Properties

Label 700.2.r.b.149.1
Level $700$
Weight $2$
Character 700.149
Analytic conductor $5.590$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 700 = 2^{2} \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 700.r (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.58952814149\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\zeta_{12})\)
Defining polynomial: \(x^{4} - x^{2} + 1\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 28)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 149.1
Root \(-0.866025 + 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 700.149
Dual form 700.2.r.b.249.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.866025 + 0.500000i) q^{3} +(1.73205 - 2.00000i) q^{7} +(-1.00000 + 1.73205i) q^{9} +O(q^{10})\) \(q+(-0.866025 + 0.500000i) q^{3} +(1.73205 - 2.00000i) q^{7} +(-1.00000 + 1.73205i) q^{9} +(1.50000 + 2.59808i) q^{11} -2.00000i q^{13} +(2.59808 - 1.50000i) q^{17} +(-0.500000 + 0.866025i) q^{19} +(-0.500000 + 2.59808i) q^{21} +(2.59808 + 1.50000i) q^{23} -5.00000i q^{27} +6.00000 q^{29} +(3.50000 + 6.06218i) q^{31} +(-2.59808 - 1.50000i) q^{33} +(0.866025 + 0.500000i) q^{37} +(1.00000 + 1.73205i) q^{39} +6.00000 q^{41} +4.00000i q^{43} +(7.79423 + 4.50000i) q^{47} +(-1.00000 - 6.92820i) q^{49} +(-1.50000 + 2.59808i) q^{51} +(-2.59808 + 1.50000i) q^{53} -1.00000i q^{57} +(4.50000 + 7.79423i) q^{59} +(0.500000 - 0.866025i) q^{61} +(1.73205 + 5.00000i) q^{63} +(-6.06218 + 3.50000i) q^{67} -3.00000 q^{69} +(0.866025 - 0.500000i) q^{73} +(7.79423 + 1.50000i) q^{77} +(-6.50000 + 11.2583i) q^{79} +(-0.500000 - 0.866025i) q^{81} -12.0000i q^{83} +(-5.19615 + 3.00000i) q^{87} +(7.50000 - 12.9904i) q^{89} +(-4.00000 - 3.46410i) q^{91} +(-6.06218 - 3.50000i) q^{93} -10.0000i q^{97} -6.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q - 4q^{9} + O(q^{10}) \) \( 4q - 4q^{9} + 6q^{11} - 2q^{19} - 2q^{21} + 24q^{29} + 14q^{31} + 4q^{39} + 24q^{41} - 4q^{49} - 6q^{51} + 18q^{59} + 2q^{61} - 12q^{69} - 26q^{79} - 2q^{81} + 30q^{89} - 16q^{91} - 24q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/700\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(351\) \(477\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(1\) \(-1\)

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
\(3\) −0.866025 + 0.500000i −0.500000 + 0.288675i −0.728714 0.684819i \(-0.759881\pi\)
0.228714 + 0.973494i \(0.426548\pi\)
\(4\) 0 0
\(5\) 0 0
\(6\) 0 0
\(7\) 1.73205 2.00000i 0.654654 0.755929i
\(8\) 0 0
\(9\) −1.00000 + 1.73205i −0.333333 + 0.577350i
\(10\) 0 0
\(11\) 1.50000 + 2.59808i 0.452267 + 0.783349i 0.998526 0.0542666i \(-0.0172821\pi\)
−0.546259 + 0.837616i \(0.683949\pi\)
\(12\) 0 0
\(13\) 2.00000i 0.554700i −0.960769 0.277350i \(-0.910544\pi\)
0.960769 0.277350i \(-0.0894562\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 2.59808 1.50000i 0.630126 0.363803i −0.150675 0.988583i \(-0.548145\pi\)
0.780801 + 0.624780i \(0.214811\pi\)
\(18\) 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
\(23\) 2.59808 + 1.50000i 0.541736 + 0.312772i 0.745782 0.666190i \(-0.232076\pi\)
−0.204046 + 0.978961i \(0.565409\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) 5.00000i 0.962250i
\(28\) 0 0
\(29\) 6.00000 1.11417 0.557086 0.830455i \(-0.311919\pi\)
0.557086 + 0.830455i \(0.311919\pi\)
\(30\) 0 0
\(31\) 3.50000 + 6.06218i 0.628619 + 1.08880i 0.987829 + 0.155543i \(0.0497126\pi\)
−0.359211 + 0.933257i \(0.616954\pi\)
\(32\) 0 0
\(33\) −2.59808 1.50000i −0.452267 0.261116i
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 0.866025 + 0.500000i 0.142374 + 0.0821995i 0.569495 0.821995i \(-0.307139\pi\)
−0.427121 + 0.904194i \(0.640472\pi\)
\(38\) 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
\(43\) 4.00000i 0.609994i 0.952353 + 0.304997i \(0.0986555\pi\)
−0.952353 + 0.304997i \(0.901344\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 7.79423 + 4.50000i 1.13691 + 0.656392i 0.945662 0.325150i \(-0.105415\pi\)
0.191243 + 0.981543i \(0.438748\pi\)
\(48\) 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
\(53\) −2.59808 + 1.50000i −0.356873 + 0.206041i −0.667708 0.744423i \(-0.732725\pi\)
0.310835 + 0.950464i \(0.399391\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 1.00000i 0.132453i
\(58\) 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
\(63\) 1.73205 + 5.00000i 0.218218 + 0.629941i
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) −6.06218 + 3.50000i −0.740613 + 0.427593i −0.822292 0.569066i \(-0.807305\pi\)
0.0816792 + 0.996659i \(0.473972\pi\)
\(68\) 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
\(73\) 0.866025 0.500000i 0.101361 0.0585206i −0.448463 0.893801i \(-0.648028\pi\)
0.549823 + 0.835281i \(0.314695\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 7.79423 + 1.50000i 0.888235 + 0.170941i
\(78\) 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
\(83\) 12.0000i 1.31717i −0.752506 0.658586i \(-0.771155\pi\)
0.752506 0.658586i \(-0.228845\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) −5.19615 + 3.00000i −0.557086 + 0.321634i
\(88\) 0 0
\(89\) 7.50000 12.9904i 0.794998 1.37698i −0.127842 0.991795i \(-0.540805\pi\)
0.922840 0.385183i \(-0.125862\pi\)
\(90\) 0 0
\(91\) −4.00000 3.46410i −0.419314 0.363137i
\(92\) 0 0
\(93\) −6.06218 3.50000i −0.628619 0.362933i
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) 10.0000i 1.01535i −0.861550 0.507673i \(-0.830506\pi\)
0.861550 0.507673i \(-0.169494\pi\)
\(98\) 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
\(103\) 9.52628 + 5.50000i 0.938652 + 0.541931i 0.889538 0.456862i \(-0.151027\pi\)
0.0491146 + 0.998793i \(0.484360\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −12.9904 7.50000i −1.25583 0.725052i −0.283567 0.958952i \(-0.591518\pi\)
−0.972261 + 0.233900i \(0.924851\pi\)
\(108\) 0 0
\(109\) −0.500000 0.866025i −0.0478913 0.0829502i 0.841086 0.540901i \(-0.181917\pi\)
−0.888977 + 0.457951i \(0.848583\pi\)
\(110\) 0 0
\(111\) −1.00000 −0.0949158
\(112\) 0 0
\(113\) 6.00000i 0.564433i −0.959351 0.282216i \(-0.908930\pi\)
0.959351 0.282216i \(-0.0910696\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) 3.46410 + 2.00000i 0.320256 + 0.184900i
\(118\) 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
\(123\) −5.19615 + 3.00000i −0.468521 + 0.270501i
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) 8.00000i 0.709885i 0.934888 + 0.354943i \(0.115500\pi\)
−0.934888 + 0.354943i \(0.884500\pi\)
\(128\) 0 0
\(129\) −2.00000 3.46410i −0.176090 0.304997i
\(130\) 0 0
\(131\) −1.50000 + 2.59808i −0.131056 + 0.226995i −0.924084 0.382190i \(-0.875170\pi\)
0.793028 + 0.609185i \(0.208503\pi\)
\(132\) 0 0
\(133\) 0.866025 + 2.50000i 0.0750939 + 0.216777i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −18.1865 + 10.5000i −1.55378 + 0.897076i −0.555952 + 0.831215i \(0.687646\pi\)
−0.997829 + 0.0658609i \(0.979021\pi\)
\(138\) 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
\(143\) 5.19615 3.00000i 0.434524 0.250873i
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) 4.33013 + 5.50000i 0.357143 + 0.453632i
\(148\) 0 0
\(149\) 1.50000 2.59808i 0.122885 0.212843i −0.798019 0.602632i \(-0.794119\pi\)
0.920904 + 0.389789i \(0.127452\pi\)
\(150\) 0 0
\(151\) −8.50000 14.7224i −0.691720 1.19809i −0.971274 0.237964i \(-0.923520\pi\)
0.279554 0.960130i \(-0.409814\pi\)
\(152\) 0 0
\(153\) 6.00000i 0.485071i
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) −11.2583 + 6.50000i −0.898513 + 0.518756i −0.876717 0.481006i \(-0.840272\pi\)
−0.0217953 + 0.999762i \(0.506938\pi\)
\(158\) 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
\(163\) 9.52628 + 5.50000i 0.746156 + 0.430793i 0.824303 0.566149i \(-0.191567\pi\)
−0.0781474 + 0.996942i \(0.524900\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 12.0000i 0.928588i −0.885681 0.464294i \(-0.846308\pi\)
0.885681 0.464294i \(-0.153692\pi\)
\(168\) 0 0
\(169\) 9.00000 0.692308
\(170\) 0 0
\(171\) −1.00000 1.73205i −0.0764719 0.132453i
\(172\) 0 0
\(173\) −7.79423 4.50000i −0.592584 0.342129i 0.173534 0.984828i \(-0.444481\pi\)
−0.766119 + 0.642699i \(0.777815\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) −7.79423 4.50000i −0.585850 0.338241i
\(178\) 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
\(183\) 1.00000i 0.0739221i
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 7.79423 + 4.50000i 0.569970 + 0.329073i
\(188\) 0 0
\(189\) −10.0000 8.66025i −0.727393 0.629941i
\(190\) 0 0
\(191\) 4.50000 7.79423i 0.325609 0.563971i −0.656027 0.754738i \(-0.727764\pi\)
0.981635 + 0.190767i \(0.0610975\pi\)
\(192\) 0 0
\(193\) −9.52628 + 5.50000i −0.685717 + 0.395899i −0.802005 0.597317i \(-0.796234\pi\)
0.116289 + 0.993215i \(0.462900\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 18.0000i 1.28245i 0.767354 + 0.641223i \(0.221573\pi\)
−0.767354 + 0.641223i \(0.778427\pi\)
\(198\) 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
\(203\) 10.3923 12.0000i 0.729397 0.842235i
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) −5.19615 + 3.00000i −0.361158 + 0.208514i
\(208\) 0 0
\(209\) −3.00000 −0.207514
\(210\) 0 0
\(211\) −4.00000 −0.275371 −0.137686 0.990476i \(-0.543966\pi\)
−0.137686 + 0.990476i \(0.543966\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 18.1865 + 3.50000i 1.23458 + 0.237595i
\(218\) 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
\(223\) 8.00000i 0.535720i −0.963458 0.267860i \(-0.913684\pi\)
0.963458 0.267860i \(-0.0863164\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −2.59808 + 1.50000i −0.172440 + 0.0995585i −0.583736 0.811943i \(-0.698410\pi\)
0.411296 + 0.911502i \(0.365076\pi\)
\(228\) 0 0
\(229\) 5.50000 9.52628i 0.363450 0.629514i −0.625076 0.780564i \(-0.714932\pi\)
0.988526 + 0.151050i \(0.0482653\pi\)
\(230\) 0 0
\(231\) −7.50000 + 2.59808i −0.493464 + 0.170941i
\(232\) 0 0
\(233\) −18.1865 10.5000i −1.19144 0.687878i −0.232806 0.972523i \(-0.574791\pi\)
−0.958633 + 0.284645i \(0.908124\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) 13.0000i 0.844441i
\(238\) 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
\(243\) 13.8564 + 8.00000i 0.888889 + 0.513200i
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 1.73205 + 1.00000i 0.110208 + 0.0636285i
\(248\) 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
\(253\) 9.00000i 0.565825i
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −2.59808 1.50000i −0.162064 0.0935674i 0.416775 0.909010i \(-0.363160\pi\)
−0.578838 + 0.815442i \(0.696494\pi\)
\(258\) 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
\(263\) 2.59808 1.50000i 0.160204 0.0924940i −0.417755 0.908560i \(-0.637183\pi\)
0.577959 + 0.816066i \(0.303849\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 15.0000i 0.917985i
\(268\) 0 0
\(269\) 1.50000 + 2.59808i 0.0914566 + 0.158408i 0.908124 0.418701i \(-0.137514\pi\)
−0.816668 + 0.577108i \(0.804181\pi\)
\(270\) 0 0
\(271\) −5.50000 + 9.52628i −0.334101 + 0.578680i −0.983312 0.181928i \(-0.941766\pi\)
0.649211 + 0.760609i \(0.275099\pi\)
\(272\) 0 0
\(273\) 5.19615 + 1.00000i 0.314485 + 0.0605228i
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) −11.2583 + 6.50000i −0.676448 + 0.390547i −0.798515 0.601975i \(-0.794381\pi\)
0.122068 + 0.992522i \(0.461047\pi\)
\(278\) 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
\(283\) −25.1147 + 14.5000i −1.49292 + 0.861936i −0.999967 0.00812260i \(-0.997414\pi\)
−0.492949 + 0.870058i \(0.664081\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 10.3923 12.0000i 0.613438 0.708338i
\(288\) 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
\(293\) 6.00000i 0.350524i −0.984522 0.175262i \(-0.943923\pi\)
0.984522 0.175262i \(-0.0560772\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) 12.9904 7.50000i 0.753778 0.435194i
\(298\) 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
\(303\) 12.9904 + 7.50000i 0.746278 + 0.430864i
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 28.0000i 1.59804i −0.601302 0.799022i \(-0.705351\pi\)
0.601302 0.799022i \(-0.294649\pi\)
\(308\) 0 0
\(309\) −11.0000 −0.625768
\(310\) 0 0
\(311\) 13.5000 + 23.3827i 0.765515 + 1.32591i 0.939974 + 0.341246i \(0.110849\pi\)
−0.174459 + 0.984664i \(0.555818\pi\)
\(312\) 0 0
\(313\) 19.9186 + 11.5000i 1.12586 + 0.650018i 0.942892 0.333099i \(-0.108094\pi\)
0.182973 + 0.983118i \(0.441428\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 7.79423 + 4.50000i 0.437767 + 0.252745i 0.702650 0.711535i \(-0.252000\pi\)
−0.264883 + 0.964281i \(0.585333\pi\)
\(318\) 0 0
\(319\) 9.00000 + 15.5885i 0.503903 + 0.872786i
\(320\) 0 0
\(321\) 15.0000 0.837218
\(322\) 0 0
\(323\) 3.00000i 0.166924i
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) 0.866025 + 0.500000i 0.0478913 + 0.0276501i
\(328\) 0 0
\(329\) 22.5000 7.79423i 1.24047 0.429710i
\(330\) 0 0
\(331\) 6.50000 11.2583i 0.357272 0.618814i −0.630232 0.776407i \(-0.717040\pi\)
0.987504 + 0.157593i \(0.0503735\pi\)
\(332\) 0 0
\(333\) −1.73205 + 1.00000i −0.0949158 + 0.0547997i
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) 34.0000i 1.85210i −0.377403 0.926049i \(-0.623183\pi\)
0.377403 0.926049i \(-0.376817\pi\)
\(338\) 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
\(343\) −15.5885 10.0000i −0.841698 0.539949i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 7.79423 4.50000i 0.418416 0.241573i −0.275983 0.961162i \(-0.589003\pi\)
0.694399 + 0.719590i \(0.255670\pi\)
\(348\) 0 0
\(349\) −26.0000 −1.39175 −0.695874 0.718164i \(-0.744983\pi\)
−0.695874 + 0.718164i \(0.744983\pi\)
\(350\) 0 0
\(351\) −10.0000 −0.533761
\(352\) 0 0
\(353\) 18.1865 10.5000i 0.967972 0.558859i 0.0693543 0.997592i \(-0.477906\pi\)
0.898617 + 0.438733i \(0.144573\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 2.59808 + 7.50000i 0.137505 + 0.396942i
\(358\) 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
\(363\) 2.00000i 0.104973i
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 4.33013 2.50000i 0.226031 0.130499i −0.382709 0.923869i \(-0.625009\pi\)
0.608740 + 0.793370i \(0.291675\pi\)
\(368\) 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
\(373\) −21.6506 12.5000i −1.12103 0.647225i −0.179364 0.983783i \(-0.557404\pi\)
−0.941663 + 0.336557i \(0.890737\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 12.0000i 0.618031i
\(378\) 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
\(383\) −28.5788 16.5000i −1.46031 0.843111i −0.461285 0.887252i \(-0.652611\pi\)
−0.999025 + 0.0441413i \(0.985945\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) −6.92820 4.00000i −0.352180 0.203331i
\(388\) 0 0
\(389\) 7.50000 + 12.9904i 0.380265 + 0.658638i 0.991100 0.133120i \(-0.0424994\pi\)
−0.610835 + 0.791758i \(0.709166\pi\)
\(390\) 0 0
\(391\) 9.00000 0.455150
\(392\) 0 0
\(393\) 3.00000i 0.151330i
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) 32.0429 + 18.5000i 1.60819 + 0.928488i 0.989775 + 0.142636i \(0.0455577\pi\)
0.618414 + 0.785853i \(0.287776\pi\)
\(398\) 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
\(403\) 12.1244 7.00000i 0.603957 0.348695i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 3.00000i 0.148704i
\(408\) 0 0
\(409\) 5.50000 + 9.52628i 0.271957 + 0.471044i 0.969363 0.245633i \(-0.0789957\pi\)
−0.697406 + 0.716677i \(0.745662\pi\)
\(410\) 0 0
\(411\) 10.5000 18.1865i 0.517927 0.897076i
\(412\) 0 0
\(413\) 23.3827 + 4.50000i 1.15059 + 0.221431i
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 17.3205 10.0000i 0.848189 0.489702i
\(418\) 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
\(423\) −15.5885 + 9.00000i −0.757937 + 0.437595i
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) −0.866025 2.50000i −0.0419099 0.120983i
\(428\) 0 0
\(429\) −3.00000 + 5.19615i −0.144841 + 0.250873i
\(430\) 0 0
\(431\) 7.50000 + 12.9904i 0.361262 + 0.625725i 0.988169 0.153370i \(-0.0490126\pi\)
−0.626907 + 0.779094i \(0.715679\pi\)
\(432\) 0 0
\(433\) 10.0000i 0.480569i 0.970702 + 0.240285i \(0.0772408\pi\)
−0.970702 + 0.240285i \(0.922759\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −2.59808 + 1.50000i −0.124283 + 0.0717547i
\(438\) 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
\(443\) −7.79423 4.50000i −0.370315 0.213801i 0.303281 0.952901i \(-0.401918\pi\)
−0.673596 + 0.739100i \(0.735251\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 3.00000i 0.141895i
\(448\) 0 0
\(449\) 18.0000 0.849473 0.424736 0.905317i \(-0.360367\pi\)
0.424736 + 0.905317i \(0.360367\pi\)
\(450\) 0 0
\(451\) 9.00000 + 15.5885i 0.423793 + 0.734032i
\(452\) 0 0
\(453\) 14.7224 + 8.50000i 0.691720 + 0.399365i
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −19.9186 11.5000i −0.931752 0.537947i −0.0443868 0.999014i \(-0.514133\pi\)
−0.887365 + 0.461067i \(0.847467\pi\)
\(458\) 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
\(463\) 16.0000i 0.743583i 0.928316 + 0.371792i \(0.121256\pi\)
−0.928316 + 0.371792i \(0.878744\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 18.1865 + 10.5000i 0.841572 + 0.485882i 0.857798 0.513986i \(-0.171832\pi\)
−0.0162260 + 0.999868i \(0.505165\pi\)
\(468\) 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
\(473\) −10.3923 + 6.00000i −0.477839 + 0.275880i
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) 6.00000i 0.274721i
\(478\) 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
\(483\) −5.19615 + 6.00000i −0.236433 + 0.273009i
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) −16.4545 + 9.50000i −0.745624 + 0.430486i −0.824110 0.566429i \(-0.808325\pi\)
0.0784867 + 0.996915i \(0.474991\pi\)
\(488\) 0 0
\(489\) −11.0000 −0.497437
\(490\) 0 0
\(491\) 24.0000 1.08310 0.541552 0.840667i \(-0.317837\pi\)
0.541552 + 0.840667i \(0.317837\pi\)
\(492\) 0 0
\(493\) 15.5885 9.00000i 0.702069 0.405340i
\(494\) 0 0
\(495\) 0 0
\(496\) 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 1.00000 \(0\)
−1.00000 \(\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) −7.79423 + 4.50000i −0.346154 + 0.199852i
\(508\) 0 0
\(509\) 1.50000 2.59808i 0.0664863 0.115158i −0.830866 0.556473i \(-0.812154\pi\)
0.897352 + 0.441315i \(0.145488\pi\)
\(510\) 0 0
\(511\) 0.500000 2.59808i 0.0221187 0.114932i
\(512\) 0 0
\(513\) 4.33013 + 2.50000i 0.191180 + 0.110378i
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 27.0000i 1.18746i
\(518\) 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
\(523\) −0.866025 0.500000i −0.0378686 0.0218635i 0.480946 0.876750i \(-0.340293\pi\)
−0.518815 + 0.854887i \(0.673627\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 18.1865 + 10.5000i 0.792218 + 0.457387i
\(528\) 0 0
\(529\) −7.00000 12.1244i −0.304348 0.527146i
\(530\) 0 0
\(531\) −18.0000 −0.781133
\(532\) 0 0
\(533\) 12.0000i 0.519778i
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) −18.1865 10.5000i −0.784807 0.453108i
\(538\) 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
\(543\) 8.66025 5.00000i 0.371647 0.214571i
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 8.00000i 0.342055i 0.985266 + 0.171028i \(0.0547087\pi\)
−0.985266 + 0.171028i \(0.945291\pi\)
\(548\) 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
\(553\) 11.2583 + 32.5000i 0.478753 + 1.38204i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −28.5788 + 16.5000i −1.21092 + 0.699127i −0.962961 0.269642i \(-0.913095\pi\)
−0.247964 + 0.968769i \(0.579761\pi\)
\(558\) 0 0
\(559\) 8.00000 0.338364
\(560\) 0 0
\(561\) −9.00000 −0.379980
\(562\) 0 0
\(563\) −7.79423 + 4.50000i −0.328488 + 0.189652i −0.655169 0.755482i \(-0.727403\pi\)
0.326682 + 0.945134i \(0.394069\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) −2.59808 0.500000i −0.109109 0.0209980i
\(568\) 0 0
\(569\) −4.50000 + 7.79423i −0.188650 + 0.326751i −0.944800 0.327647i \(-0.893744\pi\)
0.756151 + 0.654398i \(0.227078\pi\)
\(570\) 0 0
\(571\) −14.5000 25.1147i −0.606806 1.05102i −0.991763 0.128085i \(-0.959117\pi\)
0.384957 0.922934i \(-0.374216\pi\)
\(572\) 0 0
\(573\) 9.00000i 0.375980i
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) −0.866025 + 0.500000i −0.0360531 + 0.0208153i −0.517918 0.855430i \(-0.673293\pi\)
0.481865 + 0.876245i \(0.339960\pi\)
\(578\) 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
\(583\) −7.79423 4.50000i −0.322804 0.186371i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 12.0000i 0.495293i 0.968850 + 0.247647i \(0.0796572\pi\)
−0.968850 + 0.247647i \(0.920343\pi\)
\(588\) 0 0
\(589\) −7.00000 −0.288430
\(590\) 0 0
\(591\) −9.00000 15.5885i −0.370211 0.641223i
\(592\) 0 0
\(593\) −18.1865 10.5000i −0.746831 0.431183i 0.0777165 0.996976i \(-0.475237\pi\)
−0.824548 + 0.565792i \(0.808570\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 6.06218 + 3.50000i 0.248108 + 0.143245i
\(598\) 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
\(603\) 14.0000i 0.570124i
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) −40.7032 23.5000i −1.65209 0.953836i −0.976210 0.216825i \(-0.930430\pi\)
−0.675881 0.737011i \(-0.736237\pi\)
\(608\) 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
\(613\) 21.6506 12.5000i 0.874461 0.504870i 0.00563283 0.999984i \(-0.498207\pi\)
0.868828 + 0.495114i \(0.164874\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 6.00000i 0.241551i 0.992680 + 0.120775i \(0.0385381\pi\)
−0.992680 + 0.120775i \(0.961462\pi\)
\(618\) 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
\(623\) −12.9904 37.5000i −0.520449 1.50241i
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) 2.59808 1.50000i 0.103757 0.0599042i
\(628\) 0 0
\(629\) 3.00000 0.119618
\(630\) 0 0
\(631\) −16.0000 −0.636950 −0.318475 0.947931i \(-0.603171\pi\)
−0.318475 + 0.947931i \(0.603171\pi\)
\(632\) 0 0
\(633\) 3.46410 2.00000i 0.137686 0.0794929i
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) −13.8564 + 2.00000i −0.549011 + 0.0792429i
\(638\) 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
\(643\) 20.0000i 0.788723i −0.918955 0.394362i \(-0.870966\pi\)
0.918955 0.394362i \(-0.129034\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 18.1865 10.5000i 0.714986 0.412798i −0.0979182 0.995194i \(-0.531218\pi\)
0.812905 + 0.582397i \(0.197885\pi\)
\(648\) 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
\(653\) 33.7750 + 19.5000i 1.32172 + 0.763094i 0.984003 0.178154i \(-0.0570127\pi\)
0.337715 + 0.941248i \(0.390346\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 2.00000i 0.0780274i
\(658\) 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
\(663\) 5.19615 + 3.00000i 0.201802 + 0.116510i
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 15.5885 + 9.00000i 0.603587 + 0.348481i
\(668\) 0 0
\(669\) 4.00000 + 6.92820i 0.154649 + 0.267860i
\(670\) 0 0
\(671\) 3.00000 0.115814
\(672\) 0 0
\(673\) 14.0000i 0.539660i −0.962908 0.269830i \(-0.913032\pi\)
0.962908 0.269830i \(-0.0869676\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −23.3827 13.5000i −0.898670 0.518847i −0.0219013 0.999760i \(-0.506972\pi\)
−0.876768 + 0.480913i \(0.840305\pi\)
\(678\) 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
\(683\) −18.1865 + 10.5000i −0.695888 + 0.401771i −0.805814 0.592168i \(-0.798272\pi\)
0.109926 + 0.993940i \(0.464939\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) 11.0000i 0.419676i
\(688\) 0 0
\(689\) 3.00000 + 5.19615i 0.114291 + 0.197958i
\(690\) 0 0
\(691\) 6.50000 11.2583i 0.247272 0.428287i −0.715496 0.698617i \(-0.753799\pi\)
0.962768 + 0.270330i \(0.0871327\pi\)
\(692\) 0 0
\(693\) −10.3923 + 12.0000i −0.394771 + 0.455842i
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 15.5885 9.00000i 0.590455 0.340899i
\(698\) 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
\(703\) −0.866025 + 0.500000i −0.0326628 + 0.0188579i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −38.9711 7.50000i −1.46566 0.282067i
\(708\) 0 0
\(709\) −0.500000 + 0.866025i −0.0187779 + 0.0325243i −0.875262 0.483650i \(-0.839311\pi\)
0.856484 + 0.516174i \(0.172644\pi\)
\(710\) 0 0
\(711\) −13.0000 22.5167i −0.487538 0.844441i
\(712\) 0 0
\(713\) 21.0000i 0.786456i
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) −10.3923 + 6.00000i −0.388108 + 0.224074i
\(718\) 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
\(723\) −0.866025 0.500000i −0.0322078 0.0185952i
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) 32.0000i 1.18681i 0.804902 + 0.593407i \(0.202218\pi\)
−0.804902 + 0.593407i \(0.797782\pi\)
\(728\) 0 0
\(729\) −13.0000 −0.481481
\(730\) 0 0
\(731\) 6.00000 + 10.3923i 0.221918 + 0.384373i
\(732\) 0 0
\(733\) −21.6506 12.5000i −0.799684 0.461698i 0.0436764 0.999046i \(-0.486093\pi\)
−0.843361 + 0.537348i \(0.819426\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −18.1865 10.5000i −0.669910 0.386772i
\(738\) 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
\(743\) 48.0000i 1.76095i 0.474093 + 0.880475i \(0.342776\pi\)
−0.474093 + 0.880475i \(0.657224\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 20.7846 + 12.0000i 0.760469 + 0.439057i
\(748\) 0 0
\(749\) −37.5000 + 12.9904i −1.37022 + 0.474658i
\(750\) 0 0
\(751\) 12.5000 21.6506i 0.456131 0.790043i −0.542621 0.839978i \(-0.682568\pi\)
0.998752 + 0.0499348i \(0.0159013\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 2.00000i 0.0726912i 0.999339 + 0.0363456i \(0.0115717\pi\)
−0.999339 + 0.0363456i \(0.988428\pi\)
\(758\) 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
\(763\) −2.59808 0.500000i −0.0940567 0.0181012i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 15.5885 9.00000i 0.562867 0.324971i
\(768\) 0 0
\(769\) 34.0000 1.22607 0.613036 0.790055i \(-0.289948\pi\)
0.613036 + 0.790055i \(0.289948\pi\)
\(770\) 0 0
\(771\) 3.00000 0.108042
\(772\) 0 0
\(773\) 28.5788 16.5000i 1.02791 0.593464i 0.111524 0.993762i \(-0.464427\pi\)
0.916385 + 0.400298i \(0.131093\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) −1.73205 + 2.00000i −0.0621370 + 0.0717496i
\(778\) 0 0
\(779\) −3.00000 + 5.19615i −0.107486 + 0.186171i
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 30.0000i 1.07211i
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) −26.8468 + 15.5000i −0.956985 + 0.552515i −0.895244 0.445577i \(-0.852999\pi\)
−0.0617409 + 0.998092i \(0.519665\pi\)
\(788\) 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
\(793\) −1.73205 1.00000i −0.0615069 0.0355110i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 42.0000i 1.48772i 0.668338 + 0.743858i \(0.267006\pi\)
−0.668338 + 0.743858i \(0.732994\pi\)
\(798\) 0 0
\(799\) 27.0000 0.955191
\(800\) 0 0