Properties

Label 136.2.n.a.25.1
Level $136$
Weight $2$
Character 136.25
Analytic conductor $1.086$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 136 = 2^{3} \cdot 17 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 136.n (of order \(8\), degree \(4\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(1.08596546749\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\Q(\zeta_{8})\)
Defining polynomial: \(x^{4} + 1\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label 25.1
Root \(-0.707107 - 0.707107i\) of defining polynomial
Character \(\chi\) \(=\) 136.25
Dual form 136.2.n.a.49.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.292893 + 0.707107i) q^{3} +(1.70711 + 0.707107i) q^{5} +(-0.292893 + 0.121320i) q^{7} +(1.70711 + 1.70711i) q^{9} +O(q^{10})\) \(q+(-0.292893 + 0.707107i) q^{3} +(1.70711 + 0.707107i) q^{5} +(-0.292893 + 0.121320i) q^{7} +(1.70711 + 1.70711i) q^{9} +(0.292893 + 0.707107i) q^{11} +(-1.00000 + 1.00000i) q^{15} +(1.00000 - 4.00000i) q^{17} +(-1.58579 + 1.58579i) q^{19} -0.242641i q^{21} +(-2.53553 - 6.12132i) q^{23} +(-1.12132 - 1.12132i) q^{25} +(-3.82843 + 1.58579i) q^{27} +(-5.12132 - 2.12132i) q^{29} +(0.878680 - 2.12132i) q^{31} -0.585786 q^{33} -0.585786 q^{35} +(0.292893 - 0.707107i) q^{37} +(-2.29289 + 0.949747i) q^{41} +(7.24264 + 7.24264i) q^{43} +(1.70711 + 4.12132i) q^{45} -12.8284i q^{47} +(-4.87868 + 4.87868i) q^{49} +(2.53553 + 1.87868i) q^{51} +(2.17157 - 2.17157i) q^{53} +1.41421i q^{55} +(-0.656854 - 1.58579i) q^{57} +(5.58579 + 5.58579i) q^{59} +(-9.12132 + 3.77817i) q^{61} +(-0.707107 - 0.292893i) q^{63} +9.65685 q^{67} +5.07107 q^{69} +(3.70711 - 8.94975i) q^{71} +(7.36396 + 3.05025i) q^{73} +(1.12132 - 0.464466i) q^{75} +(-0.171573 - 0.171573i) q^{77} +(5.46447 + 13.1924i) q^{79} +4.07107i q^{81} +(-7.24264 + 7.24264i) q^{83} +(4.53553 - 6.12132i) q^{85} +(3.00000 - 3.00000i) q^{87} -1.65685i q^{89} +(1.24264 + 1.24264i) q^{93} +(-3.82843 + 1.58579i) q^{95} +(-14.7782 - 6.12132i) q^{97} +(-0.707107 + 1.70711i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 4 q^{3} + 4 q^{5} - 4 q^{7} + 4 q^{9} + O(q^{10}) \) \( 4 q - 4 q^{3} + 4 q^{5} - 4 q^{7} + 4 q^{9} + 4 q^{11} - 4 q^{15} + 4 q^{17} - 12 q^{19} + 4 q^{23} + 4 q^{25} - 4 q^{27} - 12 q^{29} + 12 q^{31} - 8 q^{33} - 8 q^{35} + 4 q^{37} - 12 q^{41} + 12 q^{43} + 4 q^{45} - 28 q^{49} - 4 q^{51} + 20 q^{53} + 20 q^{57} + 28 q^{59} - 28 q^{61} + 16 q^{67} - 8 q^{69} + 12 q^{71} + 4 q^{73} - 4 q^{75} - 12 q^{77} + 36 q^{79} - 12 q^{83} + 4 q^{85} + 12 q^{87} - 12 q^{93} - 4 q^{95} - 28 q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/136\mathbb{Z}\right)^\times\).

\(n\) \(69\) \(103\) \(105\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{5}{8}\right)\)

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
\(3\) −0.292893 + 0.707107i −0.169102 + 0.408248i −0.985599 0.169102i \(-0.945913\pi\)
0.816497 + 0.577350i \(0.195913\pi\)
\(4\) 0 0
\(5\) 1.70711 + 0.707107i 0.763441 + 0.316228i 0.730213 0.683220i \(-0.239421\pi\)
0.0332288 + 0.999448i \(0.489421\pi\)
\(6\) 0 0
\(7\) −0.292893 + 0.121320i −0.110703 + 0.0458548i −0.437348 0.899293i \(-0.644082\pi\)
0.326644 + 0.945147i \(0.394082\pi\)
\(8\) 0 0
\(9\) 1.70711 + 1.70711i 0.569036 + 0.569036i
\(10\) 0 0
\(11\) 0.292893 + 0.707107i 0.0883106 + 0.213201i 0.961864 0.273527i \(-0.0881903\pi\)
−0.873554 + 0.486728i \(0.838190\pi\)
\(12\) 0 0
\(13\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(14\) 0 0
\(15\) −1.00000 + 1.00000i −0.258199 + 0.258199i
\(16\) 0 0
\(17\) 1.00000 4.00000i 0.242536 0.970143i
\(18\) 0 0
\(19\) −1.58579 + 1.58579i −0.363804 + 0.363804i −0.865211 0.501407i \(-0.832816\pi\)
0.501407 + 0.865211i \(0.332816\pi\)
\(20\) 0 0
\(21\) 0.242641i 0.0529485i
\(22\) 0 0
\(23\) −2.53553 6.12132i −0.528695 1.27638i −0.932378 0.361484i \(-0.882270\pi\)
0.403683 0.914899i \(-0.367730\pi\)
\(24\) 0 0
\(25\) −1.12132 1.12132i −0.224264 0.224264i
\(26\) 0 0
\(27\) −3.82843 + 1.58579i −0.736781 + 0.305185i
\(28\) 0 0
\(29\) −5.12132 2.12132i −0.951005 0.393919i −0.147397 0.989077i \(-0.547089\pi\)
−0.803609 + 0.595158i \(0.797089\pi\)
\(30\) 0 0
\(31\) 0.878680 2.12132i 0.157816 0.381000i −0.825118 0.564960i \(-0.808892\pi\)
0.982934 + 0.183960i \(0.0588916\pi\)
\(32\) 0 0
\(33\) −0.585786 −0.101972
\(34\) 0 0
\(35\) −0.585786 −0.0990160
\(36\) 0 0
\(37\) 0.292893 0.707107i 0.0481513 0.116248i −0.897974 0.440049i \(-0.854961\pi\)
0.946125 + 0.323802i \(0.104961\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −2.29289 + 0.949747i −0.358090 + 0.148326i −0.554473 0.832202i \(-0.687080\pi\)
0.196384 + 0.980527i \(0.437080\pi\)
\(42\) 0 0
\(43\) 7.24264 + 7.24264i 1.10449 + 1.10449i 0.993862 + 0.110631i \(0.0352871\pi\)
0.110631 + 0.993862i \(0.464713\pi\)
\(44\) 0 0
\(45\) 1.70711 + 4.12132i 0.254480 + 0.614370i
\(46\) 0 0
\(47\) 12.8284i 1.87122i −0.353037 0.935609i \(-0.614851\pi\)
0.353037 0.935609i \(-0.385149\pi\)
\(48\) 0 0
\(49\) −4.87868 + 4.87868i −0.696954 + 0.696954i
\(50\) 0 0
\(51\) 2.53553 + 1.87868i 0.355046 + 0.263068i
\(52\) 0 0
\(53\) 2.17157 2.17157i 0.298288 0.298288i −0.542055 0.840343i \(-0.682353\pi\)
0.840343 + 0.542055i \(0.182353\pi\)
\(54\) 0 0
\(55\) 1.41421i 0.190693i
\(56\) 0 0
\(57\) −0.656854 1.58579i −0.0870025 0.210043i
\(58\) 0 0
\(59\) 5.58579 + 5.58579i 0.727207 + 0.727207i 0.970063 0.242855i \(-0.0780840\pi\)
−0.242855 + 0.970063i \(0.578084\pi\)
\(60\) 0 0
\(61\) −9.12132 + 3.77817i −1.16787 + 0.483746i −0.880486 0.474071i \(-0.842784\pi\)
−0.287379 + 0.957817i \(0.592784\pi\)
\(62\) 0 0
\(63\) −0.707107 0.292893i −0.0890871 0.0369011i
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) 9.65685 1.17977 0.589886 0.807486i \(-0.299173\pi\)
0.589886 + 0.807486i \(0.299173\pi\)
\(68\) 0 0
\(69\) 5.07107 0.610485
\(70\) 0 0
\(71\) 3.70711 8.94975i 0.439953 1.06214i −0.536012 0.844210i \(-0.680070\pi\)
0.975965 0.217929i \(-0.0699302\pi\)
\(72\) 0 0
\(73\) 7.36396 + 3.05025i 0.861886 + 0.357005i 0.769445 0.638713i \(-0.220533\pi\)
0.0924414 + 0.995718i \(0.470533\pi\)
\(74\) 0 0
\(75\) 1.12132 0.464466i 0.129479 0.0536319i
\(76\) 0 0
\(77\) −0.171573 0.171573i −0.0195525 0.0195525i
\(78\) 0 0
\(79\) 5.46447 + 13.1924i 0.614800 + 1.48426i 0.857670 + 0.514201i \(0.171911\pi\)
−0.242869 + 0.970059i \(0.578089\pi\)
\(80\) 0 0
\(81\) 4.07107i 0.452341i
\(82\) 0 0
\(83\) −7.24264 + 7.24264i −0.794983 + 0.794983i −0.982300 0.187317i \(-0.940021\pi\)
0.187317 + 0.982300i \(0.440021\pi\)
\(84\) 0 0
\(85\) 4.53553 6.12132i 0.491948 0.663950i
\(86\) 0 0
\(87\) 3.00000 3.00000i 0.321634 0.321634i
\(88\) 0 0
\(89\) 1.65685i 0.175626i −0.996137 0.0878131i \(-0.972012\pi\)
0.996137 0.0878131i \(-0.0279878\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) 1.24264 + 1.24264i 0.128856 + 0.128856i
\(94\) 0 0
\(95\) −3.82843 + 1.58579i −0.392788 + 0.162698i
\(96\) 0 0
\(97\) −14.7782 6.12132i −1.50050 0.621526i −0.526926 0.849911i \(-0.676655\pi\)
−0.973571 + 0.228386i \(0.926655\pi\)
\(98\) 0 0
\(99\) −0.707107 + 1.70711i −0.0710669 + 0.171571i
\(100\) 0 0
\(101\) 10.0000 0.995037 0.497519 0.867453i \(-0.334245\pi\)
0.497519 + 0.867453i \(0.334245\pi\)
\(102\) 0 0
\(103\) −2.34315 −0.230877 −0.115439 0.993315i \(-0.536827\pi\)
−0.115439 + 0.993315i \(0.536827\pi\)
\(104\) 0 0
\(105\) 0.171573 0.414214i 0.0167438 0.0404231i
\(106\) 0 0
\(107\) −13.3640 5.53553i −1.29194 0.535140i −0.372379 0.928081i \(-0.621458\pi\)
−0.919564 + 0.392940i \(0.871458\pi\)
\(108\) 0 0
\(109\) −10.7782 + 4.46447i −1.03236 + 0.427618i −0.833564 0.552422i \(-0.813704\pi\)
−0.198797 + 0.980041i \(0.563704\pi\)
\(110\) 0 0
\(111\) 0.414214 + 0.414214i 0.0393154 + 0.0393154i
\(112\) 0 0
\(113\) 3.12132 + 7.53553i 0.293629 + 0.708883i 0.999999 + 0.00104094i \(0.000331343\pi\)
−0.706370 + 0.707842i \(0.749669\pi\)
\(114\) 0 0
\(115\) 12.2426i 1.14163i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 0.192388 + 1.29289i 0.0176362 + 0.118519i
\(120\) 0 0
\(121\) 7.36396 7.36396i 0.669451 0.669451i
\(122\) 0 0
\(123\) 1.89949i 0.171272i
\(124\) 0 0
\(125\) −4.65685 11.2426i −0.416522 1.00557i
\(126\) 0 0
\(127\) −1.24264 1.24264i −0.110267 0.110267i 0.649821 0.760087i \(-0.274844\pi\)
−0.760087 + 0.649821i \(0.774844\pi\)
\(128\) 0 0
\(129\) −7.24264 + 3.00000i −0.637679 + 0.264135i
\(130\) 0 0
\(131\) −13.3640 5.53553i −1.16761 0.483642i −0.287211 0.957867i \(-0.592728\pi\)
−0.880403 + 0.474225i \(0.842728\pi\)
\(132\) 0 0
\(133\) 0.272078 0.656854i 0.0235921 0.0569565i
\(134\) 0 0
\(135\) −7.65685 −0.658997
\(136\) 0 0
\(137\) 14.0000 1.19610 0.598050 0.801459i \(-0.295942\pi\)
0.598050 + 0.801459i \(0.295942\pi\)
\(138\) 0 0
\(139\) 0.192388 0.464466i 0.0163182 0.0393955i −0.915510 0.402294i \(-0.868213\pi\)
0.931829 + 0.362899i \(0.118213\pi\)
\(140\) 0 0
\(141\) 9.07107 + 3.75736i 0.763922 + 0.316427i
\(142\) 0 0
\(143\) 0 0
\(144\) 0 0
\(145\) −7.24264 7.24264i −0.601469 0.601469i
\(146\) 0 0
\(147\) −2.02082 4.87868i −0.166674 0.402387i
\(148\) 0 0
\(149\) 6.34315i 0.519651i 0.965656 + 0.259825i \(0.0836650\pi\)
−0.965656 + 0.259825i \(0.916335\pi\)
\(150\) 0 0
\(151\) −14.0711 + 14.0711i −1.14509 + 1.14509i −0.157581 + 0.987506i \(0.550370\pi\)
−0.987506 + 0.157581i \(0.949630\pi\)
\(152\) 0 0
\(153\) 8.53553 5.12132i 0.690057 0.414034i
\(154\) 0 0
\(155\) 3.00000 3.00000i 0.240966 0.240966i
\(156\) 0 0
\(157\) 15.3137i 1.22217i −0.791566 0.611083i \(-0.790734\pi\)
0.791566 0.611083i \(-0.209266\pi\)
\(158\) 0 0
\(159\) 0.899495 + 2.17157i 0.0713346 + 0.172217i
\(160\) 0 0
\(161\) 1.48528 + 1.48528i 0.117057 + 0.117057i
\(162\) 0 0
\(163\) −4.29289 + 1.77817i −0.336245 + 0.139277i −0.544417 0.838815i \(-0.683249\pi\)
0.208171 + 0.978092i \(0.433249\pi\)
\(164\) 0 0
\(165\) −1.00000 0.414214i −0.0778499 0.0322465i
\(166\) 0 0
\(167\) −0.292893 + 0.707107i −0.0226648 + 0.0547176i −0.934807 0.355157i \(-0.884427\pi\)
0.912142 + 0.409874i \(0.134427\pi\)
\(168\) 0 0
\(169\) 13.0000 1.00000
\(170\) 0 0
\(171\) −5.41421 −0.414035
\(172\) 0 0
\(173\) −7.22183 + 17.4350i −0.549065 + 1.32556i 0.369110 + 0.929386i \(0.379663\pi\)
−0.918175 + 0.396175i \(0.870337\pi\)
\(174\) 0 0
\(175\) 0.464466 + 0.192388i 0.0351103 + 0.0145432i
\(176\) 0 0
\(177\) −5.58579 + 2.31371i −0.419853 + 0.173909i
\(178\) 0 0
\(179\) 12.8995 + 12.8995i 0.964154 + 0.964154i 0.999379 0.0352259i \(-0.0112151\pi\)
−0.0352259 + 0.999379i \(0.511215\pi\)
\(180\) 0 0
\(181\) 3.12132 + 7.53553i 0.232006 + 0.560112i 0.996413 0.0846219i \(-0.0269682\pi\)
−0.764407 + 0.644734i \(0.776968\pi\)
\(182\) 0 0
\(183\) 7.55635i 0.558581i
\(184\) 0 0
\(185\) 1.00000 1.00000i 0.0735215 0.0735215i
\(186\) 0 0
\(187\) 3.12132 0.464466i 0.228254 0.0339651i
\(188\) 0 0
\(189\) 0.928932 0.928932i 0.0675699 0.0675699i
\(190\) 0 0
\(191\) 8.82843i 0.638803i 0.947620 + 0.319401i \(0.103482\pi\)
−0.947620 + 0.319401i \(0.896518\pi\)
\(192\) 0 0
\(193\) 0.292893 + 0.707107i 0.0210829 + 0.0508987i 0.934070 0.357089i \(-0.116231\pi\)
−0.912987 + 0.407988i \(0.866231\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 11.3640 4.70711i 0.809649 0.335367i 0.0608349 0.998148i \(-0.480624\pi\)
0.748814 + 0.662780i \(0.230624\pi\)
\(198\) 0 0
\(199\) 20.7782 + 8.60660i 1.47293 + 0.610106i 0.967524 0.252778i \(-0.0813444\pi\)
0.505402 + 0.862884i \(0.331344\pi\)
\(200\) 0 0
\(201\) −2.82843 + 6.82843i −0.199502 + 0.481640i
\(202\) 0 0
\(203\) 1.75736 0.123342
\(204\) 0 0
\(205\) −4.58579 −0.320285
\(206\) 0 0
\(207\) 6.12132 14.7782i 0.425461 1.02715i
\(208\) 0 0
\(209\) −1.58579 0.656854i −0.109691 0.0454356i
\(210\) 0 0
\(211\) 24.1924 10.0208i 1.66547 0.689861i 0.666997 0.745060i \(-0.267579\pi\)
0.998475 + 0.0551988i \(0.0175792\pi\)
\(212\) 0 0
\(213\) 5.24264 + 5.24264i 0.359220 + 0.359220i
\(214\) 0 0
\(215\) 7.24264 + 17.4853i 0.493944 + 1.19249i
\(216\) 0 0
\(217\) 0.727922i 0.0494146i
\(218\) 0 0
\(219\) −4.31371 + 4.31371i −0.291493 + 0.291493i
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) −12.4142 + 12.4142i −0.831317 + 0.831317i −0.987697 0.156380i \(-0.950018\pi\)
0.156380 + 0.987697i \(0.450018\pi\)
\(224\) 0 0
\(225\) 3.82843i 0.255228i
\(226\) 0 0
\(227\) −1.36396 3.29289i −0.0905293 0.218557i 0.872129 0.489276i \(-0.162739\pi\)
−0.962659 + 0.270719i \(0.912739\pi\)
\(228\) 0 0
\(229\) −7.00000 7.00000i −0.462573 0.462573i 0.436925 0.899498i \(-0.356068\pi\)
−0.899498 + 0.436925i \(0.856068\pi\)
\(230\) 0 0
\(231\) 0.171573 0.0710678i 0.0112887 0.00467592i
\(232\) 0 0
\(233\) 0.535534 + 0.221825i 0.0350840 + 0.0145323i 0.400156 0.916447i \(-0.368956\pi\)
−0.365072 + 0.930979i \(0.618956\pi\)
\(234\) 0 0
\(235\) 9.07107 21.8995i 0.591731 1.42857i
\(236\) 0 0
\(237\) −10.9289 −0.709910
\(238\) 0 0
\(239\) 11.3137 0.731823 0.365911 0.930650i \(-0.380757\pi\)
0.365911 + 0.930650i \(0.380757\pi\)
\(240\) 0 0
\(241\) −5.36396 + 12.9497i −0.345523 + 0.834167i 0.651614 + 0.758551i \(0.274092\pi\)
−0.997137 + 0.0756158i \(0.975908\pi\)
\(242\) 0 0
\(243\) −14.3640 5.94975i −0.921449 0.381676i
\(244\) 0 0
\(245\) −11.7782 + 4.87868i −0.752480 + 0.311687i
\(246\) 0 0
\(247\) 0 0
\(248\) 0 0
\(249\) −3.00000 7.24264i −0.190117 0.458984i
\(250\) 0 0
\(251\) 0.828427i 0.0522899i −0.999658 0.0261449i \(-0.991677\pi\)
0.999658 0.0261449i \(-0.00832314\pi\)
\(252\) 0 0
\(253\) 3.58579 3.58579i 0.225436 0.225436i
\(254\) 0 0
\(255\) 3.00000 + 5.00000i 0.187867 + 0.313112i
\(256\) 0 0
\(257\) −5.82843 + 5.82843i −0.363567 + 0.363567i −0.865124 0.501557i \(-0.832761\pi\)
0.501557 + 0.865124i \(0.332761\pi\)
\(258\) 0 0
\(259\) 0.242641i 0.0150770i
\(260\) 0 0
\(261\) −5.12132 12.3640i −0.317002 0.765310i
\(262\) 0 0
\(263\) 2.75736 + 2.75736i 0.170026 + 0.170026i 0.786991 0.616965i \(-0.211638\pi\)
−0.616965 + 0.786991i \(0.711638\pi\)
\(264\) 0 0
\(265\) 5.24264 2.17157i 0.322053 0.133399i
\(266\) 0 0
\(267\) 1.17157 + 0.485281i 0.0716991 + 0.0296987i
\(268\) 0 0
\(269\) −5.36396 + 12.9497i −0.327046 + 0.789560i 0.671762 + 0.740767i \(0.265538\pi\)
−0.998809 + 0.0487934i \(0.984462\pi\)
\(270\) 0 0
\(271\) −11.3137 −0.687259 −0.343629 0.939105i \(-0.611656\pi\)
−0.343629 + 0.939105i \(0.611656\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 0.464466 1.12132i 0.0280084 0.0676182i
\(276\) 0 0
\(277\) 8.53553 + 3.53553i 0.512851 + 0.212430i 0.624073 0.781366i \(-0.285477\pi\)
−0.111223 + 0.993796i \(0.535477\pi\)
\(278\) 0 0
\(279\) 5.12132 2.12132i 0.306605 0.127000i
\(280\) 0 0
\(281\) −2.31371 2.31371i −0.138024 0.138024i 0.634719 0.772743i \(-0.281116\pi\)
−0.772743 + 0.634719i \(0.781116\pi\)
\(282\) 0 0
\(283\) −10.0503 24.2635i −0.597426 1.44231i −0.876196 0.481955i \(-0.839927\pi\)
0.278770 0.960358i \(-0.410073\pi\)
\(284\) 0 0
\(285\) 3.17157i 0.187868i
\(286\) 0 0
\(287\) 0.556349 0.556349i 0.0328403 0.0328403i
\(288\) 0 0
\(289\) −15.0000 8.00000i −0.882353 0.470588i
\(290\) 0 0
\(291\) 8.65685 8.65685i 0.507474 0.507474i
\(292\) 0 0
\(293\) 7.31371i 0.427271i 0.976913 + 0.213636i \(0.0685306\pi\)
−0.976913 + 0.213636i \(0.931469\pi\)
\(294\) 0 0
\(295\) 5.58579 + 13.4853i 0.325217 + 0.785143i
\(296\) 0 0
\(297\) −2.24264 2.24264i −0.130131 0.130131i
\(298\) 0 0
\(299\) 0 0
\(300\) 0 0
\(301\) −3.00000 1.24264i −0.172917 0.0716246i
\(302\) 0 0
\(303\) −2.92893 + 7.07107i −0.168263 + 0.406222i
\(304\) 0 0
\(305\) −18.2426 −1.04457
\(306\) 0 0
\(307\) −26.6274 −1.51971 −0.759853 0.650094i \(-0.774729\pi\)
−0.759853 + 0.650094i \(0.774729\pi\)
\(308\) 0 0
\(309\) 0.686292 1.65685i 0.0390418 0.0942551i
\(310\) 0 0
\(311\) −3.70711 1.53553i −0.210211 0.0870721i 0.275094 0.961417i \(-0.411291\pi\)
−0.485304 + 0.874345i \(0.661291\pi\)
\(312\) 0 0
\(313\) −3.94975 + 1.63604i −0.223253 + 0.0924744i −0.491506 0.870874i \(-0.663554\pi\)
0.268253 + 0.963348i \(0.413554\pi\)
\(314\) 0 0
\(315\) −1.00000 1.00000i −0.0563436 0.0563436i
\(316\) 0 0
\(317\) −6.05025 14.6066i −0.339816 0.820388i −0.997733 0.0672979i \(-0.978562\pi\)
0.657917 0.753091i \(-0.271438\pi\)
\(318\) 0 0
\(319\) 4.24264i 0.237542i
\(320\) 0 0
\(321\) 7.82843 7.82843i 0.436940 0.436940i
\(322\) 0 0
\(323\) 4.75736 + 7.92893i 0.264707 + 0.441178i
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) 8.92893i 0.493771i
\(328\) 0 0
\(329\) 1.55635 + 3.75736i 0.0858043 + 0.207150i
\(330\) 0 0
\(331\) −9.72792 9.72792i −0.534695 0.534695i 0.387271 0.921966i \(-0.373418\pi\)
−0.921966 + 0.387271i \(0.873418\pi\)
\(332\) 0 0
\(333\) 1.70711 0.707107i 0.0935489 0.0387492i
\(334\) 0 0
\(335\) 16.4853 + 6.82843i 0.900687 + 0.373077i
\(336\) 0 0
\(337\) 5.94975 14.3640i 0.324103 0.782455i −0.674904 0.737906i \(-0.735815\pi\)
0.999007 0.0445491i \(-0.0141851\pi\)
\(338\) 0 0
\(339\) −6.24264 −0.339054
\(340\) 0 0
\(341\) 1.75736 0.0951663
\(342\) 0 0
\(343\) 1.68629 4.07107i 0.0910512 0.219817i
\(344\) 0 0
\(345\) 8.65685 + 3.58579i 0.466069 + 0.193052i
\(346\) 0 0
\(347\) 5.36396 2.22183i 0.287953 0.119274i −0.234032 0.972229i \(-0.575192\pi\)
0.521984 + 0.852955i \(0.325192\pi\)
\(348\) 0 0
\(349\) −15.4853 15.4853i −0.828908 0.828908i 0.158458 0.987366i \(-0.449348\pi\)
−0.987366 + 0.158458i \(0.949348\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 24.9706i 1.32905i 0.747266 + 0.664524i \(0.231366\pi\)
−0.747266 + 0.664524i \(0.768634\pi\)
\(354\) 0 0
\(355\) 12.6569 12.6569i 0.671756 0.671756i
\(356\) 0 0
\(357\) −0.970563 0.242641i −0.0513676 0.0128419i
\(358\) 0 0
\(359\) −15.7279 + 15.7279i −0.830088 + 0.830088i −0.987528 0.157440i \(-0.949676\pi\)
0.157440 + 0.987528i \(0.449676\pi\)
\(360\) 0 0
\(361\) 13.9706i 0.735293i
\(362\) 0 0
\(363\) 3.05025 + 7.36396i 0.160097 + 0.386508i
\(364\) 0 0
\(365\) 10.4142 + 10.4142i 0.545105 + 0.545105i
\(366\) 0 0
\(367\) −1.94975 + 0.807612i −0.101776 + 0.0421570i −0.432990 0.901398i \(-0.642542\pi\)
0.331214 + 0.943555i \(0.392542\pi\)
\(368\) 0 0
\(369\) −5.53553 2.29289i −0.288168 0.119363i
\(370\) 0 0
\(371\) −0.372583 + 0.899495i −0.0193435 + 0.0466995i
\(372\) 0 0
\(373\) 35.9411 1.86096 0.930480 0.366342i \(-0.119390\pi\)
0.930480 + 0.366342i \(0.119390\pi\)
\(374\) 0 0
\(375\) 9.31371 0.480958
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) 13.9497 + 5.77817i 0.716550 + 0.296805i 0.711012 0.703180i \(-0.248237\pi\)
0.00553829 + 0.999985i \(0.498237\pi\)
\(380\) 0 0
\(381\) 1.24264 0.514719i 0.0636624 0.0263698i
\(382\) 0 0
\(383\) −7.58579 7.58579i −0.387616 0.387616i 0.486221 0.873836i \(-0.338375\pi\)
−0.873836 + 0.486221i \(0.838375\pi\)
\(384\) 0 0
\(385\) −0.171573 0.414214i −0.00874416 0.0211103i
\(386\) 0 0
\(387\) 24.7279i 1.25699i
\(388\) 0 0
\(389\) 20.3137 20.3137i 1.02995 1.02995i 0.0304083 0.999538i \(-0.490319\pi\)
0.999538 0.0304083i \(-0.00968077\pi\)
\(390\) 0 0
\(391\) −27.0208 + 4.02082i −1.36650 + 0.203341i
\(392\) 0 0
\(393\) 7.82843 7.82843i 0.394892 0.394892i
\(394\) 0 0
\(395\) 26.3848i 1.32756i
\(396\) 0 0
\(397\) 11.1213 + 26.8492i 0.558163 + 1.34752i 0.911219 + 0.411923i \(0.135143\pi\)
−0.353056 + 0.935602i \(0.614857\pi\)
\(398\) 0 0
\(399\) 0.384776 + 0.384776i 0.0192629 + 0.0192629i
\(400\) 0 0
\(401\) 25.0208 10.3640i 1.24948 0.517552i 0.342815 0.939403i \(-0.388620\pi\)
0.906665 + 0.421851i \(0.138620\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 0 0
\(405\) −2.87868 + 6.94975i −0.143043 + 0.345336i
\(406\) 0 0
\(407\) 0.585786 0.0290364
\(408\) 0 0
\(409\) 18.0000 0.890043 0.445021 0.895520i \(-0.353196\pi\)
0.445021 + 0.895520i \(0.353196\pi\)
\(410\) 0 0
\(411\) −4.10051 + 9.89949i −0.202263 + 0.488306i
\(412\) 0 0
\(413\) −2.31371 0.958369i −0.113850 0.0471583i
\(414\) 0 0
\(415\) −17.4853 + 7.24264i −0.858319 + 0.355527i
\(416\) 0 0
\(417\) 0.272078 + 0.272078i 0.0133237 + 0.0133237i
\(418\) 0 0
\(419\) −2.53553 6.12132i −0.123869 0.299046i 0.849765 0.527161i \(-0.176744\pi\)
−0.973634 + 0.228115i \(0.926744\pi\)
\(420\) 0 0
\(421\) 11.3137i 0.551396i 0.961244 + 0.275698i \(0.0889090\pi\)
−0.961244 + 0.275698i \(0.911091\pi\)
\(422\) 0 0
\(423\) 21.8995 21.8995i 1.06479 1.06479i
\(424\) 0 0
\(425\) −5.60660 + 3.36396i −0.271960 + 0.163176i
\(426\) 0 0
\(427\) 2.21320 2.21320i 0.107104 0.107104i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −0.878680 2.12132i −0.0423245 0.102180i 0.901304 0.433188i \(-0.142611\pi\)
−0.943628 + 0.331008i \(0.892611\pi\)
\(432\) 0 0
\(433\) 3.82843 + 3.82843i 0.183982 + 0.183982i 0.793089 0.609106i \(-0.208472\pi\)
−0.609106 + 0.793089i \(0.708472\pi\)
\(434\) 0 0
\(435\) 7.24264 3.00000i 0.347258 0.143839i
\(436\) 0 0
\(437\) 13.7279 + 5.68629i 0.656696 + 0.272012i
\(438\) 0 0
\(439\) −3.60660 + 8.70711i −0.172134 + 0.415568i −0.986278 0.165096i \(-0.947207\pi\)
0.814144 + 0.580663i \(0.197207\pi\)
\(440\) 0 0
\(441\) −16.6569 −0.793184
\(442\) 0 0
\(443\) −40.2843 −1.91396 −0.956982 0.290148i \(-0.906295\pi\)
−0.956982 + 0.290148i \(0.906295\pi\)
\(444\) 0 0
\(445\) 1.17157 2.82843i 0.0555379 0.134080i
\(446\) 0 0
\(447\) −4.48528 1.85786i −0.212147 0.0878740i
\(448\) 0 0
\(449\) 16.5355 6.84924i 0.780360 0.323236i 0.0432993 0.999062i \(-0.486213\pi\)
0.737061 + 0.675826i \(0.236213\pi\)
\(450\) 0 0
\(451\) −1.34315 1.34315i −0.0632463 0.0632463i
\(452\) 0 0
\(453\) −5.82843 14.0711i −0.273843 0.661116i
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −3.48528 + 3.48528i −0.163035 + 0.163035i −0.783910 0.620875i \(-0.786777\pi\)
0.620875 + 0.783910i \(0.286777\pi\)
\(458\) 0 0
\(459\) 2.51472 + 16.8995i 0.117377 + 0.788801i
\(460\) 0 0
\(461\) −2.51472 + 2.51472i −0.117122 + 0.117122i −0.763239 0.646117i \(-0.776392\pi\)
0.646117 + 0.763239i \(0.276392\pi\)
\(462\) 0 0
\(463\) 24.1421i 1.12198i −0.827823 0.560990i \(-0.810421\pi\)
0.827823 0.560990i \(-0.189579\pi\)
\(464\) 0 0
\(465\) 1.24264 + 3.00000i 0.0576261 + 0.139122i
\(466\) 0 0
\(467\) 9.58579 + 9.58579i 0.443577 + 0.443577i 0.893212 0.449635i \(-0.148446\pi\)
−0.449635 + 0.893212i \(0.648446\pi\)
\(468\) 0 0
\(469\) −2.82843 + 1.17157i −0.130605 + 0.0540982i
\(470\) 0 0
\(471\) 10.8284 + 4.48528i 0.498948 + 0.206671i
\(472\) 0 0
\(473\) −3.00000 + 7.24264i −0.137940 + 0.333017i
\(474\) 0 0
\(475\) 3.55635 0.163176
\(476\) 0 0
\(477\) 7.41421 0.339474
\(478\) 0 0
\(479\) 14.5355 35.0919i 0.664145 1.60339i −0.127100 0.991890i \(-0.540567\pi\)
0.791245 0.611499i \(-0.209433\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) 0 0
\(483\) −1.48528 + 0.615224i −0.0675826 + 0.0279936i
\(484\) 0 0
\(485\) −20.8995 20.8995i −0.948997 0.948997i
\(486\) 0 0
\(487\) −6.73654 16.2635i −0.305262 0.736968i −0.999846 0.0175559i \(-0.994412\pi\)
0.694584 0.719412i \(-0.255588\pi\)
\(488\) 0 0
\(489\) 3.55635i 0.160824i
\(490\) 0 0
\(491\) 14.4142 14.4142i 0.650504 0.650504i −0.302610 0.953114i \(-0.597858\pi\)
0.953114 + 0.302610i \(0.0978580\pi\)
\(492\) 0 0
\(493\) −13.6066 + 18.3640i −0.612811 + 0.827071i
\(494\) 0 0
\(495\) −2.41421 + 2.41421i −0.108511 + 0.108511i
\(496\) 0 0
\(497\) 3.07107i 0.137756i
\(498\) 0 0
\(499\) 6.43503 + 15.5355i 0.288071 + 0.695466i 0.999977 0.00680940i \(-0.00216752\pi\)
−0.711905 + 0.702275i \(0.752168\pi\)
\(500\) 0 0
\(501\) −0.414214 0.414214i −0.0185057 0.0185057i
\(502\) 0 0
\(503\) −0.292893 + 0.121320i −0.0130595 + 0.00540941i −0.389204 0.921152i \(-0.627250\pi\)
0.376144 + 0.926561i \(0.377250\pi\)
\(504\) 0 0
\(505\) 17.0711 + 7.07107i 0.759653 + 0.314658i
\(506\) 0 0
\(507\) −3.80761 + 9.19239i −0.169102 + 0.408248i
\(508\) 0 0
\(509\) −38.2843 −1.69692 −0.848460 0.529259i \(-0.822470\pi\)
−0.848460 + 0.529259i \(0.822470\pi\)
\(510\) 0 0
\(511\) −2.52691 −0.111784
\(512\) 0 0
\(513\) 3.55635 8.58579i 0.157017 0.379072i
\(514\) 0 0
\(515\) −4.00000 1.65685i −0.176261 0.0730097i
\(516\) 0 0
\(517\) 9.07107 3.75736i 0.398945 0.165248i
\(518\) 0 0
\(519\) −10.2132 10.2132i −0.448310 0.448310i
\(520\) 0 0
\(521\) −15.0208 36.2635i −0.658074 1.58873i −0.800775 0.598965i \(-0.795579\pi\)
0.142701 0.989766i \(-0.454421\pi\)
\(522\) 0 0
\(523\) 4.14214i 0.181123i −0.995891 0.0905615i \(-0.971134\pi\)
0.995891 0.0905615i \(-0.0288662\pi\)
\(524\) 0 0
\(525\) −0.272078 + 0.272078i −0.0118745 + 0.0118745i
\(526\) 0 0
\(527\) −7.60660 5.63604i −0.331349 0.245510i
\(528\) 0 0
\(529\) −14.7782 + 14.7782i −0.642529 + 0.642529i
\(530\) 0 0
\(531\) 19.0711i 0.827614i
\(532\) 0 0
\(533\) 0 0
\(534\) 0 0
\(535\) −18.8995 18.8995i −0.817096 0.817096i
\(536\) 0 0
\(537\) −12.8995 + 5.34315i −0.556654 + 0.230574i
\(538\) 0 0
\(539\) −4.87868 2.02082i −0.210140 0.0870427i
\(540\) 0 0
\(541\) 9.94975 24.0208i 0.427773 1.03274i −0.552219 0.833699i \(-0.686219\pi\)
0.979992 0.199036i \(-0.0637812\pi\)
\(542\) 0 0
\(543\) −6.24264 −0.267897
\(544\) 0 0
\(545\) −21.5563 −0.923373
\(546\) 0 0
\(547\) −17.2635 + 41.6777i −0.738132 + 1.78201i −0.124802 + 0.992182i \(0.539830\pi\)
−0.613330 + 0.789827i \(0.710170\pi\)
\(548\) 0 0
\(549\) −22.0208 9.12132i −0.939825 0.389288i
\(550\) 0 0
\(551\) 11.4853 4.75736i 0.489289 0.202670i
\(552\) 0 0
\(553\) −3.20101 3.20101i −0.136121 0.136121i
\(554\) 0 0
\(555\) 0.414214 + 1.00000i 0.0175824 + 0.0424476i
\(556\) 0 0
\(557\) 16.0000i 0.677942i 0.940797 + 0.338971i \(0.110079\pi\)
−0.940797 + 0.338971i \(0.889921\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 0 0
\(561\) −0.585786 + 2.34315i −0.0247319 + 0.0989277i
\(562\) 0 0
\(563\) 18.4142 18.4142i 0.776067 0.776067i −0.203093 0.979159i \(-0.565099\pi\)
0.979159 + 0.203093i \(0.0650993\pi\)
\(564\) 0 0
\(565\) 15.0711i 0.634045i
\(566\) 0 0
\(567\) −0.493903 1.19239i −0.0207420 0.0500756i
\(568\) 0 0
\(569\) −21.3431 21.3431i −0.894751 0.894751i 0.100215 0.994966i \(-0.468047\pi\)
−0.994966 + 0.100215i \(0.968047\pi\)
\(570\) 0 0
\(571\) 29.8492 12.3640i 1.24915 0.517416i 0.342589 0.939486i \(-0.388696\pi\)
0.906563 + 0.422070i \(0.138696\pi\)
\(572\) 0 0
\(573\) −6.24264 2.58579i −0.260790 0.108023i
\(574\) 0 0
\(575\) −4.02082 + 9.70711i −0.167680 + 0.404814i
\(576\) 0 0
\(577\) 14.0000 0.582828 0.291414 0.956597i \(-0.405874\pi\)
0.291414 + 0.956597i \(0.405874\pi\)
\(578\) 0 0
\(579\) −0.585786 −0.0243445
\(580\) 0 0
\(581\) 1.24264 3.00000i 0.0515534 0.124461i
\(582\) 0 0
\(583\) 2.17157 + 0.899495i 0.0899374 + 0.0372533i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 6.27208 + 6.27208i 0.258876 + 0.258876i 0.824597 0.565721i \(-0.191402\pi\)
−0.565721 + 0.824597i \(0.691402\pi\)
\(588\) 0 0
\(589\) 1.97056 + 4.75736i 0.0811956 + 0.196024i
\(590\) 0 0
\(591\) 9.41421i 0.387249i
\(592\) 0 0
\(593\) 15.3431 15.3431i 0.630067 0.630067i −0.318017 0.948085i \(-0.603017\pi\)
0.948085 + 0.318017i \(0.103017\pi\)
\(594\) 0 0
\(595\) −0.585786 + 2.34315i −0.0240149 + 0.0960596i
\(596\) 0 0
\(597\) −12.1716 + 12.1716i −0.498149 + 0.498149i
\(598\) 0 0
\(599\) 44.8284i 1.83164i −0.401589 0.915820i \(-0.631542\pi\)
0.401589 0.915820i \(-0.368458\pi\)
\(600\) 0 0
\(601\) 11.6066 + 28.0208i 0.473443 + 1.14299i 0.962631 + 0.270815i \(0.0872931\pi\)
−0.489188 + 0.872178i \(0.662707\pi\)
\(602\) 0 0
\(603\) 16.4853 + 16.4853i 0.671333 + 0.671333i
\(604\) 0 0
\(605\) 17.7782 7.36396i 0.722786 0.299388i
\(606\) 0 0
\(607\) 36.0919 + 14.9497i 1.46492 + 0.606792i 0.965695 0.259678i \(-0.0836166\pi\)
0.499229 + 0.866470i \(0.333617\pi\)
\(608\) 0 0
\(609\) −0.514719 + 1.24264i −0.0208575 + 0.0503543i
\(610\) 0 0
\(611\) 0 0
\(612\) 0 0
\(613\) −29.3137 −1.18397 −0.591985 0.805949i \(-0.701655\pi\)
−0.591985 + 0.805949i \(0.701655\pi\)
\(614\) 0 0
\(615\) 1.34315 3.24264i 0.0541609 0.130756i
\(616\) 0 0
\(617\) −22.7782 9.43503i −0.917015 0.379840i −0.126277 0.991995i \(-0.540303\pi\)
−0.790738 + 0.612155i \(0.790303\pi\)
\(618\) 0 0
\(619\) −1.94975 + 0.807612i −0.0783670 + 0.0324607i −0.421523 0.906818i \(-0.638504\pi\)
0.343156 + 0.939279i \(0.388504\pi\)
\(620\) 0 0
\(621\) 19.4142 + 19.4142i 0.779066 + 0.779066i
\(622\) 0 0
\(623\) 0.201010 + 0.485281i 0.00805330 + 0.0194424i
\(624\) 0 0
\(625\) 14.5563i 0.582254i
\(626\) 0 0
\(627\) 0.928932 0.928932i 0.0370980 0.0370980i
\(628\) 0 0
\(629\) −2.53553 1.87868i −0.101098 0.0749079i
\(630\) 0 0
\(631\) −17.3848 + 17.3848i −0.692077 + 0.692077i −0.962689 0.270612i \(-0.912774\pi\)
0.270612 + 0.962689i \(0.412774\pi\)
\(632\) 0 0
\(633\) 20.0416i 0.796583i
\(634\) 0 0
\(635\) −1.24264 3.00000i −0.0493127 0.119051i
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 21.6066 8.94975i 0.854744 0.354047i
\(640\) 0 0
\(641\) 10.8787 + 4.50610i 0.429682 + 0.177980i 0.587034 0.809563i \(-0.300296\pi\)
−0.157352 + 0.987543i \(0.550296\pi\)
\(642\) 0 0
\(643\) 15.0208 36.2635i 0.592363 1.43009i −0.288851 0.957374i \(-0.593273\pi\)
0.881214 0.472717i \(-0.156727\pi\)
\(644\) 0 0
\(645\) −14.4853 −0.570357
\(646\) 0 0
\(647\) 45.2548 1.77915 0.889576 0.456788i \(-0.151000\pi\)
0.889576 + 0.456788i \(0.151000\pi\)
\(648\) 0 0
\(649\) −2.31371 + 5.58579i −0.0908210 + 0.219261i
\(650\) 0 0
\(651\) −0.514719 0.213203i −0.0201734 0.00835610i
\(652\) 0 0
\(653\) 23.3640 9.67767i 0.914302 0.378716i 0.124600 0.992207i \(-0.460235\pi\)
0.789702 + 0.613491i \(0.210235\pi\)
\(654\) 0 0
\(655\) −18.8995 18.8995i −0.738464 0.738464i
\(656\) 0 0
\(657\) 7.36396 + 17.7782i 0.287295 + 0.693593i
\(658\) 0 0
\(659\) 22.7696i 0.886976i 0.896280 + 0.443488i \(0.146259\pi\)
−0.896280 + 0.443488i \(0.853741\pi\)
\(660\) 0 0
\(661\) −18.7990 + 18.7990i −0.731196 + 0.731196i −0.970857 0.239661i \(-0.922964\pi\)
0.239661 + 0.970857i \(0.422964\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 0.928932 0.928932i 0.0360224 0.0360224i
\(666\) 0 0
\(667\) 36.7279i 1.42211i
\(668\) 0 0
\(669\) −5.14214 12.4142i −0.198806 0.479961i
\(670\) 0 0
\(671\) −5.34315 5.34315i −0.206270 0.206270i
\(672\) 0 0
\(673\) 14.1924 5.87868i 0.547076 0.226606i −0.0919875 0.995760i \(-0.529322\pi\)
0.639064 + 0.769154i \(0.279322\pi\)
\(674\) 0 0
\(675\) 6.07107 + 2.51472i 0.233676 + 0.0967916i
\(676\) 0 0
\(677\) −3.90812 + 9.43503i −0.150201 + 0.362618i −0.981015 0.193933i \(-0.937876\pi\)
0.830814 + 0.556551i \(0.187876\pi\)
\(678\) 0 0
\(679\) 5.07107 0.194610
\(680\) 0 0
\(681\) 2.72792 0.104534
\(682\) 0 0
\(683\) −12.9792 + 31.3345i −0.496635 + 1.19898i 0.454650 + 0.890670i \(0.349764\pi\)
−0.951285 + 0.308312i \(0.900236\pi\)
\(684\) 0 0
\(685\) 23.8995 + 9.89949i 0.913153 + 0.378240i
\(686\) 0 0
\(687\) 7.00000 2.89949i 0.267067 0.110623i
\(688\) 0 0
\(689\) 0 0
\(690\) 0 0
\(691\) −12.3934 29.9203i −0.471467 1.13822i −0.963515 0.267654i \(-0.913752\pi\)
0.492048 0.870568i \(-0.336248\pi\)
\(692\) 0 0
\(693\) 0.585786i 0.0222522i
\(694\) 0 0
\(695\) 0.656854 0.656854i 0.0249159 0.0249159i
\(696\) 0 0
\(697\) 1.50610 + 10.1213i 0.0570475 + 0.383372i
\(698\) 0 0
\(699\) −0.313708 + 0.313708i −0.0118655 + 0.0118655i
\(700\) 0 0
\(701\) 28.6863i 1.08347i −0.840551 0.541733i \(-0.817768\pi\)
0.840551 0.541733i \(-0.182232\pi\)
\(702\) 0 0
\(703\) 0.656854 + 1.58579i 0.0247737 + 0.0598091i
\(704\) 0 0
\(705\) 12.8284 + 12.8284i 0.483147 + 0.483147i
\(706\) 0 0
\(707\) −2.92893 + 1.21320i −0.110154 + 0.0456272i
\(708\) 0 0
\(709\) 34.1924 + 14.1630i 1.28412 + 0.531901i 0.917228 0.398362i \(-0.130421\pi\)
0.366894 + 0.930263i \(0.380421\pi\)
\(710\) 0 0
\(711\) −13.1924 + 31.8492i −0.494753 + 1.19444i
\(712\) 0 0
\(713\) −15.2132 −0.569739
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) −3.31371 + 8.00000i −0.123753 + 0.298765i
\(718\) 0 0
\(719\) 17.9497 + 7.43503i 0.669413 + 0.277280i 0.691393 0.722479i \(-0.256997\pi\)
−0.0219807 + 0.999758i \(0.506997\pi\)
\(720\) 0 0
\(721\) 0.686292 0.284271i 0.0255588 0.0105868i
\(722\) 0 0
\(723\) −7.58579 7.58579i −0.282118 0.282118i
\(724\) 0 0
\(725\) 3.36396 + 8.12132i 0.124934 + 0.301618i
\(726\) 0 0
\(727\) 17.7990i 0.660128i 0.943959 + 0.330064i \(0.107070\pi\)
−0.943959 + 0.330064i \(0.892930\pi\)
\(728\) 0 0
\(729\) −0.221825 + 0.221825i −0.00821576 + 0.00821576i
\(730\) 0 0
\(731\) 36.2132 21.7279i 1.33939 0.803636i
\(732\) 0 0
\(733\) 17.4853 17.4853i 0.645834 0.645834i −0.306150 0.951983i \(-0.599041\pi\)
0.951983 + 0.306150i \(0.0990408\pi\)
\(734\) 0 0
\(735\) 9.75736i 0.359906i
\(736\) 0 0
\(737\) 2.82843 + 6.82843i 0.104186 + 0.251528i
\(738\) 0 0
\(739\) −6.41421 6.41421i −0.235951 0.235951i 0.579220 0.815171i \(-0.303357\pi\)
−0.815171 + 0.579220i \(0.803357\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −29.8492 12.3640i −1.09506 0.453590i −0.239293 0.970947i \(-0.576916\pi\)
−0.855769 + 0.517358i \(0.826916\pi\)
\(744\) 0 0
\(745\) −4.48528 + 10.8284i −0.164328 + 0.396723i
\(746\) 0 0
\(747\) −24.7279 −0.904747
\(748\) 0 0
\(749\) 4.58579 0.167561
\(750\) 0 0
\(751\) −9.26346 + 22.3640i −0.338028 + 0.816073i 0.659877 + 0.751374i \(0.270609\pi\)
−0.997905 + 0.0646985i \(0.979391\pi\)
\(752\) 0 0
\(753\) 0.585786 + 0.242641i 0.0213472 + 0.00884232i
\(754\) 0 0
\(755\) −33.9706 + 14.0711i −1.23632 + 0.512099i
\(756\) 0 0
\(757\) 9.97056 + 9.97056i 0.362386 + 0.362386i 0.864691 0.502305i \(-0.167514\pi\)
−0.502305 + 0.864691i \(0.667514\pi\)
\(758\) 0 0
\(759\) 1.48528 + 3.58579i 0.0539123 + 0.130156i
\(760\) 0 0
\(761\) 3.02944i 0.109817i 0.998491 + 0.0549085i \(0.0174867\pi\)
−0.998491 + 0.0549085i \(0.982513\pi\)
\(762\) 0 0
\(763\) 2.61522 2.61522i 0.0946775 0.0946775i
\(764\) 0 0
\(765\) 18.1924 2.70711i 0.657747 0.0978757i
\(766\) 0 0
\(767\) 0 0
\(768\) 0 0
\(769\) 43.5980i 1.57218i −0.618110 0.786092i \(-0.712101\pi\)
0.618110 0.786092i \(-0.287899\pi\)
\(770\) 0 0
\(771\) −2.41421 5.82843i −0.0869458 0.209906i
\(772\) 0 0
\(773\) −23.2843 23.2843i −0.837477 0.837477i 0.151049 0.988526i \(-0.451735\pi\)
−0.988526 + 0.151049i \(0.951735\pi\)
\(774\) 0 0
\(775\) −3.36396 + 1.39340i −0.120837 + 0.0500523i
\(776\) 0 0
\(777\) −0.171573 0.0710678i −0.00615514 0.00254954i
\(778\) 0 0
\(779\) 2.12994 5.14214i 0.0763131 0.184236i
\(780\) 0 0
\(781\) 7.41421 0.265301
\(782\) 0 0
\(783\) 22.9706 0.820901
\(784\) 0 0
\(785\) 10.8284 26.1421i 0.386483 0.933053i
\(786\) 0 0
\(787\) 10.4350 + 4.32233i 0.371969 + 0.154074i 0.560833 0.827929i \(-0.310481\pi\)
−0.188865 + 0.982003i \(0.560481\pi\)
\(788\) 0 0
\(789\) −2.75736 + 1.14214i −0.0981646 + 0.0406611i
\(790\) 0 0
\(791\) −1.82843 1.82843i −0.0650114 0.0650114i
\(792\) 0 0
\(793\) 0 0
\(794\) 0 0
\(795\) 4.34315i 0.154036i
\(796\) 0 0