Properties

Label 384.2.k.b.95.5
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 95.5
Root \(1.35164 - 0.416001i\) of defining polynomial
Character \(\chi\) \(=\) 384.95
Dual form 384.2.k.b.287.5

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

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

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
<
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 1.43726 + 0.966579i 0.829804 + 0.558055i
\(4\) 0 0
\(5\) −1.57184 1.57184i −0.702949 0.702949i 0.262094 0.965042i \(-0.415587\pi\)
−0.965042 + 0.262094i \(0.915587\pi\)
\(6\) 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 \(-0.672451\pi\)
0.856798 + 0.515653i \(0.172451\pi\)
\(12\) 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 \(0.0646758\pi\)
−0.979429 + 0.201790i \(0.935324\pi\)
\(18\) 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
\(21\) 3.23261 + 2.17397i 0.705412 + 0.474400i
\(22\) 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
\(27\) −1.05941 + 5.08701i −0.203884 + 0.978995i
\(28\) 0 0
\(29\) −3.23584 + 3.23584i −0.600881 + 0.600881i −0.940546 0.339665i \(-0.889686\pi\)
0.339665 + 0.940546i \(0.389686\pi\)
\(30\) 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 \(-0.793897\pi\)
−0.797600 + 0.603187i \(0.793897\pi\)
\(42\) 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
\(45\) 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 0.770765 0.637120i \(-0.219874\pi\)
−0.637120 + 0.770765i \(0.719874\pi\)
\(54\) 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 \(-0.633627\pi\)
0.913170 + 0.407579i \(0.133627\pi\)
\(60\) 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
\(69\) 2.18727 3.25238i 0.263316 0.391540i
\(70\) 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 \(-0.878185\pi\)
0.927662 0.373421i \(-0.121815\pi\)
\(74\) 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 \(0.0483941\pi\)
−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 0.835738 0.549129i \(-0.185040\pi\)
−0.549129 + 0.835738i \(0.685040\pi\)
\(84\) 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 −0.999666 0.0258621i \(-0.991767\pi\)
−0.0258621 0.999666i \(-0.508233\pi\)
\(102\) 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 \(-0.802544\pi\)
0.581301 + 0.813689i \(0.302544\pi\)
\(108\) 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 \(0.268986\pi\)
−0.663697 + 0.748002i \(0.731014\pi\)
\(114\) 0 0
\(115\) −3.55691 + 3.55691i −0.331684 + 0.331684i
\(116\) 0 0
\(117\) −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 \(-0.893142\pi\)
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 0.516801 0.856106i \(-0.327123\pi\)
−0.856106 + 0.516801i \(0.827123\pi\)
\(132\) 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 0.708276 0.705935i \(-0.249473\pi\)
−0.705935 + 0.708276i \(0.749473\pi\)
\(140\) 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 0.999545 + 0.0301744i \(0.00960626\pi\)
0.0301744 + 0.999545i \(0.490394\pi\)
\(150\) 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
\(165\) −5.11222 3.43804i −0.397986 0.267651i
\(166\) 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
\(171\) 14.7734 + 6.22315i 1.12975 + 0.475896i
\(172\) 0 0
\(173\) 16.3119 16.3119i 1.24017 1.24017i 0.280241 0.959930i \(-0.409586\pi\)
0.959930 0.280241i \(-0.0904144\pi\)
\(174\) 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 \(-0.272541\pi\)
−0.755365 + 0.655304i \(0.772541\pi\)
\(180\) 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
\(189\) −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 0.751565 0.659659i \(-0.229299\pi\)
−0.659659 + 0.751565i \(0.729299\pi\)
\(198\) 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
\(213\) 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 \(-0.743100\pi\)
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 \(0.0379668\pi\)
0.118994 + 0.992895i \(0.462033\pi\)
\(228\) 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 \(-0.494773\pi\)
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 −0.978409 0.206679i \(-0.933734\pi\)
0.206679 + 0.978409i \(0.433734\pi\)
\(252\) 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
\(261\) −12.6518 5.32946i −0.783129 0.329885i
\(262\) 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
\(267\) 10.5674 + 7.10675i 0.646716 + 0.434926i
\(268\) 0 0
\(269\) −2.76963 + 2.76963i −0.168867 + 0.168867i −0.786481 0.617614i \(-0.788099\pi\)
0.617614 + 0.786481i \(0.288099\pi\)
\(270\) 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 \(-0.268076\pi\)
0.665833 + 0.746101i \(0.268076\pi\)
\(282\) 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
\(285\) −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 0.868458 0.495762i \(-0.165111\pi\)
−0.495762 + 0.868458i \(0.665111\pi\)
\(294\) 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
\(309\) −11.6876 7.86010i −0.664887 0.447146i
\(310\) 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 \(-0.748098\pi\)
0.702870 0.711319i \(-0.251902\pi\)
\(314\) 0 0
\(315\) 5.82265 13.8227i 0.328069 0.778818i
\(316\) 0 0
\(317\) 15.5287 15.5287i 0.872178 0.872178i −0.120532 0.992709i \(-0.538460\pi\)
0.992709 + 0.120532i \(0.0384600\pi\)
\(318\) 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
\(333\) −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 −0.864135 0.503260i \(-0.832134\pi\)
0.503260 + 0.864135i \(0.332134\pi\)
\(348\) 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 \(-0.788262\pi\)
0.786796 0.617213i \(-0.211738\pi\)
\(354\) 0 0
\(355\) −17.4396 + 17.4396i −0.925600 + 0.925600i
\(356\) 0 0
\(357\) −3.61750 + 5.37907i −0.191458 + 0.284690i
\(358\) 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
\(363\) −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 \(0.237870\pi\)
−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
\(381\) 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 0.644879 0.764285i \(-0.276908\pi\)
−0.764285 + 0.644879i \(0.776908\pi\)
\(390\) 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 \(-0.958657\pi\)
0.991577 0.129517i \(-0.0413426\pi\)
\(402\) 0 0
\(403\) −4.24914 + 4.24914i −0.211665 + 0.211665i
\(404\) 0 0
\(405\) 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 \(-0.880088\pi\)
0.929878 0.367867i \(-0.119912\pi\)
\(410\) 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 −0.961578 0.274533i \(-0.911477\pi\)
−0.274533 0.961578i \(-0.588523\pi\)
\(420\) 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
\(429\) 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 −0.259749 0.965676i \(-0.583640\pi\)
0.965676 + 0.259749i \(0.0836399\pi\)
\(444\) 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
\(453\) 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 \(0.188597\pi\)
−0.829550 + 0.558433i \(0.811403\pi\)
\(458\) 0 0
\(459\) −8.46480 1.76286i −0.395103 0.0822833i
\(460\) 0 0
\(461\) 0.921303 0.921303i 0.0429094 0.0429094i −0.685327 0.728236i \(-0.740341\pi\)
0.728236 + 0.685327i \(0.240341\pi\)
\(462\) 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 0.222848 0.974853i \(-0.428465\pi\)
−0.974853 + 0.222848i \(0.928465\pi\)
\(468\) 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 −0.896355 0.443337i \(-0.853794\pi\)
0.443337 + 0.896355i \(0.353794\pi\)
\(492\) 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
\(501\) −16.4008 + 24.3872i −0.732732 + 1.08954i
\(502\) 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
\(507\) −7.84266 + 11.6617i −0.348305 + 0.517914i
\(508\) 0 0
\(509\) −16.1276 + 16.1276i −0.714842 + 0.714842i −0.967544 0.252702i \(-0.918681\pi\)
0.252702 + 0.967544i \(0.418681\pi\)
\(510\) 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 0.342248 0.939610i \(-0.388812\pi\)
−0.939610 + 0.342248i \(0.888812\pi\)
\(524\) 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 0.998311 + 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
\(549\) 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 −0.978014 0.208540i \(-0.933129\pi\)
0.208540 + 0.978014i \(0.433129\pi\)
\(558\) 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 \(-0.183907\pi\)
−0.546150 + 0.837687i \(0.683907\pi\)
\(564\) 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 0.790814 + 0.612056i \(0.209657\pi\)
0.612056 + 0.790814i \(0.290343\pi\)
\(572\) 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 0.255885 0.966707i \(-0.417633\pi\)
0.966707 0.255885i \(-0.0823667\pi\)
\(588\) 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
\(597\) −18.8270 12.6614i −0.770539 0.518198i
\(598\) 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 \(0.233642\pi\)
−0.742495 + 0.669851i \(0.766358\pi\)
\(602\) 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 \(-0.954915\pi\)
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 \(-0.442542\pi\)
0.179531 + 0.983752i \(0.442542\pi\)
\(618\) 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
\(621\) 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 \(-0.893454\pi\)
0.944501 0.328508i \(-0.106546\pi\)
\(642\) 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
\(645\) −11.4813 + 17.0722i −0.452075 + 0.672217i
\(646\) 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
\(651\) −2.84306 + 4.22752i −0.111428 + 0.165689i
\(652\) 0 0
\(653\) −24.2281 + 24.2281i −0.948121 + 0.948121i −0.998719 0.0505983i \(-0.983887\pi\)
0.0505983 + 0.998719i \(0.483887\pi\)
\(654\) 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 \(-0.165957\pi\)
−0.498067 + 0.867138i \(0.665957\pi\)
\(660\) 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
\(669\) 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 0.806423 0.591339i \(-0.201401\pi\)
−0.591339 + 0.806423i \(0.701401\pi\)
\(678\) 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 \(-0.572289\pi\)
0.974323 + 0.225155i \(0.0722887\pi\)
\(684\) 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
\(693\) 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 −0.358856 0.933393i \(-0.616833\pi\)
0.933393 + 0.358856i \(0.116833\pi\)
\(702\) 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
\(717\) −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 0.659817 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
\(741\) 35.2898 + 23.7329i 1.29640 + 0.871849i
\(742\) 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
\(747\) −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 \(0.104381\pi\)
−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 \(-0.538699\pi\)
−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 0.872665 0.488320i \(-0.162390\pi\)
−0.488320 + 0.872665i \(0.662390\pi\)
\(774\) 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
\(789\) 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 −0.658860 0.752266i \(-0.728961\pi\)
0.752266 +