Properties

Label 384.2.k.b.287.5
Level $384$
Weight $2$
Character 384.287
Analytic conductor $3.066$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $4$

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Newspace parameters

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

Newform invariants

Self dual: no
Analytic conductor: \(3.06625543762\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(i)\)
Coefficient field: 12.0.163368480538624.2
Defining polynomial: \(x^{12} - 2 x^{10} - 2 x^{8} + 16 x^{6} - 8 x^{4} - 32 x^{2} + 64\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{7} \)
Twist minimal: no (minimal twist has level 48)
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 287.5
Root \(1.35164 + 0.416001i\) of defining polynomial
Character \(\chi\) \(=\) 384.287
Dual form 384.2.k.b.95.5

$q$-expansion

\(f(q)\) \(=\) \(q+(1.43726 - 0.966579i) q^{3} +(-1.57184 + 1.57184i) q^{5} +2.24914 q^{7} +(1.13145 - 2.77846i) q^{9} +O(q^{10})\) \(q+(1.43726 - 0.966579i) q^{3} +(-1.57184 + 1.57184i) q^{5} +2.24914 q^{7} +(1.13145 - 2.77846i) q^{9} +(1.13145 + 1.13145i) q^{11} +(3.24914 - 3.24914i) q^{13} +(-0.739839 + 3.77846i) q^{15} -1.66400i q^{17} +(3.77846 + 3.77846i) q^{19} +(3.23261 - 2.17397i) q^{21} +2.26290i q^{23} +0.0586332i q^{25} +(-1.05941 - 5.08701i) q^{27} +(-3.23584 - 3.23584i) q^{29} -1.30777i q^{31} +(2.71982 + 0.532554i) q^{33} +(-3.53529 + 3.53529i) q^{35} +(-2.30777 - 2.30777i) q^{37} +(1.52932 - 7.81042i) q^{39} -10.2143 q^{41} +(-3.77846 + 3.77846i) q^{43} +(2.58884 + 6.14575i) q^{45} +3.74258 q^{47} -1.94137 q^{49} +(-1.60839 - 2.39161i) q^{51} +(0.972946 - 0.972946i) q^{53} -3.55691 q^{55} +(9.08281 + 1.77846i) q^{57} +(3.88352 + 3.88352i) q^{59} +(-4.19051 + 4.19051i) q^{61} +(2.54479 - 6.24914i) q^{63} +10.2143i q^{65} +(-8.02760 - 8.02760i) q^{67} +(2.18727 + 3.25238i) q^{69} +11.0950i q^{71} +6.38101i q^{73} +(0.0566736 + 0.0842713i) q^{75} +(2.54479 + 2.54479i) q^{77} -2.69223i q^{79} +(-6.43965 - 6.28736i) q^{81} +(2.61113 - 2.61113i) q^{83} +(2.61555 + 2.61555i) q^{85} +(-7.77846 - 1.52306i) q^{87} +7.35247 q^{89} +(7.30777 - 7.30777i) q^{91} +(-1.26407 - 1.87961i) q^{93} -11.8783 q^{95} -5.67418 q^{97} +(4.42386 - 1.86351i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12q + 2q^{3} - 8q^{7} + O(q^{10}) \) \( 12q + 2q^{3} - 8q^{7} + 4q^{13} + 12q^{19} + 8q^{21} - 10q^{27} - 4q^{33} + 4q^{37} + 20q^{39} - 12q^{43} + 12q^{45} - 20q^{49} - 24q^{51} + 24q^{55} - 12q^{61} - 28q^{67} - 4q^{69} + 34q^{75} - 4q^{81} - 32q^{85} - 60q^{87} + 56q^{91} - 28q^{93} - 8q^{97} + 52q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/384\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(133\) \(257\)
\(\chi(n)\) \(-1\) \(e\left(\frac{1}{4}\right)\) \(-1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 1.43726 0.966579i 0.829804 0.558055i
\(4\) 0 0
\(5\) −1.57184 + 1.57184i −0.702949 + 0.702949i −0.965042 0.262094i \(-0.915587\pi\)
0.262094 + 0.965042i \(0.415587\pi\)
\(6\) 0 0
\(7\) 2.24914 0.850095 0.425048 0.905171i \(-0.360257\pi\)
0.425048 + 0.905171i \(0.360257\pi\)
\(8\) 0 0
\(9\) 1.13145 2.77846i 0.377150 0.926152i
\(10\) 0 0
\(11\) 1.13145 + 1.13145i 0.341145 + 0.341145i 0.856798 0.515653i \(-0.172451\pi\)
−0.515653 + 0.856798i \(0.672451\pi\)
\(12\) 0 0
\(13\) 3.24914 3.24914i 0.901149 0.901149i −0.0943862 0.995536i \(-0.530089\pi\)
0.995536 + 0.0943862i \(0.0300889\pi\)
\(14\) 0 0
\(15\) −0.739839 + 3.77846i −0.191026 + 0.975593i
\(16\) 0 0
\(17\) 1.66400i 0.403580i −0.979429 0.201790i \(-0.935324\pi\)
0.979429 0.201790i \(-0.0646758\pi\)
\(18\) 0 0
\(19\) 3.77846 + 3.77846i 0.866838 + 0.866838i 0.992121 0.125283i \(-0.0399840\pi\)
−0.125283 + 0.992121i \(0.539984\pi\)
\(20\) 0 0
\(21\) 3.23261 2.17397i 0.705412 0.474400i
\(22\) 0 0
\(23\) 2.26290i 0.471847i 0.971772 + 0.235923i \(0.0758114\pi\)
−0.971772 + 0.235923i \(0.924189\pi\)
\(24\) 0 0
\(25\) 0.0586332i 0.0117266i
\(26\) 0 0
\(27\) −1.05941 5.08701i −0.203884 0.978995i
\(28\) 0 0
\(29\) −3.23584 3.23584i −0.600881 0.600881i 0.339665 0.940546i \(-0.389686\pi\)
−0.940546 + 0.339665i \(0.889686\pi\)
\(30\) 0 0
\(31\) 1.30777i 0.234883i −0.993080 0.117442i \(-0.962531\pi\)
0.993080 0.117442i \(-0.0374693\pi\)
\(32\) 0 0
\(33\) 2.71982 + 0.532554i 0.473461 + 0.0927058i
\(34\) 0 0
\(35\) −3.53529 + 3.53529i −0.597573 + 0.597573i
\(36\) 0 0
\(37\) −2.30777 2.30777i −0.379396 0.379396i 0.491488 0.870884i \(-0.336453\pi\)
−0.870884 + 0.491488i \(0.836453\pi\)
\(38\) 0 0
\(39\) 1.52932 7.81042i 0.244887 1.25067i
\(40\) 0 0
\(41\) −10.2143 −1.59520 −0.797600 0.603187i \(-0.793897\pi\)
−0.797600 + 0.603187i \(0.793897\pi\)
\(42\) 0 0
\(43\) −3.77846 + 3.77846i −0.576209 + 0.576209i −0.933857 0.357647i \(-0.883579\pi\)
0.357647 + 0.933857i \(0.383579\pi\)
\(44\) 0 0
\(45\) 2.58884 + 6.14575i 0.385921 + 0.916154i
\(46\) 0 0
\(47\) 3.74258 0.545911 0.272955 0.962027i \(-0.411999\pi\)
0.272955 + 0.962027i \(0.411999\pi\)
\(48\) 0 0
\(49\) −1.94137 −0.277338
\(50\) 0 0
\(51\) −1.60839 2.39161i −0.225220 0.334892i
\(52\) 0 0
\(53\) 0.972946 0.972946i 0.133644 0.133644i −0.637120 0.770765i \(-0.719874\pi\)
0.770765 + 0.637120i \(0.219874\pi\)
\(54\) 0 0
\(55\) −3.55691 −0.479614
\(56\) 0 0
\(57\) 9.08281 + 1.77846i 1.20305 + 0.235562i
\(58\) 0 0
\(59\) 3.88352 + 3.88352i 0.505591 + 0.505591i 0.913170 0.407579i \(-0.133627\pi\)
−0.407579 + 0.913170i \(0.633627\pi\)
\(60\) 0 0
\(61\) −4.19051 + 4.19051i −0.536539 + 0.536539i −0.922511 0.385971i \(-0.873866\pi\)
0.385971 + 0.922511i \(0.373866\pi\)
\(62\) 0 0
\(63\) 2.54479 6.24914i 0.320613 0.787318i
\(64\) 0 0
\(65\) 10.2143i 1.26692i
\(66\) 0 0
\(67\) −8.02760 8.02760i −0.980727 0.980727i 0.0190906 0.999818i \(-0.493923\pi\)
−0.999818 + 0.0190906i \(0.993923\pi\)
\(68\) 0 0
\(69\) 2.18727 + 3.25238i 0.263316 + 0.391540i
\(70\) 0 0
\(71\) 11.0950i 1.31674i 0.752695 + 0.658370i \(0.228754\pi\)
−0.752695 + 0.658370i \(0.771246\pi\)
\(72\) 0 0
\(73\) 6.38101i 0.746841i 0.927662 + 0.373421i \(0.121815\pi\)
−0.927662 + 0.373421i \(0.878185\pi\)
\(74\) 0 0
\(75\) 0.0566736 + 0.0842713i 0.00654410 + 0.00973081i
\(76\) 0 0
\(77\) 2.54479 + 2.54479i 0.290005 + 0.290005i
\(78\) 0 0
\(79\) 2.69223i 0.302899i −0.988465 0.151450i \(-0.951606\pi\)
0.988465 0.151450i \(-0.0483941\pi\)
\(80\) 0 0
\(81\) −6.43965 6.28736i −0.715516 0.698596i
\(82\) 0 0
\(83\) 2.61113 2.61113i 0.286608 0.286608i −0.549129 0.835738i \(-0.685040\pi\)
0.835738 + 0.549129i \(0.185040\pi\)
\(84\) 0 0
\(85\) 2.61555 + 2.61555i 0.283696 + 0.283696i
\(86\) 0 0
\(87\) −7.77846 1.52306i −0.833938 0.163289i
\(88\) 0 0
\(89\) 7.35247 0.779360 0.389680 0.920950i \(-0.372586\pi\)
0.389680 + 0.920950i \(0.372586\pi\)
\(90\) 0 0
\(91\) 7.30777 7.30777i 0.766063 0.766063i
\(92\) 0 0
\(93\) −1.26407 1.87961i −0.131078 0.194907i
\(94\) 0 0
\(95\) −11.8783 −1.21868
\(96\) 0 0
\(97\) −5.67418 −0.576126 −0.288063 0.957611i \(-0.593011\pi\)
−0.288063 + 0.957611i \(0.593011\pi\)
\(98\) 0 0
\(99\) 4.42386 1.86351i 0.444614 0.187289i
\(100\) 0 0
\(101\) −10.3064 + 10.3064i −1.02553 + 1.02553i −0.0258621 + 0.999666i \(0.508233\pi\)
−0.999666 + 0.0258621i \(0.991767\pi\)
\(102\) 0 0
\(103\) −8.13187 −0.801257 −0.400629 0.916241i \(-0.631208\pi\)
−0.400629 + 0.916241i \(0.631208\pi\)
\(104\) 0 0
\(105\) −1.66400 + 8.49828i −0.162390 + 0.829347i
\(106\) 0 0
\(107\) −2.40384 2.40384i −0.232388 0.232388i 0.581301 0.813689i \(-0.302544\pi\)
−0.813689 + 0.581301i \(0.802544\pi\)
\(108\) 0 0
\(109\) −8.92332 + 8.92332i −0.854699 + 0.854699i −0.990708 0.136009i \(-0.956573\pi\)
0.136009 + 0.990708i \(0.456573\pi\)
\(110\) 0 0
\(111\) −5.54752 1.08623i −0.526548 0.103100i
\(112\) 0 0
\(113\) 15.9027i 1.49600i −0.663697 0.748002i \(-0.731014\pi\)
0.663697 0.748002i \(-0.268986\pi\)
\(114\) 0 0
\(115\) −3.55691 3.55691i −0.331684 0.331684i
\(116\) 0 0
\(117\) −5.35136 12.7038i −0.494734 1.17447i
\(118\) 0 0
\(119\) 3.74258i 0.343081i
\(120\) 0 0
\(121\) 8.43965i 0.767241i
\(122\) 0 0
\(123\) −14.6806 + 9.87290i −1.32370 + 0.890209i
\(124\) 0 0
\(125\) −7.95137 7.95137i −0.711192 0.711192i
\(126\) 0 0
\(127\) 7.42504i 0.658866i 0.944179 + 0.329433i \(0.106858\pi\)
−0.944179 + 0.329433i \(0.893142\pi\)
\(128\) 0 0
\(129\) −1.77846 + 9.08281i −0.156584 + 0.799697i
\(130\) 0 0
\(131\) −3.88352 + 3.88352i −0.339305 + 0.339305i −0.856106 0.516801i \(-0.827123\pi\)
0.516801 + 0.856106i \(0.327123\pi\)
\(132\) 0 0
\(133\) 8.49828 + 8.49828i 0.736894 + 0.736894i
\(134\) 0 0
\(135\) 9.66119 + 6.33074i 0.831503 + 0.544864i
\(136\) 0 0
\(137\) −2.72911 −0.233164 −0.116582 0.993181i \(-0.537194\pi\)
−0.116582 + 0.993181i \(0.537194\pi\)
\(138\) 0 0
\(139\) 0.0275977 0.0275977i 0.00234080 0.00234080i −0.705935 0.708276i \(-0.749473\pi\)
0.708276 + 0.705935i \(0.249473\pi\)
\(140\) 0 0
\(141\) 5.37907 3.61750i 0.452999 0.304648i
\(142\) 0 0
\(143\) 7.35247 0.614845
\(144\) 0 0
\(145\) 10.1725 0.844777
\(146\) 0 0
\(147\) −2.79025 + 1.87649i −0.230136 + 0.154770i
\(148\) 0 0
\(149\) 12.5693 12.5693i 1.02972 1.02972i 0.0301744 0.999545i \(-0.490394\pi\)
0.999545 0.0301744i \(-0.00960626\pi\)
\(150\) 0 0
\(151\) 16.8647 1.37243 0.686214 0.727399i \(-0.259271\pi\)
0.686214 + 0.727399i \(0.259271\pi\)
\(152\) 0 0
\(153\) −4.62336 1.88273i −0.373777 0.152210i
\(154\) 0 0
\(155\) 2.05561 + 2.05561i 0.165111 + 0.165111i
\(156\) 0 0
\(157\) 5.36641 5.36641i 0.428286 0.428286i −0.459758 0.888044i \(-0.652064\pi\)
0.888044 + 0.459758i \(0.152064\pi\)
\(158\) 0 0
\(159\) 0.457950 2.33881i 0.0363178 0.185480i
\(160\) 0 0
\(161\) 5.08957i 0.401115i
\(162\) 0 0
\(163\) 8.77502 + 8.77502i 0.687313 + 0.687313i 0.961637 0.274325i \(-0.0884543\pi\)
−0.274325 + 0.961637i \(0.588454\pi\)
\(164\) 0 0
\(165\) −5.11222 + 3.43804i −0.397986 + 0.267651i
\(166\) 0 0
\(167\) 16.9678i 1.31301i −0.754321 0.656505i \(-0.772034\pi\)
0.754321 0.656505i \(-0.227966\pi\)
\(168\) 0 0
\(169\) 8.11383i 0.624141i
\(170\) 0 0
\(171\) 14.7734 6.22315i 1.12975 0.475896i
\(172\) 0 0
\(173\) 16.3119 + 16.3119i 1.24017 + 1.24017i 0.959930 + 0.280241i \(0.0904144\pi\)
0.280241 + 0.959930i \(0.409586\pi\)
\(174\) 0 0
\(175\) 0.131874i 0.00996875i
\(176\) 0 0
\(177\) 9.33537 + 1.82791i 0.701689 + 0.137394i
\(178\) 0 0
\(179\) −1.33873 + 1.33873i −0.100062 + 0.100062i −0.755365 0.655304i \(-0.772541\pi\)
0.655304 + 0.755365i \(0.272541\pi\)
\(180\) 0 0
\(181\) −10.2457 10.2457i −0.761557 0.761557i 0.215047 0.976604i \(-0.431010\pi\)
−0.976604 + 0.215047i \(0.931010\pi\)
\(182\) 0 0
\(183\) −1.97240 + 10.0733i −0.145804 + 0.744641i
\(184\) 0 0
\(185\) 7.25491 0.533391
\(186\) 0 0
\(187\) 1.88273 1.88273i 0.137679 0.137679i
\(188\) 0 0
\(189\) −2.38276 11.4414i −0.173320 0.832239i
\(190\) 0 0
\(191\) 24.5398 1.77563 0.887817 0.460197i \(-0.152221\pi\)
0.887817 + 0.460197i \(0.152221\pi\)
\(192\) 0 0
\(193\) 8.38101 0.603279 0.301639 0.953422i \(-0.402466\pi\)
0.301639 + 0.953422i \(0.402466\pi\)
\(194\) 0 0
\(195\) 9.87290 + 14.6806i 0.707013 + 1.05130i
\(196\) 0 0
\(197\) 1.28995 1.28995i 0.0919052 0.0919052i −0.659659 0.751565i \(-0.729299\pi\)
0.751565 + 0.659659i \(0.229299\pi\)
\(198\) 0 0
\(199\) −13.0992 −0.928579 −0.464290 0.885683i \(-0.653690\pi\)
−0.464290 + 0.885683i \(0.653690\pi\)
\(200\) 0 0
\(201\) −19.2971 3.77846i −1.36111 0.266512i
\(202\) 0 0
\(203\) −7.27787 7.27787i −0.510806 0.510806i
\(204\) 0 0
\(205\) 16.0552 16.0552i 1.12134 1.12134i
\(206\) 0 0
\(207\) 6.28736 + 2.56035i 0.437002 + 0.177957i
\(208\) 0 0
\(209\) 8.55026i 0.591434i
\(210\) 0 0
\(211\) 8.47068 + 8.47068i 0.583146 + 0.583146i 0.935766 0.352621i \(-0.114709\pi\)
−0.352621 + 0.935766i \(0.614709\pi\)
\(212\) 0 0
\(213\) 10.7242 + 15.9465i 0.734813 + 1.09264i
\(214\) 0 0
\(215\) 11.8783i 0.810091i
\(216\) 0 0
\(217\) 2.94137i 0.199673i
\(218\) 0 0
\(219\) 6.16776 + 9.17120i 0.416778 + 0.619732i
\(220\) 0 0
\(221\) −5.40658 5.40658i −0.363686 0.363686i
\(222\) 0 0
\(223\) 21.5715i 1.44454i 0.691613 + 0.722268i \(0.256900\pi\)
−0.691613 + 0.722268i \(0.743100\pi\)
\(224\) 0 0
\(225\) 0.162910 + 0.0663404i 0.0108606 + 0.00442269i
\(226\) 0 0
\(227\) 16.7523 16.7523i 1.11189 1.11189i 0.118994 0.992895i \(-0.462033\pi\)
0.992895 0.118994i \(-0.0379668\pi\)
\(228\) 0 0
\(229\) −3.36641 3.36641i −0.222458 0.222458i 0.587074 0.809533i \(-0.300280\pi\)
−0.809533 + 0.587074i \(0.800280\pi\)
\(230\) 0 0
\(231\) 6.11727 + 1.19779i 0.402487 + 0.0788087i
\(232\) 0 0
\(233\) 0.501329 0.0328431 0.0164216 0.999865i \(-0.494773\pi\)
0.0164216 + 0.999865i \(0.494773\pi\)
\(234\) 0 0
\(235\) −5.88273 + 5.88273i −0.383747 + 0.383747i
\(236\) 0 0
\(237\) −2.60225 3.86944i −0.169034 0.251347i
\(238\) 0 0
\(239\) −30.4585 −1.97019 −0.985097 0.171999i \(-0.944978\pi\)
−0.985097 + 0.171999i \(0.944978\pi\)
\(240\) 0 0
\(241\) −15.4948 −0.998111 −0.499055 0.866570i \(-0.666320\pi\)
−0.499055 + 0.866570i \(0.666320\pi\)
\(242\) 0 0
\(243\) −15.3327 2.81216i −0.983593 0.180400i
\(244\) 0 0
\(245\) 3.05152 3.05152i 0.194954 0.194954i
\(246\) 0 0
\(247\) 24.5535 1.56230
\(248\) 0 0
\(249\) 1.22901 6.27674i 0.0778856 0.397772i
\(250\) 0 0
\(251\) −12.2265 12.2265i −0.771730 0.771730i 0.206679 0.978409i \(-0.433734\pi\)
−0.978409 + 0.206679i \(0.933734\pi\)
\(252\) 0 0
\(253\) −2.56035 + 2.56035i −0.160968 + 0.160968i
\(254\) 0 0
\(255\) 6.28736 + 1.23109i 0.393730 + 0.0770941i
\(256\) 0 0
\(257\) 7.48515i 0.466911i −0.972367 0.233455i \(-0.924997\pi\)
0.972367 0.233455i \(-0.0750033\pi\)
\(258\) 0 0
\(259\) −5.19051 5.19051i −0.322522 0.322522i
\(260\) 0 0
\(261\) −12.6518 + 5.32946i −0.783129 + 0.329885i
\(262\) 0 0
\(263\) 10.2659i 0.633023i 0.948589 + 0.316511i \(0.102512\pi\)
−0.948589 + 0.316511i \(0.897488\pi\)
\(264\) 0 0
\(265\) 3.05863i 0.187890i
\(266\) 0 0
\(267\) 10.5674 7.10675i 0.646716 0.434926i
\(268\) 0 0
\(269\) −2.76963 2.76963i −0.168867 0.168867i 0.617614 0.786481i \(-0.288099\pi\)
−0.786481 + 0.617614i \(0.788099\pi\)
\(270\) 0 0
\(271\) 28.6854i 1.74251i −0.490830 0.871255i \(-0.663306\pi\)
0.490830 0.871255i \(-0.336694\pi\)
\(272\) 0 0
\(273\) 3.43965 17.5667i 0.208177 1.06319i
\(274\) 0 0
\(275\) −0.0663404 + 0.0663404i −0.00400048 + 0.00400048i
\(276\) 0 0
\(277\) 0.806055 + 0.806055i 0.0484311 + 0.0484311i 0.730908 0.682476i \(-0.239097\pi\)
−0.682476 + 0.730908i \(0.739097\pi\)
\(278\) 0 0
\(279\) −3.63359 1.47968i −0.217538 0.0885861i
\(280\) 0 0
\(281\) 22.3228 1.33167 0.665833 0.746101i \(-0.268076\pi\)
0.665833 + 0.746101i \(0.268076\pi\)
\(282\) 0 0
\(283\) −8.08279 + 8.08279i −0.480472 + 0.480472i −0.905282 0.424810i \(-0.860341\pi\)
0.424810 + 0.905282i \(0.360341\pi\)
\(284\) 0 0
\(285\) −17.0722 + 11.4813i −1.01127 + 0.680093i
\(286\) 0 0
\(287\) −22.9733 −1.35607
\(288\) 0 0
\(289\) 14.2311 0.837123
\(290\) 0 0
\(291\) −8.15529 + 5.48455i −0.478071 + 0.321510i
\(292\) 0 0
\(293\) 6.37953 6.37953i 0.372696 0.372696i −0.495762 0.868458i \(-0.665111\pi\)
0.868458 + 0.495762i \(0.165111\pi\)
\(294\) 0 0
\(295\) −12.2086 −0.710809
\(296\) 0 0
\(297\) 4.55702 6.95436i 0.264425 0.403533i
\(298\) 0 0
\(299\) 7.35247 + 7.35247i 0.425204 + 0.425204i
\(300\) 0 0
\(301\) −8.49828 + 8.49828i −0.489833 + 0.489833i
\(302\) 0 0
\(303\) −4.85106 + 24.7750i −0.278686 + 1.42329i
\(304\) 0 0
\(305\) 13.1736i 0.754319i
\(306\) 0 0
\(307\) 6.58795 + 6.58795i 0.375994 + 0.375994i 0.869655 0.493661i \(-0.164341\pi\)
−0.493661 + 0.869655i \(0.664341\pi\)
\(308\) 0 0
\(309\) −11.6876 + 7.86010i −0.664887 + 0.447146i
\(310\) 0 0
\(311\) 9.52861i 0.540318i 0.962816 + 0.270159i \(0.0870763\pi\)
−0.962816 + 0.270159i \(0.912924\pi\)
\(312\) 0 0
\(313\) 25.1690i 1.42264i 0.702870 + 0.711319i \(0.251902\pi\)
−0.702870 + 0.711319i \(0.748098\pi\)
\(314\) 0 0
\(315\) 5.82265 + 13.8227i 0.328069 + 0.778818i
\(316\) 0 0
\(317\) 15.5287 + 15.5287i 0.872178 + 0.872178i 0.992709 0.120532i \(-0.0384600\pi\)
−0.120532 + 0.992709i \(0.538460\pi\)
\(318\) 0 0
\(319\) 7.32238i 0.409975i
\(320\) 0 0
\(321\) −5.77846 1.13145i −0.322522 0.0631513i
\(322\) 0 0
\(323\) 6.28736 6.28736i 0.349838 0.349838i
\(324\) 0 0
\(325\) 0.190507 + 0.190507i 0.0105674 + 0.0105674i
\(326\) 0 0
\(327\) −4.20006 + 21.4503i −0.232264 + 1.18620i
\(328\) 0 0
\(329\) 8.41758 0.464076
\(330\) 0 0
\(331\) −2.58795 + 2.58795i −0.142247 + 0.142247i −0.774644 0.632397i \(-0.782071\pi\)
0.632397 + 0.774644i \(0.282071\pi\)
\(332\) 0 0
\(333\) −9.02318 + 3.80092i −0.494467 + 0.208289i
\(334\) 0 0
\(335\) 25.2362 1.37880
\(336\) 0 0
\(337\) −23.1690 −1.26210 −0.631049 0.775743i \(-0.717375\pi\)
−0.631049 + 0.775743i \(0.717375\pi\)
\(338\) 0 0
\(339\) −15.3713 22.8564i −0.834852 1.24139i
\(340\) 0 0
\(341\) 1.47968 1.47968i 0.0801291 0.0801291i
\(342\) 0 0
\(343\) −20.1104 −1.08586
\(344\) 0 0
\(345\) −8.55026 1.67418i −0.460331 0.0901349i
\(346\) 0 0
\(347\) −6.72235 6.72235i −0.360875 0.360875i 0.503260 0.864135i \(-0.332134\pi\)
−0.864135 + 0.503260i \(0.832134\pi\)
\(348\) 0 0
\(349\) 2.75086 2.75086i 0.147250 0.147250i −0.629638 0.776888i \(-0.716797\pi\)
0.776888 + 0.629638i \(0.216797\pi\)
\(350\) 0 0
\(351\) −19.9706 13.0862i −1.06595 0.698491i
\(352\) 0 0
\(353\) 23.1928i 1.23443i 0.786796 + 0.617213i \(0.211738\pi\)
−0.786796 + 0.617213i \(0.788262\pi\)
\(354\) 0 0
\(355\) −17.4396 17.4396i −0.925600 0.925600i
\(356\) 0 0
\(357\) −3.61750 5.37907i −0.191458 0.284690i
\(358\) 0 0
\(359\) 27.3664i 1.44434i −0.691713 0.722172i \(-0.743144\pi\)
0.691713 0.722172i \(-0.256856\pi\)
\(360\) 0 0
\(361\) 9.55348i 0.502815i
\(362\) 0 0
\(363\) −8.15759 12.1300i −0.428162 0.636659i
\(364\) 0 0
\(365\) −10.0299 10.0299i −0.524991 0.524991i
\(366\) 0 0
\(367\) 26.0406i 1.35931i −0.733533 0.679654i \(-0.762130\pi\)
0.733533 0.679654i \(-0.237870\pi\)
\(368\) 0 0
\(369\) −11.5569 + 28.3799i −0.601629 + 1.47740i
\(370\) 0 0
\(371\) 2.18829 2.18829i 0.113611 0.113611i
\(372\) 0 0
\(373\) 13.1319 + 13.1319i 0.679943 + 0.679943i 0.959987 0.280044i \(-0.0903492\pi\)
−0.280044 + 0.959987i \(0.590349\pi\)
\(374\) 0 0
\(375\) −19.1138 3.74258i −0.987034 0.193266i
\(376\) 0 0
\(377\) −21.0274 −1.08297
\(378\) 0 0
\(379\) 17.4526 17.4526i 0.896482 0.896482i −0.0986413 0.995123i \(-0.531450\pi\)
0.995123 + 0.0986413i \(0.0314496\pi\)
\(380\) 0 0
\(381\) 7.17689 + 10.6717i 0.367683 + 0.546729i
\(382\) 0 0
\(383\) 26.4965 1.35391 0.676953 0.736027i \(-0.263300\pi\)
0.676953 + 0.736027i \(0.263300\pi\)
\(384\) 0 0
\(385\) −8.00000 −0.407718
\(386\) 0 0
\(387\) 6.22315 + 14.7734i 0.316341 + 0.750975i
\(388\) 0 0
\(389\) −2.35506 + 2.35506i −0.119406 + 0.119406i −0.764285 0.644879i \(-0.776908\pi\)
0.644879 + 0.764285i \(0.276908\pi\)
\(390\) 0 0
\(391\) 3.76547 0.190428
\(392\) 0 0
\(393\) −1.82791 + 9.33537i −0.0922058 + 0.470907i
\(394\) 0 0
\(395\) 4.23175 + 4.23175i 0.212923 + 0.212923i
\(396\) 0 0
\(397\) −4.68879 + 4.68879i −0.235324 + 0.235324i −0.814910 0.579587i \(-0.803214\pi\)
0.579587 + 0.814910i \(0.303214\pi\)
\(398\) 0 0
\(399\) 20.4285 + 4.00000i 1.02271 + 0.200250i
\(400\) 0 0
\(401\) 5.18714i 0.259033i 0.991577 + 0.129517i \(0.0413426\pi\)
−0.991577 + 0.129517i \(0.958657\pi\)
\(402\) 0 0
\(403\) −4.24914 4.24914i −0.211665 0.211665i
\(404\) 0 0
\(405\) 20.0048 0.239367i 0.994048 0.0118943i
\(406\) 0 0
\(407\) 5.22225i 0.258858i
\(408\) 0 0
\(409\) 14.8793i 0.735734i 0.929878 + 0.367867i \(0.119912\pi\)
−0.929878 + 0.367867i \(0.880088\pi\)
\(410\) 0 0
\(411\) −3.92245 + 2.63790i −0.193480 + 0.130118i
\(412\) 0 0
\(413\) 8.73458 + 8.73458i 0.429801 + 0.429801i
\(414\) 0 0
\(415\) 8.20855i 0.402942i
\(416\) 0 0
\(417\) 0.0129898 0.0663404i 0.000636111 0.00324870i
\(418\) 0 0
\(419\) −25.3026 + 25.3026i −1.23611 + 1.23611i −0.274533 + 0.961578i \(0.588523\pi\)
−0.961578 + 0.274533i \(0.911477\pi\)
\(420\) 0 0
\(421\) −7.13187 7.13187i −0.347586 0.347586i 0.511623 0.859210i \(-0.329044\pi\)
−0.859210 + 0.511623i \(0.829044\pi\)
\(422\) 0 0
\(423\) 4.23453 10.3986i 0.205890 0.505597i
\(424\) 0 0
\(425\) 0.0975657 0.00473263
\(426\) 0 0
\(427\) −9.42504 + 9.42504i −0.456110 + 0.456110i
\(428\) 0 0
\(429\) 10.5674 7.10675i 0.510200 0.343117i
\(430\) 0 0
\(431\) −15.4882 −0.746038 −0.373019 0.927824i \(-0.621677\pi\)
−0.373019 + 0.927824i \(0.621677\pi\)
\(432\) 0 0
\(433\) 25.5500 1.22786 0.613928 0.789362i \(-0.289588\pi\)
0.613928 + 0.789362i \(0.289588\pi\)
\(434\) 0 0
\(435\) 14.6205 9.83249i 0.700999 0.471432i
\(436\) 0 0
\(437\) −8.55026 + 8.55026i −0.409014 + 0.409014i
\(438\) 0 0
\(439\) 2.63703 0.125859 0.0629293 0.998018i \(-0.479956\pi\)
0.0629293 + 0.998018i \(0.479956\pi\)
\(440\) 0 0
\(441\) −2.19656 + 5.39400i −0.104598 + 0.256857i
\(442\) 0 0
\(443\) 14.8580 + 14.8580i 0.705927 + 0.705927i 0.965676 0.259749i \(-0.0836399\pi\)
−0.259749 + 0.965676i \(0.583640\pi\)
\(444\) 0 0
\(445\) −11.5569 + 11.5569i −0.547850 + 0.547850i
\(446\) 0 0
\(447\) 5.91617 30.2147i 0.279825 1.42910i
\(448\) 0 0
\(449\) 31.7079i 1.49639i −0.663480 0.748194i \(-0.730921\pi\)
0.663480 0.748194i \(-0.269079\pi\)
\(450\) 0 0
\(451\) −11.5569 11.5569i −0.544194 0.544194i
\(452\) 0 0
\(453\) 24.2390 16.3011i 1.13885 0.765891i
\(454\) 0 0
\(455\) 22.9733i 1.07701i
\(456\) 0 0
\(457\) 23.8759i 1.11687i −0.829550 0.558433i \(-0.811403\pi\)
0.829550 0.558433i \(-0.188597\pi\)
\(458\) 0 0
\(459\) −8.46480 + 1.76286i −0.395103 + 0.0822833i
\(460\) 0 0
\(461\) 0.921303 + 0.921303i 0.0429094 + 0.0429094i 0.728236 0.685327i \(-0.240341\pi\)
−0.685327 + 0.728236i \(0.740341\pi\)
\(462\) 0 0
\(463\) 26.1510i 1.21534i 0.794190 + 0.607670i \(0.207895\pi\)
−0.794190 + 0.607670i \(0.792105\pi\)
\(464\) 0 0
\(465\) 4.94137 + 0.967542i 0.229150 + 0.0448687i
\(466\) 0 0
\(467\) −16.2510 + 16.2510i −0.752005 + 0.752005i −0.974853 0.222848i \(-0.928465\pi\)
0.222848 + 0.974853i \(0.428465\pi\)
\(468\) 0 0
\(469\) −18.0552 18.0552i −0.833711 0.833711i
\(470\) 0 0
\(471\) 2.52588 12.9000i 0.116386 0.594400i
\(472\) 0 0
\(473\) −8.55026 −0.393141
\(474\) 0 0
\(475\) −0.221543 + 0.221543i −0.0101651 + 0.0101651i
\(476\) 0 0
\(477\) −1.60245 3.80413i −0.0733712 0.174179i
\(478\) 0 0
\(479\) −11.7456 −0.536669 −0.268335 0.963326i \(-0.586473\pi\)
−0.268335 + 0.963326i \(0.586473\pi\)
\(480\) 0 0
\(481\) −14.9966 −0.683784
\(482\) 0 0
\(483\) 4.91948 + 7.31506i 0.223844 + 0.332847i
\(484\) 0 0
\(485\) 8.91891 8.91891i 0.404987 0.404987i
\(486\) 0 0
\(487\) −0.783513 −0.0355044 −0.0177522 0.999842i \(-0.505651\pi\)
−0.0177522 + 0.999842i \(0.505651\pi\)
\(488\) 0 0
\(489\) 21.0938 + 4.13026i 0.953893 + 0.186777i
\(490\) 0 0
\(491\) −10.0382 10.0382i −0.453018 0.453018i 0.443337 0.896355i \(-0.353794\pi\)
−0.896355 + 0.443337i \(0.853794\pi\)
\(492\) 0 0
\(493\) −5.38445 + 5.38445i −0.242504 + 0.242504i
\(494\) 0 0
\(495\) −4.02447 + 9.88273i −0.180886 + 0.444196i
\(496\) 0 0
\(497\) 24.9543i 1.11935i
\(498\) 0 0
\(499\) 29.9655 + 29.9655i 1.34144 + 1.34144i 0.894627 + 0.446815i \(0.147442\pi\)
0.446815 + 0.894627i \(0.352558\pi\)
\(500\) 0 0
\(501\) −16.4008 24.3872i −0.732732 1.08954i
\(502\) 0 0
\(503\) 21.7131i 0.968138i 0.875030 + 0.484069i \(0.160842\pi\)
−0.875030 + 0.484069i \(0.839158\pi\)
\(504\) 0 0
\(505\) 32.4001i 1.44179i
\(506\) 0 0
\(507\) −7.84266 11.6617i −0.348305 0.517914i
\(508\) 0 0
\(509\) −16.1276 16.1276i −0.714842 0.714842i 0.252702 0.967544i \(-0.418681\pi\)
−0.967544 + 0.252702i \(0.918681\pi\)
\(510\) 0 0
\(511\) 14.3518i 0.634886i
\(512\) 0 0
\(513\) 15.2181 23.2240i 0.671896 1.02536i
\(514\) 0 0
\(515\) 12.7820 12.7820i 0.563243 0.563243i
\(516\) 0 0
\(517\) 4.23453 + 4.23453i 0.186235 + 0.186235i
\(518\) 0 0
\(519\) 39.2112 + 7.67774i 1.72118 + 0.337015i
\(520\) 0 0
\(521\) 5.68847 0.249216 0.124608 0.992206i \(-0.460233\pi\)
0.124608 + 0.992206i \(0.460233\pi\)
\(522\) 0 0
\(523\) −13.6612 + 13.6612i −0.597362 + 0.597362i −0.939610 0.342248i \(-0.888812\pi\)
0.342248 + 0.939610i \(0.388812\pi\)
\(524\) 0 0
\(525\) 0.127467 + 0.189538i 0.00556311 + 0.00827211i
\(526\) 0 0
\(527\) −2.17614 −0.0947941
\(528\) 0 0
\(529\) 17.8793 0.777361
\(530\) 0 0
\(531\) 15.1842 6.39619i 0.658938 0.277571i
\(532\) 0 0
\(533\) −33.1876 + 33.1876i −1.43751 + 1.43751i
\(534\) 0 0
\(535\) 7.55691 0.326714
\(536\) 0 0
\(537\) −0.630120 + 3.21811i −0.0271917 + 0.138871i
\(538\) 0 0
\(539\) −2.19656 2.19656i −0.0946124 0.0946124i
\(540\) 0 0
\(541\) 24.5715 24.5715i 1.05641 1.05641i 0.0581016 0.998311i \(-0.481495\pi\)
0.998311 0.0581016i \(-0.0185047\pi\)
\(542\) 0 0
\(543\) −24.6291 4.82248i −1.05693 0.206953i
\(544\) 0 0
\(545\) 28.0521i 1.20162i
\(546\) 0 0
\(547\) −3.56990 3.56990i −0.152638 0.152638i 0.626657 0.779295i \(-0.284423\pi\)
−0.779295 + 0.626657i \(0.784423\pi\)
\(548\) 0 0
\(549\) 6.90180 + 16.3845i 0.294562 + 0.699273i
\(550\) 0 0
\(551\) 24.4530i 1.04173i
\(552\) 0 0
\(553\) 6.05520i 0.257493i
\(554\) 0 0
\(555\) 10.4272 7.01244i 0.442610 0.297662i
\(556\) 0 0
\(557\) −18.1602 18.1602i −0.769473 0.769473i 0.208540 0.978014i \(-0.433129\pi\)
−0.978014 + 0.208540i \(0.933129\pi\)
\(558\) 0 0
\(559\) 24.5535i 1.03850i
\(560\) 0 0
\(561\) 0.886172 4.52579i 0.0374142 0.191079i
\(562\) 0 0
\(563\) 6.91748 6.91748i 0.291537 0.291537i −0.546150 0.837687i \(-0.683907\pi\)
0.837687 + 0.546150i \(0.183907\pi\)
\(564\) 0 0
\(565\) 24.9966 + 24.9966i 1.05161 + 1.05161i
\(566\) 0 0
\(567\) −14.4837 14.1412i −0.608257 0.593873i
\(568\) 0 0
\(569\) −36.2961 −1.52161 −0.760807 0.648979i \(-0.775196\pi\)
−0.760807 + 0.648979i \(0.775196\pi\)
\(570\) 0 0
\(571\) 33.5224 33.5224i 1.40287 1.40287i 0.612056 0.790814i \(-0.290343\pi\)
0.790814 0.612056i \(-0.209657\pi\)
\(572\) 0 0
\(573\) 35.2701 23.7196i 1.47343 0.990901i
\(574\) 0 0
\(575\) −0.132681 −0.00553317
\(576\) 0 0
\(577\) −18.9345 −0.788253 −0.394127 0.919056i \(-0.628953\pi\)
−0.394127 + 0.919056i \(0.628953\pi\)
\(578\) 0 0
\(579\) 12.0457 8.10092i 0.500603 0.336663i
\(580\) 0 0
\(581\) 5.87279 5.87279i 0.243644 0.243644i
\(582\) 0 0
\(583\) 2.20168 0.0911842
\(584\) 0 0
\(585\) 28.3799 + 11.5569i 1.17336 + 0.477820i
\(586\) 0 0
\(587\) 29.6211 + 29.6211i 1.22259 + 1.22259i 0.966707 + 0.255885i \(0.0823667\pi\)
0.255885 + 0.966707i \(0.417633\pi\)
\(588\) 0 0
\(589\) 4.94137 4.94137i 0.203605 0.203605i
\(590\) 0 0
\(591\) 0.607159 3.10084i 0.0249752 0.127551i
\(592\) 0 0
\(593\) 21.6263i 0.888086i 0.896005 + 0.444043i \(0.146456\pi\)
−0.896005 + 0.444043i \(0.853544\pi\)
\(594\) 0 0
\(595\) 5.88273 + 5.88273i 0.241169 + 0.241169i
\(596\) 0 0
\(597\) −18.8270 + 12.6614i −0.770539 + 0.518198i
\(598\) 0 0
\(599\) 29.8079i 1.21792i 0.793201 + 0.608959i \(0.208413\pi\)
−0.793201 + 0.608959i \(0.791587\pi\)
\(600\) 0 0
\(601\) 32.8432i 1.33970i −0.742495 0.669851i \(-0.766358\pi\)
0.742495 0.669851i \(-0.233642\pi\)
\(602\) 0 0
\(603\) −31.3872 + 13.2215i −1.27818 + 0.538422i
\(604\) 0 0
\(605\) 13.2658 + 13.2658i 0.539331 + 0.539331i
\(606\) 0 0
\(607\) 6.95597i 0.282334i 0.989986 + 0.141167i \(0.0450855\pi\)
−0.989986 + 0.141167i \(0.954915\pi\)
\(608\) 0 0
\(609\) −17.4948 3.42557i −0.708927 0.138811i
\(610\) 0 0
\(611\) 12.1602 12.1602i 0.491947 0.491947i
\(612\) 0 0
\(613\) 13.5389 + 13.5389i 0.546830 + 0.546830i 0.925522 0.378693i \(-0.123626\pi\)
−0.378693 + 0.925522i \(0.623626\pi\)
\(614\) 0 0
\(615\) 7.55691 38.5942i 0.304724 1.55627i
\(616\) 0 0
\(617\) 8.91891 0.359062 0.179531 0.983752i \(-0.442542\pi\)
0.179531 + 0.983752i \(0.442542\pi\)
\(618\) 0 0
\(619\) 1.64658 1.64658i 0.0661818 0.0661818i −0.673241 0.739423i \(-0.735098\pi\)
0.739423 + 0.673241i \(0.235098\pi\)
\(620\) 0 0
\(621\) 11.5114 2.39734i 0.461936 0.0962018i
\(622\) 0 0
\(623\) 16.5367 0.662531
\(624\) 0 0
\(625\) 24.7034 0.988136
\(626\) 0 0
\(627\) 8.26451 + 12.2890i 0.330053 + 0.490774i
\(628\) 0 0
\(629\) −3.84014 + 3.84014i −0.153116 + 0.153116i
\(630\) 0 0
\(631\) 19.2457 0.766159 0.383080 0.923715i \(-0.374863\pi\)
0.383080 + 0.923715i \(0.374863\pi\)
\(632\) 0 0
\(633\) 20.3622 + 3.98701i 0.809324 + 0.158469i
\(634\) 0 0
\(635\) −11.6710 11.6710i −0.463149 0.463149i
\(636\) 0 0
\(637\) −6.30777 + 6.30777i −0.249923 + 0.249923i
\(638\) 0 0
\(639\) 30.8271 + 12.5535i 1.21950 + 0.496608i
\(640\) 0 0
\(641\) 16.6343i 0.657016i 0.944501 + 0.328508i \(0.106546\pi\)
−0.944501 + 0.328508i \(0.893454\pi\)
\(642\) 0 0
\(643\) 4.77502 + 4.77502i 0.188308 + 0.188308i 0.794964 0.606656i \(-0.207489\pi\)
−0.606656 + 0.794964i \(0.707489\pi\)
\(644\) 0 0
\(645\) −11.4813 17.0722i −0.452075 0.672217i
\(646\) 0 0
\(647\) 48.2095i 1.89531i 0.319293 + 0.947656i \(0.396555\pi\)
−0.319293 + 0.947656i \(0.603445\pi\)
\(648\) 0 0
\(649\) 8.78801i 0.344960i
\(650\) 0 0
\(651\) −2.84306 4.22752i −0.111428 0.165689i
\(652\) 0 0
\(653\) −24.2281 24.2281i −0.948121 0.948121i 0.0505983 0.998719i \(-0.483887\pi\)
−0.998719 + 0.0505983i \(0.983887\pi\)
\(654\) 0 0
\(655\) 12.2086i 0.477028i
\(656\) 0 0
\(657\) 17.7294 + 7.21979i 0.691689 + 0.281671i
\(658\) 0 0
\(659\) 9.47442 9.47442i 0.369071 0.369071i −0.498067 0.867138i \(-0.665957\pi\)
0.867138 + 0.498067i \(0.165957\pi\)
\(660\) 0 0
\(661\) −23.0406 23.0406i −0.896175 0.896175i 0.0989204 0.995095i \(-0.468461\pi\)
−0.995095 + 0.0989204i \(0.968461\pi\)
\(662\) 0 0
\(663\) −12.9966 2.54479i −0.504745 0.0988313i
\(664\) 0 0
\(665\) −26.7159 −1.03600
\(666\) 0 0
\(667\) 7.32238 7.32238i 0.283524 0.283524i
\(668\) 0 0
\(669\) 20.8506 + 31.0039i 0.806130 + 1.19868i
\(670\) 0 0
\(671\) −9.48269 −0.366075
\(672\) 0 0
\(673\) 29.7846 1.14811 0.574055 0.818816i \(-0.305369\pi\)
0.574055 + 0.818816i \(0.305369\pi\)
\(674\) 0 0
\(675\) 0.298267 0.0621166i 0.0114803 0.00239087i
\(676\) 0 0
\(677\) 5.59631 5.59631i 0.215084 0.215084i −0.591339 0.806423i \(-0.701401\pi\)
0.806423 + 0.591339i \(0.201401\pi\)
\(678\) 0 0
\(679\) −12.7620 −0.489762
\(680\) 0 0
\(681\) 7.88503 40.2699i 0.302155 1.54314i
\(682\) 0 0
\(683\) 19.5790 + 19.5790i 0.749168 + 0.749168i 0.974323 0.225155i \(-0.0722887\pi\)
−0.225155 + 0.974323i \(0.572289\pi\)
\(684\) 0 0
\(685\) 4.28973 4.28973i 0.163902 0.163902i
\(686\) 0 0
\(687\) −8.09231 1.58451i −0.308741 0.0604529i
\(688\) 0 0
\(689\) 6.32248i 0.240867i
\(690\) 0 0
\(691\) −3.98701 3.98701i −0.151673 0.151673i 0.627192 0.778865i \(-0.284204\pi\)
−0.778865 + 0.627192i \(0.784204\pi\)
\(692\) 0 0
\(693\) 9.94988 4.19129i 0.377965 0.159214i
\(694\) 0 0
\(695\) 0.0867582i 0.00329093i
\(696\) 0 0
\(697\) 16.9966i 0.643791i
\(698\) 0 0
\(699\) 0.720541 0.484574i 0.0272534 0.0183283i
\(700\) 0 0
\(701\) 15.2117 + 15.2117i 0.574537 + 0.574537i 0.933393 0.358856i \(-0.116833\pi\)
−0.358856 + 0.933393i \(0.616833\pi\)
\(702\) 0 0
\(703\) 17.4396i 0.657749i
\(704\) 0 0
\(705\) −2.76891 + 14.1412i −0.104283 + 0.532587i
\(706\) 0 0
\(707\) −23.1806 + 23.1806i −0.871796 + 0.871796i
\(708\) 0 0
\(709\) −20.3009 20.3009i −0.762416 0.762416i 0.214342 0.976759i \(-0.431239\pi\)
−0.976759 + 0.214342i \(0.931239\pi\)
\(710\) 0 0
\(711\) −7.48024 3.04612i −0.280531 0.114238i
\(712\) 0 0
\(713\) 2.95936 0.110829
\(714\) 0 0
\(715\) −11.5569 + 11.5569i −0.432204 + 0.432204i
\(716\) 0 0
\(717\) −43.7768 + 29.4405i −1.63488 + 1.09948i
\(718\) 0 0
\(719\) 3.52314 0.131391 0.0656954 0.997840i \(-0.479073\pi\)
0.0656954 + 0.997840i \(0.479073\pi\)
\(720\) 0 0
\(721\) −18.2897 −0.681145
\(722\) 0 0
\(723\) −22.2702 + 14.9770i −0.828236 + 0.557000i
\(724\) 0 0
\(725\) 0.189728 0.189728i 0.00704631 0.00704631i
\(726\) 0 0
\(727\) 20.3664 0.755348 0.377674 0.925939i \(-0.376724\pi\)
0.377674 + 0.925939i \(0.376724\pi\)
\(728\) 0 0
\(729\) −24.7553 + 10.7785i −0.916863 + 0.399202i
\(730\) 0 0
\(731\) 6.28736 + 6.28736i 0.232547 + 0.232547i
\(732\) 0 0
\(733\) −2.48024 + 2.48024i −0.0916096 + 0.0916096i −0.751426 0.659817i \(-0.770634\pi\)
0.659817 + 0.751426i \(0.270634\pi\)
\(734\) 0 0
\(735\) 1.43630 7.33537i 0.0529787 0.270569i
\(736\) 0 0
\(737\) 18.1656i 0.669140i
\(738\) 0 0
\(739\) −15.7931 15.7931i −0.580957 0.580957i 0.354209 0.935166i \(-0.384750\pi\)
−0.935166 + 0.354209i \(0.884750\pi\)
\(740\) 0 0
\(741\) 35.2898 23.7329i 1.29640 0.871849i
\(742\) 0 0
\(743\) 38.5942i 1.41588i −0.706271 0.707941i \(-0.749624\pi\)
0.706271 0.707941i \(-0.250376\pi\)
\(744\) 0 0
\(745\) 39.5139i 1.44768i
\(746\) 0 0
\(747\) −4.30055 10.2093i −0.157349 0.373537i
\(748\) 0 0
\(749\) −5.40658 5.40658i −0.197552 0.197552i
\(750\) 0 0
\(751\) 17.6527i 0.644156i −0.946713 0.322078i \(-0.895619\pi\)
0.946713 0.322078i \(-0.104381\pi\)
\(752\) 0 0
\(753\) −29.3906 5.75481i −1.07105 0.209717i
\(754\) 0 0
\(755\) −26.5086 + 26.5086i −0.964747 + 0.964747i
\(756\) 0 0
\(757\) 32.7440 + 32.7440i 1.19010 + 1.19010i 0.977039 + 0.213062i \(0.0683435\pi\)
0.213062 + 0.977039i \(0.431657\pi\)
\(758\) 0 0
\(759\) −1.20512 + 6.15468i −0.0437429 + 0.223401i
\(760\) 0 0
\(761\) −6.69113 −0.242553 −0.121277 0.992619i \(-0.538699\pi\)
−0.121277 + 0.992619i \(0.538699\pi\)
\(762\) 0 0
\(763\) −20.0698 + 20.0698i −0.726576 + 0.726576i
\(764\) 0 0
\(765\) 10.2265 4.30783i 0.369741 0.155750i
\(766\) 0 0
\(767\) 25.2362 0.911227
\(768\) 0 0
\(769\) −5.03265 −0.181482 −0.0907411 0.995875i \(-0.528924\pi\)
−0.0907411 + 0.995875i \(0.528924\pi\)
\(770\) 0 0
\(771\) −7.23499 10.7581i −0.260562 0.387445i
\(772\) 0 0
\(773\) 10.6859 10.6859i 0.384344 0.384344i −0.488320 0.872665i \(-0.662390\pi\)
0.872665 + 0.488320i \(0.162390\pi\)
\(774\) 0 0
\(775\) 0.0766789 0.00275439
\(776\) 0 0
\(777\) −12.4772 2.44309i −0.447616 0.0876452i
\(778\) 0 0
\(779\) −38.5942 38.5942i −1.38278 1.38278i
\(780\) 0 0
\(781\) −12.5535 + 12.5535i −0.449199 + 0.449199i
\(782\) 0 0
\(783\) −13.0327 + 19.8888i −0.465750 + 0.710769i
\(784\) 0 0
\(785\) 16.8703i 0.602126i
\(786\) 0 0
\(787\) −16.0974 16.0974i −0.573810 0.573810i 0.359381 0.933191i \(-0.382988\pi\)
−0.933191 + 0.359381i \(0.882988\pi\)
\(788\) 0 0
\(789\) 9.92281 + 14.7548i 0.353262 + 0.525285i
\(790\) 0 0
\(791\) 35.7675i 1.27175i
\(792\) 0 0
\(793\) 27.2311i 0.967005i
\(794\) 0 0
\(795\) 2.95641 + 4.39606i 0.104853 + 0.155912i
\(796\) 0 0
\(797\) 2.63695 + 2.63695i 0.0934055 + 0.0934055i 0.752266 0.658860i \(-0.228961\pi\)
−0.658860 +