Properties

Label 384.2.k.b.287.2
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 287.2
Root \(-1.35164 - 0.416001i\) of defining polynomial
Character \(\chi\) \(=\) 384.287
Dual form 384.2.k.b.95.2

$q$-expansion

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

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
\(3\) −0.966579 + 1.43726i −0.558055 + 0.829804i
\(4\) 0 0
\(5\) 1.57184 1.57184i 0.702949 0.702949i −0.262094 0.965042i \(-0.584413\pi\)
0.965042 + 0.262094i \(0.0844130\pi\)
\(6\) 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 0.515653 0.856798i \(-0.327549\pi\)
−0.856798 + 0.515653i \(0.827549\pi\)
\(12\) 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 \(0.0646758\pi\)
−0.979429 + 0.201790i \(0.935324\pi\)
\(18\) 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
\(21\) −2.17397 + 3.23261i −0.474400 + 0.705412i
\(22\) 0 0
\(23\) 2.26290i 0.471847i −0.971772 0.235923i \(-0.924189\pi\)
0.971772 0.235923i \(-0.0758114\pi\)
\(24\) 0 0
\(25\) 0.0586332i 0.0117266i
\(26\) 0 0
\(27\) 5.08701 + 1.05941i 0.978995 + 0.203884i
\(28\) 0 0
\(29\) 3.23584 + 3.23584i 0.600881 + 0.600881i 0.940546 0.339665i \(-0.110314\pi\)
−0.339665 + 0.940546i \(0.610314\pi\)
\(30\) 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 \(-0.206103\pi\)
0.797600 + 0.603187i \(0.206103\pi\)
\(42\) 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
\(45\) −6.14575 2.58884i −0.916154 0.385921i
\(46\) 0 0
\(47\) −3.74258 −0.545911 −0.272955 0.962027i \(-0.588001\pi\)
−0.272955 + 0.962027i \(0.588001\pi\)
\(48\) 0 0
\(49\) −1.94137 −0.277338
\(50\) 0 0
\(51\) −2.39161 1.60839i −0.334892 0.225220i
\(52\) 0 0
\(53\) −0.972946 + 0.972946i −0.133644 + 0.133644i −0.770765 0.637120i \(-0.780126\pi\)
0.637120 + 0.770765i \(0.280126\pi\)
\(54\) 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 0.407579 0.913170i \(-0.366373\pi\)
−0.913170 + 0.407579i \(0.866373\pi\)
\(60\) 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
\(69\) 3.25238 + 2.18727i 0.391540 + 0.263316i
\(70\) 0 0
\(71\) 11.0950i 1.31674i −0.752695 0.658370i \(-0.771246\pi\)
0.752695 0.658370i \(-0.228754\pi\)
\(72\) 0 0
\(73\) 6.38101i 0.746841i 0.927662 + 0.373421i \(0.121815\pi\)
−0.927662 + 0.373421i \(0.878185\pi\)
\(74\) 0 0
\(75\) −0.0842713 0.0566736i −0.00973081 0.00654410i
\(76\) 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 −0.835738 0.549129i \(-0.814960\pi\)
0.549129 + 0.835738i \(0.314960\pi\)
\(84\) 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 \(-0.627414\pi\)
−0.389680 + 0.920950i \(0.627414\pi\)
\(90\) 0 0
\(91\) 7.30777 7.30777i 0.766063 0.766063i
\(92\) 0 0
\(93\) 1.87961 + 1.26407i 0.194907 + 0.131078i
\(94\) 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
\(99\) −1.86351 + 4.42386i −0.187289 + 0.444614i
\(100\) 0 0
\(101\) 10.3064 10.3064i 1.02553 1.02553i 0.0258621 0.999666i \(-0.491767\pi\)
0.999666 0.0258621i \(-0.00823308\pi\)
\(102\) 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 0.813689 0.581301i \(-0.197456\pi\)
−0.581301 + 0.813689i \(0.697456\pi\)
\(108\) 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 \(0.268986\pi\)
−0.663697 + 0.748002i \(0.731014\pi\)
\(114\) 0 0
\(115\) −3.55691 3.55691i −0.331684 0.331684i
\(116\) 0 0
\(117\) −12.7038 5.35136i −1.17447 0.494734i
\(118\) 0 0
\(119\) 3.74258i 0.343081i
\(120\) 0 0
\(121\) 8.43965i 0.767241i
\(122\) 0 0
\(123\) −9.87290 + 14.6806i −0.890209 + 1.32370i
\(124\) 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 −0.516801 0.856106i \(-0.672877\pi\)
0.856106 + 0.516801i \(0.172877\pi\)
\(132\) 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 \(-0.462806\pi\)
0.116582 + 0.993181i \(0.462806\pi\)
\(138\) 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
\(141\) 3.61750 5.37907i 0.304648 0.452999i
\(142\) 0 0
\(143\) −7.35247 −0.614845
\(144\) 0 0
\(145\) 10.1725 0.844777
\(146\) 0 0
\(147\) 1.87649 2.79025i 0.154770 0.230136i
\(148\) 0 0
\(149\) −12.5693 + 12.5693i −1.02972 + 1.02972i −0.0301744 + 0.999545i \(0.509606\pi\)
−0.999545 + 0.0301744i \(0.990394\pi\)
\(150\) 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
\(165\) 3.43804 5.11222i 0.267651 0.397986i
\(166\) 0 0
\(167\) 16.9678i 1.31301i 0.754321 + 0.656505i \(0.227966\pi\)
−0.754321 + 0.656505i \(0.772034\pi\)
\(168\) 0 0
\(169\) 8.11383i 0.624141i
\(170\) 0 0
\(171\) 6.22315 14.7734i 0.475896 1.12975i
\(172\) 0 0
\(173\) −16.3119 16.3119i −1.24017 1.24017i −0.959930 0.280241i \(-0.909586\pi\)
−0.280241 0.959930i \(-0.590414\pi\)
\(174\) 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 −0.655304 0.755365i \(-0.727459\pi\)
0.755365 + 0.655304i \(0.227459\pi\)
\(180\) 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
\(189\) 11.4414 + 2.38276i 0.832239 + 0.173320i
\(190\) 0 0
\(191\) −24.5398 −1.77563 −0.887817 0.460197i \(-0.847779\pi\)
−0.887817 + 0.460197i \(0.847779\pi\)
\(192\) 0 0
\(193\) 8.38101 0.603279 0.301639 0.953422i \(-0.402466\pi\)
0.301639 + 0.953422i \(0.402466\pi\)
\(194\) 0 0
\(195\) 14.6806 + 9.87290i 1.05130 + 0.707013i
\(196\) 0 0
\(197\) −1.28995 + 1.28995i −0.0919052 + 0.0919052i −0.751565 0.659659i \(-0.770701\pi\)
0.659659 + 0.751565i \(0.270701\pi\)
\(198\) 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
\(213\) 15.9465 + 10.7242i 1.09264 + 0.734813i
\(214\) 0 0
\(215\) 11.8783i 0.810091i
\(216\) 0 0
\(217\) 2.94137i 0.199673i
\(218\) 0 0
\(219\) −9.17120 6.16776i −0.619732 0.416778i
\(220\) 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 \(0.537967\pi\)
−0.992895 + 0.118994i \(0.962033\pi\)
\(228\) 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 \(-0.505227\pi\)
−0.0164216 + 0.999865i \(0.505227\pi\)
\(234\) 0 0
\(235\) −5.88273 + 5.88273i −0.383747 + 0.383747i
\(236\) 0 0
\(237\) 3.86944 + 2.60225i 0.251347 + 0.169034i
\(238\) 0 0
\(239\) 30.4585 1.97019 0.985097 0.171999i \(-0.0550225\pi\)
0.985097 + 0.171999i \(0.0550225\pi\)
\(240\) 0 0
\(241\) −15.4948 −0.998111 −0.499055 0.866570i \(-0.666320\pi\)
−0.499055 + 0.866570i \(0.666320\pi\)
\(242\) 0 0
\(243\) −2.81216 15.3327i −0.180400 0.983593i
\(244\) 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 0.978409 0.206679i \(-0.0662656\pi\)
−0.206679 + 0.978409i \(0.566266\pi\)
\(252\) 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 \(0.0750033\pi\)
−0.972367 + 0.233455i \(0.924997\pi\)
\(258\) 0 0
\(259\) −5.19051 5.19051i −0.322522 0.322522i
\(260\) 0 0
\(261\) 5.32946 12.6518i 0.329885 0.783129i
\(262\) 0 0
\(263\) 10.2659i 0.633023i −0.948589 0.316511i \(-0.897488\pi\)
0.948589 0.316511i \(-0.102512\pi\)
\(264\) 0 0
\(265\) 3.05863i 0.187890i
\(266\) 0 0
\(267\) 7.10675 10.5674i 0.434926 0.646716i
\(268\) 0 0
\(269\) 2.76963 + 2.76963i 0.168867 + 0.168867i 0.786481 0.617614i \(-0.211901\pi\)
−0.617614 + 0.786481i \(0.711901\pi\)
\(270\) 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 \(-0.731924\pi\)
−0.665833 + 0.746101i \(0.731924\pi\)
\(282\) 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
\(285\) −11.4813 + 17.0722i −0.680093 + 1.01127i
\(286\) 0 0
\(287\) 22.9733 1.35607
\(288\) 0 0
\(289\) 14.2311 0.837123
\(290\) 0 0
\(291\) 5.48455 8.15529i 0.321510 0.478071i
\(292\) 0 0
\(293\) −6.37953 + 6.37953i −0.372696 + 0.372696i −0.868458 0.495762i \(-0.834889\pi\)
0.495762 + 0.868458i \(0.334889\pi\)
\(294\) 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
\(309\) 7.86010 11.6876i 0.447146 0.664887i
\(310\) 0 0
\(311\) 9.52861i 0.540318i −0.962816 0.270159i \(-0.912924\pi\)
0.962816 0.270159i \(-0.0870763\pi\)
\(312\) 0 0
\(313\) 25.1690i 1.42264i 0.702870 + 0.711319i \(0.251902\pi\)
−0.702870 + 0.711319i \(0.748098\pi\)
\(314\) 0 0
\(315\) −13.8227 5.82265i −0.778818 0.328069i
\(316\) 0 0
\(317\) −15.5287 15.5287i −0.872178 0.872178i 0.120532 0.992709i \(-0.461540\pi\)
−0.992709 + 0.120532i \(0.961540\pi\)
\(318\) 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
\(333\) −3.80092 + 9.02318i −0.208289 + 0.494467i
\(334\) 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
\(339\) −22.8564 15.3713i −1.24139 0.834852i
\(340\) 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 0.864135 0.503260i \(-0.167866\pi\)
−0.503260 + 0.864135i \(0.667866\pi\)
\(348\) 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 \(-0.788262\pi\)
0.786796 0.617213i \(-0.211738\pi\)
\(354\) 0 0
\(355\) −17.4396 17.4396i −0.925600 0.925600i
\(356\) 0 0
\(357\) −5.37907 3.61750i −0.284690 0.191458i
\(358\) 0 0
\(359\) 27.3664i 1.44434i 0.691713 + 0.722172i \(0.256856\pi\)
−0.691713 + 0.722172i \(0.743144\pi\)
\(360\) 0 0
\(361\) 9.55348i 0.502815i
\(362\) 0 0
\(363\) 12.1300 + 8.15759i 0.636659 + 0.428162i
\(364\) 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
\(381\) −10.6717 7.17689i −0.546729 0.367683i
\(382\) 0 0
\(383\) −26.4965 −1.35391 −0.676953 0.736027i \(-0.736700\pi\)
−0.676953 + 0.736027i \(0.736700\pi\)
\(384\) 0 0
\(385\) −8.00000 −0.407718
\(386\) 0 0
\(387\) 14.7734 + 6.22315i 0.750975 + 0.316341i
\(388\) 0 0
\(389\) 2.35506 2.35506i 0.119406 0.119406i −0.644879 0.764285i \(-0.723092\pi\)
0.764285 + 0.644879i \(0.223092\pi\)
\(390\) 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 \(-0.958657\pi\)
0.991577 0.129517i \(-0.0413426\pi\)
\(402\) 0 0
\(403\) −4.24914 4.24914i −0.211665 0.211665i
\(404\) 0 0
\(405\) −0.239367 + 20.0048i −0.0118943 + 0.994048i
\(406\) 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
\(411\) −2.63790 + 3.92245i −0.130118 + 0.193480i
\(412\) 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 \(-0.411477\pi\)
0.961578 0.274533i \(-0.0885232\pi\)
\(420\) 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
\(429\) 7.10675 10.5674i 0.343117 0.510200i
\(430\) 0 0
\(431\) 15.4882 0.746038 0.373019 0.927824i \(-0.378323\pi\)
0.373019 + 0.927824i \(0.378323\pi\)
\(432\) 0 0
\(433\) 25.5500 1.22786 0.613928 0.789362i \(-0.289588\pi\)
0.613928 + 0.789362i \(0.289588\pi\)
\(434\) 0 0
\(435\) −9.83249 + 14.6205i −0.471432 + 0.700999i
\(436\) 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 0.259749 0.965676i \(-0.416360\pi\)
−0.965676 + 0.259749i \(0.916360\pi\)
\(444\) 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 \(0.269079\pi\)
−0.663480 + 0.748194i \(0.730921\pi\)
\(450\) 0 0
\(451\) −11.5569 11.5569i −0.544194 0.544194i
\(452\) 0 0
\(453\) −16.3011 + 24.2390i −0.765891 + 1.13885i
\(454\) 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
\(459\) −1.76286 + 8.46480i −0.0822833 + 0.395103i
\(460\) 0 0
\(461\) −0.921303 0.921303i −0.0429094 0.0429094i 0.685327 0.728236i \(-0.259659\pi\)
−0.728236 + 0.685327i \(0.759659\pi\)
\(462\) 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 −0.222848 0.974853i \(-0.571535\pi\)
0.974853 + 0.222848i \(0.0715355\pi\)
\(468\) 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
\(477\) 3.80413 + 1.60245i 0.174179 + 0.0733712i
\(478\) 0 0
\(479\) 11.7456 0.536669 0.268335 0.963326i \(-0.413527\pi\)
0.268335 + 0.963326i \(0.413527\pi\)
\(480\) 0 0
\(481\) −14.9966 −0.683784
\(482\) 0 0
\(483\) 7.31506 + 4.91948i 0.332847 + 0.223844i
\(484\) 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 0.896355 0.443337i \(-0.146206\pi\)
−0.443337 + 0.896355i \(0.646206\pi\)
\(492\) 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
\(501\) −24.3872 16.4008i −1.08954 0.732732i
\(502\) 0 0
\(503\) 21.7131i 0.968138i −0.875030 0.484069i \(-0.839158\pi\)
0.875030 0.484069i \(-0.160842\pi\)
\(504\) 0 0
\(505\) 32.4001i 1.44179i
\(506\) 0 0
\(507\) 11.6617 + 7.84266i 0.517914 + 0.348305i
\(508\) 0 0
\(509\) 16.1276 + 16.1276i 0.714842 + 0.714842i 0.967544 0.252702i \(-0.0813192\pi\)
−0.252702 + 0.967544i \(0.581319\pi\)
\(510\) 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 \(-0.539767\pi\)
−0.124608 + 0.992206i \(0.539767\pi\)
\(522\) 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
\(525\) −0.189538 0.127467i −0.00827211 0.00556311i
\(526\) 0 0
\(527\) 2.17614 0.0947941
\(528\) 0 0
\(529\) 17.8793 0.777361
\(530\) 0 0
\(531\) −6.39619 + 15.1842i −0.277571 + 0.658938i
\(532\) 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
\(549\) 16.3845 + 6.90180i 0.699273 + 0.294562i
\(550\) 0 0
\(551\) 24.4530i 1.04173i
\(552\) 0 0
\(553\) 6.05520i 0.257493i
\(554\) 0 0
\(555\) 7.01244 10.4272i 0.297662 0.442610i
\(556\) 0 0
\(557\) 18.1602 + 18.1602i 0.769473 + 0.769473i 0.978014 0.208540i \(-0.0668713\pi\)
−0.208540 + 0.978014i \(0.566871\pi\)
\(558\) 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 −0.837687 0.546150i \(-0.816093\pi\)
0.546150 + 0.837687i \(0.316093\pi\)
\(564\) 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 \(-0.224804\pi\)
0.760807 + 0.648979i \(0.224804\pi\)
\(570\) 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
\(573\) 23.7196 35.2701i 0.990901 1.47343i
\(574\) 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
\(579\) −8.10092 + 12.0457i −0.336663 + 0.500603i
\(580\) 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 \(-0.917633\pi\)
−0.255885 0.966707i \(-0.582367\pi\)
\(588\) 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 \(-0.853544\pi\)
0.896005 0.444043i \(-0.146456\pi\)
\(594\) 0 0
\(595\) 5.88273 + 5.88273i 0.241169 + 0.241169i
\(596\) 0 0
\(597\) 12.6614 18.8270i 0.518198 0.770539i
\(598\) 0 0
\(599\) 29.8079i 1.21792i −0.793201 0.608959i \(-0.791587\pi\)
0.793201 0.608959i \(-0.208413\pi\)
\(600\) 0 0
\(601\) 32.8432i 1.33970i −0.742495 0.669851i \(-0.766358\pi\)
0.742495 0.669851i \(-0.233642\pi\)
\(602\) 0 0
\(603\) −13.2215 + 31.3872i −0.538422 + 1.27818i
\(604\) 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 \(-0.557458\pi\)
−0.179531 + 0.983752i \(0.557458\pi\)
\(618\) 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
\(621\) 2.39734 11.5114i 0.0962018 0.461936i
\(622\) 0 0
\(623\) −16.5367 −0.662531
\(624\) 0 0
\(625\) 24.7034 0.988136
\(626\) 0 0
\(627\) 12.2890 + 8.26451i 0.490774 + 0.330053i
\(628\) 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 \(-0.893454\pi\)
0.944501 0.328508i \(-0.106546\pi\)
\(642\) 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
\(645\) −17.0722 11.4813i −0.672217 0.452075i
\(646\) 0 0
\(647\) 48.2095i 1.89531i −0.319293 0.947656i \(-0.603445\pi\)
0.319293 0.947656i \(-0.396555\pi\)
\(648\) 0 0
\(649\) 8.78801i 0.344960i
\(650\) 0 0
\(651\) 4.22752 + 2.84306i 0.165689 + 0.111428i
\(652\) 0 0
\(653\) 24.2281 + 24.2281i 0.948121 + 0.948121i 0.998719 0.0505983i \(-0.0161128\pi\)
−0.0505983 + 0.998719i \(0.516113\pi\)
\(654\) 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 −0.867138 0.498067i \(-0.834043\pi\)
0.498067 + 0.867138i \(0.334043\pi\)
\(660\) 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
\(669\) −31.0039 20.8506i −1.19868 0.806130i
\(670\) 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
\(675\) −0.0621166 + 0.298267i −0.00239087 + 0.0114803i
\(676\) 0 0
\(677\) −5.59631 + 5.59631i −0.215084 + 0.215084i −0.806423 0.591339i \(-0.798599\pi\)
0.591339 + 0.806423i \(0.298599\pi\)
\(678\) 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 0.225155 0.974323i \(-0.427711\pi\)
−0.974323 + 0.225155i \(0.927711\pi\)
\(684\) 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
\(693\) −4.19129 + 9.94988i −0.159214 + 0.377965i
\(694\) 0 0
\(695\) 0.0867582i 0.00329093i
\(696\) 0 0
\(697\) 16.9966i 0.643791i
\(698\) 0 0
\(699\) 0.484574 0.720541i 0.0183283 0.0272534i
\(700\) 0 0
\(701\) −15.2117 15.2117i −0.574537 0.574537i 0.358856 0.933393i \(-0.383167\pi\)
−0.933393 + 0.358856i \(0.883167\pi\)
\(702\) 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
\(717\) −29.4405 + 43.7768i −1.09948 + 1.63488i
\(718\) 0 0
\(719\) −3.52314 −0.131391 −0.0656954 0.997840i \(-0.520927\pi\)
−0.0656954 + 0.997840i \(0.520927\pi\)
\(720\) 0 0
\(721\) −18.2897 −0.681145
\(722\) 0 0
\(723\) 14.9770 22.2702i 0.557000 0.828236i
\(724\) 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
\(741\) −23.7329 + 35.2898i −0.871849 + 1.29640i
\(742\) 0 0
\(743\) 38.5942i 1.41588i 0.706271 + 0.707941i \(0.250376\pi\)
−0.706271 + 0.707941i \(0.749624\pi\)
\(744\) 0 0
\(745\) 39.5139i 1.44768i
\(746\) 0 0
\(747\) 10.2093 + 4.30055i 0.373537 + 0.157349i
\(748\) 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 \(-0.461301\pi\)
0.121277 + 0.992619i \(0.461301\pi\)
\(762\) 0 0
\(763\) −20.0698 + 20.0698i −0.726576 + 0.726576i
\(764\) 0 0
\(765\) 4.30783 10.2265i 0.155750 0.369741i
\(766\) 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
\(771\) −10.7581 7.23499i −0.387445 0.260562i
\(772\) 0 0
\(773\) −10.6859 + 10.6859i −0.384344 + 0.384344i −0.872665 0.488320i \(-0.837610\pi\)
0.488320 + 0.872665i \(0.337610\pi\)
\(774\) 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
\(789\) 14.7548 + 9.92281i 0.525285 + 0.353262i
\(790\) 0 0
\(791\) 35.7675i 1.27175i
\(792\) 0 0
\(793\) 27.2311i 0.967005i
\(794\) 0 0
\(795\) −4.39606 2.95641i −0.155912 0.104853i
\(796\) 0 0
\(797\) −2.63695 2.63695i −0.0934055 0.0934055i 0.658860 0.752266i \(-0.271039\pi\)