Properties

Label 112.2.i.b.65.1
Level $112$
Weight $2$
Character 112.65
Analytic conductor $0.894$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 112 = 2^{4} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 112.i (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(0.894324502638\)
Analytic rank: \(0\)
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: no (minimal twist has level 28)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 65.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 112.65
Dual form 112.2.i.b.81.1

$q$-expansion

\(f(q)\) \(=\) \(q+(0.500000 + 0.866025i) q^{3} +(-1.50000 + 2.59808i) q^{5} +(2.00000 + 1.73205i) q^{7} +(1.00000 - 1.73205i) q^{9} +O(q^{10})\) \(q+(0.500000 + 0.866025i) q^{3} +(-1.50000 + 2.59808i) q^{5} +(2.00000 + 1.73205i) q^{7} +(1.00000 - 1.73205i) q^{9} +(-1.50000 - 2.59808i) q^{11} +2.00000 q^{13} -3.00000 q^{15} +(-1.50000 - 2.59808i) q^{17} +(-0.500000 + 0.866025i) q^{19} +(-0.500000 + 2.59808i) q^{21} +(1.50000 - 2.59808i) q^{23} +(-2.00000 - 3.46410i) q^{25} +5.00000 q^{27} -6.00000 q^{29} +(-3.50000 - 6.06218i) q^{31} +(1.50000 - 2.59808i) q^{33} +(-7.50000 + 2.59808i) q^{35} +(0.500000 - 0.866025i) q^{37} +(1.00000 + 1.73205i) q^{39} +6.00000 q^{41} +4.00000 q^{43} +(3.00000 + 5.19615i) q^{45} +(-4.50000 + 7.79423i) q^{47} +(1.00000 + 6.92820i) q^{49} +(1.50000 - 2.59808i) q^{51} +(-1.50000 - 2.59808i) q^{53} +9.00000 q^{55} -1.00000 q^{57} +(4.50000 + 7.79423i) q^{59} +(0.500000 - 0.866025i) q^{61} +(5.00000 - 1.73205i) q^{63} +(-3.00000 + 5.19615i) q^{65} +(-3.50000 - 6.06218i) q^{67} +3.00000 q^{69} +(0.500000 + 0.866025i) q^{73} +(2.00000 - 3.46410i) q^{75} +(1.50000 - 7.79423i) q^{77} +(-6.50000 + 11.2583i) q^{79} +(-0.500000 - 0.866025i) q^{81} -12.0000 q^{83} +9.00000 q^{85} +(-3.00000 - 5.19615i) q^{87} +(-7.50000 + 12.9904i) q^{89} +(4.00000 + 3.46410i) q^{91} +(3.50000 - 6.06218i) q^{93} +(-1.50000 - 2.59808i) q^{95} -10.0000 q^{97} -6.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q + q^{3} - 3q^{5} + 4q^{7} + 2q^{9} + O(q^{10}) \) \( 2q + q^{3} - 3q^{5} + 4q^{7} + 2q^{9} - 3q^{11} + 4q^{13} - 6q^{15} - 3q^{17} - q^{19} - q^{21} + 3q^{23} - 4q^{25} + 10q^{27} - 12q^{29} - 7q^{31} + 3q^{33} - 15q^{35} + q^{37} + 2q^{39} + 12q^{41} + 8q^{43} + 6q^{45} - 9q^{47} + 2q^{49} + 3q^{51} - 3q^{53} + 18q^{55} - 2q^{57} + 9q^{59} + q^{61} + 10q^{63} - 6q^{65} - 7q^{67} + 6q^{69} + q^{73} + 4q^{75} + 3q^{77} - 13q^{79} - q^{81} - 24q^{83} + 18q^{85} - 6q^{87} - 15q^{89} + 8q^{91} + 7q^{93} - 3q^{95} - 20q^{97} - 12q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/112\mathbb{Z}\right)^\times\).

\(n\) \(15\) \(17\) \(85\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\) \(1\)

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
\(3\) 0.500000 + 0.866025i 0.288675 + 0.500000i 0.973494 0.228714i \(-0.0734519\pi\)
−0.684819 + 0.728714i \(0.740119\pi\)
\(4\) 0 0
\(5\) −1.50000 + 2.59808i −0.670820 + 1.16190i 0.306851 + 0.951757i \(0.400725\pi\)
−0.977672 + 0.210138i \(0.932609\pi\)
\(6\) 0 0
\(7\) 2.00000 + 1.73205i 0.755929 + 0.654654i
\(8\) 0 0
\(9\) 1.00000 1.73205i 0.333333 0.577350i
\(10\) 0 0
\(11\) −1.50000 2.59808i −0.452267 0.783349i 0.546259 0.837616i \(-0.316051\pi\)
−0.998526 + 0.0542666i \(0.982718\pi\)
\(12\) 0 0
\(13\) 2.00000 0.554700 0.277350 0.960769i \(-0.410544\pi\)
0.277350 + 0.960769i \(0.410544\pi\)
\(14\) 0 0
\(15\) −3.00000 −0.774597
\(16\) 0 0
\(17\) −1.50000 2.59808i −0.363803 0.630126i 0.624780 0.780801i \(-0.285189\pi\)
−0.988583 + 0.150675i \(0.951855\pi\)
\(18\) 0 0
\(19\) −0.500000 + 0.866025i −0.114708 + 0.198680i −0.917663 0.397360i \(-0.869927\pi\)
0.802955 + 0.596040i \(0.203260\pi\)
\(20\) 0 0
\(21\) −0.500000 + 2.59808i −0.109109 + 0.566947i
\(22\) 0 0
\(23\) 1.50000 2.59808i 0.312772 0.541736i −0.666190 0.745782i \(-0.732076\pi\)
0.978961 + 0.204046i \(0.0654092\pi\)
\(24\) 0 0
\(25\) −2.00000 3.46410i −0.400000 0.692820i
\(26\) 0 0
\(27\) 5.00000 0.962250
\(28\) 0 0
\(29\) −6.00000 −1.11417 −0.557086 0.830455i \(-0.688081\pi\)
−0.557086 + 0.830455i \(0.688081\pi\)
\(30\) 0 0
\(31\) −3.50000 6.06218i −0.628619 1.08880i −0.987829 0.155543i \(-0.950287\pi\)
0.359211 0.933257i \(-0.383046\pi\)
\(32\) 0 0
\(33\) 1.50000 2.59808i 0.261116 0.452267i
\(34\) 0 0
\(35\) −7.50000 + 2.59808i −1.26773 + 0.439155i
\(36\) 0 0
\(37\) 0.500000 0.866025i 0.0821995 0.142374i −0.821995 0.569495i \(-0.807139\pi\)
0.904194 + 0.427121i \(0.140472\pi\)
\(38\) 0 0
\(39\) 1.00000 + 1.73205i 0.160128 + 0.277350i
\(40\) 0 0
\(41\) 6.00000 0.937043 0.468521 0.883452i \(-0.344787\pi\)
0.468521 + 0.883452i \(0.344787\pi\)
\(42\) 0 0
\(43\) 4.00000 0.609994 0.304997 0.952353i \(-0.401344\pi\)
0.304997 + 0.952353i \(0.401344\pi\)
\(44\) 0 0
\(45\) 3.00000 + 5.19615i 0.447214 + 0.774597i
\(46\) 0 0
\(47\) −4.50000 + 7.79423i −0.656392 + 1.13691i 0.325150 + 0.945662i \(0.394585\pi\)
−0.981543 + 0.191243i \(0.938748\pi\)
\(48\) 0 0
\(49\) 1.00000 + 6.92820i 0.142857 + 0.989743i
\(50\) 0 0
\(51\) 1.50000 2.59808i 0.210042 0.363803i
\(52\) 0 0
\(53\) −1.50000 2.59808i −0.206041 0.356873i 0.744423 0.667708i \(-0.232725\pi\)
−0.950464 + 0.310835i \(0.899391\pi\)
\(54\) 0 0
\(55\) 9.00000 1.21356
\(56\) 0 0
\(57\) −1.00000 −0.132453
\(58\) 0 0
\(59\) 4.50000 + 7.79423i 0.585850 + 1.01472i 0.994769 + 0.102151i \(0.0325726\pi\)
−0.408919 + 0.912571i \(0.634094\pi\)
\(60\) 0 0
\(61\) 0.500000 0.866025i 0.0640184 0.110883i −0.832240 0.554416i \(-0.812942\pi\)
0.896258 + 0.443533i \(0.146275\pi\)
\(62\) 0 0
\(63\) 5.00000 1.73205i 0.629941 0.218218i
\(64\) 0 0
\(65\) −3.00000 + 5.19615i −0.372104 + 0.644503i
\(66\) 0 0
\(67\) −3.50000 6.06218i −0.427593 0.740613i 0.569066 0.822292i \(-0.307305\pi\)
−0.996659 + 0.0816792i \(0.973972\pi\)
\(68\) 0 0
\(69\) 3.00000 0.361158
\(70\) 0 0
\(71\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(72\) 0 0
\(73\) 0.500000 + 0.866025i 0.0585206 + 0.101361i 0.893801 0.448463i \(-0.148028\pi\)
−0.835281 + 0.549823i \(0.814695\pi\)
\(74\) 0 0
\(75\) 2.00000 3.46410i 0.230940 0.400000i
\(76\) 0 0
\(77\) 1.50000 7.79423i 0.170941 0.888235i
\(78\) 0 0
\(79\) −6.50000 + 11.2583i −0.731307 + 1.26666i 0.225018 + 0.974355i \(0.427756\pi\)
−0.956325 + 0.292306i \(0.905577\pi\)
\(80\) 0 0
\(81\) −0.500000 0.866025i −0.0555556 0.0962250i
\(82\) 0 0
\(83\) −12.0000 −1.31717 −0.658586 0.752506i \(-0.728845\pi\)
−0.658586 + 0.752506i \(0.728845\pi\)
\(84\) 0 0
\(85\) 9.00000 0.976187
\(86\) 0 0
\(87\) −3.00000 5.19615i −0.321634 0.557086i
\(88\) 0 0
\(89\) −7.50000 + 12.9904i −0.794998 + 1.37698i 0.127842 + 0.991795i \(0.459195\pi\)
−0.922840 + 0.385183i \(0.874138\pi\)
\(90\) 0 0
\(91\) 4.00000 + 3.46410i 0.419314 + 0.363137i
\(92\) 0 0
\(93\) 3.50000 6.06218i 0.362933 0.628619i
\(94\) 0 0
\(95\) −1.50000 2.59808i −0.153897 0.266557i
\(96\) 0 0
\(97\) −10.0000 −1.01535 −0.507673 0.861550i \(-0.669494\pi\)
−0.507673 + 0.861550i \(0.669494\pi\)
\(98\) 0 0
\(99\) −6.00000 −0.603023
\(100\) 0 0
\(101\) −7.50000 12.9904i −0.746278 1.29259i −0.949595 0.313478i \(-0.898506\pi\)
0.203317 0.979113i \(-0.434828\pi\)
\(102\) 0 0
\(103\) 5.50000 9.52628i 0.541931 0.938652i −0.456862 0.889538i \(-0.651027\pi\)
0.998793 0.0491146i \(-0.0156400\pi\)
\(104\) 0 0
\(105\) −6.00000 5.19615i −0.585540 0.507093i
\(106\) 0 0
\(107\) 7.50000 12.9904i 0.725052 1.25583i −0.233900 0.972261i \(-0.575149\pi\)
0.958952 0.283567i \(-0.0915178\pi\)
\(108\) 0 0
\(109\) 0.500000 + 0.866025i 0.0478913 + 0.0829502i 0.888977 0.457951i \(-0.151417\pi\)
−0.841086 + 0.540901i \(0.818083\pi\)
\(110\) 0 0
\(111\) 1.00000 0.0949158
\(112\) 0 0
\(113\) 6.00000 0.564433 0.282216 0.959351i \(-0.408930\pi\)
0.282216 + 0.959351i \(0.408930\pi\)
\(114\) 0 0
\(115\) 4.50000 + 7.79423i 0.419627 + 0.726816i
\(116\) 0 0
\(117\) 2.00000 3.46410i 0.184900 0.320256i
\(118\) 0 0
\(119\) 1.50000 7.79423i 0.137505 0.714496i
\(120\) 0 0
\(121\) 1.00000 1.73205i 0.0909091 0.157459i
\(122\) 0 0
\(123\) 3.00000 + 5.19615i 0.270501 + 0.468521i
\(124\) 0 0
\(125\) −3.00000 −0.268328
\(126\) 0 0
\(127\) −8.00000 −0.709885 −0.354943 0.934888i \(-0.615500\pi\)
−0.354943 + 0.934888i \(0.615500\pi\)
\(128\) 0 0
\(129\) 2.00000 + 3.46410i 0.176090 + 0.304997i
\(130\) 0 0
\(131\) 1.50000 2.59808i 0.131056 0.226995i −0.793028 0.609185i \(-0.791497\pi\)
0.924084 + 0.382190i \(0.124830\pi\)
\(132\) 0 0
\(133\) −2.50000 + 0.866025i −0.216777 + 0.0750939i
\(134\) 0 0
\(135\) −7.50000 + 12.9904i −0.645497 + 1.11803i
\(136\) 0 0
\(137\) 10.5000 + 18.1865i 0.897076 + 1.55378i 0.831215 + 0.555952i \(0.187646\pi\)
0.0658609 + 0.997829i \(0.479021\pi\)
\(138\) 0 0
\(139\) −20.0000 −1.69638 −0.848189 0.529694i \(-0.822307\pi\)
−0.848189 + 0.529694i \(0.822307\pi\)
\(140\) 0 0
\(141\) −9.00000 −0.757937
\(142\) 0 0
\(143\) −3.00000 5.19615i −0.250873 0.434524i
\(144\) 0 0
\(145\) 9.00000 15.5885i 0.747409 1.29455i
\(146\) 0 0
\(147\) −5.50000 + 4.33013i −0.453632 + 0.357143i
\(148\) 0 0
\(149\) −1.50000 + 2.59808i −0.122885 + 0.212843i −0.920904 0.389789i \(-0.872548\pi\)
0.798019 + 0.602632i \(0.205881\pi\)
\(150\) 0 0
\(151\) 8.50000 + 14.7224i 0.691720 + 1.19809i 0.971274 + 0.237964i \(0.0764802\pi\)
−0.279554 + 0.960130i \(0.590186\pi\)
\(152\) 0 0
\(153\) −6.00000 −0.485071
\(154\) 0 0
\(155\) 21.0000 1.68676
\(156\) 0 0
\(157\) 6.50000 + 11.2583i 0.518756 + 0.898513i 0.999762 + 0.0217953i \(0.00693820\pi\)
−0.481006 + 0.876717i \(0.659728\pi\)
\(158\) 0 0
\(159\) 1.50000 2.59808i 0.118958 0.206041i
\(160\) 0 0
\(161\) 7.50000 2.59808i 0.591083 0.204757i
\(162\) 0 0
\(163\) 5.50000 9.52628i 0.430793 0.746156i −0.566149 0.824303i \(-0.691567\pi\)
0.996942 + 0.0781474i \(0.0249005\pi\)
\(164\) 0 0
\(165\) 4.50000 + 7.79423i 0.350325 + 0.606780i
\(166\) 0 0
\(167\) 12.0000 0.928588 0.464294 0.885681i \(-0.346308\pi\)
0.464294 + 0.885681i \(0.346308\pi\)
\(168\) 0 0
\(169\) −9.00000 −0.692308
\(170\) 0 0
\(171\) 1.00000 + 1.73205i 0.0764719 + 0.132453i
\(172\) 0 0
\(173\) 4.50000 7.79423i 0.342129 0.592584i −0.642699 0.766119i \(-0.722185\pi\)
0.984828 + 0.173534i \(0.0555188\pi\)
\(174\) 0 0
\(175\) 2.00000 10.3923i 0.151186 0.785584i
\(176\) 0 0
\(177\) −4.50000 + 7.79423i −0.338241 + 0.585850i
\(178\) 0 0
\(179\) 10.5000 + 18.1865i 0.784807 + 1.35933i 0.929114 + 0.369792i \(0.120571\pi\)
−0.144308 + 0.989533i \(0.546095\pi\)
\(180\) 0 0
\(181\) −10.0000 −0.743294 −0.371647 0.928374i \(-0.621207\pi\)
−0.371647 + 0.928374i \(0.621207\pi\)
\(182\) 0 0
\(183\) 1.00000 0.0739221
\(184\) 0 0
\(185\) 1.50000 + 2.59808i 0.110282 + 0.191014i
\(186\) 0 0
\(187\) −4.50000 + 7.79423i −0.329073 + 0.569970i
\(188\) 0 0
\(189\) 10.0000 + 8.66025i 0.727393 + 0.629941i
\(190\) 0 0
\(191\) −4.50000 + 7.79423i −0.325609 + 0.563971i −0.981635 0.190767i \(-0.938902\pi\)
0.656027 + 0.754738i \(0.272236\pi\)
\(192\) 0 0
\(193\) −5.50000 9.52628i −0.395899 0.685717i 0.597317 0.802005i \(-0.296234\pi\)
−0.993215 + 0.116289i \(0.962900\pi\)
\(194\) 0 0
\(195\) −6.00000 −0.429669
\(196\) 0 0
\(197\) 18.0000 1.28245 0.641223 0.767354i \(-0.278427\pi\)
0.641223 + 0.767354i \(0.278427\pi\)
\(198\) 0 0
\(199\) −3.50000 6.06218i −0.248108 0.429736i 0.714893 0.699234i \(-0.246476\pi\)
−0.963001 + 0.269498i \(0.913142\pi\)
\(200\) 0 0
\(201\) 3.50000 6.06218i 0.246871 0.427593i
\(202\) 0 0
\(203\) −12.0000 10.3923i −0.842235 0.729397i
\(204\) 0 0
\(205\) −9.00000 + 15.5885i −0.628587 + 1.08875i
\(206\) 0 0
\(207\) −3.00000 5.19615i −0.208514 0.361158i
\(208\) 0 0
\(209\) 3.00000 0.207514
\(210\) 0 0
\(211\) 4.00000 0.275371 0.137686 0.990476i \(-0.456034\pi\)
0.137686 + 0.990476i \(0.456034\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −6.00000 + 10.3923i −0.409197 + 0.708749i
\(216\) 0 0
\(217\) 3.50000 18.1865i 0.237595 1.23458i
\(218\) 0 0
\(219\) −0.500000 + 0.866025i −0.0337869 + 0.0585206i
\(220\) 0 0
\(221\) −3.00000 5.19615i −0.201802 0.349531i
\(222\) 0 0
\(223\) −8.00000 −0.535720 −0.267860 0.963458i \(-0.586316\pi\)
−0.267860 + 0.963458i \(0.586316\pi\)
\(224\) 0 0
\(225\) −8.00000 −0.533333
\(226\) 0 0
\(227\) −1.50000 2.59808i −0.0995585 0.172440i 0.811943 0.583736i \(-0.198410\pi\)
−0.911502 + 0.411296i \(0.865076\pi\)
\(228\) 0 0
\(229\) −5.50000 + 9.52628i −0.363450 + 0.629514i −0.988526 0.151050i \(-0.951735\pi\)
0.625076 + 0.780564i \(0.285068\pi\)
\(230\) 0 0
\(231\) 7.50000 2.59808i 0.493464 0.170941i
\(232\) 0 0
\(233\) 10.5000 18.1865i 0.687878 1.19144i −0.284645 0.958633i \(-0.591876\pi\)
0.972523 0.232806i \(-0.0747909\pi\)
\(234\) 0 0
\(235\) −13.5000 23.3827i −0.880643 1.52532i
\(236\) 0 0
\(237\) −13.0000 −0.844441
\(238\) 0 0
\(239\) 12.0000 0.776215 0.388108 0.921614i \(-0.373129\pi\)
0.388108 + 0.921614i \(0.373129\pi\)
\(240\) 0 0
\(241\) 0.500000 + 0.866025i 0.0322078 + 0.0557856i 0.881680 0.471848i \(-0.156413\pi\)
−0.849472 + 0.527633i \(0.823079\pi\)
\(242\) 0 0
\(243\) 8.00000 13.8564i 0.513200 0.888889i
\(244\) 0 0
\(245\) −19.5000 7.79423i −1.24581 0.497955i
\(246\) 0 0
\(247\) −1.00000 + 1.73205i −0.0636285 + 0.110208i
\(248\) 0 0
\(249\) −6.00000 10.3923i −0.380235 0.658586i
\(250\) 0 0
\(251\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(252\) 0 0
\(253\) −9.00000 −0.565825
\(254\) 0 0
\(255\) 4.50000 + 7.79423i 0.281801 + 0.488094i
\(256\) 0 0
\(257\) −1.50000 + 2.59808i −0.0935674 + 0.162064i −0.909010 0.416775i \(-0.863160\pi\)
0.815442 + 0.578838i \(0.196494\pi\)
\(258\) 0 0
\(259\) 2.50000 0.866025i 0.155342 0.0538122i
\(260\) 0 0
\(261\) −6.00000 + 10.3923i −0.371391 + 0.643268i
\(262\) 0 0
\(263\) −1.50000 2.59808i −0.0924940 0.160204i 0.816066 0.577959i \(-0.196151\pi\)
−0.908560 + 0.417755i \(0.862817\pi\)
\(264\) 0 0
\(265\) 9.00000 0.552866
\(266\) 0 0
\(267\) −15.0000 −0.917985
\(268\) 0 0
\(269\) −1.50000 2.59808i −0.0914566 0.158408i 0.816668 0.577108i \(-0.195819\pi\)
−0.908124 + 0.418701i \(0.862486\pi\)
\(270\) 0 0
\(271\) 5.50000 9.52628i 0.334101 0.578680i −0.649211 0.760609i \(-0.724901\pi\)
0.983312 + 0.181928i \(0.0582339\pi\)
\(272\) 0 0
\(273\) −1.00000 + 5.19615i −0.0605228 + 0.314485i
\(274\) 0 0
\(275\) −6.00000 + 10.3923i −0.361814 + 0.626680i
\(276\) 0 0
\(277\) 6.50000 + 11.2583i 0.390547 + 0.676448i 0.992522 0.122068i \(-0.0389525\pi\)
−0.601975 + 0.798515i \(0.705619\pi\)
\(278\) 0 0
\(279\) −14.0000 −0.838158
\(280\) 0 0
\(281\) 30.0000 1.78965 0.894825 0.446417i \(-0.147300\pi\)
0.894825 + 0.446417i \(0.147300\pi\)
\(282\) 0 0
\(283\) 14.5000 + 25.1147i 0.861936 + 1.49292i 0.870058 + 0.492949i \(0.164081\pi\)
−0.00812260 + 0.999967i \(0.502586\pi\)
\(284\) 0 0
\(285\) 1.50000 2.59808i 0.0888523 0.153897i
\(286\) 0 0
\(287\) 12.0000 + 10.3923i 0.708338 + 0.613438i
\(288\) 0 0
\(289\) 4.00000 6.92820i 0.235294 0.407541i
\(290\) 0 0
\(291\) −5.00000 8.66025i −0.293105 0.507673i
\(292\) 0 0
\(293\) 6.00000 0.350524 0.175262 0.984522i \(-0.443923\pi\)
0.175262 + 0.984522i \(0.443923\pi\)
\(294\) 0 0
\(295\) −27.0000 −1.57200
\(296\) 0 0
\(297\) −7.50000 12.9904i −0.435194 0.753778i
\(298\) 0 0
\(299\) 3.00000 5.19615i 0.173494 0.300501i
\(300\) 0 0
\(301\) 8.00000 + 6.92820i 0.461112 + 0.399335i
\(302\) 0 0
\(303\) 7.50000 12.9904i 0.430864 0.746278i
\(304\) 0 0
\(305\) 1.50000 + 2.59808i 0.0858898 + 0.148765i
\(306\) 0 0
\(307\) 28.0000 1.59804 0.799022 0.601302i \(-0.205351\pi\)
0.799022 + 0.601302i \(0.205351\pi\)
\(308\) 0 0
\(309\) 11.0000 0.625768
\(310\) 0 0
\(311\) −13.5000 23.3827i −0.765515 1.32591i −0.939974 0.341246i \(-0.889151\pi\)
0.174459 0.984664i \(-0.444182\pi\)
\(312\) 0 0
\(313\) −11.5000 + 19.9186i −0.650018 + 1.12586i 0.333099 + 0.942892i \(0.391906\pi\)
−0.983118 + 0.182973i \(0.941428\pi\)
\(314\) 0 0
\(315\) −3.00000 + 15.5885i −0.169031 + 0.878310i
\(316\) 0 0
\(317\) 4.50000 7.79423i 0.252745 0.437767i −0.711535 0.702650i \(-0.752000\pi\)
0.964281 + 0.264883i \(0.0853332\pi\)
\(318\) 0 0
\(319\) 9.00000 + 15.5885i 0.503903 + 0.872786i
\(320\) 0 0
\(321\) 15.0000 0.837218
\(322\) 0 0
\(323\) 3.00000 0.166924
\(324\) 0 0
\(325\) −4.00000 6.92820i −0.221880 0.384308i
\(326\) 0 0
\(327\) −0.500000 + 0.866025i −0.0276501 + 0.0478913i
\(328\) 0 0
\(329\) −22.5000 + 7.79423i −1.24047 + 0.429710i
\(330\) 0 0
\(331\) −6.50000 + 11.2583i −0.357272 + 0.618814i −0.987504 0.157593i \(-0.949627\pi\)
0.630232 + 0.776407i \(0.282960\pi\)
\(332\) 0 0
\(333\) −1.00000 1.73205i −0.0547997 0.0949158i
\(334\) 0 0
\(335\) 21.0000 1.14735
\(336\) 0 0
\(337\) −34.0000 −1.85210 −0.926049 0.377403i \(-0.876817\pi\)
−0.926049 + 0.377403i \(0.876817\pi\)
\(338\) 0 0
\(339\) 3.00000 + 5.19615i 0.162938 + 0.282216i
\(340\) 0 0
\(341\) −10.5000 + 18.1865i −0.568607 + 0.984856i
\(342\) 0 0
\(343\) −10.0000 + 15.5885i −0.539949 + 0.841698i
\(344\) 0 0
\(345\) −4.50000 + 7.79423i −0.242272 + 0.419627i
\(346\) 0 0
\(347\) 4.50000 + 7.79423i 0.241573 + 0.418416i 0.961162 0.275983i \(-0.0890035\pi\)
−0.719590 + 0.694399i \(0.755670\pi\)
\(348\) 0 0
\(349\) 26.0000 1.39175 0.695874 0.718164i \(-0.255017\pi\)
0.695874 + 0.718164i \(0.255017\pi\)
\(350\) 0 0
\(351\) 10.0000 0.533761
\(352\) 0 0
\(353\) 10.5000 + 18.1865i 0.558859 + 0.967972i 0.997592 + 0.0693543i \(0.0220939\pi\)
−0.438733 + 0.898617i \(0.644573\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 7.50000 2.59808i 0.396942 0.137505i
\(358\) 0 0
\(359\) 7.50000 12.9904i 0.395835 0.685606i −0.597372 0.801964i \(-0.703789\pi\)
0.993207 + 0.116358i \(0.0371219\pi\)
\(360\) 0 0
\(361\) 9.00000 + 15.5885i 0.473684 + 0.820445i
\(362\) 0 0
\(363\) 2.00000 0.104973
\(364\) 0 0
\(365\) −3.00000 −0.157027
\(366\) 0 0
\(367\) 2.50000 + 4.33013i 0.130499 + 0.226031i 0.923869 0.382709i \(-0.125009\pi\)
−0.793370 + 0.608740i \(0.791675\pi\)
\(368\) 0 0
\(369\) 6.00000 10.3923i 0.312348 0.541002i
\(370\) 0 0
\(371\) 1.50000 7.79423i 0.0778761 0.404656i
\(372\) 0 0
\(373\) 12.5000 21.6506i 0.647225 1.12103i −0.336557 0.941663i \(-0.609263\pi\)
0.983783 0.179364i \(-0.0574041\pi\)
\(374\) 0 0
\(375\) −1.50000 2.59808i −0.0774597 0.134164i
\(376\) 0 0
\(377\) −12.0000 −0.618031
\(378\) 0 0
\(379\) −8.00000 −0.410932 −0.205466 0.978664i \(-0.565871\pi\)
−0.205466 + 0.978664i \(0.565871\pi\)
\(380\) 0 0
\(381\) −4.00000 6.92820i −0.204926 0.354943i
\(382\) 0 0
\(383\) −16.5000 + 28.5788i −0.843111 + 1.46031i 0.0441413 + 0.999025i \(0.485945\pi\)
−0.887252 + 0.461285i \(0.847389\pi\)
\(384\) 0 0
\(385\) 18.0000 + 15.5885i 0.917365 + 0.794461i
\(386\) 0 0
\(387\) 4.00000 6.92820i 0.203331 0.352180i
\(388\) 0 0
\(389\) −7.50000 12.9904i −0.380265 0.658638i 0.610835 0.791758i \(-0.290834\pi\)
−0.991100 + 0.133120i \(0.957501\pi\)
\(390\) 0 0
\(391\) −9.00000 −0.455150
\(392\) 0 0
\(393\) 3.00000 0.151330
\(394\) 0 0
\(395\) −19.5000 33.7750i −0.981151 1.69940i
\(396\) 0 0
\(397\) 18.5000 32.0429i 0.928488 1.60819i 0.142636 0.989775i \(-0.454442\pi\)
0.785853 0.618414i \(-0.212224\pi\)
\(398\) 0 0
\(399\) −2.00000 1.73205i −0.100125 0.0867110i
\(400\) 0 0
\(401\) −1.50000 + 2.59808i −0.0749064 + 0.129742i −0.901046 0.433724i \(-0.857199\pi\)
0.826139 + 0.563466i \(0.190532\pi\)
\(402\) 0 0
\(403\) −7.00000 12.1244i −0.348695 0.603957i
\(404\) 0 0
\(405\) 3.00000 0.149071
\(406\) 0 0
\(407\) −3.00000 −0.148704
\(408\) 0 0
\(409\) −5.50000 9.52628i −0.271957 0.471044i 0.697406 0.716677i \(-0.254338\pi\)
−0.969363 + 0.245633i \(0.921004\pi\)
\(410\) 0 0
\(411\) −10.5000 + 18.1865i −0.517927 + 0.897076i
\(412\) 0 0
\(413\) −4.50000 + 23.3827i −0.221431 + 1.15059i
\(414\) 0 0
\(415\) 18.0000 31.1769i 0.883585 1.53041i
\(416\) 0 0
\(417\) −10.0000 17.3205i −0.489702 0.848189i
\(418\) 0 0
\(419\) 12.0000 0.586238 0.293119 0.956076i \(-0.405307\pi\)
0.293119 + 0.956076i \(0.405307\pi\)
\(420\) 0 0
\(421\) −22.0000 −1.07221 −0.536107 0.844150i \(-0.680106\pi\)
−0.536107 + 0.844150i \(0.680106\pi\)
\(422\) 0 0
\(423\) 9.00000 + 15.5885i 0.437595 + 0.757937i
\(424\) 0 0
\(425\) −6.00000 + 10.3923i −0.291043 + 0.504101i
\(426\) 0 0
\(427\) 2.50000 0.866025i 0.120983 0.0419099i
\(428\) 0 0
\(429\) 3.00000 5.19615i 0.144841 0.250873i
\(430\) 0 0
\(431\) −7.50000 12.9904i −0.361262 0.625725i 0.626907 0.779094i \(-0.284321\pi\)
−0.988169 + 0.153370i \(0.950987\pi\)
\(432\) 0 0
\(433\) −10.0000 −0.480569 −0.240285 0.970702i \(-0.577241\pi\)
−0.240285 + 0.970702i \(0.577241\pi\)
\(434\) 0 0
\(435\) 18.0000 0.863034
\(436\) 0 0
\(437\) 1.50000 + 2.59808i 0.0717547 + 0.124283i
\(438\) 0 0
\(439\) −0.500000 + 0.866025i −0.0238637 + 0.0413331i −0.877711 0.479191i \(-0.840930\pi\)
0.853847 + 0.520524i \(0.174263\pi\)
\(440\) 0 0
\(441\) 13.0000 + 5.19615i 0.619048 + 0.247436i
\(442\) 0 0
\(443\) −4.50000 + 7.79423i −0.213801 + 0.370315i −0.952901 0.303281i \(-0.901918\pi\)
0.739100 + 0.673596i \(0.235251\pi\)
\(444\) 0 0
\(445\) −22.5000 38.9711i −1.06660 1.84741i
\(446\) 0 0
\(447\) −3.00000 −0.141895
\(448\) 0 0
\(449\) −18.0000 −0.849473 −0.424736 0.905317i \(-0.639633\pi\)
−0.424736 + 0.905317i \(0.639633\pi\)
\(450\) 0 0
\(451\) −9.00000 15.5885i −0.423793 0.734032i
\(452\) 0 0
\(453\) −8.50000 + 14.7224i −0.399365 + 0.691720i
\(454\) 0 0
\(455\) −15.0000 + 5.19615i −0.703211 + 0.243599i
\(456\) 0 0
\(457\) −11.5000 + 19.9186i −0.537947 + 0.931752i 0.461067 + 0.887365i \(0.347467\pi\)
−0.999014 + 0.0443868i \(0.985867\pi\)
\(458\) 0 0
\(459\) −7.50000 12.9904i −0.350070 0.606339i
\(460\) 0 0
\(461\) −6.00000 −0.279448 −0.139724 0.990190i \(-0.544622\pi\)
−0.139724 + 0.990190i \(0.544622\pi\)
\(462\) 0 0
\(463\) 16.0000 0.743583 0.371792 0.928316i \(-0.378744\pi\)
0.371792 + 0.928316i \(0.378744\pi\)
\(464\) 0 0
\(465\) 10.5000 + 18.1865i 0.486926 + 0.843380i
\(466\) 0 0
\(467\) −10.5000 + 18.1865i −0.485882 + 0.841572i −0.999868 0.0162260i \(-0.994835\pi\)
0.513986 + 0.857798i \(0.328168\pi\)
\(468\) 0 0
\(469\) 3.50000 18.1865i 0.161615 0.839776i
\(470\) 0 0
\(471\) −6.50000 + 11.2583i −0.299504 + 0.518756i
\(472\) 0 0
\(473\) −6.00000 10.3923i −0.275880 0.477839i
\(474\) 0 0
\(475\) 4.00000 0.183533
\(476\) 0 0
\(477\) −6.00000 −0.274721
\(478\) 0 0
\(479\) −1.50000 2.59808i −0.0685367 0.118709i 0.829721 0.558179i \(-0.188500\pi\)
−0.898257 + 0.439470i \(0.855166\pi\)
\(480\) 0 0
\(481\) 1.00000 1.73205i 0.0455961 0.0789747i
\(482\) 0 0
\(483\) 6.00000 + 5.19615i 0.273009 + 0.236433i
\(484\) 0 0
\(485\) 15.0000 25.9808i 0.681115 1.17973i
\(486\) 0 0
\(487\) −9.50000 16.4545i −0.430486 0.745624i 0.566429 0.824110i \(-0.308325\pi\)
−0.996915 + 0.0784867i \(0.974991\pi\)
\(488\) 0 0
\(489\) 11.0000 0.497437
\(490\) 0 0
\(491\) −24.0000 −1.08310 −0.541552 0.840667i \(-0.682163\pi\)
−0.541552 + 0.840667i \(0.682163\pi\)
\(492\) 0 0
\(493\) 9.00000 + 15.5885i 0.405340 + 0.702069i
\(494\) 0 0
\(495\) 9.00000 15.5885i 0.404520 0.700649i
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) 5.50000 9.52628i 0.246214 0.426455i −0.716258 0.697835i \(-0.754147\pi\)
0.962472 + 0.271380i \(0.0874801\pi\)
\(500\) 0 0
\(501\) 6.00000 + 10.3923i 0.268060 + 0.464294i
\(502\) 0 0
\(503\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(504\) 0 0
\(505\) 45.0000 2.00247
\(506\) 0 0
\(507\) −4.50000 7.79423i −0.199852 0.346154i
\(508\) 0 0
\(509\) −1.50000 + 2.59808i −0.0664863 + 0.115158i −0.897352 0.441315i \(-0.854512\pi\)
0.830866 + 0.556473i \(0.187846\pi\)
\(510\) 0 0
\(511\) −0.500000 + 2.59808i −0.0221187 + 0.114932i
\(512\) 0 0
\(513\) −2.50000 + 4.33013i −0.110378 + 0.191180i
\(514\) 0 0
\(515\) 16.5000 + 28.5788i 0.727077 + 1.25933i
\(516\) 0 0
\(517\) 27.0000 1.18746
\(518\) 0 0
\(519\) 9.00000 0.395056
\(520\) 0 0
\(521\) −19.5000 33.7750i −0.854311 1.47971i −0.877283 0.479973i \(-0.840646\pi\)
0.0229727 0.999736i \(-0.492687\pi\)
\(522\) 0 0
\(523\) −0.500000 + 0.866025i −0.0218635 + 0.0378686i −0.876750 0.480946i \(-0.840293\pi\)
0.854887 + 0.518815i \(0.173627\pi\)
\(524\) 0 0
\(525\) 10.0000 3.46410i 0.436436 0.151186i
\(526\) 0 0
\(527\) −10.5000 + 18.1865i −0.457387 + 0.792218i
\(528\) 0 0
\(529\) 7.00000 + 12.1244i 0.304348 + 0.527146i
\(530\) 0 0
\(531\) 18.0000 0.781133
\(532\) 0 0
\(533\) 12.0000 0.519778
\(534\) 0 0
\(535\) 22.5000 + 38.9711i 0.972760 + 1.68487i
\(536\) 0 0
\(537\) −10.5000 + 18.1865i −0.453108 + 0.784807i
\(538\) 0 0
\(539\) 16.5000 12.9904i 0.710705 0.559535i
\(540\) 0 0
\(541\) −17.5000 + 30.3109i −0.752384 + 1.30317i 0.194281 + 0.980946i \(0.437763\pi\)
−0.946664 + 0.322221i \(0.895571\pi\)
\(542\) 0 0
\(543\) −5.00000 8.66025i −0.214571 0.371647i
\(544\) 0 0
\(545\) −3.00000 −0.128506
\(546\) 0 0
\(547\) −8.00000 −0.342055 −0.171028 0.985266i \(-0.554709\pi\)
−0.171028 + 0.985266i \(0.554709\pi\)
\(548\) 0 0
\(549\) −1.00000 1.73205i −0.0426790 0.0739221i
\(550\) 0 0
\(551\) 3.00000 5.19615i 0.127804 0.221364i
\(552\) 0 0
\(553\) −32.5000 + 11.2583i −1.38204 + 0.478753i
\(554\) 0 0
\(555\) −1.50000 + 2.59808i −0.0636715 + 0.110282i
\(556\) 0 0
\(557\) 16.5000 + 28.5788i 0.699127 + 1.21092i 0.968769 + 0.247964i \(0.0797613\pi\)
−0.269642 + 0.962961i \(0.586905\pi\)
\(558\) 0 0
\(559\) 8.00000 0.338364
\(560\) 0 0
\(561\) −9.00000 −0.379980
\(562\) 0 0
\(563\) 4.50000 + 7.79423i 0.189652 + 0.328488i 0.945134 0.326682i \(-0.105931\pi\)
−0.755482 + 0.655169i \(0.772597\pi\)
\(564\) 0 0
\(565\) −9.00000 + 15.5885i −0.378633 + 0.655811i
\(566\) 0 0
\(567\) 0.500000 2.59808i 0.0209980 0.109109i
\(568\) 0 0
\(569\) 4.50000 7.79423i 0.188650 0.326751i −0.756151 0.654398i \(-0.772922\pi\)
0.944800 + 0.327647i \(0.106256\pi\)
\(570\) 0 0
\(571\) 14.5000 + 25.1147i 0.606806 + 1.05102i 0.991763 + 0.128085i \(0.0408829\pi\)
−0.384957 + 0.922934i \(0.625784\pi\)
\(572\) 0 0
\(573\) −9.00000 −0.375980
\(574\) 0 0
\(575\) −12.0000 −0.500435
\(576\) 0 0
\(577\) 0.500000 + 0.866025i 0.0208153 + 0.0360531i 0.876245 0.481865i \(-0.160040\pi\)
−0.855430 + 0.517918i \(0.826707\pi\)
\(578\) 0 0
\(579\) 5.50000 9.52628i 0.228572 0.395899i
\(580\) 0 0
\(581\) −24.0000 20.7846i −0.995688 0.862291i
\(582\) 0 0
\(583\) −4.50000 + 7.79423i −0.186371 + 0.322804i
\(584\) 0 0
\(585\) 6.00000 + 10.3923i 0.248069 + 0.429669i
\(586\) 0 0
\(587\) −12.0000 −0.495293 −0.247647 0.968850i \(-0.579657\pi\)
−0.247647 + 0.968850i \(0.579657\pi\)
\(588\) 0 0
\(589\) 7.00000 0.288430
\(590\) 0 0
\(591\) 9.00000 + 15.5885i 0.370211 + 0.641223i
\(592\) 0 0
\(593\) 10.5000 18.1865i 0.431183 0.746831i −0.565792 0.824548i \(-0.691430\pi\)
0.996976 + 0.0777165i \(0.0247629\pi\)
\(594\) 0 0
\(595\) 18.0000 + 15.5885i 0.737928 + 0.639064i
\(596\) 0 0
\(597\) 3.50000 6.06218i 0.143245 0.248108i
\(598\) 0 0
\(599\) −13.5000 23.3827i −0.551595 0.955391i −0.998160 0.0606393i \(-0.980686\pi\)
0.446565 0.894751i \(-0.352647\pi\)
\(600\) 0 0
\(601\) 14.0000 0.571072 0.285536 0.958368i \(-0.407828\pi\)
0.285536 + 0.958368i \(0.407828\pi\)
\(602\) 0 0
\(603\) −14.0000 −0.570124
\(604\) 0 0
\(605\) 3.00000 + 5.19615i 0.121967 + 0.211254i
\(606\) 0 0
\(607\) 23.5000 40.7032i 0.953836 1.65209i 0.216825 0.976210i \(-0.430430\pi\)
0.737011 0.675881i \(-0.236237\pi\)
\(608\) 0 0
\(609\) 3.00000 15.5885i 0.121566 0.631676i
\(610\) 0 0
\(611\) −9.00000 + 15.5885i −0.364101 + 0.630641i
\(612\) 0 0
\(613\) 12.5000 + 21.6506i 0.504870 + 0.874461i 0.999984 + 0.00563283i \(0.00179300\pi\)
−0.495114 + 0.868828i \(0.664874\pi\)
\(614\) 0 0
\(615\) −18.0000 −0.725830
\(616\) 0 0
\(617\) 6.00000 0.241551 0.120775 0.992680i \(-0.461462\pi\)
0.120775 + 0.992680i \(0.461462\pi\)
\(618\) 0 0
\(619\) −15.5000 26.8468i −0.622998 1.07906i −0.988924 0.148420i \(-0.952581\pi\)
0.365927 0.930644i \(-0.380752\pi\)
\(620\) 0 0
\(621\) 7.50000 12.9904i 0.300965 0.521286i
\(622\) 0 0
\(623\) −37.5000 + 12.9904i −1.50241 + 0.520449i
\(624\) 0 0
\(625\) 14.5000 25.1147i 0.580000 1.00459i
\(626\) 0 0
\(627\) 1.50000 + 2.59808i 0.0599042 + 0.103757i
\(628\) 0 0
\(629\) −3.00000 −0.119618
\(630\) 0 0
\(631\) 16.0000 0.636950 0.318475 0.947931i \(-0.396829\pi\)
0.318475 + 0.947931i \(0.396829\pi\)
\(632\) 0 0
\(633\) 2.00000 + 3.46410i 0.0794929 + 0.137686i
\(634\) 0 0
\(635\) 12.0000 20.7846i 0.476205 0.824812i
\(636\) 0 0
\(637\) 2.00000 + 13.8564i 0.0792429 + 0.549011i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −7.50000 12.9904i −0.296232 0.513089i 0.679039 0.734103i \(-0.262397\pi\)
−0.975271 + 0.221013i \(0.929064\pi\)
\(642\) 0 0
\(643\) −20.0000 −0.788723 −0.394362 0.918955i \(-0.629034\pi\)
−0.394362 + 0.918955i \(0.629034\pi\)
\(644\) 0 0
\(645\) −12.0000 −0.472500
\(646\) 0 0
\(647\) 10.5000 + 18.1865i 0.412798 + 0.714986i 0.995194 0.0979182i \(-0.0312184\pi\)
−0.582397 + 0.812905i \(0.697885\pi\)
\(648\) 0 0
\(649\) 13.5000 23.3827i 0.529921 0.917851i
\(650\) 0 0
\(651\) 17.5000 6.06218i 0.685879 0.237595i
\(652\) 0 0
\(653\) −19.5000 + 33.7750i −0.763094 + 1.32172i 0.178154 + 0.984003i \(0.442987\pi\)
−0.941248 + 0.337715i \(0.890346\pi\)
\(654\) 0 0
\(655\) 4.50000 + 7.79423i 0.175830 + 0.304546i
\(656\) 0 0
\(657\) 2.00000 0.0780274
\(658\) 0 0
\(659\) −12.0000 −0.467454 −0.233727 0.972302i \(-0.575092\pi\)
−0.233727 + 0.972302i \(0.575092\pi\)
\(660\) 0 0
\(661\) −5.50000 9.52628i −0.213925 0.370529i 0.739014 0.673690i \(-0.235292\pi\)
−0.952940 + 0.303160i \(0.901958\pi\)
\(662\) 0 0
\(663\) 3.00000 5.19615i 0.116510 0.201802i
\(664\) 0 0
\(665\) 1.50000 7.79423i 0.0581675 0.302247i
\(666\) 0 0
\(667\) −9.00000 + 15.5885i −0.348481 + 0.603587i
\(668\) 0 0
\(669\) −4.00000 6.92820i −0.154649 0.267860i
\(670\) 0 0
\(671\) −3.00000 −0.115814
\(672\) 0 0
\(673\) 14.0000 0.539660 0.269830 0.962908i \(-0.413032\pi\)
0.269830 + 0.962908i \(0.413032\pi\)
\(674\) 0 0
\(675\) −10.0000 17.3205i −0.384900 0.666667i
\(676\) 0 0
\(677\) −13.5000 + 23.3827i −0.518847 + 0.898670i 0.480913 + 0.876768i \(0.340305\pi\)
−0.999760 + 0.0219013i \(0.993028\pi\)
\(678\) 0 0
\(679\) −20.0000 17.3205i −0.767530 0.664700i
\(680\) 0 0
\(681\) 1.50000 2.59808i 0.0574801 0.0995585i
\(682\) 0 0
\(683\) 10.5000 + 18.1865i 0.401771 + 0.695888i 0.993940 0.109926i \(-0.0350613\pi\)
−0.592168 + 0.805814i \(0.701728\pi\)
\(684\) 0 0
\(685\) −63.0000 −2.40711
\(686\) 0 0
\(687\) −11.0000 −0.419676
\(688\) 0 0
\(689\) −3.00000 5.19615i −0.114291 0.197958i
\(690\) 0 0
\(691\) −6.50000 + 11.2583i −0.247272 + 0.428287i −0.962768 0.270330i \(-0.912867\pi\)
0.715496 + 0.698617i \(0.246201\pi\)
\(692\) 0 0
\(693\) −12.0000 10.3923i −0.455842 0.394771i
\(694\) 0 0
\(695\) 30.0000 51.9615i 1.13796 1.97101i
\(696\) 0 0
\(697\) −9.00000 15.5885i −0.340899 0.590455i
\(698\) 0 0
\(699\) 21.0000 0.794293
\(700\) 0 0
\(701\) −18.0000 −0.679851 −0.339925 0.940452i \(-0.610402\pi\)
−0.339925 + 0.940452i \(0.610402\pi\)
\(702\) 0 0
\(703\) 0.500000 + 0.866025i 0.0188579 + 0.0326628i
\(704\) 0 0
\(705\) 13.5000 23.3827i 0.508439 0.880643i
\(706\) 0 0
\(707\) 7.50000 38.9711i 0.282067 1.46566i
\(708\) 0 0
\(709\) 0.500000 0.866025i 0.0187779 0.0325243i −0.856484 0.516174i \(-0.827356\pi\)
0.875262 + 0.483650i \(0.160689\pi\)
\(710\) 0 0
\(711\) 13.0000 + 22.5167i 0.487538 + 0.844441i
\(712\) 0 0
\(713\) −21.0000 −0.786456
\(714\) 0 0
\(715\) 18.0000 0.673162
\(716\) 0 0
\(717\) 6.00000 + 10.3923i 0.224074 + 0.388108i
\(718\) 0 0
\(719\) −10.5000 + 18.1865i −0.391584 + 0.678243i −0.992659 0.120950i \(-0.961406\pi\)
0.601075 + 0.799193i \(0.294739\pi\)
\(720\) 0 0
\(721\) 27.5000 9.52628i 1.02415 0.354777i
\(722\) 0 0
\(723\) −0.500000 + 0.866025i −0.0185952 + 0.0322078i
\(724\) 0 0
\(725\) 12.0000 + 20.7846i 0.445669 + 0.771921i
\(726\) 0 0
\(727\) −32.0000 −1.18681 −0.593407 0.804902i \(-0.702218\pi\)
−0.593407 + 0.804902i \(0.702218\pi\)
\(728\) 0 0
\(729\) 13.0000 0.481481
\(730\) 0 0
\(731\) −6.00000 10.3923i −0.221918 0.384373i
\(732\) 0 0
\(733\) 12.5000 21.6506i 0.461698 0.799684i −0.537348 0.843361i \(-0.680574\pi\)
0.999046 + 0.0436764i \(0.0139070\pi\)
\(734\) 0 0
\(735\) −3.00000 20.7846i −0.110657 0.766652i
\(736\) 0 0
\(737\) −10.5000 + 18.1865i −0.386772 + 0.669910i
\(738\) 0 0
\(739\) −9.50000 16.4545i −0.349463 0.605288i 0.636691 0.771119i \(-0.280303\pi\)
−0.986154 + 0.165831i \(0.946969\pi\)
\(740\) 0 0
\(741\) −2.00000 −0.0734718
\(742\) 0 0
\(743\) 48.0000 1.76095 0.880475 0.474093i \(-0.157224\pi\)
0.880475 + 0.474093i \(0.157224\pi\)
\(744\) 0 0
\(745\) −4.50000 7.79423i −0.164867 0.285558i
\(746\) 0 0
\(747\) −12.0000 + 20.7846i −0.439057 + 0.760469i
\(748\) 0 0
\(749\) 37.5000 12.9904i 1.37022 0.474658i
\(750\) 0 0
\(751\) −12.5000 + 21.6506i −0.456131 + 0.790043i −0.998752 0.0499348i \(-0.984099\pi\)
0.542621 + 0.839978i \(0.317432\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −51.0000 −1.85608
\(756\) 0 0
\(757\) 2.00000 0.0726912 0.0363456 0.999339i \(-0.488428\pi\)
0.0363456 + 0.999339i \(0.488428\pi\)
\(758\) 0 0
\(759\) −4.50000 7.79423i −0.163340 0.282913i
\(760\) 0 0
\(761\) −1.50000 + 2.59808i −0.0543750 + 0.0941802i −0.891932 0.452170i \(-0.850650\pi\)
0.837557 + 0.546350i \(0.183983\pi\)
\(762\) 0 0
\(763\) −0.500000 + 2.59808i −0.0181012 + 0.0940567i
\(764\) 0 0
\(765\) 9.00000 15.5885i 0.325396 0.563602i
\(766\) 0 0
\(767\) 9.00000 + 15.5885i 0.324971 + 0.562867i
\(768\) 0 0
\(769\) −34.0000 −1.22607 −0.613036 0.790055i \(-0.710052\pi\)
−0.613036 + 0.790055i \(0.710052\pi\)
\(770\) 0 0
\(771\) −3.00000 −0.108042
\(772\) 0 0
\(773\) 16.5000 + 28.5788i 0.593464 + 1.02791i 0.993762 + 0.111524i \(0.0355733\pi\)
−0.400298 + 0.916385i \(0.631093\pi\)
\(774\) 0 0
\(775\) −14.0000 + 24.2487i −0.502895 + 0.871039i
\(776\) 0 0
\(777\) 2.00000 + 1.73205i 0.0717496 + 0.0621370i
\(778\) 0 0
\(779\) −3.00000 + 5.19615i −0.107486 + 0.186171i
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) −30.0000 −1.07211
\(784\) 0 0
\(785\) −39.0000 −1.39197
\(786\) 0 0
\(787\) −15.5000 26.8468i −0.552515 0.956985i −0.998092 0.0617409i \(-0.980335\pi\)
0.445577 0.895244i \(-0.352999\pi\)
\(788\) 0 0
\(789\) 1.50000 2.59808i 0.0534014 0.0924940i
\(790\) 0 0
\(791\) 12.0000 + 10.3923i 0.426671 + 0.369508i
\(792\) 0 0
\(793\) 1.00000 1.73205i 0.0355110 0.0615069i
\(794\) 0 0
\(795\) 4.50000 + 7.79423i 0.159599 + 0.276433i
\(796\) 0 0