Properties

Label 672.2.q.a.193.1
Level $672$
Weight $2$
Character 672.193
Analytic conductor $5.366$
Analytic rank $1$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 672 = 2^{5} \cdot 3 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 672.q (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.36594701583\)
Analytic rank: \(1\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Defining polynomial: \(x^{2} - x + 1\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 193.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 672.193
Dual form 672.2.q.a.289.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.500000 + 0.866025i) q^{3} +(-1.50000 - 2.59808i) q^{5} +(0.500000 + 2.59808i) q^{7} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\) \(q+(-0.500000 + 0.866025i) q^{3} +(-1.50000 - 2.59808i) q^{5} +(0.500000 + 2.59808i) q^{7} +(-0.500000 - 0.866025i) q^{9} +(0.500000 - 0.866025i) q^{11} -4.00000 q^{13} +3.00000 q^{15} +(-2.00000 + 3.46410i) q^{17} +(-2.50000 - 0.866025i) q^{21} +(-4.00000 - 6.92820i) q^{23} +(-2.00000 + 3.46410i) q^{25} +1.00000 q^{27} -7.00000 q^{29} +(-5.50000 + 9.52628i) q^{31} +(0.500000 + 0.866025i) q^{33} +(6.00000 - 5.19615i) q^{35} +(-2.00000 - 3.46410i) q^{37} +(2.00000 - 3.46410i) q^{39} -4.00000 q^{41} -2.00000 q^{43} +(-1.50000 + 2.59808i) q^{45} +(1.00000 + 1.73205i) q^{47} +(-6.50000 + 2.59808i) q^{49} +(-2.00000 - 3.46410i) q^{51} +(5.50000 - 9.52628i) q^{53} -3.00000 q^{55} +(-3.50000 + 6.06218i) q^{59} +(-5.00000 - 8.66025i) q^{61} +(2.00000 - 1.73205i) q^{63} +(6.00000 + 10.3923i) q^{65} +(-5.00000 + 8.66025i) q^{67} +8.00000 q^{69} +6.00000 q^{71} +(3.00000 - 5.19615i) q^{73} +(-2.00000 - 3.46410i) q^{75} +(2.50000 + 0.866025i) q^{77} +(-5.50000 - 9.52628i) q^{79} +(-0.500000 + 0.866025i) q^{81} +11.0000 q^{83} +12.0000 q^{85} +(3.50000 - 6.06218i) q^{87} +(-3.00000 - 5.19615i) q^{89} +(-2.00000 - 10.3923i) q^{91} +(-5.50000 - 9.52628i) q^{93} +7.00000 q^{97} -1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q - q^{3} - 3q^{5} + q^{7} - q^{9} + O(q^{10}) \) \( 2q - q^{3} - 3q^{5} + q^{7} - q^{9} + q^{11} - 8q^{13} + 6q^{15} - 4q^{17} - 5q^{21} - 8q^{23} - 4q^{25} + 2q^{27} - 14q^{29} - 11q^{31} + q^{33} + 12q^{35} - 4q^{37} + 4q^{39} - 8q^{41} - 4q^{43} - 3q^{45} + 2q^{47} - 13q^{49} - 4q^{51} + 11q^{53} - 6q^{55} - 7q^{59} - 10q^{61} + 4q^{63} + 12q^{65} - 10q^{67} + 16q^{69} + 12q^{71} + 6q^{73} - 4q^{75} + 5q^{77} - 11q^{79} - q^{81} + 22q^{83} + 24q^{85} + 7q^{87} - 6q^{89} - 4q^{91} - 11q^{93} + 14q^{97} - 2q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/672\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(421\) \(449\) \(577\)
\(\chi(n)\) \(1\) \(1\) \(1\) \(e\left(\frac{2}{3}\right)\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −0.500000 + 0.866025i −0.288675 + 0.500000i
\(4\) 0 0
\(5\) −1.50000 2.59808i −0.670820 1.16190i −0.977672 0.210138i \(-0.932609\pi\)
0.306851 0.951757i \(-0.400725\pi\)
\(6\) 0 0
\(7\) 0.500000 + 2.59808i 0.188982 + 0.981981i
\(8\) 0 0
\(9\) −0.500000 0.866025i −0.166667 0.288675i
\(10\) 0 0
\(11\) 0.500000 0.866025i 0.150756 0.261116i −0.780750 0.624844i \(-0.785163\pi\)
0.931505 + 0.363727i \(0.118496\pi\)
\(12\) 0 0
\(13\) −4.00000 −1.10940 −0.554700 0.832050i \(-0.687167\pi\)
−0.554700 + 0.832050i \(0.687167\pi\)
\(14\) 0 0
\(15\) 3.00000 0.774597
\(16\) 0 0
\(17\) −2.00000 + 3.46410i −0.485071 + 0.840168i −0.999853 0.0171533i \(-0.994540\pi\)
0.514782 + 0.857321i \(0.327873\pi\)
\(18\) 0 0
\(19\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(20\) 0 0
\(21\) −2.50000 0.866025i −0.545545 0.188982i
\(22\) 0 0
\(23\) −4.00000 6.92820i −0.834058 1.44463i −0.894795 0.446476i \(-0.852679\pi\)
0.0607377 0.998154i \(-0.480655\pi\)
\(24\) 0 0
\(25\) −2.00000 + 3.46410i −0.400000 + 0.692820i
\(26\) 0 0
\(27\) 1.00000 0.192450
\(28\) 0 0
\(29\) −7.00000 −1.29987 −0.649934 0.759991i \(-0.725203\pi\)
−0.649934 + 0.759991i \(0.725203\pi\)
\(30\) 0 0
\(31\) −5.50000 + 9.52628i −0.987829 + 1.71097i −0.359211 + 0.933257i \(0.616954\pi\)
−0.628619 + 0.777714i \(0.716379\pi\)
\(32\) 0 0
\(33\) 0.500000 + 0.866025i 0.0870388 + 0.150756i
\(34\) 0 0
\(35\) 6.00000 5.19615i 1.01419 0.878310i
\(36\) 0 0
\(37\) −2.00000 3.46410i −0.328798 0.569495i 0.653476 0.756948i \(-0.273310\pi\)
−0.982274 + 0.187453i \(0.939977\pi\)
\(38\) 0 0
\(39\) 2.00000 3.46410i 0.320256 0.554700i
\(40\) 0 0
\(41\) −4.00000 −0.624695 −0.312348 0.949968i \(-0.601115\pi\)
−0.312348 + 0.949968i \(0.601115\pi\)
\(42\) 0 0
\(43\) −2.00000 −0.304997 −0.152499 0.988304i \(-0.548732\pi\)
−0.152499 + 0.988304i \(0.548732\pi\)
\(44\) 0 0
\(45\) −1.50000 + 2.59808i −0.223607 + 0.387298i
\(46\) 0 0
\(47\) 1.00000 + 1.73205i 0.145865 + 0.252646i 0.929695 0.368329i \(-0.120070\pi\)
−0.783830 + 0.620975i \(0.786737\pi\)
\(48\) 0 0
\(49\) −6.50000 + 2.59808i −0.928571 + 0.371154i
\(50\) 0 0
\(51\) −2.00000 3.46410i −0.280056 0.485071i
\(52\) 0 0
\(53\) 5.50000 9.52628i 0.755483 1.30854i −0.189651 0.981852i \(-0.560736\pi\)
0.945134 0.326683i \(-0.105931\pi\)
\(54\) 0 0
\(55\) −3.00000 −0.404520
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −3.50000 + 6.06218i −0.455661 + 0.789228i −0.998726 0.0504625i \(-0.983930\pi\)
0.543065 + 0.839691i \(0.317264\pi\)
\(60\) 0 0
\(61\) −5.00000 8.66025i −0.640184 1.10883i −0.985391 0.170305i \(-0.945525\pi\)
0.345207 0.938527i \(-0.387809\pi\)
\(62\) 0 0
\(63\) 2.00000 1.73205i 0.251976 0.218218i
\(64\) 0 0
\(65\) 6.00000 + 10.3923i 0.744208 + 1.28901i
\(66\) 0 0
\(67\) −5.00000 + 8.66025i −0.610847 + 1.05802i 0.380251 + 0.924883i \(0.375838\pi\)
−0.991098 + 0.133135i \(0.957496\pi\)
\(68\) 0 0
\(69\) 8.00000 0.963087
\(70\) 0 0
\(71\) 6.00000 0.712069 0.356034 0.934473i \(-0.384129\pi\)
0.356034 + 0.934473i \(0.384129\pi\)
\(72\) 0 0
\(73\) 3.00000 5.19615i 0.351123 0.608164i −0.635323 0.772246i \(-0.719133\pi\)
0.986447 + 0.164083i \(0.0524664\pi\)
\(74\) 0 0
\(75\) −2.00000 3.46410i −0.230940 0.400000i
\(76\) 0 0
\(77\) 2.50000 + 0.866025i 0.284901 + 0.0986928i
\(78\) 0 0
\(79\) −5.50000 9.52628i −0.618798 1.07179i −0.989705 0.143120i \(-0.954286\pi\)
0.370907 0.928670i \(-0.379047\pi\)
\(80\) 0 0
\(81\) −0.500000 + 0.866025i −0.0555556 + 0.0962250i
\(82\) 0 0
\(83\) 11.0000 1.20741 0.603703 0.797209i \(-0.293691\pi\)
0.603703 + 0.797209i \(0.293691\pi\)
\(84\) 0 0
\(85\) 12.0000 1.30158
\(86\) 0 0
\(87\) 3.50000 6.06218i 0.375239 0.649934i
\(88\) 0 0
\(89\) −3.00000 5.19615i −0.317999 0.550791i 0.662071 0.749441i \(-0.269678\pi\)
−0.980071 + 0.198650i \(0.936344\pi\)
\(90\) 0 0
\(91\) −2.00000 10.3923i −0.209657 1.08941i
\(92\) 0 0
\(93\) −5.50000 9.52628i −0.570323 0.987829i
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) 7.00000 0.710742 0.355371 0.934725i \(-0.384354\pi\)
0.355371 + 0.934725i \(0.384354\pi\)
\(98\) 0 0
\(99\) −1.00000 −0.100504
\(100\) 0 0
\(101\) −3.00000 + 5.19615i −0.298511 + 0.517036i −0.975796 0.218685i \(-0.929823\pi\)
0.677284 + 0.735721i \(0.263157\pi\)
\(102\) 0 0
\(103\) 8.00000 + 13.8564i 0.788263 + 1.36531i 0.927030 + 0.374987i \(0.122353\pi\)
−0.138767 + 0.990325i \(0.544314\pi\)
\(104\) 0 0
\(105\) 1.50000 + 7.79423i 0.146385 + 0.760639i
\(106\) 0 0
\(107\) 3.50000 + 6.06218i 0.338358 + 0.586053i 0.984124 0.177482i \(-0.0567953\pi\)
−0.645766 + 0.763535i \(0.723462\pi\)
\(108\) 0 0
\(109\) −5.00000 + 8.66025i −0.478913 + 0.829502i −0.999708 0.0241802i \(-0.992302\pi\)
0.520794 + 0.853682i \(0.325636\pi\)
\(110\) 0 0
\(111\) 4.00000 0.379663
\(112\) 0 0
\(113\) 12.0000 1.12887 0.564433 0.825479i \(-0.309095\pi\)
0.564433 + 0.825479i \(0.309095\pi\)
\(114\) 0 0
\(115\) −12.0000 + 20.7846i −1.11901 + 1.93817i
\(116\) 0 0
\(117\) 2.00000 + 3.46410i 0.184900 + 0.320256i
\(118\) 0 0
\(119\) −10.0000 3.46410i −0.916698 0.317554i
\(120\) 0 0
\(121\) 5.00000 + 8.66025i 0.454545 + 0.787296i
\(122\) 0 0
\(123\) 2.00000 3.46410i 0.180334 0.312348i
\(124\) 0 0
\(125\) −3.00000 −0.268328
\(126\) 0 0
\(127\) 17.0000 1.50851 0.754253 0.656584i \(-0.227999\pi\)
0.754253 + 0.656584i \(0.227999\pi\)
\(128\) 0 0
\(129\) 1.00000 1.73205i 0.0880451 0.152499i
\(130\) 0 0
\(131\) −1.50000 2.59808i −0.131056 0.226995i 0.793028 0.609185i \(-0.208503\pi\)
−0.924084 + 0.382190i \(0.875170\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) −1.50000 2.59808i −0.129099 0.223607i
\(136\) 0 0
\(137\) 1.00000 1.73205i 0.0854358 0.147979i −0.820141 0.572161i \(-0.806105\pi\)
0.905577 + 0.424182i \(0.139438\pi\)
\(138\) 0 0
\(139\) −22.0000 −1.86602 −0.933008 0.359856i \(-0.882826\pi\)
−0.933008 + 0.359856i \(0.882826\pi\)
\(140\) 0 0
\(141\) −2.00000 −0.168430
\(142\) 0 0
\(143\) −2.00000 + 3.46410i −0.167248 + 0.289683i
\(144\) 0 0
\(145\) 10.5000 + 18.1865i 0.871978 + 1.51031i
\(146\) 0 0
\(147\) 1.00000 6.92820i 0.0824786 0.571429i
\(148\) 0 0
\(149\) 3.00000 + 5.19615i 0.245770 + 0.425685i 0.962348 0.271821i \(-0.0876260\pi\)
−0.716578 + 0.697507i \(0.754293\pi\)
\(150\) 0 0
\(151\) −5.50000 + 9.52628i −0.447584 + 0.775238i −0.998228 0.0595022i \(-0.981049\pi\)
0.550645 + 0.834740i \(0.314382\pi\)
\(152\) 0 0
\(153\) 4.00000 0.323381
\(154\) 0 0
\(155\) 33.0000 2.65062
\(156\) 0 0
\(157\) 6.00000 10.3923i 0.478852 0.829396i −0.520854 0.853646i \(-0.674386\pi\)
0.999706 + 0.0242497i \(0.00771967\pi\)
\(158\) 0 0
\(159\) 5.50000 + 9.52628i 0.436178 + 0.755483i
\(160\) 0 0
\(161\) 16.0000 13.8564i 1.26098 1.09204i
\(162\) 0 0
\(163\) 4.00000 + 6.92820i 0.313304 + 0.542659i 0.979076 0.203497i \(-0.0652307\pi\)
−0.665771 + 0.746156i \(0.731897\pi\)
\(164\) 0 0
\(165\) 1.50000 2.59808i 0.116775 0.202260i
\(166\) 0 0
\(167\) −22.0000 −1.70241 −0.851206 0.524832i \(-0.824128\pi\)
−0.851206 + 0.524832i \(0.824128\pi\)
\(168\) 0 0
\(169\) 3.00000 0.230769
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 3.00000 + 5.19615i 0.228086 + 0.395056i 0.957241 0.289292i \(-0.0934200\pi\)
−0.729155 + 0.684349i \(0.760087\pi\)
\(174\) 0 0
\(175\) −10.0000 3.46410i −0.755929 0.261861i
\(176\) 0 0
\(177\) −3.50000 6.06218i −0.263076 0.455661i
\(178\) 0 0
\(179\) 6.00000 10.3923i 0.448461 0.776757i −0.549825 0.835280i \(-0.685306\pi\)
0.998286 + 0.0585225i \(0.0186389\pi\)
\(180\) 0 0
\(181\) 12.0000 0.891953 0.445976 0.895045i \(-0.352856\pi\)
0.445976 + 0.895045i \(0.352856\pi\)
\(182\) 0 0
\(183\) 10.0000 0.739221
\(184\) 0 0
\(185\) −6.00000 + 10.3923i −0.441129 + 0.764057i
\(186\) 0 0
\(187\) 2.00000 + 3.46410i 0.146254 + 0.253320i
\(188\) 0 0
\(189\) 0.500000 + 2.59808i 0.0363696 + 0.188982i
\(190\) 0 0
\(191\) −12.0000 20.7846i −0.868290 1.50392i −0.863743 0.503932i \(-0.831886\pi\)
−0.00454614 0.999990i \(-0.501447\pi\)
\(192\) 0 0
\(193\) 9.50000 16.4545i 0.683825 1.18442i −0.289980 0.957033i \(-0.593649\pi\)
0.973805 0.227387i \(-0.0730182\pi\)
\(194\) 0 0
\(195\) −12.0000 −0.859338
\(196\) 0 0
\(197\) 6.00000 0.427482 0.213741 0.976890i \(-0.431435\pi\)
0.213741 + 0.976890i \(0.431435\pi\)
\(198\) 0 0
\(199\) 10.0000 17.3205i 0.708881 1.22782i −0.256391 0.966573i \(-0.582534\pi\)
0.965272 0.261245i \(-0.0841331\pi\)
\(200\) 0 0
\(201\) −5.00000 8.66025i −0.352673 0.610847i
\(202\) 0 0
\(203\) −3.50000 18.1865i −0.245652 1.27644i
\(204\) 0 0
\(205\) 6.00000 + 10.3923i 0.419058 + 0.725830i
\(206\) 0 0
\(207\) −4.00000 + 6.92820i −0.278019 + 0.481543i
\(208\) 0 0
\(209\) 0 0
\(210\) 0 0
\(211\) 2.00000 0.137686 0.0688428 0.997628i \(-0.478069\pi\)
0.0688428 + 0.997628i \(0.478069\pi\)
\(212\) 0 0
\(213\) −3.00000 + 5.19615i −0.205557 + 0.356034i
\(214\) 0 0
\(215\) 3.00000 + 5.19615i 0.204598 + 0.354375i
\(216\) 0 0
\(217\) −27.5000 9.52628i −1.86682 0.646686i
\(218\) 0 0
\(219\) 3.00000 + 5.19615i 0.202721 + 0.351123i
\(220\) 0 0
\(221\) 8.00000 13.8564i 0.538138 0.932083i
\(222\) 0 0
\(223\) 9.00000 0.602685 0.301342 0.953516i \(-0.402565\pi\)
0.301342 + 0.953516i \(0.402565\pi\)
\(224\) 0 0
\(225\) 4.00000 0.266667
\(226\) 0 0
\(227\) 3.50000 6.06218i 0.232303 0.402361i −0.726182 0.687502i \(-0.758707\pi\)
0.958485 + 0.285141i \(0.0920405\pi\)
\(228\) 0 0
\(229\) 4.00000 + 6.92820i 0.264327 + 0.457829i 0.967387 0.253302i \(-0.0815167\pi\)
−0.703060 + 0.711131i \(0.748183\pi\)
\(230\) 0 0
\(231\) −2.00000 + 1.73205i −0.131590 + 0.113961i
\(232\) 0 0
\(233\) −6.00000 10.3923i −0.393073 0.680823i 0.599780 0.800165i \(-0.295255\pi\)
−0.992853 + 0.119342i \(0.961921\pi\)
\(234\) 0 0
\(235\) 3.00000 5.19615i 0.195698 0.338960i
\(236\) 0 0
\(237\) 11.0000 0.714527
\(238\) 0 0
\(239\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(240\) 0 0
\(241\) 12.5000 21.6506i 0.805196 1.39464i −0.110963 0.993825i \(-0.535394\pi\)
0.916159 0.400815i \(-0.131273\pi\)
\(242\) 0 0
\(243\) −0.500000 0.866025i −0.0320750 0.0555556i
\(244\) 0 0
\(245\) 16.5000 + 12.9904i 1.05415 + 0.829925i
\(246\) 0 0
\(247\) 0 0
\(248\) 0 0
\(249\) −5.50000 + 9.52628i −0.348548 + 0.603703i
\(250\) 0 0
\(251\) −25.0000 −1.57799 −0.788993 0.614402i \(-0.789397\pi\)
−0.788993 + 0.614402i \(0.789397\pi\)
\(252\) 0 0
\(253\) −8.00000 −0.502956
\(254\) 0 0
\(255\) −6.00000 + 10.3923i −0.375735 + 0.650791i
\(256\) 0 0
\(257\) −7.00000 12.1244i −0.436648 0.756297i 0.560781 0.827964i \(-0.310501\pi\)
−0.997429 + 0.0716680i \(0.977168\pi\)
\(258\) 0 0
\(259\) 8.00000 6.92820i 0.497096 0.430498i
\(260\) 0 0
\(261\) 3.50000 + 6.06218i 0.216645 + 0.375239i
\(262\) 0 0
\(263\) −13.0000 + 22.5167i −0.801614 + 1.38844i 0.116939 + 0.993139i \(0.462692\pi\)
−0.918553 + 0.395298i \(0.870641\pi\)
\(264\) 0 0
\(265\) −33.0000 −2.02717
\(266\) 0 0
\(267\) 6.00000 0.367194
\(268\) 0 0
\(269\) −10.5000 + 18.1865i −0.640196 + 1.10885i 0.345192 + 0.938532i \(0.387814\pi\)
−0.985389 + 0.170321i \(0.945520\pi\)
\(270\) 0 0
\(271\) 0.500000 + 0.866025i 0.0303728 + 0.0526073i 0.880812 0.473466i \(-0.156997\pi\)
−0.850439 + 0.526073i \(0.823664\pi\)
\(272\) 0 0
\(273\) 10.0000 + 3.46410i 0.605228 + 0.209657i
\(274\) 0 0
\(275\) 2.00000 + 3.46410i 0.120605 + 0.208893i
\(276\) 0 0
\(277\) −16.0000 + 27.7128i −0.961347 + 1.66510i −0.242222 + 0.970221i \(0.577876\pi\)
−0.719125 + 0.694881i \(0.755457\pi\)
\(278\) 0 0
\(279\) 11.0000 0.658553
\(280\) 0 0
\(281\) −30.0000 −1.78965 −0.894825 0.446417i \(-0.852700\pi\)
−0.894825 + 0.446417i \(0.852700\pi\)
\(282\) 0 0
\(283\) 1.00000 1.73205i 0.0594438 0.102960i −0.834772 0.550596i \(-0.814401\pi\)
0.894216 + 0.447636i \(0.147734\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −2.00000 10.3923i −0.118056 0.613438i
\(288\) 0 0
\(289\) 0.500000 + 0.866025i 0.0294118 + 0.0509427i
\(290\) 0 0
\(291\) −3.50000 + 6.06218i −0.205174 + 0.355371i
\(292\) 0 0
\(293\) −7.00000 −0.408944 −0.204472 0.978872i \(-0.565548\pi\)
−0.204472 + 0.978872i \(0.565548\pi\)
\(294\) 0 0
\(295\) 21.0000 1.22267
\(296\) 0 0
\(297\) 0.500000 0.866025i 0.0290129 0.0502519i
\(298\) 0 0
\(299\) 16.0000 + 27.7128i 0.925304 + 1.60267i
\(300\) 0 0
\(301\) −1.00000 5.19615i −0.0576390 0.299501i
\(302\) 0 0
\(303\) −3.00000 5.19615i −0.172345 0.298511i
\(304\) 0 0
\(305\) −15.0000 + 25.9808i −0.858898 + 1.48765i
\(306\) 0 0
\(307\) −8.00000 −0.456584 −0.228292 0.973593i \(-0.573314\pi\)
−0.228292 + 0.973593i \(0.573314\pi\)
\(308\) 0 0
\(309\) −16.0000 −0.910208
\(310\) 0 0
\(311\) −6.00000 + 10.3923i −0.340229 + 0.589294i −0.984475 0.175525i \(-0.943838\pi\)
0.644246 + 0.764818i \(0.277171\pi\)
\(312\) 0 0
\(313\) −0.500000 0.866025i −0.0282617 0.0489506i 0.851549 0.524276i \(-0.175664\pi\)
−0.879810 + 0.475325i \(0.842331\pi\)
\(314\) 0 0
\(315\) −7.50000 2.59808i −0.422577 0.146385i
\(316\) 0 0
\(317\) −8.50000 14.7224i −0.477408 0.826894i 0.522257 0.852788i \(-0.325090\pi\)
−0.999665 + 0.0258939i \(0.991757\pi\)
\(318\) 0 0
\(319\) −3.50000 + 6.06218i −0.195962 + 0.339417i
\(320\) 0 0
\(321\) −7.00000 −0.390702
\(322\) 0 0
\(323\) 0 0
\(324\) 0 0
\(325\) 8.00000 13.8564i 0.443760 0.768615i
\(326\) 0 0
\(327\) −5.00000 8.66025i −0.276501 0.478913i
\(328\) 0 0
\(329\) −4.00000 + 3.46410i −0.220527 + 0.190982i
\(330\) 0 0
\(331\) −6.00000 10.3923i −0.329790 0.571213i 0.652680 0.757634i \(-0.273645\pi\)
−0.982470 + 0.186421i \(0.940311\pi\)
\(332\) 0 0
\(333\) −2.00000 + 3.46410i −0.109599 + 0.189832i
\(334\) 0 0
\(335\) 30.0000 1.63908
\(336\) 0 0
\(337\) −15.0000 −0.817102 −0.408551 0.912735i \(-0.633966\pi\)
−0.408551 + 0.912735i \(0.633966\pi\)
\(338\) 0 0
\(339\) −6.00000 + 10.3923i −0.325875 + 0.564433i
\(340\) 0 0
\(341\) 5.50000 + 9.52628i 0.297842 + 0.515877i
\(342\) 0 0
\(343\) −10.0000 15.5885i −0.539949 0.841698i
\(344\) 0 0
\(345\) −12.0000 20.7846i −0.646058 1.11901i
\(346\) 0 0
\(347\) −6.00000 + 10.3923i −0.322097 + 0.557888i −0.980921 0.194409i \(-0.937721\pi\)
0.658824 + 0.752297i \(0.271054\pi\)
\(348\) 0 0
\(349\) −34.0000 −1.81998 −0.909989 0.414632i \(-0.863910\pi\)
−0.909989 + 0.414632i \(0.863910\pi\)
\(350\) 0 0
\(351\) −4.00000 −0.213504
\(352\) 0 0
\(353\) 12.0000 20.7846i 0.638696 1.10625i −0.347024 0.937856i \(-0.612808\pi\)
0.985719 0.168397i \(-0.0538590\pi\)
\(354\) 0 0
\(355\) −9.00000 15.5885i −0.477670 0.827349i
\(356\) 0 0
\(357\) 8.00000 6.92820i 0.423405 0.366679i
\(358\) 0 0
\(359\) −1.00000 1.73205i −0.0527780 0.0914141i 0.838429 0.545010i \(-0.183474\pi\)
−0.891207 + 0.453596i \(0.850141\pi\)
\(360\) 0 0
\(361\) 9.50000 16.4545i 0.500000 0.866025i
\(362\) 0 0
\(363\) −10.0000 −0.524864
\(364\) 0 0
\(365\) −18.0000 −0.942163
\(366\) 0 0
\(367\) −8.50000 + 14.7224i −0.443696 + 0.768505i −0.997960 0.0638362i \(-0.979666\pi\)
0.554264 + 0.832341i \(0.313000\pi\)
\(368\) 0 0
\(369\) 2.00000 + 3.46410i 0.104116 + 0.180334i
\(370\) 0 0
\(371\) 27.5000 + 9.52628i 1.42773 + 0.494580i
\(372\) 0 0
\(373\) 6.00000 + 10.3923i 0.310668 + 0.538093i 0.978507 0.206213i \(-0.0661139\pi\)
−0.667839 + 0.744306i \(0.732781\pi\)
\(374\) 0 0
\(375\) 1.50000 2.59808i 0.0774597 0.134164i
\(376\) 0 0
\(377\) 28.0000 1.44207
\(378\) 0 0
\(379\) 28.0000 1.43826 0.719132 0.694874i \(-0.244540\pi\)
0.719132 + 0.694874i \(0.244540\pi\)
\(380\) 0 0
\(381\) −8.50000 + 14.7224i −0.435468 + 0.754253i
\(382\) 0 0
\(383\) −1.00000 1.73205i −0.0510976 0.0885037i 0.839345 0.543599i \(-0.182939\pi\)
−0.890443 + 0.455095i \(0.849605\pi\)
\(384\) 0 0
\(385\) −1.50000 7.79423i −0.0764471 0.397231i
\(386\) 0 0
\(387\) 1.00000 + 1.73205i 0.0508329 + 0.0880451i
\(388\) 0 0
\(389\) 3.00000 5.19615i 0.152106 0.263455i −0.779895 0.625910i \(-0.784728\pi\)
0.932002 + 0.362454i \(0.118061\pi\)
\(390\) 0 0
\(391\) 32.0000 1.61831
\(392\) 0 0
\(393\) 3.00000 0.151330
\(394\) 0 0
\(395\) −16.5000 + 28.5788i −0.830205 + 1.43796i
\(396\) 0 0
\(397\) 2.00000 + 3.46410i 0.100377 + 0.173858i 0.911840 0.410546i \(-0.134662\pi\)
−0.811463 + 0.584404i \(0.801328\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −8.00000 13.8564i −0.399501 0.691956i 0.594163 0.804344i \(-0.297483\pi\)
−0.993664 + 0.112388i \(0.964150\pi\)
\(402\) 0 0
\(403\) 22.0000 38.1051i 1.09590 1.89815i
\(404\) 0 0
\(405\) 3.00000 0.149071
\(406\) 0 0
\(407\) −4.00000 −0.198273
\(408\) 0 0
\(409\) −3.50000 + 6.06218i −0.173064 + 0.299755i −0.939490 0.342578i \(-0.888700\pi\)
0.766426 + 0.642333i \(0.222033\pi\)
\(410\) 0 0
\(411\) 1.00000 + 1.73205i 0.0493264 + 0.0854358i
\(412\) 0 0
\(413\) −17.5000 6.06218i −0.861119 0.298300i
\(414\) 0 0
\(415\) −16.5000 28.5788i −0.809953 1.40288i
\(416\) 0 0
\(417\) 11.0000 19.0526i 0.538672 0.933008i
\(418\) 0 0
\(419\) −24.0000 −1.17248 −0.586238 0.810139i \(-0.699392\pi\)
−0.586238 + 0.810139i \(0.699392\pi\)
\(420\) 0 0
\(421\) 30.0000 1.46211 0.731055 0.682318i \(-0.239028\pi\)
0.731055 + 0.682318i \(0.239028\pi\)
\(422\) 0 0
\(423\) 1.00000 1.73205i 0.0486217 0.0842152i
\(424\) 0 0
\(425\) −8.00000 13.8564i −0.388057 0.672134i
\(426\) 0 0
\(427\) 20.0000 17.3205i 0.967868 0.838198i
\(428\) 0 0
\(429\) −2.00000 3.46410i −0.0965609 0.167248i
\(430\) 0 0
\(431\) −4.00000 + 6.92820i −0.192673 + 0.333720i −0.946135 0.323772i \(-0.895049\pi\)
0.753462 + 0.657491i \(0.228382\pi\)
\(432\) 0 0
\(433\) −2.00000 −0.0961139 −0.0480569 0.998845i \(-0.515303\pi\)
−0.0480569 + 0.998845i \(0.515303\pi\)
\(434\) 0 0
\(435\) −21.0000 −1.00687
\(436\) 0 0
\(437\) 0 0
\(438\) 0 0
\(439\) −7.50000 12.9904i −0.357955 0.619997i 0.629664 0.776868i \(-0.283193\pi\)
−0.987619 + 0.156871i \(0.949859\pi\)
\(440\) 0 0
\(441\) 5.50000 + 4.33013i 0.261905 + 0.206197i
\(442\) 0 0
\(443\) 10.5000 + 18.1865i 0.498870 + 0.864068i 0.999999 0.00130426i \(-0.000415158\pi\)
−0.501129 + 0.865373i \(0.667082\pi\)
\(444\) 0 0
\(445\) −9.00000 + 15.5885i −0.426641 + 0.738964i
\(446\) 0 0
\(447\) −6.00000 −0.283790
\(448\) 0 0
\(449\) −12.0000 −0.566315 −0.283158 0.959073i \(-0.591382\pi\)
−0.283158 + 0.959073i \(0.591382\pi\)
\(450\) 0 0
\(451\) −2.00000 + 3.46410i −0.0941763 + 0.163118i
\(452\) 0 0
\(453\) −5.50000 9.52628i −0.258413 0.447584i
\(454\) 0 0
\(455\) −24.0000 + 20.7846i −1.12514 + 0.974398i
\(456\) 0 0
\(457\) 8.50000 + 14.7224i 0.397613 + 0.688686i 0.993431 0.114433i \(-0.0365053\pi\)
−0.595818 + 0.803120i \(0.703172\pi\)
\(458\) 0 0
\(459\) −2.00000 + 3.46410i −0.0933520 + 0.161690i
\(460\) 0 0
\(461\) −2.00000 −0.0931493 −0.0465746 0.998915i \(-0.514831\pi\)
−0.0465746 + 0.998915i \(0.514831\pi\)
\(462\) 0 0
\(463\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(464\) 0 0
\(465\) −16.5000 + 28.5788i −0.765169 + 1.32531i
\(466\) 0 0
\(467\) −6.00000 10.3923i −0.277647 0.480899i 0.693153 0.720791i \(-0.256221\pi\)
−0.970799 + 0.239892i \(0.922888\pi\)
\(468\) 0 0
\(469\) −25.0000 8.66025i −1.15439 0.399893i
\(470\) 0 0
\(471\) 6.00000 + 10.3923i 0.276465 + 0.478852i
\(472\) 0 0
\(473\) −1.00000 + 1.73205i −0.0459800 + 0.0796398i
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) −11.0000 −0.503655
\(478\) 0 0
\(479\) −3.00000 + 5.19615i −0.137073 + 0.237418i −0.926388 0.376571i \(-0.877103\pi\)
0.789314 + 0.613990i \(0.210436\pi\)
\(480\) 0 0
\(481\) 8.00000 + 13.8564i 0.364769 + 0.631798i
\(482\) 0 0
\(483\) 4.00000 + 20.7846i 0.182006 + 0.945732i
\(484\) 0 0
\(485\) −10.5000 18.1865i −0.476780 0.825808i
\(486\) 0 0
\(487\) 1.50000 2.59808i 0.0679715 0.117730i −0.830037 0.557709i \(-0.811681\pi\)
0.898008 + 0.439979i \(0.145014\pi\)
\(488\) 0 0
\(489\) −8.00000 −0.361773
\(490\) 0 0
\(491\) −37.0000 −1.66979 −0.834893 0.550412i \(-0.814471\pi\)
−0.834893 + 0.550412i \(0.814471\pi\)
\(492\) 0 0
\(493\) 14.0000 24.2487i 0.630528 1.09211i
\(494\) 0 0
\(495\) 1.50000 + 2.59808i 0.0674200 + 0.116775i
\(496\) 0 0
\(497\) 3.00000 + 15.5885i 0.134568 + 0.699238i
\(498\) 0 0
\(499\) −5.00000 8.66025i −0.223831 0.387686i 0.732137 0.681157i \(-0.238523\pi\)
−0.955968 + 0.293471i \(0.905190\pi\)
\(500\) 0 0
\(501\) 11.0000 19.0526i 0.491444 0.851206i
\(502\) 0 0
\(503\) 32.0000 1.42681 0.713405 0.700752i \(-0.247152\pi\)
0.713405 + 0.700752i \(0.247152\pi\)
\(504\) 0 0
\(505\) 18.0000 0.800989
\(506\) 0 0
\(507\) −1.50000 + 2.59808i −0.0666173 + 0.115385i
\(508\) 0 0
\(509\) 21.5000 + 37.2391i 0.952971 + 1.65059i 0.738945 + 0.673766i \(0.235324\pi\)
0.214026 + 0.976828i \(0.431342\pi\)
\(510\) 0 0
\(511\) 15.0000 + 5.19615i 0.663561 + 0.229864i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 24.0000 41.5692i 1.05757 1.83176i
\(516\) 0 0
\(517\) 2.00000 0.0879599
\(518\) 0 0
\(519\) −6.00000 −0.263371
\(520\) 0 0
\(521\) −7.00000 + 12.1244i −0.306676 + 0.531178i −0.977633 0.210318i \(-0.932550\pi\)
0.670957 + 0.741496i \(0.265883\pi\)
\(522\) 0 0
\(523\) 10.0000 + 17.3205i 0.437269 + 0.757373i 0.997478 0.0709788i \(-0.0226123\pi\)
−0.560208 + 0.828352i \(0.689279\pi\)
\(524\) 0 0
\(525\) 8.00000 6.92820i 0.349149 0.302372i
\(526\) 0 0
\(527\) −22.0000 38.1051i −0.958335 1.65989i
\(528\) 0 0
\(529\) −20.5000 + 35.5070i −0.891304 + 1.54378i
\(530\) 0 0
\(531\) 7.00000 0.303774
\(532\) 0 0
\(533\) 16.0000 0.693037
\(534\) 0 0
\(535\) 10.5000 18.1865i 0.453955 0.786272i
\(536\) 0 0
\(537\) 6.00000 + 10.3923i 0.258919 + 0.448461i
\(538\) 0 0
\(539\) −1.00000 + 6.92820i −0.0430730 + 0.298419i
\(540\) 0 0
\(541\) 15.0000 + 25.9808i 0.644900 + 1.11700i 0.984325 + 0.176367i \(0.0564345\pi\)
−0.339424 + 0.940633i \(0.610232\pi\)
\(542\) 0 0
\(543\) −6.00000 + 10.3923i −0.257485 + 0.445976i
\(544\) 0 0
\(545\) 30.0000 1.28506
\(546\) 0 0
\(547\) −20.0000 −0.855138 −0.427569 0.903983i \(-0.640630\pi\)
−0.427569 + 0.903983i \(0.640630\pi\)
\(548\) 0 0
\(549\) −5.00000 + 8.66025i −0.213395 + 0.369611i
\(550\) 0 0
\(551\) 0 0
\(552\) 0 0
\(553\) 22.0000 19.0526i 0.935535 0.810197i
\(554\) 0 0
\(555\) −6.00000 10.3923i −0.254686 0.441129i
\(556\) 0 0
\(557\) −1.50000 + 2.59808i −0.0635570 + 0.110084i −0.896053 0.443947i \(-0.853578\pi\)
0.832496 + 0.554031i \(0.186911\pi\)
\(558\) 0 0
\(559\) 8.00000 0.338364
\(560\) 0 0
\(561\) −4.00000 −0.168880
\(562\) 0 0
\(563\) −9.50000 + 16.4545i −0.400377 + 0.693474i −0.993771 0.111438i \(-0.964454\pi\)
0.593394 + 0.804912i \(0.297788\pi\)
\(564\) 0 0
\(565\) −18.0000 31.1769i −0.757266 1.31162i
\(566\) 0 0
\(567\) −2.50000 0.866025i −0.104990 0.0363696i
\(568\) 0 0
\(569\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(570\) 0 0
\(571\) 11.0000 19.0526i 0.460336 0.797325i −0.538642 0.842535i \(-0.681062\pi\)
0.998978 + 0.0452101i \(0.0143957\pi\)
\(572\) 0 0
\(573\) 24.0000 1.00261
\(574\) 0 0
\(575\) 32.0000 1.33449
\(576\) 0 0
\(577\) 8.50000 14.7224i 0.353860 0.612903i −0.633062 0.774101i \(-0.718202\pi\)
0.986922 + 0.161198i \(0.0515357\pi\)
\(578\) 0 0
\(579\) 9.50000 + 16.4545i 0.394807 + 0.683825i
\(580\) 0 0
\(581\) 5.50000 + 28.5788i 0.228178 + 1.18565i
\(582\) 0 0
\(583\) −5.50000 9.52628i −0.227787 0.394538i
\(584\) 0 0
\(585\) 6.00000 10.3923i 0.248069 0.429669i
\(586\) 0 0
\(587\) −15.0000 −0.619116 −0.309558 0.950881i \(-0.600181\pi\)
−0.309558 + 0.950881i \(0.600181\pi\)
\(588\) 0 0
\(589\) 0 0
\(590\) 0 0
\(591\) −3.00000 + 5.19615i −0.123404 + 0.213741i
\(592\) 0 0
\(593\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(594\) 0 0
\(595\) 6.00000 + 31.1769i 0.245976 + 1.27813i
\(596\) 0 0
\(597\) 10.0000 + 17.3205i 0.409273 + 0.708881i
\(598\) 0 0
\(599\) −9.00000 + 15.5885i −0.367730 + 0.636927i −0.989210 0.146503i \(-0.953198\pi\)
0.621480 + 0.783430i \(0.286532\pi\)
\(600\) 0 0
\(601\) −37.0000 −1.50926 −0.754631 0.656150i \(-0.772184\pi\)
−0.754631 + 0.656150i \(0.772184\pi\)
\(602\) 0 0
\(603\) 10.0000 0.407231
\(604\) 0 0
\(605\) 15.0000 25.9808i 0.609837 1.05627i
\(606\) 0 0
\(607\) 13.5000 + 23.3827i 0.547948 + 0.949074i 0.998415 + 0.0562808i \(0.0179242\pi\)
−0.450467 + 0.892793i \(0.648742\pi\)
\(608\) 0 0
\(609\) 17.5000 + 6.06218i 0.709136 + 0.245652i
\(610\) 0 0
\(611\) −4.00000 6.92820i −0.161823 0.280285i
\(612\) 0 0
\(613\) 8.00000 13.8564i 0.323117 0.559655i −0.658012 0.753007i \(-0.728603\pi\)
0.981129 + 0.193352i \(0.0619359\pi\)
\(614\) 0 0
\(615\) −12.0000 −0.483887
\(616\) 0 0
\(617\) 22.0000 0.885687 0.442843 0.896599i \(-0.353970\pi\)
0.442843 + 0.896599i \(0.353970\pi\)
\(618\) 0 0
\(619\) 11.0000 19.0526i 0.442127 0.765787i −0.555720 0.831370i \(-0.687557\pi\)
0.997847 + 0.0655827i \(0.0208906\pi\)
\(620\) 0 0
\(621\) −4.00000 6.92820i −0.160514 0.278019i
\(622\) 0 0
\(623\) 12.0000 10.3923i 0.480770 0.416359i
\(624\) 0 0
\(625\) 14.5000 + 25.1147i 0.580000 + 1.00459i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 16.0000 0.637962
\(630\) 0 0
\(631\) −43.0000 −1.71180 −0.855901 0.517139i \(-0.826997\pi\)
−0.855901 + 0.517139i \(0.826997\pi\)
\(632\) 0 0
\(633\) −1.00000 + 1.73205i −0.0397464 + 0.0688428i
\(634\) 0 0
\(635\) −25.5000 44.1673i −1.01194 1.75273i
\(636\) 0 0
\(637\) 26.0000 10.3923i 1.03016 0.411758i
\(638\) 0 0
\(639\) −3.00000 5.19615i −0.118678 0.205557i
\(640\) 0 0
\(641\) 5.00000 8.66025i 0.197488 0.342059i −0.750225 0.661182i \(-0.770055\pi\)
0.947713 + 0.319123i \(0.103388\pi\)
\(642\) 0 0
\(643\) 2.00000 0.0788723 0.0394362 0.999222i \(-0.487444\pi\)
0.0394362 + 0.999222i \(0.487444\pi\)
\(644\) 0 0
\(645\) −6.00000 −0.236250
\(646\) 0 0
\(647\) 15.0000 25.9808i 0.589711 1.02141i −0.404559 0.914512i \(-0.632575\pi\)
0.994270 0.106897i \(-0.0340916\pi\)
\(648\) 0 0
\(649\) 3.50000 + 6.06218i 0.137387 + 0.237961i
\(650\) 0 0
\(651\) 22.0000 19.0526i 0.862248 0.746729i
\(652\) 0 0
\(653\) −21.5000 37.2391i −0.841360 1.45728i −0.888745 0.458402i \(-0.848422\pi\)
0.0473852 0.998877i \(-0.484911\pi\)
\(654\) 0 0
\(655\) −4.50000 + 7.79423i −0.175830 + 0.304546i
\(656\) 0 0
\(657\) −6.00000 −0.234082
\(658\) 0 0
\(659\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(660\) 0 0
\(661\) 21.0000 36.3731i 0.816805 1.41475i −0.0912190 0.995831i \(-0.529076\pi\)
0.908024 0.418917i \(-0.137590\pi\)
\(662\) 0 0
\(663\) 8.00000 + 13.8564i 0.310694 + 0.538138i
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 28.0000 + 48.4974i 1.08416 + 1.87783i
\(668\) 0 0
\(669\) −4.50000 + 7.79423i −0.173980 + 0.301342i
\(670\) 0 0
\(671\) −10.0000 −0.386046
\(672\) 0 0
\(673\) 45.0000 1.73462 0.867311 0.497766i \(-0.165846\pi\)
0.867311 + 0.497766i \(0.165846\pi\)
\(674\) 0 0
\(675\) −2.00000 + 3.46410i −0.0769800 + 0.133333i
\(676\) 0 0
\(677\) −7.50000 12.9904i −0.288248 0.499261i 0.685143 0.728408i \(-0.259740\pi\)
−0.973392 + 0.229147i \(0.926406\pi\)
\(678\) 0 0
\(679\) 3.50000 + 18.1865i 0.134318 + 0.697935i
\(680\) 0 0
\(681\) 3.50000 + 6.06218i 0.134120 + 0.232303i
\(682\) 0 0
\(683\) −10.5000 + 18.1865i −0.401771 + 0.695888i −0.993940 0.109926i \(-0.964939\pi\)
0.592168 + 0.805814i \(0.298272\pi\)
\(684\) 0 0
\(685\) −6.00000 −0.229248
\(686\) 0 0
\(687\) −8.00000 −0.305219
\(688\) 0 0
\(689\) −22.0000 + 38.1051i −0.838133 + 1.45169i
\(690\) 0 0
\(691\) −10.0000 17.3205i −0.380418 0.658903i 0.610704 0.791859i \(-0.290887\pi\)
−0.991122 + 0.132956i \(0.957553\pi\)
\(692\) 0 0
\(693\) −0.500000 2.59808i −0.0189934 0.0986928i
\(694\) 0 0
\(695\) 33.0000 + 57.1577i 1.25176 + 2.16811i
\(696\) 0 0
\(697\) 8.00000 13.8564i 0.303022 0.524849i
\(698\) 0 0
\(699\) 12.0000 0.453882
\(700\) 0 0
\(701\) 33.0000 1.24639 0.623196 0.782065i \(-0.285834\pi\)
0.623196 + 0.782065i \(0.285834\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) 0 0
\(705\) 3.00000 + 5.19615i 0.112987 + 0.195698i
\(706\) 0 0
\(707\) −15.0000 5.19615i −0.564133 0.195421i
\(708\) 0 0
\(709\) 17.0000 + 29.4449i 0.638448 + 1.10583i 0.985773 + 0.168080i \(0.0537568\pi\)
−0.347325 + 0.937745i \(0.612910\pi\)
\(710\) 0 0
\(711\) −5.50000 + 9.52628i −0.206266 + 0.357263i
\(712\) 0 0
\(713\) 88.0000 3.29563
\(714\) 0 0
\(715\) 12.0000 0.448775
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 9.00000 + 15.5885i 0.335643 + 0.581351i 0.983608 0.180319i \(-0.0577130\pi\)
−0.647965 + 0.761670i \(0.724380\pi\)
\(720\) 0 0
\(721\) −32.0000 + 27.7128i −1.19174 + 1.03208i
\(722\) 0 0
\(723\) 12.5000 + 21.6506i 0.464880 + 0.805196i
\(724\) 0 0
\(725\) 14.0000 24.2487i 0.519947 0.900575i
\(726\) 0 0
\(727\) 7.00000 0.259616 0.129808 0.991539i \(-0.458564\pi\)
0.129808 + 0.991539i \(0.458564\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) 4.00000 6.92820i 0.147945 0.256249i
\(732\) 0 0
\(733\) −7.00000 12.1244i −0.258551 0.447823i 0.707303 0.706910i \(-0.249912\pi\)
−0.965854 + 0.259087i \(0.916578\pi\)
\(734\) 0 0
\(735\) −19.5000 + 7.79423i −0.719268 + 0.287494i
\(736\) 0 0
\(737\) 5.00000 + 8.66025i 0.184177 + 0.319005i
\(738\) 0 0
\(739\) −17.0000 + 29.4449i −0.625355 + 1.08315i 0.363117 + 0.931744i \(0.381713\pi\)
−0.988472 + 0.151403i \(0.951621\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −50.0000 −1.83432 −0.917161 0.398517i \(-0.869525\pi\)
−0.917161 + 0.398517i \(0.869525\pi\)
\(744\) 0 0
\(745\) 9.00000 15.5885i 0.329734 0.571117i
\(746\) 0 0
\(747\) −5.50000 9.52628i −0.201234 0.348548i
\(748\) 0 0
\(749\) −14.0000 + 12.1244i −0.511549 + 0.443014i
\(750\) 0 0
\(751\) 1.50000 + 2.59808i 0.0547358 + 0.0948051i 0.892095 0.451848i \(-0.149235\pi\)
−0.837359 + 0.546653i \(0.815902\pi\)
\(752\) 0 0
\(753\) 12.5000 21.6506i 0.455525 0.788993i
\(754\) 0 0
\(755\) 33.0000 1.20099
\(756\) 0 0
\(757\) −14.0000 −0.508839 −0.254419 0.967094i \(-0.581884\pi\)
−0.254419 + 0.967094i \(0.581884\pi\)
\(758\) 0 0
\(759\) 4.00000 6.92820i 0.145191 0.251478i
\(760\) 0 0
\(761\) 6.00000 + 10.3923i 0.217500 + 0.376721i 0.954043 0.299670i \(-0.0968765\pi\)
−0.736543 + 0.676391i \(0.763543\pi\)
\(762\) 0 0
\(763\) −25.0000 8.66025i −0.905061 0.313522i
\(764\) 0 0
\(765\) −6.00000 10.3923i −0.216930 0.375735i
\(766\) 0 0
\(767\) 14.0000 24.2487i 0.505511 0.875570i
\(768\) 0 0
\(769\) −3.00000 −0.108183 −0.0540914 0.998536i \(-0.517226\pi\)
−0.0540914 + 0.998536i \(0.517226\pi\)
\(770\) 0 0
\(771\) 14.0000 0.504198
\(772\) 0 0
\(773\) −15.0000 + 25.9808i −0.539513 + 0.934463i 0.459418 + 0.888220i \(0.348058\pi\)
−0.998930 + 0.0462427i \(0.985275\pi\)
\(774\) 0 0
\(775\) −22.0000 38.1051i −0.790263 1.36878i
\(776\) 0 0
\(777\) 2.00000 + 10.3923i 0.0717496 + 0.372822i
\(778\) 0 0
\(779\) 0 0
\(780\) 0 0
\(781\) 3.00000 5.19615i 0.107348 0.185933i
\(782\) 0 0
\(783\) −7.00000 −0.250160
\(784\) 0 0
\(785\) −36.0000 −1.28490
\(786\) 0 0
\(787\) 17.0000 29.4449i 0.605985 1.04960i −0.385911 0.922536i \(-0.626113\pi\)
0.991895 0.127060i \(-0.0405540\pi\)
\(788\) 0 0
\(789\) −13.0000 22.5167i −0.462812 0.801614i
\(790\) 0 0
\(791\) 6.00000 + 31.1769i 0.213335 + 1.10852i
\(792\) 0 0
\(793\) 20.0000 + 34.6410i 0.710221 + 1.23014i
\(794\) 0 0
\(795\) 16.5000 28.5788i 0.585195 1.01359i
\(796\) 0 0
\(797\) −25.0000 −0.885545