Properties

Label 384.2.k.b.95.2
Level $384$
Weight $2$
Character 384.95
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 95.2
Root \(-1.35164 + 0.416001i\) of defining polynomial
Character \(\chi\) \(=\) 384.95
Dual form 384.2.k.b.287.2

$q$-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 \(\left(\mathbb{Z}/384\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(133\) \(257\)
\(\chi(n)\) \(-1\) \(e\left(\frac{3}{4}\right)\) \(-1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −0.966579 1.43726i −0.558055 0.829804i
\(4\) 0 0
\(5\) 1.57184 + 1.57184i 0.702949 + 0.702949i 0.965042 0.262094i \(-0.0844130\pi\)
−0.262094 + 0.965042i \(0.584413\pi\)
\(6\) 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 \(-0.827549\pi\)
0.515653 + 0.856798i \(0.327549\pi\)
\(12\) 0 0
\(13\) 3.24914 + 3.24914i 0.901149 + 0.901149i 0.995536 0.0943862i \(-0.0300889\pi\)
−0.0943862 + 0.995536i \(0.530089\pi\)
\(14\) 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 −0.125283 0.992121i \(-0.539984\pi\)
0.992121 + 0.125283i \(0.0399840\pi\)
\(20\) 0 0
\(21\) −2.17397 3.23261i −0.474400 0.705412i
\(22\) 0 0
\(23\) 2.26290i 0.471847i 0.971772 + 0.235923i \(0.0758114\pi\)
−0.971772 + 0.235923i \(0.924189\pi\)
\(24\) 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 −0.339665 0.940546i \(-0.610314\pi\)
0.940546 + 0.339665i \(0.110314\pi\)
\(30\) 0 0
\(31\) 1.30777i 0.234883i 0.993080 + 0.117442i \(0.0374693\pi\)
−0.993080 + 0.117442i \(0.962531\pi\)
\(32\) 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 −0.870884 0.491488i \(-0.836453\pi\)
0.491488 + 0.870884i \(0.336453\pi\)
\(38\) 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 0.357647 0.933857i \(-0.383579\pi\)
−0.933857 + 0.357647i \(0.883579\pi\)
\(44\) 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 0.637120 0.770765i \(-0.280126\pi\)
−0.770765 + 0.637120i \(0.780126\pi\)
\(54\) 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 \(-0.866373\pi\)
0.407579 + 0.913170i \(0.366373\pi\)
\(60\) 0 0
\(61\) −4.19051 4.19051i −0.536539 0.536539i 0.385971 0.922511i \(-0.373866\pi\)
−0.922511 + 0.385971i \(0.873866\pi\)
\(62\) 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 −0.999818 0.0190906i \(-0.993923\pi\)
0.0190906 + 0.999818i \(0.493923\pi\)
\(68\) 0 0
\(69\) 3.25238 2.18727i 0.391540 0.263316i
\(70\) 0 0
\(71\) 11.0950i 1.31674i 0.752695 + 0.658370i \(0.228754\pi\)
−0.752695 + 0.658370i \(0.771246\pi\)
\(72\) 0 0
\(73\) 6.38101i 0.746841i −0.927662 0.373421i \(-0.878185\pi\)
0.927662 0.373421i \(-0.121815\pi\)
\(74\) 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 \(0.0483941\pi\)
−0.988465 + 0.151450i \(0.951606\pi\)
\(80\) 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 \(-0.314960\pi\)
−0.835738 + 0.549129i \(0.814960\pi\)
\(84\) 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 0.999666 + 0.0258621i \(0.00823308\pi\)
0.0258621 + 0.999666i \(0.491767\pi\)
\(102\) 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 \(-0.697456\pi\)
0.813689 + 0.581301i \(0.197456\pi\)
\(108\) 0 0
\(109\) −8.92332 8.92332i −0.854699 0.854699i 0.136009 0.990708i \(-0.456573\pi\)
−0.990708 + 0.136009i \(0.956573\pi\)
\(110\) 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
\(117\) −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 \(-0.893142\pi\)
0.944179 0.329433i \(-0.106858\pi\)
\(128\) 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 \(-0.172877\pi\)
−0.516801 + 0.856106i \(0.672877\pi\)
\(132\) 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 0.708276 0.705935i \(-0.249473\pi\)
−0.705935 + 0.708276i \(0.749473\pi\)
\(140\) 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 −0.999545 0.0301744i \(-0.990394\pi\)
−0.0301744 0.999545i \(-0.509606\pi\)
\(150\) 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 0.888044 0.459758i \(-0.152064\pi\)
−0.459758 + 0.888044i \(0.652064\pi\)
\(158\) 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 −0.274325 0.961637i \(-0.588454\pi\)
0.961637 + 0.274325i \(0.0884543\pi\)
\(164\) 0 0
\(165\) 3.43804 + 5.11222i 0.267651 + 0.397986i
\(166\) 0 0
\(167\) 16.9678i 1.31301i −0.754321 0.656505i \(-0.772034\pi\)
0.754321 0.656505i \(-0.227966\pi\)
\(168\) 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 −0.280241 + 0.959930i \(0.590414\pi\)
−0.959930 + 0.280241i \(0.909586\pi\)
\(174\) 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 \(-0.227459\pi\)
−0.655304 + 0.755365i \(0.727459\pi\)
\(180\) 0 0
\(181\) −10.2457 + 10.2457i −0.761557 + 0.761557i −0.976604 0.215047i \(-0.931010\pi\)
0.215047 + 0.976604i \(0.431010\pi\)
\(182\) 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 0.659659 0.751565i \(-0.270701\pi\)
−0.751565 + 0.659659i \(0.770701\pi\)
\(198\) 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 −0.352621 0.935766i \(-0.614709\pi\)
0.935766 + 0.352621i \(0.114709\pi\)
\(212\) 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 \(-0.743100\pi\)
0.691613 0.722268i \(-0.256900\pi\)
\(224\) 0 0
\(225\) 0.162910 + 0.0663404i 0.0108606 + 0.00442269i
\(226\) 0 0
\(227\) −16.7523 16.7523i −1.11189 1.11189i −0.992895 0.118994i \(-0.962033\pi\)
−0.118994 0.992895i \(-0.537967\pi\)
\(228\) 0 0
\(229\) −3.36641 + 3.36641i −0.222458 + 0.222458i −0.809533 0.587074i \(-0.800280\pi\)
0.587074 + 0.809533i \(0.300280\pi\)
\(230\) 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 −0.206679 0.978409i \(-0.566266\pi\)
0.978409 + 0.206679i \(0.0662656\pi\)
\(252\) 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
\(261\) 5.32946 + 12.6518i 0.329885 + 0.783129i
\(262\) 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
\(267\) 7.10675 + 10.5674i 0.434926 + 0.646716i
\(268\) 0 0
\(269\) 2.76963 2.76963i 0.168867 0.168867i −0.617614 0.786481i \(-0.711901\pi\)
0.786481 + 0.617614i \(0.211901\pi\)
\(270\) 0 0
\(271\) 28.6854i 1.74251i 0.490830 + 0.871255i \(0.336694\pi\)
−0.490830 + 0.871255i \(0.663306\pi\)
\(272\) 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 −0.682476 0.730908i \(-0.739097\pi\)
0.730908 + 0.682476i \(0.239097\pi\)
\(278\) 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 0.424810 0.905282i \(-0.360341\pi\)
−0.905282 + 0.424810i \(0.860341\pi\)
\(284\) 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 0.495762 0.868458i \(-0.334889\pi\)
−0.868458 + 0.495762i \(0.834889\pi\)
\(294\) 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 −0.493661 0.869655i \(-0.664341\pi\)
0.869655 + 0.493661i \(0.164341\pi\)
\(308\) 0 0
\(309\) 7.86010 + 11.6876i 0.447146 + 0.664887i
\(310\) 0 0
\(311\) 9.52861i 0.540318i 0.962816 + 0.270159i \(0.0870763\pi\)
−0.962816 + 0.270159i \(0.912924\pi\)
\(312\) 0 0
\(313\) 25.1690i 1.42264i −0.702870 0.711319i \(-0.748098\pi\)
0.702870 0.711319i \(-0.251902\pi\)
\(314\) 0 0
\(315\) −13.8227 + 5.82265i −0.778818 + 0.328069i
\(316\) 0 0
\(317\) −15.5287 + 15.5287i −0.872178 + 0.872178i −0.992709 0.120532i \(-0.961540\pi\)
0.120532 + 0.992709i \(0.461540\pi\)
\(318\) 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 0.632397 0.774644i \(-0.282071\pi\)
−0.774644 + 0.632397i \(0.782071\pi\)
\(332\) 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 −0.503260 0.864135i \(-0.667866\pi\)
0.864135 + 0.503260i \(0.167866\pi\)
\(348\) 0 0
\(349\) 2.75086 + 2.75086i 0.147250 + 0.147250i 0.776888 0.629638i \(-0.216797\pi\)
−0.629638 + 0.776888i \(0.716797\pi\)
\(350\) 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
\(357\) −5.37907 + 3.61750i −0.284690 + 0.191458i
\(358\) 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
\(363\) 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 \(0.237870\pi\)
−0.733533 + 0.679654i \(0.762130\pi\)
\(368\) 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 −0.280044 0.959987i \(-0.590349\pi\)
0.959987 + 0.280044i \(0.0903492\pi\)
\(374\) 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 0.995123 0.0986413i \(-0.0314496\pi\)
−0.0986413 + 0.995123i \(0.531450\pi\)
\(380\) 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 0.764285 0.644879i \(-0.223092\pi\)
−0.644879 + 0.764285i \(0.723092\pi\)
\(390\) 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 0.579587 0.814910i \(-0.303214\pi\)
−0.814910 + 0.579587i \(0.803214\pi\)
\(398\) 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
\(405\) −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 \(-0.880088\pi\)
0.929878 0.367867i \(-0.119912\pi\)
\(410\) 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 0.961578 + 0.274533i \(0.0885232\pi\)
0.274533 + 0.961578i \(0.411477\pi\)
\(420\) 0 0
\(421\) −7.13187 + 7.13187i −0.347586 + 0.347586i −0.859210 0.511623i \(-0.829044\pi\)
0.511623 + 0.859210i \(0.329044\pi\)
\(422\) 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 −0.965676 0.259749i \(-0.916360\pi\)
0.259749 + 0.965676i \(0.416360\pi\)
\(444\) 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
\(453\) −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 \(0.188597\pi\)
−0.829550 + 0.558433i \(0.811403\pi\)
\(458\) 0 0
\(459\) −1.76286 8.46480i −0.0822833 0.395103i
\(460\) 0 0
\(461\) −0.921303 + 0.921303i −0.0429094 + 0.0429094i −0.728236 0.685327i \(-0.759659\pi\)
0.685327 + 0.728236i \(0.259659\pi\)
\(462\) 0 0
\(463\) 26.1510i 1.21534i −0.794190 0.607670i \(-0.792105\pi\)
0.794190 0.607670i \(-0.207895\pi\)
\(464\) 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 \(-0.0715355\pi\)
−0.222848 + 0.974853i \(0.571535\pi\)
\(468\) 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 −0.443337 0.896355i \(-0.646206\pi\)
0.896355 + 0.443337i \(0.146206\pi\)
\(492\) 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 0.446815 0.894627i \(-0.352558\pi\)
0.894627 0.446815i \(-0.147442\pi\)
\(500\) 0 0
\(501\) −24.3872 + 16.4008i −1.08954 + 0.732732i
\(502\) 0 0
\(503\) 21.7131i 0.968138i 0.875030 + 0.484069i \(0.160842\pi\)
−0.875030 + 0.484069i \(0.839158\pi\)
\(504\) 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 −0.252702 0.967544i \(-0.581319\pi\)
0.967544 + 0.252702i \(0.0813192\pi\)
\(510\) 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 0.342248 0.939610i \(-0.388812\pi\)
−0.939610 + 0.342248i \(0.888812\pi\)
\(524\) 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 0.998311 + 0.0581016i \(0.0185047\pi\)
0.0581016 + 0.998311i \(0.481495\pi\)
\(542\) 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 −0.779295 0.626657i \(-0.784423\pi\)
0.626657 + 0.779295i \(0.284423\pi\)
\(548\) 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 −0.208540 0.978014i \(-0.566871\pi\)
0.978014 + 0.208540i \(0.0668713\pi\)
\(558\) 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 \(-0.316093\pi\)
−0.837687 + 0.546150i \(0.816093\pi\)
\(564\) 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 0.790814 + 0.612056i \(0.209657\pi\)
0.612056 + 0.790814i \(0.290343\pi\)
\(572\) 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 −0.255885 + 0.966707i \(0.582367\pi\)
−0.966707 + 0.255885i \(0.917633\pi\)
\(588\) 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
\(597\) 12.6614 + 18.8270i 0.518198 + 0.770539i
\(598\) 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 \(0.233642\pi\)
−0.742495 + 0.669851i \(0.766358\pi\)
\(602\) 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 \(-0.954915\pi\)
0.989986 0.141167i \(-0.0450855\pi\)
\(608\) 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 −0.378693 0.925522i \(-0.623626\pi\)
0.925522 + 0.378693i \(0.123626\pi\)
\(614\) 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 0.739423 0.673241i \(-0.235098\pi\)
−0.673241 + 0.739423i \(0.735098\pi\)
\(620\) 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 \(0.106546\pi\)
−0.944501 + 0.328508i \(0.893454\pi\)
\(642\) 0 0
\(643\) 4.77502 4.77502i 0.188308 0.188308i −0.606656 0.794964i \(-0.707489\pi\)
0.794964 + 0.606656i \(0.207489\pi\)
\(644\) 0 0
\(645\) −17.0722 + 11.4813i −0.672217 + 0.452075i
\(646\) 0 0
\(647\) 48.2095i 1.89531i 0.319293 + 0.947656i \(0.396555\pi\)
−0.319293 + 0.947656i \(0.603445\pi\)
\(648\) 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 −0.0505983 0.998719i \(-0.516113\pi\)
0.998719 + 0.0505983i \(0.0161128\pi\)
\(654\) 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 \(-0.334043\pi\)
−0.867138 + 0.498067i \(0.834043\pi\)
\(660\) 0 0
\(661\) −23.0406 + 23.0406i −0.896175 + 0.896175i −0.995095 0.0989204i \(-0.968461\pi\)
0.0989204 + 0.995095i \(0.468461\pi\)
\(662\) 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 0.591339 0.806423i \(-0.298599\pi\)
−0.806423 + 0.591339i \(0.798599\pi\)
\(678\) 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 \(-0.927711\pi\)
0.225155 + 0.974323i \(0.427711\pi\)
\(684\) 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 −0.778865 0.627192i \(-0.784204\pi\)
0.627192 + 0.778865i \(0.284204\pi\)
\(692\) 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 −0.933393 0.358856i \(-0.883167\pi\)
0.358856 + 0.933393i \(0.383167\pi\)
\(702\) 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 −0.976759 0.214342i \(-0.931239\pi\)
0.214342 + 0.976759i \(0.431239\pi\)
\(710\) 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 0.659817 0.751426i \(-0.270634\pi\)
−0.751426 + 0.659817i \(0.770634\pi\)
\(734\) 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 −0.935166 0.354209i \(-0.884750\pi\)
0.354209 + 0.935166i \(0.384750\pi\)
\(740\) 0 0
\(741\) −23.7329 35.2898i −0.871849 1.29640i
\(742\) 0 0
\(743\) 38.5942i 1.41588i −0.706271 0.707941i \(-0.749624\pi\)
0.706271 0.707941i \(-0.250376\pi\)
\(744\) 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 \(0.104381\pi\)
−0.946713 + 0.322078i \(0.895619\pi\)
\(752\) 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 0.213062 0.977039i \(-0.431657\pi\)
0.977039 0.213062i \(-0.0683435\pi\)
\(758\) 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 0.488320 0.872665i \(-0.337610\pi\)
−0.872665 + 0.488320i \(0.837610\pi\)
\(774\) 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 −0.933191 0.359381i \(-0.882988\pi\)
0.359381 + 0.933191i \(0.382988\pi\)
\(788\) 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 −0.752266 0.658860i \(-0.771039\pi\)