Properties

Label 640.2.j.d.607.3
Level $640$
Weight $2$
Character 640.607
Analytic conductor $5.110$
Analytic rank $0$
Dimension $18$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 640 = 2^{7} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 640.j (of order \(4\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.11042572936\)
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 607.3
Root \(0.482716 + 1.32928i\) of defining polynomial
Character \(\chi\) \(=\) 640.607
Dual form 640.2.j.d.543.7

$q$-expansion

\(f(q)\) \(=\) \(q-1.39319i q^{3} +(-0.535339 + 2.17104i) q^{5} +(-2.13436 - 2.13436i) q^{7} +1.05903 q^{9} +O(q^{10})\) \(q-1.39319i q^{3} +(-0.535339 + 2.17104i) q^{5} +(-2.13436 - 2.13436i) q^{7} +1.05903 q^{9} +(-2.17074 - 2.17074i) q^{11} -1.54663 q^{13} +(3.02466 + 0.745827i) q^{15} +(-3.86386 - 3.86386i) q^{17} +(0.0136865 + 0.0136865i) q^{19} +(-2.97357 + 2.97357i) q^{21} +(-3.15240 + 3.15240i) q^{23} +(-4.42682 - 2.32449i) q^{25} -5.65499i q^{27} +(3.33787 - 3.33787i) q^{29} -8.92639i q^{31} +(-3.02424 + 3.02424i) q^{33} +(5.77640 - 3.49118i) q^{35} -7.24737 q^{37} +2.15475i q^{39} +10.3771i q^{41} +2.02975 q^{43} +(-0.566942 + 2.29920i) q^{45} +(-3.34313 + 3.34313i) q^{47} +2.11103i q^{49} +(-5.38308 + 5.38308i) q^{51} -7.30702i q^{53} +(5.87483 - 3.55067i) q^{55} +(0.0190679 - 0.0190679i) q^{57} +(-3.52732 + 3.52732i) q^{59} +(-1.41629 - 1.41629i) q^{61} +(-2.26036 - 2.26036i) q^{63} +(0.827973 - 3.35780i) q^{65} -0.748197 q^{67} +(4.39187 + 4.39187i) q^{69} -0.269603 q^{71} +(-0.811870 - 0.811870i) q^{73} +(-3.23844 + 6.16739i) q^{75} +9.26628i q^{77} +2.80567 q^{79} -4.70135 q^{81} +12.8279i q^{83} +(10.4571 - 6.32012i) q^{85} +(-4.65027 - 4.65027i) q^{87} +13.3732 q^{89} +(3.30108 + 3.30108i) q^{91} -12.4361 q^{93} +(-0.0370409 + 0.0223871i) q^{95} +(6.33466 + 6.33466i) q^{97} +(-2.29888 - 2.29888i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 18 q + 4 q^{5} + 2 q^{7} - 10 q^{9} + O(q^{10}) \) \( 18 q + 4 q^{5} + 2 q^{7} - 10 q^{9} + 2 q^{11} + 20 q^{15} - 6 q^{17} - 2 q^{19} + 16 q^{21} - 2 q^{23} + 6 q^{25} + 14 q^{29} - 8 q^{33} + 6 q^{35} - 8 q^{37} + 44 q^{43} + 4 q^{45} - 38 q^{47} - 8 q^{51} - 6 q^{55} + 24 q^{57} + 10 q^{59} - 14 q^{61} + 6 q^{63} - 12 q^{67} - 32 q^{69} + 24 q^{71} + 14 q^{73} - 64 q^{75} + 16 q^{79} + 2 q^{81} + 10 q^{85} + 24 q^{87} - 12 q^{89} - 16 q^{93} - 34 q^{95} + 18 q^{97} + 22 q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/640\mathbb{Z}\right)^\times\).

\(n\) \(257\) \(261\) \(511\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(e\left(\frac{3}{4}\right)\) \(-1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 1.39319i 0.804356i −0.915561 0.402178i \(-0.868253\pi\)
0.915561 0.402178i \(-0.131747\pi\)
\(4\) 0 0
\(5\) −0.535339 + 2.17104i −0.239411 + 0.970918i
\(6\) 0 0
\(7\) −2.13436 2.13436i −0.806714 0.806714i 0.177421 0.984135i \(-0.443225\pi\)
−0.984135 + 0.177421i \(0.943225\pi\)
\(8\) 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
\(13\) −1.54663 −0.428958 −0.214479 0.976729i \(-0.568805\pi\)
−0.214479 + 0.976729i \(0.568805\pi\)
\(14\) 0 0
\(15\) 3.02466 + 0.745827i 0.780964 + 0.192572i
\(16\) 0 0
\(17\) −3.86386 3.86386i −0.937125 0.937125i 0.0610123 0.998137i \(-0.480567\pi\)
−0.998137 + 0.0610123i \(0.980567\pi\)
\(18\) 0 0
\(19\) 0.0136865 + 0.0136865i 0.00313991 + 0.00313991i 0.708675 0.705535i \(-0.249293\pi\)
−0.705535 + 0.708675i \(0.749293\pi\)
\(20\) 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 \(-0.903872\pi\)
0.297425 + 0.954745i \(0.403872\pi\)
\(24\) 0 0
\(25\) −4.42682 2.32449i −0.885365 0.464897i
\(26\) 0 0
\(27\) 5.65499i 1.08830i
\(28\) 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 \(-0.703975\pi\)
0.597843 0.801613i \(-0.296025\pi\)
\(32\) 0 0
\(33\) −3.02424 + 3.02424i −0.526452 + 0.526452i
\(34\) 0 0
\(35\) 5.77640 3.49118i 0.976390 0.590117i
\(36\) 0 0
\(37\) −7.24737 −1.19146 −0.595730 0.803184i \(-0.703137\pi\)
−0.595730 + 0.803184i \(0.703137\pi\)
\(38\) 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
\(43\) 2.02975 0.309534 0.154767 0.987951i \(-0.450537\pi\)
0.154767 + 0.987951i \(0.450537\pi\)
\(44\) 0 0
\(45\) −0.566942 + 2.29920i −0.0845147 + 0.342745i
\(46\) 0 0
\(47\) −3.34313 + 3.34313i −0.487646 + 0.487646i −0.907563 0.419917i \(-0.862059\pi\)
0.419917 + 0.907563i \(0.362059\pi\)
\(48\) 0 0
\(49\) 2.11103i 0.301575i
\(50\) 0 0
\(51\) −5.38308 + 5.38308i −0.753782 + 0.753782i
\(52\) 0 0
\(53\) 7.30702i 1.00370i −0.864956 0.501848i \(-0.832654\pi\)
0.864956 0.501848i \(-0.167346\pi\)
\(54\) 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 −0.898399 0.439181i \(-0.855269\pi\)
0.439181 + 0.898399i \(0.355269\pi\)
\(60\) 0 0
\(61\) −1.41629 1.41629i −0.181338 0.181338i 0.610601 0.791939i \(-0.290928\pi\)
−0.791939 + 0.610601i \(0.790928\pi\)
\(62\) 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
\(67\) −0.748197 −0.0914068 −0.0457034 0.998955i \(-0.514553\pi\)
−0.0457034 + 0.998955i \(0.514553\pi\)
\(68\) 0 0
\(69\) 4.39187 + 4.39187i 0.528719 + 0.528719i
\(70\) 0 0
\(71\) −0.269603 −0.0319960 −0.0159980 0.999872i \(-0.505093\pi\)
−0.0159980 + 0.999872i \(0.505093\pi\)
\(72\) 0 0
\(73\) −0.811870 0.811870i −0.0950222 0.0950222i 0.657998 0.753020i \(-0.271404\pi\)
−0.753020 + 0.657998i \(0.771404\pi\)
\(74\) 0 0
\(75\) −3.23844 + 6.16739i −0.373943 + 0.712149i
\(76\) 0 0
\(77\) 9.26628i 1.05599i
\(78\) 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
\(83\) 12.8279i 1.40804i 0.710178 + 0.704022i \(0.248614\pi\)
−0.710178 + 0.704022i \(0.751386\pi\)
\(84\) 0 0
\(85\) 10.4571 6.32012i 1.13423 0.685514i
\(86\) 0 0
\(87\) −4.65027 4.65027i −0.498561 0.498561i
\(88\) 0 0
\(89\) 13.3732 1.41755 0.708777 0.705432i \(-0.249247\pi\)
0.708777 + 0.705432i \(0.249247\pi\)
\(90\) 0 0
\(91\) 3.30108 + 3.30108i 0.346047 + 0.346047i
\(92\) 0 0
\(93\) −12.4361 −1.28957
\(94\) 0 0
\(95\) −0.0370409 + 0.0223871i −0.00380032 + 0.00229686i
\(96\) 0 0
\(97\) 6.33466 + 6.33466i 0.643187 + 0.643187i 0.951338 0.308151i \(-0.0997101\pi\)
−0.308151 + 0.951338i \(0.599710\pi\)
\(98\) 0 0
\(99\) −2.29888 2.29888i −0.231046 0.231046i
\(100\) 0 0
\(101\) 3.78129 3.78129i 0.376252 0.376252i −0.493496 0.869748i \(-0.664281\pi\)
0.869748 + 0.493496i \(0.164281\pi\)
\(102\) 0 0
\(103\) 10.7199 10.7199i 1.05626 1.05626i 0.0579430 0.998320i \(-0.481546\pi\)
0.998320 0.0579430i \(-0.0184542\pi\)
\(104\) 0 0
\(105\) −4.86386 8.04760i −0.474665 0.785365i
\(106\) 0 0
\(107\) 10.9109i 1.05479i −0.849619 0.527397i \(-0.823168\pi\)
0.849619 0.527397i \(-0.176832\pi\)
\(108\) 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 −0.438767 0.898601i \(-0.644585\pi\)
0.898601 + 0.438767i \(0.144585\pi\)
\(114\) 0 0
\(115\) −5.15637 8.53157i −0.480834 0.795573i
\(116\) 0 0
\(117\) −1.63793 −0.151427
\(118\) 0 0
\(119\) 16.4938i 1.51198i
\(120\) 0 0
\(121\) 1.57582i 0.143256i
\(122\) 0 0
\(123\) 14.4572 1.30356
\(124\) 0 0
\(125\) 7.41640 8.36642i 0.663343 0.748315i
\(126\) 0 0
\(127\) −1.38586 + 1.38586i −0.122975 + 0.122975i −0.765916 0.642941i \(-0.777714\pi\)
0.642941 + 0.765916i \(0.277714\pi\)
\(128\) 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
\(133\) 0.0584241i 0.00506601i
\(134\) 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 \(-0.639632\pi\)
0.905319 + 0.424732i \(0.139632\pi\)
\(138\) 0 0
\(139\) −12.1022 + 12.1022i −1.02650 + 1.02650i −0.0268584 + 0.999639i \(0.508550\pi\)
−0.999639 + 0.0268584i \(0.991450\pi\)
\(140\) 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
\(147\) 2.94105 0.242574
\(148\) 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 \(-0.819228\pi\)
−0.843025 + 0.537874i \(0.819228\pi\)
\(152\) 0 0
\(153\) −4.09196 4.09196i −0.330815 0.330815i
\(154\) 0 0
\(155\) 19.3795 + 4.77865i 1.55660 + 0.383830i
\(156\) 0 0
\(157\) 5.72312i 0.456755i 0.973573 + 0.228377i \(0.0733420\pi\)
−0.973573 + 0.228377i \(0.926658\pi\)
\(158\) 0 0
\(159\) −10.1800 −0.807329
\(160\) 0 0
\(161\) 13.4567 1.06054
\(162\) 0 0
\(163\) 17.9900i 1.40909i −0.709662 0.704543i \(-0.751152\pi\)
0.709662 0.704543i \(-0.248848\pi\)
\(164\) 0 0
\(165\) −4.94675 8.18473i −0.385104 0.637181i
\(166\) 0 0
\(167\) 2.39642 + 2.39642i 0.185441 + 0.185441i 0.793722 0.608281i \(-0.208141\pi\)
−0.608281 + 0.793722i \(0.708141\pi\)
\(168\) 0 0
\(169\) −10.6079 −0.815995
\(170\) 0 0
\(171\) 0.0144945 + 0.0144945i 0.00110842 + 0.00110842i
\(172\) 0 0
\(173\) 9.45205 0.718626 0.359313 0.933217i \(-0.383011\pi\)
0.359313 + 0.933217i \(0.383011\pi\)
\(174\) 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 0.993728 0.111824i \(-0.0356691\pi\)
−0.111824 + 0.993728i \(0.535669\pi\)
\(180\) 0 0
\(181\) −2.54155 + 2.54155i −0.188912 + 0.188912i −0.795225 0.606314i \(-0.792648\pi\)
0.606314 + 0.795225i \(0.292648\pi\)
\(182\) 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
\(187\) 16.7748i 1.22670i
\(188\) 0 0
\(189\) −12.0698 + 12.0698i −0.877949 + 0.877949i
\(190\) 0 0
\(191\) 5.46421i 0.395376i 0.980265 + 0.197688i \(0.0633433\pi\)
−0.980265 + 0.197688i \(0.936657\pi\)
\(192\) 0 0
\(193\) 4.82485 4.82485i 0.347300 0.347300i −0.511803 0.859103i \(-0.671022\pi\)
0.859103 + 0.511803i \(0.171022\pi\)
\(194\) 0 0
\(195\) −4.67804 1.15352i −0.335001 0.0826053i
\(196\) 0 0
\(197\) −2.94582 −0.209881 −0.104941 0.994478i \(-0.533465\pi\)
−0.104941 + 0.994478i \(0.533465\pi\)
\(198\) 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
\(203\) −14.2485 −1.00005
\(204\) 0 0
\(205\) −22.5291 5.55526i −1.57350 0.387996i
\(206\) 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
\(213\) 0.375608i 0.0257362i
\(214\) 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 0.667142 0.744930i \(-0.267517\pi\)
−0.744930 + 0.667142i \(0.767517\pi\)
\(224\) 0 0
\(225\) −4.68815 2.46171i −0.312543 0.164114i
\(226\) 0 0
\(227\) −12.8161 −0.850632 −0.425316 0.905045i \(-0.639837\pi\)
−0.425316 + 0.905045i \(0.639837\pi\)
\(228\) 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 \(-0.245519\pi\)
−0.697083 + 0.716990i \(0.745519\pi\)
\(234\) 0 0
\(235\) −5.46836 9.04777i −0.356716 0.590212i
\(236\) 0 0
\(237\) 3.90881i 0.253905i
\(238\) 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
\(243\) 10.4151i 0.668129i
\(244\) 0 0
\(245\) −4.58312 1.13012i −0.292805 0.0722004i
\(246\) 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
\(253\) 13.6860 0.860433
\(254\) 0 0
\(255\) −8.80511 14.5687i −0.551397 0.912325i
\(256\) 0 0
\(257\) −14.7989 14.7989i −0.923131 0.923131i 0.0741183 0.997249i \(-0.476386\pi\)
−0.997249 + 0.0741183i \(0.976386\pi\)
\(258\) 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 \(-0.578129\pi\)
0.970029 + 0.242991i \(0.0781285\pi\)
\(264\) 0 0
\(265\) 15.8638 + 3.91173i 0.974507 + 0.240296i
\(266\) 0 0
\(267\) 18.6313i 1.14022i
\(268\) 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 \(-0.805850\pi\)
0.819683 0.572818i \(-0.194150\pi\)
\(272\) 0 0
\(273\) 4.59901 4.59901i 0.278345 0.278345i
\(274\) 0 0
\(275\) 4.56362 + 14.6553i 0.275197 + 0.883748i
\(276\) 0 0
\(277\) −9.91909 −0.595980 −0.297990 0.954569i \(-0.596316\pi\)
−0.297990 + 0.954569i \(0.596316\pi\)
\(278\) 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
\(283\) 3.42364 0.203514 0.101757 0.994809i \(-0.467554\pi\)
0.101757 + 0.994809i \(0.467554\pi\)
\(284\) 0 0
\(285\) 0.0311893 + 0.0516049i 0.00184750 + 0.00305681i
\(286\) 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
\(293\) 2.66471i 0.155674i 0.996966 + 0.0778369i \(0.0248013\pi\)
−0.996966 + 0.0778369i \(0.975199\pi\)
\(294\) 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
\(307\) −10.5554 −0.602430 −0.301215 0.953556i \(-0.597392\pi\)
−0.301215 + 0.953556i \(0.597392\pi\)
\(308\) 0 0
\(309\) −14.9348 14.9348i −0.849612 0.849612i
\(310\) 0 0
\(311\) −20.4762 −1.16110 −0.580550 0.814225i \(-0.697162\pi\)
−0.580550 + 0.814225i \(0.697162\pi\)
\(312\) 0 0
\(313\) 2.82393 + 2.82393i 0.159618 + 0.159618i 0.782397 0.622780i \(-0.213997\pi\)
−0.622780 + 0.782397i \(0.713997\pi\)
\(314\) 0 0
\(315\) 6.11740 3.69727i 0.344676 0.208318i
\(316\) 0 0
\(317\) 20.2533i 1.13754i −0.822497 0.568769i \(-0.807420\pi\)
0.822497 0.568769i \(-0.192580\pi\)
\(318\) 0 0
\(319\) −14.4913 −0.811354
\(320\) 0 0
\(321\) −15.2009 −0.848430
\(322\) 0 0
\(323\) 0.105766i 0.00588497i
\(324\) 0 0
\(325\) 6.84667 + 3.59512i 0.379785 + 0.199422i
\(326\) 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
\(333\) −7.67521 −0.420599
\(334\) 0 0
\(335\) 0.400539 1.62437i 0.0218838 0.0887485i
\(336\) 0 0
\(337\) −5.89449 5.89449i −0.321093 0.321093i 0.528093 0.849186i \(-0.322907\pi\)
−0.849186 + 0.528093i \(0.822907\pi\)
\(338\) 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
\(347\) 11.4626i 0.615346i 0.951492 + 0.307673i \(0.0995502\pi\)
−0.951492 + 0.307673i \(0.900450\pi\)
\(348\) 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 −0.999845 0.0175800i \(-0.994404\pi\)
0.0175800 + 0.999845i \(0.494404\pi\)
\(354\) 0 0
\(355\) 0.144329 0.585320i 0.00766020 0.0310655i
\(356\) 0 0
\(357\) 22.9789 1.21617
\(358\) 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
\(363\) −2.19541 −0.115229
\(364\) 0 0
\(365\) 2.19723 1.32798i 0.115008 0.0695095i
\(366\) 0 0
\(367\) 5.37489 5.37489i 0.280567 0.280567i −0.552768 0.833335i \(-0.686428\pi\)
0.833335 + 0.552768i \(0.186428\pi\)
\(368\) 0 0
\(369\) 10.9897i 0.572100i
\(370\) 0 0
\(371\) −15.5958 + 15.5958i −0.809696 + 0.809696i
\(372\) 0 0
\(373\) 3.24424i 0.167980i 0.996467 + 0.0839902i \(0.0267664\pi\)
−0.996467 + 0.0839902i \(0.973234\pi\)
\(374\) 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 \(-0.364522\pi\)
0.910785 0.412882i \(-0.135478\pi\)
\(380\) 0 0
\(381\) 1.93076 + 1.93076i 0.0989160 + 0.0989160i
\(382\) 0 0
\(383\) 0.418091 + 0.418091i 0.0213634 + 0.0213634i 0.717708 0.696344i \(-0.245191\pi\)
−0.696344 + 0.717708i \(0.745191\pi\)
\(384\) 0 0
\(385\) −20.1175 4.96060i −1.02528 0.252816i
\(386\) 0 0
\(387\) 2.14957 0.109269
\(388\) 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
\(395\) −1.50198 + 6.09121i −0.0755730 + 0.306482i
\(396\) 0 0
\(397\) 13.8391i 0.694564i 0.937761 + 0.347282i \(0.112895\pi\)
−0.937761 + 0.347282i \(0.887105\pi\)
\(398\) 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
\(403\) 13.8058i 0.687718i
\(404\) 0 0
\(405\) 2.51682 10.2068i 0.125062 0.507181i
\(406\) 0 0
\(407\) 15.7321 + 15.7321i 0.779813 + 0.779813i
\(408\) 0 0
\(409\) −18.2875 −0.904259 −0.452130 0.891952i \(-0.649336\pi\)
−0.452130 + 0.891952i \(0.649336\pi\)
\(410\) 0 0
\(411\) −7.83684 7.83684i −0.386563 0.386563i
\(412\) 0 0
\(413\) 15.0572 0.740915
\(414\) 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 0.143563 0.989641i \(-0.454144\pi\)
−0.989641 + 0.143563i \(0.954144\pi\)
\(420\) 0 0
\(421\) −11.5457 + 11.5457i −0.562703 + 0.562703i −0.930074 0.367372i \(-0.880258\pi\)
0.367372 + 0.930074i \(0.380258\pi\)
\(422\) 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
\(427\) 6.04577i 0.292576i
\(428\) 0 0
\(429\) 4.67738 4.67738i 0.225826 0.225826i
\(430\) 0 0
\(431\) 15.9479i 0.768185i 0.923295 + 0.384093i \(0.125486\pi\)
−0.923295 + 0.384093i \(0.874514\pi\)
\(432\) 0 0
\(433\) 3.52109 3.52109i 0.169213 0.169213i −0.617420 0.786633i \(-0.711822\pi\)
0.786633 + 0.617420i \(0.211822\pi\)
\(434\) 0 0
\(435\) 12.5854 7.60645i 0.603423 0.364701i
\(436\) 0 0
\(437\) −0.0862907 −0.00412784
\(438\) 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
\(443\) −27.0992 −1.28752 −0.643761 0.765226i \(-0.722627\pi\)
−0.643761 + 0.765226i \(0.722627\pi\)
\(444\) 0 0
\(445\) −7.15919 + 29.0337i −0.339378 + 1.37633i
\(446\) 0 0
\(447\) 18.8903 18.8903i 0.893478 0.893478i
\(448\) 0 0
\(449\) 41.0879i 1.93906i −0.244976 0.969529i \(-0.578780\pi\)
0.244976 0.969529i \(-0.421220\pi\)
\(450\) 0 0
\(451\) 22.5259 22.5259i 1.06070 1.06070i
\(452\) 0 0
\(453\) 28.8648i 1.35619i
\(454\) 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 \(-0.543777\pi\)
0.990558 + 0.137096i \(0.0437769\pi\)
\(458\) 0 0
\(459\) −21.8501 + 21.8501i −1.01988 + 1.01988i
\(460\) 0 0
\(461\) −6.68802 6.68802i −0.311492 0.311492i 0.533995 0.845488i \(-0.320690\pi\)
−0.845488 + 0.533995i \(0.820690\pi\)
\(462\) 0 0
\(463\) 28.6926 + 28.6926i 1.33346 + 1.33346i 0.902254 + 0.431205i \(0.141911\pi\)
0.431205 + 0.902254i \(0.358089\pi\)
\(464\) 0 0
\(465\) 6.65754 26.9993i 0.308736 1.25206i
\(466\) 0 0
\(467\) 32.4161 1.50004 0.750018 0.661417i \(-0.230045\pi\)
0.750018 + 0.661417i \(0.230045\pi\)
\(468\) 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
\(475\) −0.0287737 0.0924020i −0.00132023 0.00423970i
\(476\) 0 0
\(477\) 7.73837i 0.354316i
\(478\) 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
\(483\) 18.7477i 0.853051i
\(484\) 0 0
\(485\) −17.1440 + 10.3616i −0.778468 + 0.470496i
\(486\) 0 0
\(487\) −11.7773 11.7773i −0.533681 0.533681i 0.387985 0.921666i \(-0.373171\pi\)
−0.921666 + 0.387985i \(0.873171\pi\)
\(488\) 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
\(493\) −25.7941 −1.16171
\(494\) 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 0.380353 0.924841i \(-0.375802\pi\)
−0.924841 + 0.380353i \(0.875802\pi\)
\(500\) 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 \(-0.887455\pi\)
0.346250 + 0.938142i \(0.387455\pi\)
\(504\) 0 0
\(505\) 6.18505 + 10.2336i 0.275231 + 0.455389i
\(506\) 0 0
\(507\) 14.7788i 0.656350i
\(508\) 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
\(515\) 17.5345 + 29.0121i 0.772664 + 1.27843i
\(516\) 0 0
\(517\) 14.5141 0.638329
\(518\) 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
\(523\) 25.9463 1.13455 0.567276 0.823528i \(-0.307997\pi\)
0.567276 + 0.823528i \(0.307997\pi\)
\(524\) 0 0
\(525\) 20.0755 6.25144i 0.876165 0.272835i
\(526\) 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
\(533\) 16.0495i 0.695182i
\(534\) 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 0.604428 0.796660i \(-0.293402\pi\)
−0.796660 + 0.604428i \(0.793402\pi\)
\(542\) 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
\(547\) −15.5964 −0.666853 −0.333426 0.942776i \(-0.608205\pi\)
−0.333426 + 0.942776i \(0.608205\pi\)
\(548\) 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
\(555\) −21.9209 5.40529i −0.930488 0.229442i
\(556\) 0 0
\(557\) 15.5348i 0.658231i −0.944290 0.329116i \(-0.893249\pi\)
0.944290 0.329116i \(-0.106751\pi\)
\(558\) 0 0
\(559\) −3.13928 −0.132777
\(560\) 0 0
\(561\) 23.3705 0.986703
\(562\) 0 0
\(563\) 24.3087i 1.02449i 0.858839 + 0.512245i \(0.171186\pi\)
−0.858839 + 0.512245i \(0.828814\pi\)
\(564\) 0 0
\(565\) 7.99547 + 13.2291i 0.336372 + 0.556550i
\(566\) 0 0
\(567\) 10.0344 + 10.0344i 0.421405 + 0.421405i
\(568\) 0 0
\(569\) 0.187259 0.00785029 0.00392515 0.999992i \(-0.498751\pi\)
0.00392515 + 0.999992i \(0.498751\pi\)
\(570\) 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
\(573\) 7.61266 0.318023
\(574\) 0 0
\(575\) 21.2828 6.62740i 0.887554 0.276382i
\(576\) 0 0
\(577\) −1.53648 1.53648i −0.0639645 0.0639645i 0.674401 0.738365i \(-0.264402\pi\)
−0.738365 + 0.674401i \(0.764402\pi\)
\(578\) 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
\(587\) 3.06150i 0.126362i 0.998002 + 0.0631808i \(0.0201245\pi\)
−0.998002 + 0.0631808i \(0.979876\pi\)
\(588\) 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 −0.990747 0.135718i \(-0.956666\pi\)
0.135718 + 0.990747i \(0.456666\pi\)
\(594\) 0 0
\(595\) −35.8087 8.82977i −1.46801 0.361985i
\(596\) 0 0
\(597\) 2.99005 0.122375
\(598\) 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
\(603\) −0.792365 −0.0322676
\(604\) 0 0
\(605\) 3.42116 + 0.843598i 0.139090 + 0.0342971i
\(606\) 0 0
\(607\) −28.8294 + 28.8294i −1.17015 + 1.17015i −0.187975 + 0.982174i \(0.560193\pi\)
−0.982174 + 0.187975i \(0.939807\pi\)
\(608\) 0 0
\(609\) 19.8507i 0.804393i
\(610\) 0 0
\(611\) 5.17059 5.17059i 0.209180 0.209180i
\(612\) 0 0
\(613\) 38.7980i 1.56704i −0.621369 0.783518i \(-0.713423\pi\)
0.621369 0.783518i \(-0.286577\pi\)
\(614\) 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 \(-0.814479\pi\)
0.550391 + 0.834907i \(0.314479\pi\)
\(618\) 0 0
\(619\) 28.1001 28.1001i 1.12944 1.12944i 0.139172 0.990268i \(-0.455556\pi\)
0.990268 0.139172i \(-0.0444440\pi\)
\(620\) 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
\(627\) −0.0827827 −0.00330602
\(628\) 0 0
\(629\) 28.0029 + 28.0029i 1.11655 + 1.11655i
\(630\) 0 0
\(631\) 38.2613 1.52316 0.761580 0.648071i \(-0.224424\pi\)
0.761580 + 0.648071i \(0.224424\pi\)
\(632\) 0 0
\(633\) 7.72420 + 7.72420i 0.307010 + 0.307010i
\(634\) 0 0
\(635\) −2.26685 3.75067i −0.0899574 0.148841i
\(636\) 0 0
\(637\) 3.26498i 0.129363i
\(638\) 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
\(643\) 8.74864i 0.345013i 0.985008 + 0.172506i \(0.0551866\pi\)
−0.985008 + 0.172506i \(0.944813\pi\)
\(644\) 0 0
\(645\) 6.13931 + 1.51384i 0.241735 + 0.0596076i
\(646\) 0 0
\(647\) 8.84125 + 8.84125i 0.347585 + 0.347585i 0.859209 0.511624i \(-0.170956\pi\)
−0.511624 + 0.859209i \(0.670956\pi\)
\(648\) 0 0
\(649\) 15.3137 0.601117
\(650\) 0 0
\(651\) 26.5432 + 26.5432i 1.04031 + 1.04031i
\(652\) 0 0
\(653\) 20.7854 0.813396 0.406698 0.913563i \(-0.366680\pi\)
0.406698 + 0.913563i \(0.366680\pi\)
\(654\) 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 0.398003 0.917384i \(-0.369703\pi\)
−0.917384 + 0.398003i \(0.869703\pi\)
\(660\) 0 0
\(661\) 30.5831 30.5831i 1.18954 1.18954i 0.212350 0.977194i \(-0.431888\pi\)
0.977194 0.212350i \(-0.0681116\pi\)
\(662\) 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
\(667\) 21.0446i 0.814848i
\(668\) 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 0.170652 0.985331i \(-0.445413\pi\)
0.985331 0.170652i \(-0.0545873\pi\)
\(674\) 0 0
\(675\) −13.1449 + 25.0336i −0.505949 + 0.963545i
\(676\) 0 0
\(677\) 33.4274 1.28472 0.642360 0.766403i \(-0.277956\pi\)
0.642360 + 0.766403i \(0.277956\pi\)
\(678\) 0 0
\(679\) 27.0409i 1.03774i
\(680\) 0 0
\(681\) 17.8551i 0.684211i
\(682\) 0 0
\(683\) 4.07583 0.155957 0.0779787 0.996955i \(-0.475153\pi\)
0.0779787 + 0.996955i \(0.475153\pi\)
\(684\) 0 0
\(685\) 9.20102 + 15.2237i 0.351553 + 0.581668i
\(686\) 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
\(693\) 9.81330i 0.372776i
\(694\) 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 0.447418 0.894325i \(-0.352344\pi\)
−0.894325 + 0.447418i \(0.852344\pi\)
\(702\) 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
\(707\) −16.1413 −0.607056
\(708\) 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
\(715\) −9.08620 + 5.49158i −0.339805 + 0.205373i
\(716\) 0 0
\(717\) 17.4282i 0.650868i
\(718\) 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
\(723\) 27.2751i 1.01437i
\(724\) 0 0
\(725\) −22.5350 + 7.01733i −0.836928 + 0.260617i
\(726\) 0 0
\(727\) 28.6014 + 28.6014i 1.06077 + 1.06077i 0.998030 + 0.0627368i \(0.0199829\pi\)
0.0627368 + 0.998030i \(0.480017\pi\)
\(728\) 0 0
\(729\) −28.6142 −1.05979
\(730\) 0 0
\(731\) −7.84269 7.84269i −0.290072 0.290072i
\(732\) 0 0
\(733\) −18.7069 −0.690956 −0.345478 0.938427i \(-0.612283\pi\)
−0.345478 + 0.938427i \(0.612283\pi\)
\(734\) 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 \(0.108175\pi\)
0.333337 + 0.942808i \(0.391825\pi\)
\(740\) 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 \(-0.527913\pi\)
0.996157 + 0.0875803i \(0.0279134\pi\)
\(744\) 0 0
\(745\) −36.6959 + 22.1785i −1.34443 + 0.812558i
\(746\) 0 0
\(747\) 13.5852i 0.497055i
\(748\) 0 0
\(749\) −23.2878 + 23.2878i −0.850917 + 0.850917i
\(750\) 0 0
\(751\) 45.2370i 1.65072i −0.564606 0.825361i \(-0.690972\pi\)
0.564606 0.825361i \(-0.309028\pi\)
\(752\) 0 0
\(753\) −7.21340 + 7.21340i −0.262871 + 0.262871i
\(754\) 0 0
\(755\) 11.0914 44.9808i 0.403659 1.63702i
\(756\) 0 0
\(757\) −6.44058 −0.234087 −0.117044 0.993127i \(-0.537342\pi\)
−0.117044 + 0.993127i \(0.537342\pi\)
\(758\) 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
\(763\) −38.9367 −1.40960
\(764\) 0 0
\(765\) 11.0744 6.69322i 0.400395 0.241994i
\(766\) 0 0
\(767\) 5.45546 5.45546i 0.196985 0.196985i
\(768\) 0 0
\(769\) 46.8513i 1.68950i −0.535159 0.844751i \(-0.679748\pi\)
0.535159 0.844751i \(-0.320252\pi\)
\(770\) 0 0
\(771\) −20.6176 + 20.6176i −0.742526 + 0.742526i
\(772\) 0 0
\(773\) 10.9964i 0.395513i 0.980251 + 0.197756i \(0.0633655\pi\)
−0.980251 + 0.197756i \(0.936635\pi\)
\(774\) 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
\(787\) 25.5190 0.909653 0.454826 0.890580i \(-0.349701\pi\)
0.454826 + 0.890580i \(0.349701\pi\)
\(788\) 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
\(795\) 5.44977 22.1013i 0.193283 0.783851i
\(796\) 0 0
\(797\) 13.3808i 0.473972i 0.971513 + 0.236986i \(0.0761595\pi\)
−0.971513 + 0.236986i