Properties

Label 672.2.q.l.193.1
Level $672$
Weight $2$
Character 672.193
Analytic conductor $5.366$
Analytic rank $0$
Dimension $6$
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: \(0\)
Dimension: \(6\)
Relative dimension: \(3\) over \(\Q(\zeta_{3})\)
Coefficient field: 6.0.1156923.1
Defining polynomial: \(x^{6} - 3 x^{5} + 12 x^{4} - 19 x^{3} + 27 x^{2} - 18 x + 4\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 193.1
Root \(0.500000 + 0.0585812i\) of defining polynomial
Character \(\chi\) \(=\) 672.193
Dual form 672.2.q.l.289.1

$q$-expansion

\(f(q)\) \(=\) \(q+(0.500000 - 0.866025i) q^{3} +(-1.37328 - 2.37860i) q^{5} +(2.64510 + 0.0585812i) q^{7} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\) \(q+(0.500000 - 0.866025i) q^{3} +(-1.37328 - 2.37860i) q^{5} +(2.64510 + 0.0585812i) q^{7} +(-0.500000 - 0.866025i) q^{9} +(0.771819 - 1.33683i) q^{11} +6.03677 q^{13} -2.74657 q^{15} +(-3.74657 + 6.48925i) q^{17} +(-3.01839 - 5.22800i) q^{19} +(1.37328 - 2.26144i) q^{21} +(-3.74657 - 6.48925i) q^{23} +(-1.27182 + 2.20285i) q^{25} -1.00000 q^{27} +1.25343 q^{29} +(2.64510 - 4.58145i) q^{31} +(-0.771819 - 1.33683i) q^{33} +(-3.49314 - 6.37208i) q^{35} +(-2.47475 - 4.28639i) q^{37} +(3.01839 - 5.22800i) q^{39} -5.08727 q^{41} -3.45636 q^{43} +(-1.37328 + 2.37860i) q^{45} +(4.74657 + 8.22130i) q^{47} +(6.99314 + 0.309906i) q^{49} +(3.74657 + 6.48925i) q^{51} +(1.91692 - 3.32021i) q^{53} -4.23970 q^{55} -6.03677 q^{57} +(2.77182 - 4.80093i) q^{59} +(7.29021 + 12.6270i) q^{61} +(-1.27182 - 2.32002i) q^{63} +(-8.29021 - 14.3591i) q^{65} +(-2.01839 + 3.49595i) q^{67} -7.49314 q^{69} +5.49314 q^{71} +(-6.27182 + 10.8631i) q^{73} +(1.27182 + 2.20285i) q^{75} +(2.11985 - 3.49084i) q^{77} +(-3.89853 - 6.75246i) q^{79} +(-0.500000 + 0.866025i) q^{81} +6.52991 q^{83} +20.5804 q^{85} +(0.626716 - 1.08550i) q^{87} +(4.74657 + 8.22130i) q^{89} +(15.9679 + 0.353641i) q^{91} +(-2.64510 - 4.58145i) q^{93} +(-8.29021 + 14.3591i) q^{95} +1.54364 q^{97} -1.54364 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6q + 3q^{3} + 3q^{7} - 3q^{9} + O(q^{10}) \) \( 6q + 3q^{3} + 3q^{7} - 3q^{9} - 6q^{13} - 6q^{17} + 3q^{19} - 6q^{23} - 3q^{25} - 6q^{27} + 24q^{29} + 3q^{31} + 12q^{35} - 3q^{37} - 3q^{39} - 12q^{41} - 30q^{43} + 12q^{47} + 9q^{49} + 6q^{51} - 6q^{53} + 24q^{55} + 6q^{57} + 12q^{59} + 18q^{61} - 3q^{63} - 24q^{65} + 9q^{67} - 12q^{69} - 33q^{73} + 3q^{75} - 12q^{77} - 27q^{79} - 3q^{81} - 36q^{83} + 72q^{85} + 12q^{87} + 12q^{89} + 51q^{91} - 3q^{93} - 24q^{95} + O(q^{100}) \)

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
\(5\) −1.37328 2.37860i −0.614151 1.06374i −0.990533 0.137277i \(-0.956165\pi\)
0.376381 0.926465i \(-0.377168\pi\)
\(6\) 0 0
\(7\) 2.64510 + 0.0585812i 0.999755 + 0.0221416i
\(8\) 0 0
\(9\) −0.500000 0.866025i −0.166667 0.288675i
\(10\) 0 0
\(11\) 0.771819 1.33683i 0.232712 0.403069i −0.725893 0.687807i \(-0.758573\pi\)
0.958605 + 0.284738i \(0.0919067\pi\)
\(12\) 0 0
\(13\) 6.03677 1.67430 0.837150 0.546974i \(-0.184220\pi\)
0.837150 + 0.546974i \(0.184220\pi\)
\(14\) 0 0
\(15\) −2.74657 −0.709161
\(16\) 0 0
\(17\) −3.74657 + 6.48925i −0.908676 + 1.57387i −0.0927713 + 0.995687i \(0.529573\pi\)
−0.815905 + 0.578186i \(0.803761\pi\)
\(18\) 0 0
\(19\) −3.01839 5.22800i −0.692465 1.19939i −0.971028 0.238967i \(-0.923191\pi\)
0.278562 0.960418i \(-0.410142\pi\)
\(20\) 0 0
\(21\) 1.37328 2.26144i 0.299675 0.493486i
\(22\) 0 0
\(23\) −3.74657 6.48925i −0.781213 1.35310i −0.931235 0.364419i \(-0.881268\pi\)
0.150022 0.988683i \(-0.452066\pi\)
\(24\) 0 0
\(25\) −1.27182 + 2.20285i −0.254364 + 0.440571i
\(26\) 0 0
\(27\) −1.00000 −0.192450
\(28\) 0 0
\(29\) 1.25343 0.232756 0.116378 0.993205i \(-0.462872\pi\)
0.116378 + 0.993205i \(0.462872\pi\)
\(30\) 0 0
\(31\) 2.64510 4.58145i 0.475074 0.822853i −0.524518 0.851399i \(-0.675754\pi\)
0.999592 + 0.0285462i \(0.00908778\pi\)
\(32\) 0 0
\(33\) −0.771819 1.33683i −0.134356 0.232712i
\(34\) 0 0
\(35\) −3.49314 6.37208i −0.590448 1.07708i
\(36\) 0 0
\(37\) −2.47475 4.28639i −0.406846 0.704679i 0.587688 0.809088i \(-0.300038\pi\)
−0.994534 + 0.104409i \(0.966705\pi\)
\(38\) 0 0
\(39\) 3.01839 5.22800i 0.483329 0.837150i
\(40\) 0 0
\(41\) −5.08727 −0.794499 −0.397249 0.917711i \(-0.630035\pi\)
−0.397249 + 0.917711i \(0.630035\pi\)
\(42\) 0 0
\(43\) −3.45636 −0.527090 −0.263545 0.964647i \(-0.584892\pi\)
−0.263545 + 0.964647i \(0.584892\pi\)
\(44\) 0 0
\(45\) −1.37328 + 2.37860i −0.204717 + 0.354580i
\(46\) 0 0
\(47\) 4.74657 + 8.22130i 0.692358 + 1.19920i 0.971063 + 0.238823i \(0.0767615\pi\)
−0.278705 + 0.960377i \(0.589905\pi\)
\(48\) 0 0
\(49\) 6.99314 + 0.309906i 0.999019 + 0.0442723i
\(50\) 0 0
\(51\) 3.74657 + 6.48925i 0.524624 + 0.908676i
\(52\) 0 0
\(53\) 1.91692 3.32021i 0.263309 0.456065i −0.703810 0.710388i \(-0.748519\pi\)
0.967119 + 0.254323i \(0.0818527\pi\)
\(54\) 0 0
\(55\) −4.23970 −0.571682
\(56\) 0 0
\(57\) −6.03677 −0.799590
\(58\) 0 0
\(59\) 2.77182 4.80093i 0.360860 0.625028i −0.627243 0.778824i \(-0.715817\pi\)
0.988103 + 0.153796i \(0.0491499\pi\)
\(60\) 0 0
\(61\) 7.29021 + 12.6270i 0.933415 + 1.61672i 0.777436 + 0.628962i \(0.216520\pi\)
0.155979 + 0.987760i \(0.450147\pi\)
\(62\) 0 0
\(63\) −1.27182 2.32002i −0.160234 0.292295i
\(64\) 0 0
\(65\) −8.29021 14.3591i −1.02827 1.78102i
\(66\) 0 0
\(67\) −2.01839 + 3.49595i −0.246585 + 0.427098i −0.962576 0.271012i \(-0.912642\pi\)
0.715991 + 0.698110i \(0.245975\pi\)
\(68\) 0 0
\(69\) −7.49314 −0.902068
\(70\) 0 0
\(71\) 5.49314 0.651915 0.325958 0.945384i \(-0.394313\pi\)
0.325958 + 0.945384i \(0.394313\pi\)
\(72\) 0 0
\(73\) −6.27182 + 10.8631i −0.734061 + 1.27143i 0.221073 + 0.975257i \(0.429044\pi\)
−0.955134 + 0.296173i \(0.904289\pi\)
\(74\) 0 0
\(75\) 1.27182 + 2.20285i 0.146857 + 0.254364i
\(76\) 0 0
\(77\) 2.11985 3.49084i 0.241580 0.397818i
\(78\) 0 0
\(79\) −3.89853 6.75246i −0.438619 0.759711i 0.558964 0.829192i \(-0.311199\pi\)
−0.997583 + 0.0694809i \(0.977866\pi\)
\(80\) 0 0
\(81\) −0.500000 + 0.866025i −0.0555556 + 0.0962250i
\(82\) 0 0
\(83\) 6.52991 0.716751 0.358375 0.933578i \(-0.383331\pi\)
0.358375 + 0.933578i \(0.383331\pi\)
\(84\) 0 0
\(85\) 20.5804 2.23226
\(86\) 0 0
\(87\) 0.626716 1.08550i 0.0671910 0.116378i
\(88\) 0 0
\(89\) 4.74657 + 8.22130i 0.503135 + 0.871456i 0.999993 + 0.00362404i \(0.00115357\pi\)
−0.496858 + 0.867832i \(0.665513\pi\)
\(90\) 0 0
\(91\) 15.9679 + 0.353641i 1.67389 + 0.0370717i
\(92\) 0 0
\(93\) −2.64510 4.58145i −0.274284 0.475074i
\(94\) 0 0
\(95\) −8.29021 + 14.3591i −0.850557 + 1.47321i
\(96\) 0 0
\(97\) 1.54364 0.156733 0.0783663 0.996925i \(-0.475030\pi\)
0.0783663 + 0.996925i \(0.475030\pi\)
\(98\) 0 0
\(99\) −1.54364 −0.155141
\(100\) 0 0
\(101\) 1.29021 2.23470i 0.128380 0.222361i −0.794669 0.607043i \(-0.792356\pi\)
0.923049 + 0.384682i \(0.125689\pi\)
\(102\) 0 0
\(103\) 3.27182 + 5.66696i 0.322382 + 0.558382i 0.980979 0.194114i \(-0.0621832\pi\)
−0.658597 + 0.752496i \(0.728850\pi\)
\(104\) 0 0
\(105\) −7.26496 0.160897i −0.708987 0.0157020i
\(106\) 0 0
\(107\) −2.26496 3.92302i −0.218961 0.379252i 0.735529 0.677493i \(-0.236934\pi\)
−0.954491 + 0.298241i \(0.903600\pi\)
\(108\) 0 0
\(109\) 3.22132 5.57949i 0.308546 0.534418i −0.669498 0.742814i \(-0.733491\pi\)
0.978045 + 0.208396i \(0.0668242\pi\)
\(110\) 0 0
\(111\) −4.94950 −0.469786
\(112\) 0 0
\(113\) 8.00000 0.752577 0.376288 0.926503i \(-0.377200\pi\)
0.376288 + 0.926503i \(0.377200\pi\)
\(114\) 0 0
\(115\) −10.2902 + 17.8232i −0.959567 + 1.66202i
\(116\) 0 0
\(117\) −3.01839 5.22800i −0.279050 0.483329i
\(118\) 0 0
\(119\) −10.2902 + 16.9452i −0.943302 + 1.55337i
\(120\) 0 0
\(121\) 4.30859 + 7.46270i 0.391690 + 0.678427i
\(122\) 0 0
\(123\) −2.54364 + 4.40571i −0.229352 + 0.397249i
\(124\) 0 0
\(125\) −6.74657 −0.603431
\(126\) 0 0
\(127\) −3.79707 −0.336935 −0.168468 0.985707i \(-0.553882\pi\)
−0.168468 + 0.985707i \(0.553882\pi\)
\(128\) 0 0
\(129\) −1.72818 + 2.99330i −0.152158 + 0.263545i
\(130\) 0 0
\(131\) 0.771819 + 1.33683i 0.0674341 + 0.116799i 0.897771 0.440462i \(-0.145185\pi\)
−0.830337 + 0.557262i \(0.811852\pi\)
\(132\) 0 0
\(133\) −7.67768 14.0054i −0.665739 1.21442i
\(134\) 0 0
\(135\) 1.37328 + 2.37860i 0.118193 + 0.204717i
\(136\) 0 0
\(137\) −0.746568 + 1.29309i −0.0637836 + 0.110476i −0.896154 0.443744i \(-0.853650\pi\)
0.832370 + 0.554220i \(0.186983\pi\)
\(138\) 0 0
\(139\) 2.94950 0.250173 0.125087 0.992146i \(-0.460079\pi\)
0.125087 + 0.992146i \(0.460079\pi\)
\(140\) 0 0
\(141\) 9.49314 0.799466
\(142\) 0 0
\(143\) 4.65929 8.07013i 0.389630 0.674858i
\(144\) 0 0
\(145\) −1.72132 2.98141i −0.142948 0.247593i
\(146\) 0 0
\(147\) 3.76496 5.90128i 0.310528 0.486729i
\(148\) 0 0
\(149\) 0.746568 + 1.29309i 0.0611613 + 0.105934i 0.894985 0.446097i \(-0.147186\pi\)
−0.833823 + 0.552031i \(0.813853\pi\)
\(150\) 0 0
\(151\) 4.86642 8.42889i 0.396024 0.685933i −0.597208 0.802087i \(-0.703723\pi\)
0.993231 + 0.116154i \(0.0370565\pi\)
\(152\) 0 0
\(153\) 7.49314 0.605784
\(154\) 0 0
\(155\) −14.5299 −1.16707
\(156\) 0 0
\(157\) −4.54364 + 7.86981i −0.362622 + 0.628079i −0.988391 0.151929i \(-0.951452\pi\)
0.625770 + 0.780008i \(0.284785\pi\)
\(158\) 0 0
\(159\) −1.91692 3.32021i −0.152022 0.263309i
\(160\) 0 0
\(161\) −9.52991 17.3842i −0.751062 1.37007i
\(162\) 0 0
\(163\) 9.78334 + 16.9452i 0.766290 + 1.32725i 0.939562 + 0.342380i \(0.111233\pi\)
−0.173271 + 0.984874i \(0.555434\pi\)
\(164\) 0 0
\(165\) −2.11985 + 3.67169i −0.165030 + 0.285841i
\(166\) 0 0
\(167\) 11.8990 0.920772 0.460386 0.887719i \(-0.347711\pi\)
0.460386 + 0.887719i \(0.347711\pi\)
\(168\) 0 0
\(169\) 23.4426 1.80328
\(170\) 0 0
\(171\) −3.01839 + 5.22800i −0.230822 + 0.399795i
\(172\) 0 0
\(173\) −1.29021 2.23470i −0.0980925 0.169901i 0.812803 0.582539i \(-0.197941\pi\)
−0.910895 + 0.412638i \(0.864607\pi\)
\(174\) 0 0
\(175\) −3.49314 + 5.75227i −0.264056 + 0.434831i
\(176\) 0 0
\(177\) −2.77182 4.80093i −0.208343 0.360860i
\(178\) 0 0
\(179\) −1.49314 + 2.58619i −0.111602 + 0.193301i −0.916416 0.400226i \(-0.868932\pi\)
0.804814 + 0.593527i \(0.202265\pi\)
\(180\) 0 0
\(181\) −10.5436 −0.783702 −0.391851 0.920029i \(-0.628165\pi\)
−0.391851 + 0.920029i \(0.628165\pi\)
\(182\) 0 0
\(183\) 14.5804 1.07781
\(184\) 0 0
\(185\) −6.79707 + 11.7729i −0.499730 + 0.865559i
\(186\) 0 0
\(187\) 5.78334 + 10.0170i 0.422920 + 0.732519i
\(188\) 0 0
\(189\) −2.64510 0.0585812i −0.192403 0.00426115i
\(190\) 0 0
\(191\) 8.58041 + 14.8617i 0.620857 + 1.07536i 0.989327 + 0.145716i \(0.0465485\pi\)
−0.368470 + 0.929640i \(0.620118\pi\)
\(192\) 0 0
\(193\) −5.44950 + 9.43881i −0.392264 + 0.679420i −0.992748 0.120216i \(-0.961641\pi\)
0.600484 + 0.799637i \(0.294975\pi\)
\(194\) 0 0
\(195\) −16.5804 −1.18735
\(196\) 0 0
\(197\) 5.41959 0.386130 0.193065 0.981186i \(-0.438157\pi\)
0.193065 + 0.981186i \(0.438157\pi\)
\(198\) 0 0
\(199\) −11.4931 + 19.9067i −0.814727 + 1.41115i 0.0947970 + 0.995497i \(0.469780\pi\)
−0.909524 + 0.415652i \(0.863554\pi\)
\(200\) 0 0
\(201\) 2.01839 + 3.49595i 0.142366 + 0.246585i
\(202\) 0 0
\(203\) 3.31546 + 0.0734275i 0.232699 + 0.00515360i
\(204\) 0 0
\(205\) 6.98627 + 12.1006i 0.487942 + 0.845141i
\(206\) 0 0
\(207\) −3.74657 + 6.48925i −0.260404 + 0.451034i
\(208\) 0 0
\(209\) −9.31859 −0.644580
\(210\) 0 0
\(211\) −3.08727 −0.212537 −0.106268 0.994337i \(-0.533890\pi\)
−0.106268 + 0.994337i \(0.533890\pi\)
\(212\) 0 0
\(213\) 2.74657 4.75720i 0.188192 0.325958i
\(214\) 0 0
\(215\) 4.74657 + 8.22130i 0.323713 + 0.560688i
\(216\) 0 0
\(217\) 7.26496 11.9635i 0.493177 0.812132i
\(218\) 0 0
\(219\) 6.27182 + 10.8631i 0.423810 + 0.734061i
\(220\) 0 0
\(221\) −22.6172 + 39.1741i −1.52140 + 2.63514i
\(222\) 0 0
\(223\) 22.7466 1.52322 0.761611 0.648034i \(-0.224409\pi\)
0.761611 + 0.648034i \(0.224409\pi\)
\(224\) 0 0
\(225\) 2.54364 0.169576
\(226\) 0 0
\(227\) 11.3017 19.5752i 0.750122 1.29925i −0.197641 0.980274i \(-0.563328\pi\)
0.947763 0.318975i \(-0.103339\pi\)
\(228\) 0 0
\(229\) 5.67768 + 9.83403i 0.375192 + 0.649851i 0.990356 0.138548i \(-0.0442435\pi\)
−0.615164 + 0.788399i \(0.710910\pi\)
\(230\) 0 0
\(231\) −1.96323 3.58126i −0.129171 0.235630i
\(232\) 0 0
\(233\) −1.70979 2.96145i −0.112012 0.194011i 0.804569 0.593859i \(-0.202396\pi\)
−0.916582 + 0.399848i \(0.869063\pi\)
\(234\) 0 0
\(235\) 13.0368 22.5804i 0.850425 1.47298i
\(236\) 0 0
\(237\) −7.79707 −0.506474
\(238\) 0 0
\(239\) 7.49314 0.484691 0.242345 0.970190i \(-0.422083\pi\)
0.242345 + 0.970190i \(0.422083\pi\)
\(240\) 0 0
\(241\) 9.30173 16.1111i 0.599177 1.03781i −0.393766 0.919211i \(-0.628828\pi\)
0.992943 0.118594i \(-0.0378388\pi\)
\(242\) 0 0
\(243\) 0.500000 + 0.866025i 0.0320750 + 0.0555556i
\(244\) 0 0
\(245\) −8.86642 17.0594i −0.566455 1.08989i
\(246\) 0 0
\(247\) −18.2213 31.5602i −1.15939 2.00813i
\(248\) 0 0
\(249\) 3.26496 5.65507i 0.206908 0.358375i
\(250\) 0 0
\(251\) −24.5299 −1.54831 −0.774157 0.632994i \(-0.781826\pi\)
−0.774157 + 0.632994i \(0.781826\pi\)
\(252\) 0 0
\(253\) −11.5667 −0.727191
\(254\) 0 0
\(255\) 10.2902 17.8232i 0.644398 1.11613i
\(256\) 0 0
\(257\) 8.74657 + 15.1495i 0.545596 + 0.945000i 0.998569 + 0.0534758i \(0.0170300\pi\)
−0.452973 + 0.891524i \(0.649637\pi\)
\(258\) 0 0
\(259\) −6.29487 11.4829i −0.391144 0.713514i
\(260\) 0 0
\(261\) −0.626716 1.08550i −0.0387927 0.0671910i
\(262\) 0 0
\(263\) −6.74657 + 11.6854i −0.416011 + 0.720553i −0.995534 0.0944035i \(-0.969906\pi\)
0.579523 + 0.814956i \(0.303239\pi\)
\(264\) 0 0
\(265\) −10.5299 −0.646847
\(266\) 0 0
\(267\) 9.49314 0.580971
\(268\) 0 0
\(269\) −3.17035 + 5.49121i −0.193300 + 0.334805i −0.946342 0.323167i \(-0.895252\pi\)
0.753042 + 0.657972i \(0.228586\pi\)
\(270\) 0 0
\(271\) −10.1199 17.5281i −0.614737 1.06476i −0.990431 0.138012i \(-0.955929\pi\)
0.375693 0.926744i \(-0.377405\pi\)
\(272\) 0 0
\(273\) 8.29021 13.6518i 0.501746 0.826243i
\(274\) 0 0
\(275\) 1.96323 + 3.40041i 0.118387 + 0.205052i
\(276\) 0 0
\(277\) 1.27182 2.20285i 0.0764162 0.132357i −0.825285 0.564716i \(-0.808986\pi\)
0.901701 + 0.432360i \(0.142319\pi\)
\(278\) 0 0
\(279\) −5.29021 −0.316716
\(280\) 0 0
\(281\) 26.5804 1.58565 0.792827 0.609447i \(-0.208608\pi\)
0.792827 + 0.609447i \(0.208608\pi\)
\(282\) 0 0
\(283\) −10.2718 + 17.7913i −0.610596 + 1.05758i 0.380544 + 0.924763i \(0.375737\pi\)
−0.991140 + 0.132821i \(0.957597\pi\)
\(284\) 0 0
\(285\) 8.29021 + 14.3591i 0.491069 + 0.850557i
\(286\) 0 0
\(287\) −13.4564 0.298018i −0.794304 0.0175915i
\(288\) 0 0
\(289\) −19.5735 33.9024i −1.15139 1.99426i
\(290\) 0 0
\(291\) 0.771819 1.33683i 0.0452448 0.0783663i
\(292\) 0 0
\(293\) 5.25343 0.306909 0.153454 0.988156i \(-0.450960\pi\)
0.153454 + 0.988156i \(0.450960\pi\)
\(294\) 0 0
\(295\) −15.2260 −0.886491
\(296\) 0 0
\(297\) −0.771819 + 1.33683i −0.0447855 + 0.0775707i
\(298\) 0 0
\(299\) −22.6172 39.1741i −1.30799 2.26550i
\(300\) 0 0
\(301\) −9.14243 0.202478i −0.526961 0.0116706i
\(302\) 0 0
\(303\) −1.29021 2.23470i −0.0741204 0.128380i
\(304\) 0 0
\(305\) 20.0230 34.6809i 1.14652 1.98582i
\(306\) 0 0
\(307\) −14.8485 −0.847449 −0.423724 0.905791i \(-0.639277\pi\)
−0.423724 + 0.905791i \(0.639277\pi\)
\(308\) 0 0
\(309\) 6.54364 0.372255
\(310\) 0 0
\(311\) −0.949499 + 1.64458i −0.0538412 + 0.0932556i −0.891690 0.452647i \(-0.850480\pi\)
0.837849 + 0.545903i \(0.183813\pi\)
\(312\) 0 0
\(313\) 0.0436371 + 0.0755817i 0.00246652 + 0.00427213i 0.867256 0.497862i \(-0.165882\pi\)
−0.864790 + 0.502135i \(0.832548\pi\)
\(314\) 0 0
\(315\) −3.77182 + 6.21119i −0.212518 + 0.349961i
\(316\) 0 0
\(317\) −4.11985 7.13579i −0.231394 0.400786i 0.726825 0.686823i \(-0.240995\pi\)
−0.958219 + 0.286037i \(0.907662\pi\)
\(318\) 0 0
\(319\) 0.967422 1.67562i 0.0541652 0.0938169i
\(320\) 0 0
\(321\) −4.52991 −0.252835
\(322\) 0 0
\(323\) 45.2344 2.51691
\(324\) 0 0
\(325\) −7.67768 + 13.2981i −0.425881 + 0.737648i
\(326\) 0 0
\(327\) −3.22132 5.57949i −0.178139 0.308546i
\(328\) 0 0
\(329\) 12.0735 + 22.0242i 0.665636 + 1.21424i
\(330\) 0 0
\(331\) −2.76496 4.78904i −0.151976 0.263230i 0.779978 0.625807i \(-0.215230\pi\)
−0.931954 + 0.362577i \(0.881897\pi\)
\(332\) 0 0
\(333\) −2.47475 + 4.28639i −0.135615 + 0.234893i
\(334\) 0 0
\(335\) 11.0873 0.605763
\(336\) 0 0
\(337\) 7.17455 0.390823 0.195411 0.980721i \(-0.437396\pi\)
0.195411 + 0.980721i \(0.437396\pi\)
\(338\) 0 0
\(339\) 4.00000 6.92820i 0.217250 0.376288i
\(340\) 0 0
\(341\) −4.08308 7.07210i −0.221111 0.382976i
\(342\) 0 0
\(343\) 18.4794 + 1.22940i 0.997794 + 0.0663814i
\(344\) 0 0
\(345\) 10.2902 + 17.8232i 0.554006 + 0.959567i
\(346\) 0 0
\(347\) 12.0368 20.8483i 0.646168 1.11920i −0.337863 0.941195i \(-0.609704\pi\)
0.984030 0.178000i \(-0.0569627\pi\)
\(348\) 0 0
\(349\) −31.1608 −1.66800 −0.834000 0.551764i \(-0.813955\pi\)
−0.834000 + 0.551764i \(0.813955\pi\)
\(350\) 0 0
\(351\) −6.03677 −0.322219
\(352\) 0 0
\(353\) 5.08727 8.81142i 0.270768 0.468984i −0.698290 0.715814i \(-0.746056\pi\)
0.969059 + 0.246830i \(0.0793889\pi\)
\(354\) 0 0
\(355\) −7.54364 13.0660i −0.400375 0.693469i
\(356\) 0 0
\(357\) 9.52991 + 17.3842i 0.504376 + 0.920070i
\(358\) 0 0
\(359\) −16.1240 27.9277i −0.850995 1.47397i −0.880312 0.474396i \(-0.842667\pi\)
0.0293169 0.999570i \(-0.490667\pi\)
\(360\) 0 0
\(361\) −8.72132 + 15.1058i −0.459017 + 0.795040i
\(362\) 0 0
\(363\) 8.61718 0.452285
\(364\) 0 0
\(365\) 34.4520 1.80330
\(366\) 0 0
\(367\) 1.93531 3.35205i 0.101022 0.174976i −0.811084 0.584930i \(-0.801122\pi\)
0.912106 + 0.409954i \(0.134455\pi\)
\(368\) 0 0
\(369\) 2.54364 + 4.40571i 0.132416 + 0.229352i
\(370\) 0 0
\(371\) 5.26496 8.66999i 0.273343 0.450123i
\(372\) 0 0
\(373\) −17.3454 30.0431i −0.898109 1.55557i −0.829909 0.557899i \(-0.811608\pi\)
−0.0682000 0.997672i \(-0.521726\pi\)
\(374\) 0 0
\(375\) −3.37328 + 5.84270i −0.174196 + 0.301716i
\(376\) 0 0
\(377\) 7.56668 0.389704
\(378\) 0 0
\(379\) −13.4564 −0.691207 −0.345603 0.938381i \(-0.612326\pi\)
−0.345603 + 0.938381i \(0.612326\pi\)
\(380\) 0 0
\(381\) −1.89853 + 3.28836i −0.0972649 + 0.168468i
\(382\) 0 0
\(383\) 2.08727 + 3.61527i 0.106655 + 0.184731i 0.914413 0.404782i \(-0.132653\pi\)
−0.807758 + 0.589514i \(0.799319\pi\)
\(384\) 0 0
\(385\) −11.2145 0.248367i −0.571542 0.0126579i
\(386\) 0 0
\(387\) 1.72818 + 2.99330i 0.0878484 + 0.152158i
\(388\) 0 0
\(389\) 9.32698 16.1548i 0.472897 0.819081i −0.526622 0.850099i \(-0.676542\pi\)
0.999519 + 0.0310185i \(0.00987507\pi\)
\(390\) 0 0
\(391\) 56.1471 2.83948
\(392\) 0 0
\(393\) 1.54364 0.0778662
\(394\) 0 0
\(395\) −10.7076 + 18.5461i −0.538757 + 0.933155i
\(396\) 0 0
\(397\) 0.728181 + 1.26125i 0.0365464 + 0.0633002i 0.883720 0.468016i \(-0.155031\pi\)
−0.847174 + 0.531316i \(0.821698\pi\)
\(398\) 0 0
\(399\) −15.9679 0.353641i −0.799394 0.0177042i
\(400\) 0 0
\(401\) 14.6172 + 25.3177i 0.729947 + 1.26431i 0.956905 + 0.290401i \(0.0937888\pi\)
−0.226958 + 0.973905i \(0.572878\pi\)
\(402\) 0 0
\(403\) 15.9679 27.6572i 0.795417 1.37770i
\(404\) 0 0
\(405\) 2.74657 0.136478
\(406\) 0 0
\(407\) −7.64023 −0.378712
\(408\) 0 0
\(409\) −13.0299 + 22.5685i −0.644288 + 1.11594i 0.340178 + 0.940361i \(0.389513\pi\)
−0.984466 + 0.175578i \(0.943821\pi\)
\(410\) 0 0
\(411\) 0.746568 + 1.29309i 0.0368255 + 0.0637836i
\(412\) 0 0
\(413\) 7.61299 12.5366i 0.374611 0.616885i
\(414\) 0 0
\(415\) −8.96742 15.5320i −0.440193 0.762437i
\(416\) 0 0
\(417\) 1.47475 2.55434i 0.0722188 0.125087i
\(418\) 0 0
\(419\) −32.8853 −1.60655 −0.803275 0.595608i \(-0.796911\pi\)
−0.803275 + 0.595608i \(0.796911\pi\)
\(420\) 0 0
\(421\) −17.1976 −0.838160 −0.419080 0.907949i \(-0.637647\pi\)
−0.419080 + 0.907949i \(0.637647\pi\)
\(422\) 0 0
\(423\) 4.74657 8.22130i 0.230786 0.399733i
\(424\) 0 0
\(425\) −9.52991 16.5063i −0.462269 0.800673i
\(426\) 0 0
\(427\) 18.5436 + 33.8268i 0.897389 + 1.63699i
\(428\) 0 0
\(429\) −4.65929 8.07013i −0.224953 0.389630i
\(430\) 0 0
\(431\) 1.49314 2.58619i 0.0719219 0.124572i −0.827822 0.560991i \(-0.810420\pi\)
0.899744 + 0.436419i \(0.143753\pi\)
\(432\) 0 0
\(433\) 18.4426 0.886297 0.443148 0.896448i \(-0.353862\pi\)
0.443148 + 0.896448i \(0.353862\pi\)
\(434\) 0 0
\(435\) −3.44264 −0.165062
\(436\) 0 0
\(437\) −22.6172 + 39.1741i −1.08193 + 1.87395i
\(438\) 0 0
\(439\) 0.286010 + 0.495384i 0.0136505 + 0.0236434i 0.872770 0.488132i \(-0.162321\pi\)
−0.859119 + 0.511775i \(0.828988\pi\)
\(440\) 0 0
\(441\) −3.22818 6.21119i −0.153723 0.295771i
\(442\) 0 0
\(443\) 18.2650 + 31.6358i 0.867794 + 1.50306i 0.864246 + 0.503070i \(0.167796\pi\)
0.00354850 + 0.999994i \(0.498870\pi\)
\(444\) 0 0
\(445\) 13.0368 22.5804i 0.618002 1.07041i
\(446\) 0 0
\(447\) 1.49314 0.0706229
\(448\) 0 0
\(449\) −22.5530 −1.06434 −0.532170 0.846638i \(-0.678623\pi\)
−0.532170 + 0.846638i \(0.678623\pi\)
\(450\) 0 0
\(451\) −3.92645 + 6.80082i −0.184889 + 0.320238i
\(452\) 0 0
\(453\) −4.86642 8.42889i −0.228644 0.396024i
\(454\) 0 0
\(455\) −21.0873 38.4668i −0.988587 1.80335i
\(456\) 0 0
\(457\) −10.1172 17.5235i −0.473262 0.819714i 0.526270 0.850318i \(-0.323590\pi\)
−0.999532 + 0.0306040i \(0.990257\pi\)
\(458\) 0 0
\(459\) 3.74657 6.48925i 0.174875 0.302892i
\(460\) 0 0
\(461\) 25.4931 1.18733 0.593667 0.804711i \(-0.297680\pi\)
0.593667 + 0.804711i \(0.297680\pi\)
\(462\) 0 0
\(463\) 7.70446 0.358057 0.179028 0.983844i \(-0.442705\pi\)
0.179028 + 0.983844i \(0.442705\pi\)
\(464\) 0 0
\(465\) −7.26496 + 12.5833i −0.336904 + 0.583535i
\(466\) 0 0
\(467\) 18.0735 + 31.3043i 0.836344 + 1.44859i 0.892931 + 0.450193i \(0.148645\pi\)
−0.0565874 + 0.998398i \(0.518022\pi\)
\(468\) 0 0
\(469\) −5.54364 + 9.12890i −0.255981 + 0.421534i
\(470\) 0 0
\(471\) 4.54364 + 7.86981i 0.209360 + 0.362622i
\(472\) 0 0
\(473\) −2.66769 + 4.62057i −0.122660 + 0.212454i
\(474\) 0 0
\(475\) 15.3554 0.704552
\(476\) 0 0
\(477\) −3.83384 −0.175540
\(478\) 0 0
\(479\) 13.2902 23.0193i 0.607245 1.05178i −0.384447 0.923147i \(-0.625608\pi\)
0.991692 0.128632i \(-0.0410587\pi\)
\(480\) 0 0
\(481\) −14.9395 25.8760i −0.681183 1.17984i
\(482\) 0 0
\(483\) −19.8201 0.438957i −0.901846 0.0199732i
\(484\) 0 0
\(485\) −2.11985 3.67169i −0.0962575 0.166723i
\(486\) 0 0
\(487\) −20.2118 + 35.0078i −0.915883 + 1.58636i −0.110281 + 0.993900i \(0.535175\pi\)
−0.805603 + 0.592456i \(0.798158\pi\)
\(488\) 0 0
\(489\) 19.5667 0.884836
\(490\) 0 0
\(491\) −14.6309 −0.660284 −0.330142 0.943931i \(-0.607097\pi\)
−0.330142 + 0.943931i \(0.607097\pi\)
\(492\) 0 0
\(493\) −4.69607 + 8.13383i −0.211500 + 0.366329i
\(494\) 0 0
\(495\) 2.11985 + 3.67169i 0.0952803 + 0.165030i
\(496\) 0 0
\(497\) 14.5299 + 0.321794i 0.651756 + 0.0144344i
\(498\) 0 0
\(499\) −18.0552 31.2725i −0.808260 1.39995i −0.914068 0.405561i \(-0.867076\pi\)
0.105808 0.994387i \(-0.466257\pi\)
\(500\) 0 0
\(501\) 5.94950 10.3048i 0.265804 0.460386i
\(502\) 0 0
\(503\) −19.4931 −0.869156 −0.434578 0.900634i \(-0.643102\pi\)
−0.434578 + 0.900634i \(0.643102\pi\)
\(504\) 0 0
\(505\) −7.08727 −0.315380
\(506\) 0 0
\(507\) 11.7213 20.3019i 0.520562 0.901640i
\(508\) 0 0
\(509\) 11.9537 + 20.7044i 0.529838 + 0.917707i 0.999394 + 0.0348040i \(0.0110807\pi\)
−0.469556 + 0.882903i \(0.655586\pi\)
\(510\) 0 0
\(511\) −17.2260 + 28.3666i −0.762032 + 1.25487i
\(512\) 0 0
\(513\) 3.01839 + 5.22800i 0.133265 + 0.230822i
\(514\) 0 0
\(515\) 8.98627 15.5647i 0.395982 0.685862i
\(516\) 0 0
\(517\) 14.6540 0.644480
\(518\) 0 0
\(519\) −2.58041 −0.113267
\(520\) 0 0
\(521\) 3.54364 6.13776i 0.155250 0.268900i −0.777900 0.628388i \(-0.783715\pi\)
0.933150 + 0.359488i \(0.117048\pi\)
\(522\) 0 0
\(523\) −14.3737 24.8961i −0.628520 1.08863i −0.987849 0.155418i \(-0.950328\pi\)
0.359329 0.933211i \(-0.383006\pi\)
\(524\) 0 0
\(525\) 3.23504 + 5.90128i 0.141189 + 0.257553i
\(526\) 0 0
\(527\) 19.8201 + 34.3294i 0.863378 + 1.49541i
\(528\) 0 0
\(529\) −16.5735 + 28.7062i −0.720589 + 1.24810i
\(530\) 0 0
\(531\) −5.54364 −0.240573
\(532\) 0 0
\(533\) −30.7107 −1.33023
\(534\) 0 0
\(535\) −6.22085 + 10.7748i −0.268951 + 0.465837i
\(536\) 0 0
\(537\) 1.49314 + 2.58619i 0.0644336 + 0.111602i
\(538\) 0 0
\(539\) 5.81172 9.10944i 0.250329 0.392371i
\(540\) 0 0
\(541\) 3.51152 + 6.08214i 0.150972 + 0.261491i 0.931585 0.363523i \(-0.118426\pi\)
−0.780613 + 0.625015i \(0.785093\pi\)
\(542\) 0 0
\(543\) −5.27182 + 9.13106i −0.226235 + 0.391851i
\(544\) 0 0
\(545\) −17.6951 −0.757976
\(546\) 0 0
\(547\) −5.59414 −0.239188 −0.119594 0.992823i \(-0.538159\pi\)
−0.119594 + 0.992823i \(0.538159\pi\)
\(548\) 0 0
\(549\) 7.29021 12.6270i 0.311138 0.538907i
\(550\) 0 0
\(551\) −3.78334 6.55294i −0.161176 0.279165i
\(552\) 0 0
\(553\) −9.91646 18.0893i −0.421691 0.769237i
\(554\) 0 0
\(555\) 6.79707 + 11.7729i 0.288520 + 0.499730i
\(556\) 0 0
\(557\) −14.3228 + 24.8078i −0.606876 + 1.05114i 0.384876 + 0.922968i \(0.374244\pi\)
−0.991752 + 0.128172i \(0.959089\pi\)
\(558\) 0 0
\(559\) −20.8653 −0.882507
\(560\) 0 0
\(561\) 11.5667 0.488346
\(562\) 0 0
\(563\) −9.94637 + 17.2276i −0.419189 + 0.726057i −0.995858 0.0909207i \(-0.971019\pi\)
0.576669 + 0.816978i \(0.304352\pi\)
\(564\) 0 0
\(565\) −10.9863 19.0288i −0.462196 0.800547i
\(566\) 0 0
\(567\) −1.37328 + 2.26144i −0.0576725 + 0.0949714i
\(568\) 0 0
\(569\) −17.8201 30.8653i −0.747058 1.29394i −0.949227 0.314592i \(-0.898132\pi\)
0.202169 0.979351i \(-0.435201\pi\)
\(570\) 0 0
\(571\) −13.8385 + 23.9690i −0.579123 + 1.00307i 0.416457 + 0.909155i \(0.363272\pi\)
−0.995580 + 0.0939155i \(0.970062\pi\)
\(572\) 0 0
\(573\) 17.1608 0.716904
\(574\) 0 0
\(575\) 19.0598 0.794849
\(576\) 0 0
\(577\) 3.00686 5.20804i 0.125177 0.216814i −0.796625 0.604474i \(-0.793383\pi\)
0.921802 + 0.387660i \(0.126717\pi\)
\(578\) 0 0
\(579\) 5.44950 + 9.43881i 0.226473 + 0.392264i
\(580\) 0 0
\(581\) 17.2723 + 0.382530i 0.716575 + 0.0158700i
\(582\) 0 0
\(583\) −2.95903 5.12519i −0.122551 0.212264i
\(584\) 0 0
\(585\) −8.29021 + 14.3591i −0.342758 + 0.593674i
\(586\) 0 0
\(587\) −15.5436 −0.641555 −0.320777 0.947155i \(-0.603944\pi\)
−0.320777 + 0.947155i \(0.603944\pi\)
\(588\) 0 0
\(589\) −31.9358 −1.31589
\(590\) 0 0
\(591\) 2.70979 4.69350i 0.111466 0.193065i
\(592\) 0 0
\(593\) 24.3270 + 42.1356i 0.998989 + 1.73030i 0.538421 + 0.842676i \(0.319021\pi\)
0.460568 + 0.887624i \(0.347646\pi\)
\(594\) 0 0
\(595\) 54.4373 + 1.20562i 2.23171 + 0.0494258i
\(596\) 0 0
\(597\) 11.4931 + 19.9067i 0.470383 + 0.814727i
\(598\) 0 0
\(599\) −10.4564 + 18.1110i −0.427235 + 0.739993i −0.996626 0.0820735i \(-0.973846\pi\)
0.569391 + 0.822067i \(0.307179\pi\)
\(600\) 0 0
\(601\) −7.98627 −0.325767 −0.162883 0.986645i \(-0.552079\pi\)
−0.162883 + 0.986645i \(0.552079\pi\)
\(602\) 0 0
\(603\) 4.03677 0.164390
\(604\) 0 0
\(605\) 11.8338 20.4968i 0.481114 0.833314i
\(606\) 0 0
\(607\) 1.35490 + 2.34675i 0.0549936 + 0.0952517i 0.892212 0.451618i \(-0.149153\pi\)
−0.837218 + 0.546869i \(0.815819\pi\)
\(608\) 0 0
\(609\) 1.72132 2.83456i 0.0697513 0.114862i
\(610\) 0 0
\(611\) 28.6540 + 49.6301i 1.15922 + 2.00782i
\(612\) 0 0
\(613\) 8.25343 14.2954i 0.333353 0.577384i −0.649814 0.760093i \(-0.725153\pi\)
0.983167 + 0.182709i \(0.0584866\pi\)
\(614\) 0 0
\(615\) 13.9725 0.563427
\(616\) 0 0
\(617\) −23.1608 −0.932420 −0.466210 0.884674i \(-0.654381\pi\)
−0.466210 + 0.884674i \(0.654381\pi\)
\(618\) 0 0
\(619\) −14.7145 + 25.4862i −0.591424 + 1.02438i 0.402617 + 0.915369i \(0.368101\pi\)
−0.994041 + 0.109008i \(0.965233\pi\)
\(620\) 0 0
\(621\) 3.74657 + 6.48925i 0.150345 + 0.260404i
\(622\) 0 0
\(623\) 12.0735 + 22.0242i 0.483716 + 0.882382i
\(624\) 0 0
\(625\) 15.6240 + 27.0616i 0.624962 + 1.08247i
\(626\) 0 0
\(627\) −4.65929 + 8.07013i −0.186074 + 0.322290i
\(628\) 0 0
\(629\) 37.0873 1.47877
\(630\) 0 0
\(631\) 35.7054 1.42141 0.710705 0.703491i \(-0.248376\pi\)
0.710705 + 0.703491i \(0.248376\pi\)
\(632\) 0 0
\(633\) −1.54364 + 2.67366i −0.0613541 + 0.106268i
\(634\) 0 0
\(635\) 5.21445 + 9.03170i 0.206929 + 0.358412i
\(636\) 0 0
\(637\) 42.2160 + 1.87083i 1.67266 + 0.0741252i
\(638\) 0 0
\(639\) −2.74657 4.75720i −0.108653 0.188192i
\(640\) 0 0
\(641\) 1.68141 2.91229i 0.0664118 0.115029i −0.830908 0.556410i \(-0.812178\pi\)
0.897319 + 0.441382i \(0.145512\pi\)
\(642\) 0 0
\(643\) −10.2113 −0.402695 −0.201348 0.979520i \(-0.564532\pi\)
−0.201348 + 0.979520i \(0.564532\pi\)
\(644\) 0 0
\(645\) 9.49314 0.373792
\(646\) 0 0
\(647\) −10.2765 + 17.7994i −0.404010 + 0.699766i −0.994206 0.107494i \(-0.965717\pi\)
0.590196 + 0.807260i \(0.299051\pi\)
\(648\) 0 0
\(649\) −4.27868 7.41089i −0.167953 0.290903i
\(650\) 0 0
\(651\) −6.72818 12.2734i −0.263698 0.481031i
\(652\) 0 0
\(653\) 5.67722 + 9.83323i 0.222167 + 0.384804i 0.955466 0.295102i \(-0.0953538\pi\)
−0.733299 + 0.679906i \(0.762020\pi\)
\(654\) 0 0
\(655\) 2.11985 3.67169i 0.0828295 0.143465i
\(656\) 0 0
\(657\) 12.5436 0.489374
\(658\) 0 0
\(659\) −21.2344 −0.827174 −0.413587 0.910465i \(-0.635724\pi\)
−0.413587 + 0.910465i \(0.635724\pi\)
\(660\) 0 0
\(661\) 14.4610 25.0472i 0.562469 0.974224i −0.434812 0.900521i \(-0.643185\pi\)
0.997280 0.0737028i \(-0.0234816\pi\)
\(662\) 0 0
\(663\) 22.6172 + 39.1741i 0.878379 + 1.52140i
\(664\) 0 0
\(665\) −22.7696 + 37.4955i −0.882968 + 1.45401i
\(666\) 0 0
\(667\) −4.69607 8.13383i −0.181832 0.314943i
\(668\) 0 0
\(669\) 11.3733 19.6991i 0.439717 0.761611i
\(670\) 0 0
\(671\) 22.5069 0.868868
\(672\) 0 0
\(673\) −34.2618 −1.32070 −0.660348 0.750960i \(-0.729591\pi\)
−0.660348 + 0.750960i \(0.729591\pi\)
\(674\) 0 0
\(675\) 1.27182 2.20285i 0.0489523 0.0847879i
\(676\) 0 0
\(677\) −17.3733 30.0914i −0.667710 1.15651i −0.978543 0.206042i \(-0.933941\pi\)
0.310833 0.950464i \(-0.399392\pi\)
\(678\) 0 0
\(679\) 4.08308 + 0.0904281i 0.156694 + 0.00347031i
\(680\) 0 0
\(681\) −11.3017 19.5752i −0.433083 0.750122i
\(682\) 0 0
\(683\) 0.140907 0.244058i 0.00539166 0.00933863i −0.863317 0.504662i \(-0.831617\pi\)
0.868709 + 0.495323i \(0.164950\pi\)
\(684\) 0 0
\(685\) 4.10100 0.156691
\(686\) 0 0
\(687\) 11.3554 0.433234
\(688\) 0 0
\(689\) 11.5720 20.0433i 0.440859 0.763590i
\(690\) 0 0
\(691\) 17.2076 + 29.8044i 0.654608 + 1.13381i 0.981992 + 0.188922i \(0.0604995\pi\)
−0.327384 + 0.944891i \(0.606167\pi\)
\(692\) 0 0
\(693\) −4.08308 0.0904281i −0.155103 0.00343508i
\(694\) 0 0
\(695\) −4.05050 7.01567i −0.153644 0.266120i
\(696\) 0 0
\(697\) 19.0598 33.0126i 0.721942 1.25044i
\(698\) 0 0
\(699\) −3.41959 −0.129341
\(700\) 0 0
\(701\) −0.498472 −0.0188270 −0.00941352 0.999956i \(-0.502996\pi\)
−0.00941352 + 0.999956i \(0.502996\pi\)
\(702\) 0 0
\(703\) −14.9395 + 25.8760i −0.563454 + 0.975931i
\(704\) 0 0
\(705\) −13.0368 22.5804i −0.490993 0.850425i
\(706\) 0 0
\(707\) 3.54364 5.83543i 0.133272 0.219464i
\(708\) 0 0
\(709\) 2.08727 + 3.61527i 0.0783892 + 0.135774i 0.902555 0.430574i \(-0.141689\pi\)
−0.824166 + 0.566348i \(0.808356\pi\)
\(710\) 0 0
\(711\) −3.89853 + 6.75246i −0.146206 + 0.253237i
\(712\) 0 0
\(713\) −39.6402 −1.48454
\(714\) 0 0
\(715\) −25.5941 −0.957166
\(716\) 0 0
\(717\) 3.74657 6.48925i 0.139918 0.242345i
\(718\) 0 0
\(719\) −0.493136 0.854137i −0.0183909 0.0318540i 0.856683 0.515842i \(-0.172521\pi\)
−0.875074 + 0.483988i \(0.839188\pi\)
\(720\) 0 0
\(721\) 8.32232 + 15.1813i 0.309939 + 0.565383i
\(722\) 0 0
\(723\) −9.30173 16.1111i −0.345935 0.599177i
\(724\) 0 0
\(725\) −1.59414 + 2.76113i −0.0592048 + 0.102546i
\(726\) 0 0
\(727\) 34.9304 1.29550 0.647749 0.761854i \(-0.275711\pi\)
0.647749 + 0.761854i \(0.275711\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) 12.9495 22.4292i 0.478955 0.829574i
\(732\) 0 0
\(733\) −2.56202 4.43756i −0.0946305 0.163905i 0.814824 0.579709i \(-0.196834\pi\)
−0.909454 + 0.415804i \(0.863500\pi\)
\(734\) 0 0
\(735\) −19.2071 0.851179i −0.708466 0.0313962i
\(736\) 0 0
\(737\) 3.11566 + 5.39648i 0.114767 + 0.198782i
\(738\) 0 0
\(739\) −8.46102 + 14.6549i −0.311244 + 0.539090i −0.978632 0.205620i \(-0.934079\pi\)
0.667388 + 0.744710i \(0.267412\pi\)
\(740\) 0 0
\(741\) −36.4426 −1.33875
\(742\) 0 0
\(743\) −6.81172 −0.249898 −0.124949 0.992163i \(-0.539877\pi\)
−0.124949 + 0.992163i \(0.539877\pi\)
\(744\) 0 0
\(745\) 2.05050 3.55157i 0.0751245 0.130120i
\(746\) 0 0
\(747\) −3.26496 5.65507i −0.119458 0.206908i
\(748\) 0 0
\(749\) −5.76122 10.5095i −0.210511 0.384008i
\(750\) 0 0
\(751\) −13.0877 22.6686i −0.477578 0.827190i 0.522091 0.852890i \(-0.325152\pi\)
−0.999670 + 0.0256996i \(0.991819\pi\)
\(752\) 0 0
\(753\) −12.2650 + 21.2435i −0.446960 + 0.774157i
\(754\) 0 0
\(755\) −26.7319 −0.972874
\(756\) 0 0
\(757\) 49.7138 1.80688 0.903439 0.428717i \(-0.141034\pi\)
0.903439 + 0.428717i \(0.141034\pi\)
\(758\) 0 0
\(759\) −5.78334 + 10.0170i −0.209922 + 0.363596i
\(760\) 0 0
\(761\) 6.32698 + 10.9586i 0.229353 + 0.397251i 0.957616 0.288046i \(-0.0930057\pi\)
−0.728264 + 0.685297i \(0.759672\pi\)
\(762\) 0 0
\(763\) 8.84757 14.5696i 0.320304 0.527455i
\(764\) 0 0
\(765\) −10.2902 17.8232i −0.372043 0.644398i
\(766\) 0 0
\(767\) 16.7328 28.9821i 0.604188 1.04648i
\(768\) 0 0
\(769\) −20.2344 −0.729670 −0.364835 0.931072i \(-0.618875\pi\)
−0.364835 + 0.931072i \(0.618875\pi\)
\(770\) 0 0
\(771\) 17.4931 0.630000
\(772\) 0 0
\(773\) 9.87062 17.0964i 0.355021 0.614915i −0.632100 0.774887i \(-0.717807\pi\)
0.987122 + 0.159972i \(0.0511402\pi\)
\(774\) 0 0
\(775\) 6.72818 + 11.6536i 0.241683 + 0.418608i
\(776\) 0 0
\(777\) −13.0919 0.289947i −0.469671 0.0104018i
\(778\) 0 0
\(779\) 15.3554 + 26.5963i 0.550163 + 0.952910i
\(780\) 0 0
\(781\) 4.23970 7.34338i 0.151709 0.262767i
\(782\) 0 0
\(783\) −1.25343 −0.0447940
\(784\) 0 0
\(785\) 24.9588 0.890818
\(786\) 0 0
\(787\) −8.45636 + 14.6469i −0.301437 + 0.522104i −0.976462 0.215691i \(-0.930800\pi\)
0.675025 + 0.737795i \(0.264133\pi\)
\(788\) 0 0
\(789\) 6.74657 + 11.6854i 0.240184 + 0.416011i
\(790\) 0 0
\(791\) 21.1608 + 0.468649i 0.752392 + 0.0166633i
\(792\) 0 0
\(793\) 44.0093 + 76.2264i 1.56282 + 2.70688i
\(794\) 0 0
\(795\) −5.26496 + 9.11917i −0.186729 + 0.323424i
\(796\) 0 0
\(797\) 3.48475 0.123436 0.0617180 0.998094i \(-0.480342\pi\)
0.0617180 + 0.998094i \(0.480342\pi\)