Properties

Label 804.2.q.b.25.6
Level 804
Weight 2
Character 804.25
Analytic conductor 6.420
Analytic rank 0
Dimension 60
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) = \( 804 = 2^{2} \cdot 3 \cdot 67 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 804.q (of order \(11\), degree \(10\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.41997232251\)
Analytic rank: \(0\)
Dimension: \(60\)
Relative dimension: \(6\) over \(\Q(\zeta_{11})\)
Coefficient ring index: multiple of None
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label 25.6
Character \(\chi\) = 804.25
Dual form 804.2.q.b.193.6

$q$-expansion

\(f(q)\) \(=\) \(q+(0.654861 - 0.755750i) q^{3} +(2.59336 - 1.66665i) q^{5} +(0.180977 + 1.25872i) q^{7} +(-0.142315 - 0.989821i) q^{9} +O(q^{10})\) \(q+(0.654861 - 0.755750i) q^{3} +(2.59336 - 1.66665i) q^{5} +(0.180977 + 1.25872i) q^{7} +(-0.142315 - 0.989821i) q^{9} +(4.04726 - 2.60101i) q^{11} +(-2.03230 + 4.45011i) q^{13} +(0.438719 - 3.05136i) q^{15} +(3.53314 + 1.03742i) q^{17} +(0.417152 - 2.90136i) q^{19} +(1.06979 + 0.687514i) q^{21} +(-1.78008 + 2.05432i) q^{23} +(1.87072 - 4.09630i) q^{25} +(-0.841254 - 0.540641i) q^{27} +1.04126 q^{29} +(-1.99390 - 4.36603i) q^{31} +(0.684674 - 4.76201i) q^{33} +(2.56719 + 2.96269i) q^{35} -7.59300 q^{37} +(2.03230 + 4.45011i) q^{39} +(-4.78280 - 1.40436i) q^{41} +(10.2741 + 3.01674i) q^{43} +(-2.01876 - 2.32977i) q^{45} +(-0.421438 + 0.486365i) q^{47} +(5.16482 - 1.51653i) q^{49} +(3.09774 - 1.99080i) q^{51} +(-13.4486 + 3.94887i) q^{53} +(6.16101 - 13.4907i) q^{55} +(-1.91952 - 2.21525i) q^{57} +(-1.53624 - 3.36389i) q^{59} +(-0.360924 - 0.231952i) q^{61} +(1.22015 - 0.358269i) q^{63} +(2.14630 + 14.9279i) q^{65} +(-5.33324 - 6.20939i) q^{67} +(0.386848 + 2.69059i) q^{69} +(9.46015 - 2.77775i) q^{71} +(-0.916042 - 0.588705i) q^{73} +(-1.87072 - 4.09630i) q^{75} +(4.00641 + 4.62365i) q^{77} +(1.64183 - 3.59510i) q^{79} +(-0.959493 + 0.281733i) q^{81} +(-4.80142 + 3.08568i) q^{83} +(10.8917 - 3.19810i) q^{85} +(0.681883 - 0.786935i) q^{87} +(8.42570 + 9.72377i) q^{89} +(-5.96924 - 1.75273i) q^{91} +(-4.60536 - 1.35225i) q^{93} +(-3.75372 - 8.21951i) q^{95} -5.06821 q^{97} +(-3.15052 - 3.63590i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 60q + 6q^{3} + 2q^{5} + 2q^{7} - 6q^{9} + O(q^{10}) \) \( 60q + 6q^{3} + 2q^{5} + 2q^{7} - 6q^{9} - 11q^{11} - 2q^{13} + 9q^{15} + 21q^{17} + 10q^{19} - 2q^{21} - 10q^{23} - 36q^{25} + 6q^{27} + 4q^{29} - 24q^{31} - 32q^{35} + 2q^{37} + 2q^{39} + 10q^{41} + 23q^{43} + 2q^{45} + 66q^{47} + 34q^{49} + 23q^{51} - 13q^{53} + 27q^{55} + q^{57} + 35q^{59} + 56q^{61} - 9q^{63} + 48q^{65} + 13q^{67} + 10q^{69} + 76q^{71} - q^{73} + 36q^{75} - 38q^{77} - 46q^{79} - 6q^{81} - 26q^{83} + 42q^{85} + 7q^{87} + 58q^{89} - 40q^{91} - 9q^{93} - 29q^{95} - 46q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/804\mathbb{Z}\right)^\times\).

\(n\) \(269\) \(337\) \(403\)
\(\chi(n)\) \(1\) \(e\left(\frac{5}{11}\right)\) \(1\)

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
\(3\) 0.654861 0.755750i 0.378084 0.436332i
\(4\) 0 0
\(5\) 2.59336 1.66665i 1.15979 0.745349i 0.188222 0.982126i \(-0.439728\pi\)
0.971564 + 0.236777i \(0.0760912\pi\)
\(6\) 0 0
\(7\) 0.180977 + 1.25872i 0.0684028 + 0.475752i 0.995014 + 0.0997319i \(0.0317985\pi\)
−0.926612 + 0.376020i \(0.877292\pi\)
\(8\) 0 0
\(9\) −0.142315 0.989821i −0.0474383 0.329940i
\(10\) 0 0
\(11\) 4.04726 2.60101i 1.22029 0.784235i 0.237942 0.971279i \(-0.423527\pi\)
0.982352 + 0.187044i \(0.0598907\pi\)
\(12\) 0 0
\(13\) −2.03230 + 4.45011i −0.563658 + 1.23424i 0.386449 + 0.922311i \(0.373702\pi\)
−0.950106 + 0.311927i \(0.899026\pi\)
\(14\) 0 0
\(15\) 0.438719 3.05136i 0.113277 0.787857i
\(16\) 0 0
\(17\) 3.53314 + 1.03742i 0.856911 + 0.251612i 0.680539 0.732712i \(-0.261746\pi\)
0.176372 + 0.984324i \(0.443564\pi\)
\(18\) 0 0
\(19\) 0.417152 2.90136i 0.0957013 0.665617i −0.884343 0.466838i \(-0.845393\pi\)
0.980044 0.198779i \(-0.0636977\pi\)
\(20\) 0 0
\(21\) 1.06979 + 0.687514i 0.233448 + 0.150028i
\(22\) 0 0
\(23\) −1.78008 + 2.05432i −0.371172 + 0.428355i −0.910352 0.413836i \(-0.864189\pi\)
0.539180 + 0.842191i \(0.318734\pi\)
\(24\) 0 0
\(25\) 1.87072 4.09630i 0.374143 0.819259i
\(26\) 0 0
\(27\) −0.841254 0.540641i −0.161899 0.104046i
\(28\) 0 0
\(29\) 1.04126 0.193358 0.0966790 0.995316i \(-0.469178\pi\)
0.0966790 + 0.995316i \(0.469178\pi\)
\(30\) 0 0
\(31\) −1.99390 4.36603i −0.358115 0.784163i −0.999851 0.0172375i \(-0.994513\pi\)
0.641736 0.766925i \(-0.278214\pi\)
\(32\) 0 0
\(33\) 0.684674 4.76201i 0.119187 0.828960i
\(34\) 0 0
\(35\) 2.56719 + 2.96269i 0.433934 + 0.500786i
\(36\) 0 0
\(37\) −7.59300 −1.24828 −0.624141 0.781312i \(-0.714551\pi\)
−0.624141 + 0.781312i \(0.714551\pi\)
\(38\) 0 0
\(39\) 2.03230 + 4.45011i 0.325428 + 0.712588i
\(40\) 0 0
\(41\) −4.78280 1.40436i −0.746948 0.219324i −0.113960 0.993485i \(-0.536354\pi\)
−0.632988 + 0.774162i \(0.718172\pi\)
\(42\) 0 0
\(43\) 10.2741 + 3.01674i 1.56678 + 0.460049i 0.946063 0.323983i \(-0.105022\pi\)
0.620721 + 0.784032i \(0.286840\pi\)
\(44\) 0 0
\(45\) −2.01876 2.32977i −0.300939 0.347302i
\(46\) 0 0
\(47\) −0.421438 + 0.486365i −0.0614731 + 0.0709437i −0.785653 0.618667i \(-0.787673\pi\)
0.724180 + 0.689611i \(0.242218\pi\)
\(48\) 0 0
\(49\) 5.16482 1.51653i 0.737832 0.216647i
\(50\) 0 0
\(51\) 3.09774 1.99080i 0.433771 0.278768i
\(52\) 0 0
\(53\) −13.4486 + 3.94887i −1.84731 + 0.542418i −0.847373 + 0.530998i \(0.821817\pi\)
−0.999935 + 0.0114203i \(0.996365\pi\)
\(54\) 0 0
\(55\) 6.16101 13.4907i 0.830751 1.81909i
\(56\) 0 0
\(57\) −1.91952 2.21525i −0.254247 0.293417i
\(58\) 0 0
\(59\) −1.53624 3.36389i −0.200001 0.437941i 0.782883 0.622170i \(-0.213749\pi\)
−0.982883 + 0.184229i \(0.941021\pi\)
\(60\) 0 0
\(61\) −0.360924 0.231952i −0.0462116 0.0296984i 0.517331 0.855785i \(-0.326926\pi\)
−0.563543 + 0.826087i \(0.690562\pi\)
\(62\) 0 0
\(63\) 1.22015 0.358269i 0.153725 0.0451377i
\(64\) 0 0
\(65\) 2.14630 + 14.9279i 0.266216 + 1.85157i
\(66\) 0 0
\(67\) −5.33324 6.20939i −0.651559 0.758598i
\(68\) 0 0
\(69\) 0.386848 + 2.69059i 0.0465710 + 0.323908i
\(70\) 0 0
\(71\) 9.46015 2.77775i 1.12271 0.329658i 0.332874 0.942971i \(-0.391982\pi\)
0.789840 + 0.613313i \(0.210164\pi\)
\(72\) 0 0
\(73\) −0.916042 0.588705i −0.107215 0.0689027i 0.485935 0.873995i \(-0.338479\pi\)
−0.593149 + 0.805092i \(0.702116\pi\)
\(74\) 0 0
\(75\) −1.87072 4.09630i −0.216012 0.473000i
\(76\) 0 0
\(77\) 4.00641 + 4.62365i 0.456573 + 0.526913i
\(78\) 0 0
\(79\) 1.64183 3.59510i 0.184720 0.404480i −0.794505 0.607258i \(-0.792270\pi\)
0.979225 + 0.202778i \(0.0649969\pi\)
\(80\) 0 0
\(81\) −0.959493 + 0.281733i −0.106610 + 0.0313036i
\(82\) 0 0
\(83\) −4.80142 + 3.08568i −0.527024 + 0.338698i −0.776945 0.629568i \(-0.783232\pi\)
0.249921 + 0.968266i \(0.419595\pi\)
\(84\) 0 0
\(85\) 10.8917 3.19810i 1.18137 0.346882i
\(86\) 0 0
\(87\) 0.681883 0.786935i 0.0731056 0.0843683i
\(88\) 0 0
\(89\) 8.42570 + 9.72377i 0.893122 + 1.03072i 0.999338 + 0.0363747i \(0.0115810\pi\)
−0.106216 + 0.994343i \(0.533874\pi\)
\(90\) 0 0
\(91\) −5.96924 1.75273i −0.625747 0.183736i
\(92\) 0 0
\(93\) −4.60536 1.35225i −0.477553 0.140222i
\(94\) 0 0
\(95\) −3.75372 8.21951i −0.385124 0.843304i
\(96\) 0 0
\(97\) −5.06821 −0.514598 −0.257299 0.966332i \(-0.582833\pi\)
−0.257299 + 0.966332i \(0.582833\pi\)
\(98\) 0 0
\(99\) −3.15052 3.63590i −0.316640 0.365422i
\(100\) 0 0
\(101\) 1.61568 11.2373i 0.160766 1.11815i −0.736429 0.676515i \(-0.763489\pi\)
0.897195 0.441635i \(-0.145601\pi\)
\(102\) 0 0
\(103\) 3.99109 + 8.73926i 0.393253 + 0.861105i 0.997910 + 0.0646185i \(0.0205830\pi\)
−0.604657 + 0.796486i \(0.706690\pi\)
\(104\) 0 0
\(105\) 3.92020 0.382573
\(106\) 0 0
\(107\) 1.67901 + 1.07903i 0.162316 + 0.104314i 0.619277 0.785173i \(-0.287426\pi\)
−0.456961 + 0.889487i \(0.651062\pi\)
\(108\) 0 0
\(109\) −6.37773 + 13.9653i −0.610876 + 1.33763i 0.311097 + 0.950378i \(0.399304\pi\)
−0.921973 + 0.387254i \(0.873424\pi\)
\(110\) 0 0
\(111\) −4.97236 + 5.73841i −0.471955 + 0.544666i
\(112\) 0 0
\(113\) 10.4150 + 6.69331i 0.979760 + 0.629654i 0.929399 0.369077i \(-0.120326\pi\)
0.0503616 + 0.998731i \(0.483963\pi\)
\(114\) 0 0
\(115\) −1.19255 + 8.29436i −0.111206 + 0.773453i
\(116\) 0 0
\(117\) 4.69404 + 1.37829i 0.433964 + 0.127423i
\(118\) 0 0
\(119\) −0.666410 + 4.63498i −0.0610897 + 0.424888i
\(120\) 0 0
\(121\) 5.04545 11.0480i 0.458677 1.00436i
\(122\) 0 0
\(123\) −4.19341 + 2.69494i −0.378107 + 0.242995i
\(124\) 0 0
\(125\) 0.217935 + 1.51577i 0.0194927 + 0.135575i
\(126\) 0 0
\(127\) −2.42585 16.8721i −0.215259 1.49716i −0.755221 0.655470i \(-0.772471\pi\)
0.539962 0.841689i \(-0.318439\pi\)
\(128\) 0 0
\(129\) 9.00800 5.78909i 0.793110 0.509701i
\(130\) 0 0
\(131\) −7.73740 + 8.92944i −0.676020 + 0.780169i −0.985306 0.170801i \(-0.945365\pi\)
0.309286 + 0.950969i \(0.399910\pi\)
\(132\) 0 0
\(133\) 3.72749 0.323215
\(134\) 0 0
\(135\) −3.08273 −0.265319
\(136\) 0 0
\(137\) −14.9842 + 17.2927i −1.28019 + 1.47742i −0.480512 + 0.876988i \(0.659549\pi\)
−0.799678 + 0.600429i \(0.794996\pi\)
\(138\) 0 0
\(139\) 7.20148 4.62811i 0.610822 0.392551i −0.198344 0.980133i \(-0.563556\pi\)
0.809165 + 0.587581i \(0.199920\pi\)
\(140\) 0 0
\(141\) 0.0915872 + 0.637003i 0.00771304 + 0.0536454i
\(142\) 0 0
\(143\) 3.34957 + 23.2968i 0.280105 + 1.94817i
\(144\) 0 0
\(145\) 2.70038 1.73543i 0.224254 0.144119i
\(146\) 0 0
\(147\) 2.23612 4.89643i 0.184432 0.403851i
\(148\) 0 0
\(149\) −1.62615 + 11.3101i −0.133220 + 0.926563i 0.808100 + 0.589046i \(0.200496\pi\)
−0.941319 + 0.337517i \(0.890413\pi\)
\(150\) 0 0
\(151\) −10.0782 2.95922i −0.820150 0.240818i −0.155369 0.987856i \(-0.549657\pi\)
−0.664781 + 0.747039i \(0.731475\pi\)
\(152\) 0 0
\(153\) 0.524045 3.64481i 0.0423665 0.294666i
\(154\) 0 0
\(155\) −12.4476 7.99956i −0.999812 0.642540i
\(156\) 0 0
\(157\) −10.8095 + 12.4749i −0.862694 + 0.995602i 0.137293 + 0.990530i \(0.456160\pi\)
−0.999987 + 0.00507169i \(0.998386\pi\)
\(158\) 0 0
\(159\) −5.82261 + 12.7497i −0.461763 + 1.01112i
\(160\) 0 0
\(161\) −2.90797 1.86884i −0.229180 0.147285i
\(162\) 0 0
\(163\) −23.8950 −1.87160 −0.935798 0.352535i \(-0.885320\pi\)
−0.935798 + 0.352535i \(0.885320\pi\)
\(164\) 0 0
\(165\) −6.16101 13.4907i −0.479634 1.05025i
\(166\) 0 0
\(167\) 0.111829 0.777790i 0.00865361 0.0601872i −0.985037 0.172343i \(-0.944866\pi\)
0.993691 + 0.112155i \(0.0357755\pi\)
\(168\) 0 0
\(169\) −7.16004 8.26313i −0.550772 0.635625i
\(170\) 0 0
\(171\) −2.93119 −0.224154
\(172\) 0 0
\(173\) 4.29923 + 9.41400i 0.326864 + 0.715733i 0.999711 0.0240491i \(-0.00765580\pi\)
−0.672846 + 0.739782i \(0.734929\pi\)
\(174\) 0 0
\(175\) 5.49465 + 1.61338i 0.415357 + 0.121960i
\(176\) 0 0
\(177\) −3.54828 1.04187i −0.266705 0.0783116i
\(178\) 0 0
\(179\) −3.23301 3.73109i −0.241647 0.278875i 0.621952 0.783056i \(-0.286340\pi\)
−0.863598 + 0.504181i \(0.831795\pi\)
\(180\) 0 0
\(181\) −7.78046 + 8.97913i −0.578317 + 0.667413i −0.967242 0.253856i \(-0.918301\pi\)
0.388925 + 0.921269i \(0.372846\pi\)
\(182\) 0 0
\(183\) −0.411653 + 0.120872i −0.0304303 + 0.00893513i
\(184\) 0 0
\(185\) −19.6914 + 12.6549i −1.44774 + 0.930406i
\(186\) 0 0
\(187\) 16.9979 4.99102i 1.24301 0.364980i
\(188\) 0 0
\(189\) 0.528269 1.15675i 0.0384259 0.0841410i
\(190\) 0 0
\(191\) −8.72050 10.0640i −0.630993 0.728205i 0.346762 0.937953i \(-0.387281\pi\)
−0.977755 + 0.209748i \(0.932736\pi\)
\(192\) 0 0
\(193\) 0.745307 + 1.63200i 0.0536484 + 0.117474i 0.934558 0.355811i \(-0.115795\pi\)
−0.880909 + 0.473285i \(0.843068\pi\)
\(194\) 0 0
\(195\) 12.6873 + 8.15360i 0.908553 + 0.583892i
\(196\) 0 0
\(197\) 2.10277 0.617430i 0.149816 0.0439900i −0.205965 0.978559i \(-0.566033\pi\)
0.355781 + 0.934569i \(0.384215\pi\)
\(198\) 0 0
\(199\) −0.277162 1.92770i −0.0196475 0.136651i 0.977637 0.210301i \(-0.0674444\pi\)
−0.997284 + 0.0736498i \(0.976535\pi\)
\(200\) 0 0
\(201\) −8.18527 0.0356889i −0.577345 0.00251730i
\(202\) 0 0
\(203\) 0.188445 + 1.31066i 0.0132262 + 0.0919905i
\(204\) 0 0
\(205\) −14.7441 + 4.32926i −1.02977 + 0.302369i
\(206\) 0 0
\(207\) 2.28674 + 1.46960i 0.158939 + 0.102144i
\(208\) 0 0
\(209\) −5.85815 12.8276i −0.405217 0.887300i
\(210\) 0 0
\(211\) 14.5033 + 16.7377i 0.998450 + 1.15227i 0.988331 + 0.152324i \(0.0486756\pi\)
0.0101191 + 0.999949i \(0.496779\pi\)
\(212\) 0 0
\(213\) 4.09580 8.96855i 0.280639 0.614515i
\(214\) 0 0
\(215\) 31.6723 9.29982i 2.16003 0.634242i
\(216\) 0 0
\(217\) 5.13477 3.29992i 0.348571 0.224013i
\(218\) 0 0
\(219\) −1.04479 + 0.306779i −0.0706006 + 0.0207302i
\(220\) 0 0
\(221\) −11.7970 + 13.6145i −0.793554 + 0.915810i
\(222\) 0 0
\(223\) 4.00925 + 4.62692i 0.268479 + 0.309842i 0.873940 0.486033i \(-0.161557\pi\)
−0.605461 + 0.795875i \(0.707011\pi\)
\(224\) 0 0
\(225\) −4.32083 1.26871i −0.288056 0.0845807i
\(226\) 0 0
\(227\) −17.9113 5.25922i −1.18881 0.349067i −0.373247 0.927732i \(-0.621756\pi\)
−0.815565 + 0.578666i \(0.803574\pi\)
\(228\) 0 0
\(229\) −6.31208 13.8215i −0.417114 0.913352i −0.995245 0.0974077i \(-0.968945\pi\)
0.578131 0.815944i \(-0.303782\pi\)
\(230\) 0 0
\(231\) 6.11796 0.402532
\(232\) 0 0
\(233\) 13.6117 + 15.7088i 0.891734 + 1.02912i 0.999390 + 0.0349282i \(0.0111202\pi\)
−0.107655 + 0.994188i \(0.534334\pi\)
\(234\) 0 0
\(235\) −0.282339 + 1.96371i −0.0184178 + 0.128098i
\(236\) 0 0
\(237\) −1.64183 3.59510i −0.106648 0.233527i
\(238\) 0 0
\(239\) 14.7158 0.951884 0.475942 0.879477i \(-0.342107\pi\)
0.475942 + 0.879477i \(0.342107\pi\)
\(240\) 0 0
\(241\) 8.08049 + 5.19301i 0.520510 + 0.334511i 0.774374 0.632729i \(-0.218065\pi\)
−0.253864 + 0.967240i \(0.581701\pi\)
\(242\) 0 0
\(243\) −0.415415 + 0.909632i −0.0266489 + 0.0583529i
\(244\) 0 0
\(245\) 10.8667 12.5409i 0.694250 0.801207i
\(246\) 0 0
\(247\) 12.0636 + 7.75279i 0.767587 + 0.493298i
\(248\) 0 0
\(249\) −0.812256 + 5.64936i −0.0514746 + 0.358014i
\(250\) 0 0
\(251\) 17.5860 + 5.16370i 1.11002 + 0.325930i 0.784824 0.619718i \(-0.212753\pi\)
0.325191 + 0.945648i \(0.394571\pi\)
\(252\) 0 0
\(253\) −1.86112 + 12.9444i −0.117008 + 0.813805i
\(254\) 0 0
\(255\) 4.71560 10.3257i 0.295302 0.646622i
\(256\) 0 0
\(257\) 14.2898 9.18347i 0.891370 0.572849i −0.0128490 0.999917i \(-0.504090\pi\)
0.904219 + 0.427069i \(0.140454\pi\)
\(258\) 0 0
\(259\) −1.37416 9.55747i −0.0853860 0.593872i
\(260\) 0 0
\(261\) −0.148187 1.03067i −0.00917257 0.0637966i
\(262\) 0 0
\(263\) −2.84893 + 1.83089i −0.175672 + 0.112898i −0.625522 0.780207i \(-0.715114\pi\)
0.449850 + 0.893104i \(0.351478\pi\)
\(264\) 0 0
\(265\) −28.2957 + 32.6550i −1.73819 + 2.00598i
\(266\) 0 0
\(267\) 12.8664 0.787411
\(268\) 0 0
\(269\) −14.2503 −0.868854 −0.434427 0.900707i \(-0.643049\pi\)
−0.434427 + 0.900707i \(0.643049\pi\)
\(270\) 0 0
\(271\) −12.8182 + 14.7930i −0.778652 + 0.898612i −0.997011 0.0772562i \(-0.975384\pi\)
0.218359 + 0.975868i \(0.429930\pi\)
\(272\) 0 0
\(273\) −5.23365 + 3.36346i −0.316755 + 0.203566i
\(274\) 0 0
\(275\) −3.08326 21.4445i −0.185927 1.29315i
\(276\) 0 0
\(277\) −2.33591 16.2466i −0.140351 0.976164i −0.931293 0.364272i \(-0.881318\pi\)
0.790942 0.611892i \(-0.209591\pi\)
\(278\) 0 0
\(279\) −4.03783 + 2.59496i −0.241739 + 0.155356i
\(280\) 0 0
\(281\) −9.90941 + 21.6986i −0.591146 + 1.29443i 0.343601 + 0.939116i \(0.388353\pi\)
−0.934747 + 0.355313i \(0.884374\pi\)
\(282\) 0 0
\(283\) 1.59471 11.0915i 0.0947957 0.659318i −0.885914 0.463849i \(-0.846468\pi\)
0.980710 0.195469i \(-0.0626230\pi\)
\(284\) 0 0
\(285\) −8.67006 2.54576i −0.513570 0.150798i
\(286\) 0 0
\(287\) 0.902118 6.27437i 0.0532504 0.370364i
\(288\) 0 0
\(289\) −2.89450 1.86018i −0.170265 0.109423i
\(290\) 0 0
\(291\) −3.31897 + 3.83030i −0.194561 + 0.224536i
\(292\) 0 0
\(293\) 0.510917 1.11875i 0.0298481 0.0653582i −0.894121 0.447826i \(-0.852198\pi\)
0.923969 + 0.382468i \(0.124926\pi\)
\(294\) 0 0
\(295\) −9.59044 6.16340i −0.558377 0.358847i
\(296\) 0 0
\(297\) −4.81098 −0.279162
\(298\) 0 0
\(299\) −5.52430 12.0965i −0.319478 0.699560i
\(300\) 0 0
\(301\) −1.93787 + 13.4782i −0.111697 + 0.776869i
\(302\) 0 0
\(303\) −7.43452 8.57989i −0.427102 0.492902i
\(304\) 0 0
\(305\) −1.32259 −0.0757313
\(306\) 0 0
\(307\) 1.31587 + 2.88135i 0.0751006 + 0.164447i 0.943458 0.331491i \(-0.107552\pi\)
−0.868358 + 0.495938i \(0.834824\pi\)
\(308\) 0 0
\(309\) 9.21830 + 2.70674i 0.524410 + 0.153981i
\(310\) 0 0
\(311\) −1.69351 0.497260i −0.0960303 0.0281970i 0.233364 0.972389i \(-0.425026\pi\)
−0.329395 + 0.944192i \(0.606845\pi\)
\(312\) 0 0
\(313\) −14.5048 16.7394i −0.819860 0.946169i 0.179433 0.983770i \(-0.442574\pi\)
−0.999293 + 0.0376013i \(0.988028\pi\)
\(314\) 0 0
\(315\) 2.56719 2.96269i 0.144645 0.166929i
\(316\) 0 0
\(317\) 17.9688 5.27612i 1.00923 0.296336i 0.264991 0.964251i \(-0.414631\pi\)
0.744238 + 0.667915i \(0.232813\pi\)
\(318\) 0 0
\(319\) 4.21427 2.70834i 0.235954 0.151638i
\(320\) 0 0
\(321\) 1.91500 0.562294i 0.106885 0.0313842i
\(322\) 0 0
\(323\) 4.48379 9.81813i 0.249485 0.546295i
\(324\) 0 0
\(325\) 14.4271 + 16.6498i 0.800272 + 0.923563i
\(326\) 0 0
\(327\) 6.37773 + 13.9653i 0.352690 + 0.772282i
\(328\) 0 0
\(329\) −0.688469 0.442452i −0.0379565 0.0243932i
\(330\) 0 0
\(331\) −16.7690 + 4.92382i −0.921707 + 0.270638i −0.707961 0.706252i \(-0.750385\pi\)
−0.213746 + 0.976889i \(0.568567\pi\)
\(332\) 0 0
\(333\) 1.08060 + 7.51572i 0.0592163 + 0.411859i
\(334\) 0 0
\(335\) −24.1799 7.21453i −1.32109 0.394172i
\(336\) 0 0
\(337\) −4.04964 28.1659i −0.220598 1.53429i −0.735786 0.677214i \(-0.763187\pi\)
0.515188 0.857077i \(-0.327722\pi\)
\(338\) 0 0
\(339\) 11.8788 3.48794i 0.645170 0.189439i
\(340\) 0 0
\(341\) −19.4259 12.4843i −1.05197 0.676063i
\(342\) 0 0
\(343\) 6.54148 + 14.3238i 0.353207 + 0.773415i
\(344\) 0 0
\(345\) 5.48750 + 6.33292i 0.295437 + 0.340953i
\(346\) 0 0
\(347\) 14.4794 31.7054i 0.777294 1.70204i 0.0674033 0.997726i \(-0.478529\pi\)
0.709891 0.704311i \(-0.248744\pi\)
\(348\) 0 0
\(349\) −2.45689 + 0.721408i −0.131514 + 0.0386161i −0.346827 0.937929i \(-0.612741\pi\)
0.215313 + 0.976545i \(0.430923\pi\)
\(350\) 0 0
\(351\) 4.11559 2.64493i 0.219674 0.141176i
\(352\) 0 0
\(353\) 14.6377 4.29803i 0.779088 0.228761i 0.132075 0.991240i \(-0.457836\pi\)
0.647013 + 0.762479i \(0.276018\pi\)
\(354\) 0 0
\(355\) 19.9040 22.9705i 1.05640 1.21915i
\(356\) 0 0
\(357\) 3.06648 + 3.53891i 0.162295 + 0.187299i
\(358\) 0 0
\(359\) 2.91575 + 0.856143i 0.153888 + 0.0451855i 0.357769 0.933810i \(-0.383538\pi\)
−0.203881 + 0.978996i \(0.565356\pi\)
\(360\) 0 0
\(361\) 9.98651 + 2.93230i 0.525606 + 0.154332i
\(362\) 0 0
\(363\) −5.04545 11.0480i −0.264817 0.579869i
\(364\) 0 0
\(365\) −3.35679 −0.175703
\(366\) 0 0
\(367\) 23.2388 + 26.8190i 1.21305 + 1.39994i 0.891484 + 0.453052i \(0.149665\pi\)
0.321570 + 0.946886i \(0.395790\pi\)
\(368\) 0 0
\(369\) −0.709399 + 4.93398i −0.0369299 + 0.256853i
\(370\) 0 0
\(371\) −7.40441 16.2134i −0.384418 0.841757i
\(372\) 0 0
\(373\) 11.9975 0.621208 0.310604 0.950539i \(-0.399469\pi\)
0.310604 + 0.950539i \(0.399469\pi\)
\(374\) 0 0
\(375\) 1.28826 + 0.827915i 0.0665255 + 0.0427534i
\(376\) 0 0
\(377\) −2.11616 + 4.63374i −0.108988 + 0.238650i
\(378\) 0 0
\(379\) −4.01398 + 4.63237i −0.206184 + 0.237949i −0.849418 0.527721i \(-0.823047\pi\)
0.643234 + 0.765670i \(0.277592\pi\)
\(380\) 0 0
\(381\) −14.3397 9.21556i −0.734645 0.472128i
\(382\) 0 0
\(383\) −2.01495 + 14.0143i −0.102959 + 0.716098i 0.871314 + 0.490727i \(0.163269\pi\)
−0.974273 + 0.225371i \(0.927640\pi\)
\(384\) 0 0
\(385\) 18.0961 + 5.31349i 0.922261 + 0.270800i
\(386\) 0 0
\(387\) 1.52388 10.5988i 0.0774633 0.538769i
\(388\) 0 0
\(389\) 5.25897 11.5155i 0.266640 0.583861i −0.728194 0.685371i \(-0.759640\pi\)
0.994835 + 0.101510i \(0.0323674\pi\)
\(390\) 0 0
\(391\) −8.42045 + 5.41150i −0.425841 + 0.273671i
\(392\) 0 0
\(393\) 1.68150 + 11.6951i 0.0848204 + 0.589939i
\(394\) 0 0
\(395\) −1.73393 12.0597i −0.0872434 0.606791i
\(396\) 0 0
\(397\) 12.8115 8.23348i 0.642993 0.413227i −0.178107 0.984011i \(-0.556997\pi\)
0.821100 + 0.570785i \(0.193361\pi\)
\(398\) 0 0
\(399\) 2.44099 2.81705i 0.122202 0.141029i
\(400\) 0 0
\(401\) 24.5289 1.22492 0.612458 0.790503i \(-0.290181\pi\)
0.612458 + 0.790503i \(0.290181\pi\)
\(402\) 0 0
\(403\) 23.4815 1.16970
\(404\) 0 0
\(405\) −2.01876 + 2.32977i −0.100313 + 0.115767i
\(406\) 0 0
\(407\) −30.7308 + 19.7495i −1.52327 + 0.978947i
\(408\) 0 0
\(409\) −5.43426 37.7961i −0.268707 1.86890i −0.460778 0.887515i \(-0.652430\pi\)
0.192072 0.981381i \(-0.438479\pi\)
\(410\) 0 0
\(411\) 3.25639 + 22.6487i 0.160626 + 1.11718i
\(412\) 0 0
\(413\) 3.95617 2.54248i 0.194671 0.125107i
\(414\) 0 0
\(415\) −7.30905 + 16.0046i −0.358787 + 0.785634i
\(416\) 0 0
\(417\) 1.21827 8.47328i 0.0596591 0.414938i
\(418\) 0 0
\(419\) 27.2080 + 7.98899i 1.32920 + 0.390288i 0.867804 0.496907i \(-0.165531\pi\)
0.461395 + 0.887195i \(0.347349\pi\)
\(420\) 0 0
\(421\) 4.22583 29.3913i 0.205954 1.43244i −0.580231 0.814452i \(-0.697038\pi\)
0.786185 0.617991i \(-0.212053\pi\)
\(422\) 0 0
\(423\) 0.541392 + 0.347931i 0.0263234 + 0.0169170i
\(424\) 0 0
\(425\) 10.8591 12.5321i 0.526743 0.607894i
\(426\) 0 0
\(427\) 0.226644 0.496281i 0.0109681 0.0240167i
\(428\) 0 0
\(429\) 19.8000 + 12.7247i 0.955954 + 0.614354i
\(430\) 0 0
\(431\) 6.47892 0.312079 0.156039 0.987751i \(-0.450127\pi\)
0.156039 + 0.987751i \(0.450127\pi\)
\(432\) 0 0
\(433\) −2.39442 5.24305i −0.115069 0.251965i 0.843331 0.537394i \(-0.180591\pi\)
−0.958400 + 0.285429i \(0.907864\pi\)
\(434\) 0 0
\(435\) 0.456822 3.17727i 0.0219030 0.152338i
\(436\) 0 0
\(437\) 5.21775 + 6.02160i 0.249599 + 0.288052i
\(438\) 0 0
\(439\) −4.65641 −0.222238 −0.111119 0.993807i \(-0.535444\pi\)
−0.111119 + 0.993807i \(0.535444\pi\)
\(440\) 0 0
\(441\) −2.23612 4.89643i −0.106482 0.233163i
\(442\) 0 0
\(443\) 8.51652 + 2.50068i 0.404632 + 0.118811i 0.477714 0.878515i \(-0.341465\pi\)
−0.0730823 + 0.997326i \(0.523284\pi\)
\(444\) 0 0
\(445\) 38.0570 + 11.1745i 1.80408 + 0.529724i
\(446\) 0 0
\(447\) 7.48273 + 8.63553i 0.353921 + 0.408446i
\(448\) 0 0
\(449\) −17.9050 + 20.6634i −0.844987 + 0.975167i −0.999919 0.0127581i \(-0.995939\pi\)
0.154932 + 0.987925i \(0.450484\pi\)
\(450\) 0 0
\(451\) −23.0100 + 6.75634i −1.08350 + 0.318144i
\(452\) 0 0
\(453\) −8.83623 + 5.67870i −0.415162 + 0.266809i
\(454\) 0 0
\(455\) −18.4016 + 5.40319i −0.862680 + 0.253306i
\(456\) 0 0
\(457\) 9.62141 21.0680i 0.450071 0.985517i −0.539569 0.841942i \(-0.681413\pi\)
0.989639 0.143576i \(-0.0458601\pi\)
\(458\) 0 0
\(459\) −2.41139 2.78289i −0.112554 0.129894i
\(460\) 0 0
\(461\) −4.96332 10.8681i −0.231165 0.506180i 0.758131 0.652102i \(-0.226113\pi\)
−0.989296 + 0.145922i \(0.953385\pi\)
\(462\) 0 0
\(463\) 32.4444 + 20.8508i 1.50782 + 0.969018i 0.993793 + 0.111245i \(0.0354837\pi\)
0.514028 + 0.857773i \(0.328153\pi\)
\(464\) 0 0
\(465\) −14.1971 + 4.16864i −0.658374 + 0.193316i
\(466\) 0 0
\(467\) −5.19324 36.1198i −0.240315 1.67142i −0.650564 0.759451i \(-0.725468\pi\)
0.410250 0.911973i \(-0.365442\pi\)
\(468\) 0 0
\(469\) 6.85070 7.83682i 0.316336 0.361871i
\(470\) 0 0
\(471\) 2.34913 + 16.3386i 0.108242 + 0.752843i
\(472\) 0 0
\(473\) 49.4285 14.5135i 2.27272 0.667332i
\(474\) 0 0
\(475\) −11.1044 7.13639i −0.509507 0.327440i
\(476\) 0 0
\(477\) 5.82261 + 12.7497i 0.266599 + 0.583770i
\(478\) 0 0
\(479\) −22.2276 25.6520i −1.01560 1.17207i −0.985003 0.172536i \(-0.944804\pi\)
−0.0305996 0.999532i \(-0.509742\pi\)
\(480\) 0 0
\(481\) 15.4312 33.7897i 0.703603 1.54068i
\(482\) 0 0
\(483\) −3.31669 + 0.973867i −0.150914 + 0.0443125i
\(484\) 0 0
\(485\) −13.1437 + 8.44694i −0.596824 + 0.383556i
\(486\) 0 0
\(487\) −24.6310 + 7.23233i −1.11614 + 0.327728i −0.787246 0.616639i \(-0.788494\pi\)
−0.328893 + 0.944367i \(0.606676\pi\)
\(488\) 0 0
\(489\) −15.6479 + 18.0586i −0.707621 + 0.816638i
\(490\) 0 0
\(491\) −9.24794 10.6727i −0.417354 0.481652i 0.507675 0.861549i \(-0.330505\pi\)
−0.925029 + 0.379897i \(0.875960\pi\)
\(492\) 0 0
\(493\) 3.67893 + 1.08023i 0.165691 + 0.0486512i
\(494\) 0 0
\(495\) −14.2302 4.17837i −0.639601 0.187804i
\(496\) 0 0
\(497\) 5.20848 + 11.4050i 0.233632 + 0.511584i
\(498\) 0 0
\(499\) 40.7494 1.82419 0.912096 0.409977i \(-0.134463\pi\)
0.912096 + 0.409977i \(0.134463\pi\)
\(500\) 0 0
\(501\) −0.514582 0.593859i −0.0229898 0.0265317i
\(502\) 0 0
\(503\) 2.37212 16.4985i 0.105768 0.735631i −0.866060 0.499940i \(-0.833355\pi\)
0.971828 0.235691i \(-0.0757354\pi\)
\(504\) 0 0
\(505\) −14.5386 31.8351i −0.646958 1.41664i
\(506\) 0 0
\(507\) −10.9337 −0.485582
\(508\) 0 0
\(509\) 11.1243 + 7.14915i 0.493076 + 0.316880i 0.763441 0.645877i \(-0.223508\pi\)
−0.270366 + 0.962758i \(0.587145\pi\)
\(510\) 0 0
\(511\) 0.575233 1.25958i 0.0254468 0.0557207i
\(512\) 0 0
\(513\) −1.91952 + 2.21525i −0.0847490 + 0.0978055i
\(514\) 0 0
\(515\) 24.9156 + 16.0123i 1.09791 + 0.705586i
\(516\) 0 0
\(517\) −0.440625 + 3.06461i −0.0193787 + 0.134781i
\(518\) 0 0
\(519\) 9.93002 + 2.91572i 0.435880 + 0.127986i
\(520\) 0 0
\(521\) 5.40923 37.6220i 0.236983 1.64825i −0.429745 0.902950i \(-0.641397\pi\)
0.666728 0.745301i \(-0.267694\pi\)
\(522\) 0 0
\(523\) 5.04096 11.0382i 0.220426 0.482665i −0.766821 0.641861i \(-0.778163\pi\)
0.987247 + 0.159196i \(0.0508901\pi\)
\(524\) 0 0
\(525\) 4.81754 3.09604i 0.210255 0.135122i
\(526\) 0 0
\(527\) −2.51530 17.4943i −0.109568 0.762064i
\(528\) 0 0
\(529\) 2.22169 + 15.4522i 0.0965953 + 0.671835i
\(530\) 0 0
\(531\) −3.11102 + 1.99933i −0.135007 + 0.0867635i
\(532\) 0 0
\(533\) 15.9696 18.4299i 0.691721 0.798288i
\(534\) 0 0
\(535\) 6.15265 0.266002
\(536\) 0 0
\(537\) −4.93694 −0.213045
\(538\) 0 0
\(539\) 16.9589 19.5716i 0.730470 0.843007i
\(540\) 0 0
\(541\) −2.11613 + 1.35995i −0.0909795 + 0.0584690i −0.585340 0.810788i \(-0.699039\pi\)
0.494360 + 0.869257i \(0.335402\pi\)
\(542\) 0 0
\(543\) 1.69085 + 11.7602i 0.0725615 + 0.504677i
\(544\) 0 0
\(545\) 6.73551 + 46.8465i 0.288518 + 2.00668i
\(546\) 0 0
\(547\) 9.88371 6.35187i 0.422597 0.271586i −0.312011 0.950078i \(-0.601003\pi\)
0.734608 + 0.678492i \(0.237366\pi\)
\(548\) 0 0
\(549\) −0.178226 + 0.390261i −0.00760651 + 0.0166559i
\(550\) 0 0
\(551\) 0.434366 3.02108i 0.0185046 0.128702i
\(552\) 0 0
\(553\) 4.82236 + 1.41597i 0.205067 + 0.0602132i
\(554\) 0 0
\(555\) −3.33119 + 23.1689i −0.141401 + 0.983467i
\(556\) 0 0
\(557\) 2.00543 + 1.28881i 0.0849730 + 0.0546088i 0.582437 0.812876i \(-0.302099\pi\)
−0.497464 + 0.867484i \(0.665735\pi\)
\(558\) 0 0
\(559\) −34.3048 + 39.5899i −1.45094 + 1.67447i
\(560\) 0 0
\(561\) 7.35927 16.1146i 0.310709 0.680357i
\(562\) 0 0
\(563\) −8.96275 5.76001i −0.377735 0.242756i 0.337972 0.941156i \(-0.390259\pi\)
−0.715707 + 0.698401i \(0.753895\pi\)
\(564\) 0 0
\(565\) 38.1653 1.60562
\(566\) 0 0
\(567\) −0.528269 1.15675i −0.0221852 0.0485788i
\(568\) 0 0
\(569\) −2.18735 + 15.2134i −0.0916986 + 0.637778i 0.891197 + 0.453616i \(0.149866\pi\)
−0.982896 + 0.184162i \(0.941043\pi\)
\(570\) 0 0
\(571\) −1.60634 1.85382i −0.0672233 0.0775799i 0.721142 0.692788i \(-0.243618\pi\)
−0.788365 + 0.615208i \(0.789072\pi\)
\(572\) 0 0
\(573\) −13.3166 −0.556308
\(574\) 0 0
\(575\) 5.08508 + 11.1348i 0.212063 + 0.464352i
\(576\) 0 0
\(577\) −43.6503 12.8169i −1.81719 0.533574i −0.818051 0.575146i \(-0.804945\pi\)
−0.999135 + 0.0415724i \(0.986763\pi\)
\(578\) 0 0
\(579\) 1.72145 + 0.505464i 0.0715411 + 0.0210064i
\(580\) 0 0
\(581\) −4.75296 5.48521i −0.197186 0.227565i
\(582\) 0 0
\(583\) −44.1589 + 50.9621i −1.82887 + 2.11063i
\(584\) 0 0
\(585\) 14.4705 4.24891i 0.598280 0.175671i
\(586\) 0 0
\(587\) 14.3865 9.24563i 0.593794 0.381608i −0.208955 0.977925i \(-0.567006\pi\)
0.802749 + 0.596317i \(0.203370\pi\)
\(588\) 0 0
\(589\) −13.4992 + 3.96372i −0.556224 + 0.163322i
\(590\) 0 0
\(591\) 0.910401 1.99350i 0.0374489 0.0820016i
\(592\) 0 0
\(593\) 3.52838 + 4.07196i 0.144893 + 0.167216i 0.823557 0.567233i \(-0.191986\pi\)
−0.678664 + 0.734449i \(0.737441\pi\)
\(594\) 0 0
\(595\) 5.99666 + 13.1309i 0.245839 + 0.538313i
\(596\) 0 0
\(597\) −1.63836 1.05291i −0.0670537 0.0430928i
\(598\) 0 0
\(599\) −21.7579 + 6.38868i −0.889002 + 0.261035i −0.694178 0.719804i \(-0.744232\pi\)
−0.194824 + 0.980838i \(0.562414\pi\)
\(600\) 0 0
\(601\) −2.39915 16.6864i −0.0978632 0.680653i −0.978407 0.206688i \(-0.933731\pi\)
0.880544 0.473965i \(-0.157178\pi\)
\(602\) 0 0
\(603\) −5.38719 + 6.16265i −0.219383 + 0.250962i
\(604\) 0 0
\(605\) −5.32849 37.0604i −0.216634 1.50672i
\(606\) 0 0
\(607\) −35.1356 + 10.3167i −1.42611 + 0.418743i −0.901566 0.432641i \(-0.857582\pi\)
−0.524542 + 0.851384i \(0.675764\pi\)
\(608\) 0 0
\(609\) 1.11394 + 0.715884i 0.0451390 + 0.0290091i
\(610\) 0 0
\(611\) −1.30789 2.86388i −0.0529116 0.115860i
\(612\) 0 0
\(613\) −23.5183 27.1416i −0.949895 1.09624i −0.995258 0.0972665i \(-0.968990\pi\)
0.0453636 0.998971i \(-0.485555\pi\)
\(614\) 0 0
\(615\) −6.38350 + 13.9779i −0.257408 + 0.563644i
\(616\) 0 0
\(617\) −15.6019 + 4.58113i −0.628109 + 0.184429i −0.580268 0.814426i \(-0.697052\pi\)
−0.0478407 + 0.998855i \(0.515234\pi\)
\(618\) 0 0
\(619\) −22.4566 + 14.4319i −0.902605 + 0.580069i −0.907562 0.419919i \(-0.862059\pi\)
0.00495671 + 0.999988i \(0.498422\pi\)
\(620\) 0 0
\(621\) 2.60814 0.765820i 0.104661 0.0307313i
\(622\) 0 0
\(623\) −10.7147 + 12.3654i −0.429274 + 0.495408i
\(624\) 0 0
\(625\) 17.8364 + 20.5844i 0.713458 + 0.823374i
\(626\) 0 0
\(627\) −13.5307 3.97297i −0.540364 0.158665i
\(628\) 0 0
\(629\) −26.8271 7.87715i −1.06967 0.314083i
\(630\) 0 0
\(631\) −7.12104 15.5929i −0.283484 0.620744i 0.713301 0.700857i \(-0.247199\pi\)
−0.996786 + 0.0801133i \(0.974472\pi\)
\(632\) 0 0
\(633\) 22.1472 0.880271
\(634\) 0 0
\(635\) −34.4111 39.7125i −1.36556 1.57594i
\(636\) 0 0
\(637\) −3.74773 + 26.0661i −0.148491 + 1.03277i
\(638\) 0 0
\(639\) −4.09580 8.96855i −0.162027 0.354790i
\(640\) 0 0
\(641\) −24.9820 −0.986730 −0.493365 0.869823i \(-0.664233\pi\)
−0.493365 + 0.869823i \(0.664233\pi\)
\(642\) 0 0
\(643\) −2.60332 1.67305i −0.102665 0.0659787i 0.488301 0.872675i \(-0.337617\pi\)
−0.590966 + 0.806697i \(0.701253\pi\)
\(644\) 0 0
\(645\) 13.7126 30.0264i 0.539933 1.18229i
\(646\) 0 0
\(647\) −4.46857 + 5.15700i −0.175678 + 0.202743i −0.836759 0.547572i \(-0.815552\pi\)
0.661081 + 0.750314i \(0.270098\pi\)
\(648\) 0 0
\(649\) −14.9671 9.61875i −0.587508 0.377569i
\(650\) 0 0
\(651\) 0.868649 6.04159i 0.0340450 0.236788i
\(652\) 0 0
\(653\) −31.3221 9.19699i −1.22573 0.359906i −0.396091 0.918211i \(-0.629634\pi\)
−0.829636 + 0.558305i \(0.811452\pi\)
\(654\) 0 0
\(655\) −5.18361 + 36.0528i −0.202540 + 1.40870i
\(656\) 0 0
\(657\) −0.452346 + 0.990500i −0.0176477 + 0.0386431i
\(658\) 0 0
\(659\) −2.57002 + 1.65165i −0.100114 + 0.0643391i −0.589740 0.807593i \(-0.700770\pi\)
0.489626 + 0.871933i \(0.337133\pi\)
\(660\) 0 0
\(661\) 0.336948 + 2.34352i 0.0131058 + 0.0911526i 0.995324 0.0965876i \(-0.0307928\pi\)
−0.982219 + 0.187740i \(0.939884\pi\)
\(662\) 0 0
\(663\) 2.56374 + 17.8312i 0.0995673 + 0.692506i
\(664\) 0 0
\(665\) 9.66674 6.21243i 0.374860 0.240908i
\(666\) 0 0
\(667\) −1.85353 + 2.13909i −0.0717690 + 0.0828259i
\(668\) 0 0
\(669\) 6.12230 0.236702
\(670\) 0 0
\(671\) −2.06406 −0.0796823
\(672\) 0 0
\(673\) −8.44622 + 9.74746i −0.325578 + 0.375737i −0.894815 0.446436i \(-0.852693\pi\)
0.569238 + 0.822173i \(0.307238\pi\)
\(674\) 0 0
\(675\) −3.78837 + 2.43464i −0.145814 + 0.0937093i
\(676\) 0 0
\(677\) 4.82467 + 33.5563i 0.185427 + 1.28968i 0.843667 + 0.536867i \(0.180392\pi\)
−0.658240 + 0.752808i \(0.728699\pi\)
\(678\) 0 0
\(679\) −0.917228 6.37946i −0.0352000 0.244821i
\(680\) 0 0
\(681\) −15.7040 + 10.0924i −0.601780 + 0.386740i
\(682\) 0 0
\(683\) −14.9751 + 32.7909i −0.573006 + 1.25471i 0.372175 + 0.928163i \(0.378612\pi\)
−0.945181 + 0.326546i \(0.894115\pi\)
\(684\) 0 0
\(685\) −10.0386 + 69.8198i −0.383554 + 2.66768i
\(686\) 0 0
\(687\) −14.5791 4.28082i −0.556229 0.163324i
\(688\) 0 0
\(689\) 9.75866 67.8730i 0.371775 2.58576i
\(690\) 0 0
\(691\) −21.4045 13.7558i −0.814266 0.523297i 0.0659768 0.997821i \(-0.478984\pi\)
−0.880242 + 0.474524i \(0.842620\pi\)
\(692\) 0 0
\(693\) 4.00641 4.62365i 0.152191 0.175638i
\(694\) 0 0
\(695\) 10.9626 24.0047i 0.415835 0.910551i
\(696\) 0 0
\(697\) −15.4414 9.92357i −0.584884 0.375882i
\(698\) 0 0
\(699\) 20.7857 0.786187
\(700\) 0 0
\(701\) 2.60479 + 5.70369i 0.0983816 + 0.215426i 0.952423 0.304780i \(-0.0985828\pi\)
−0.854041 + 0.520205i \(0.825856\pi\)
\(702\) 0 0
\(703\) −3.16744 + 22.0300i −0.119462 + 0.830877i
\(704\) 0 0
\(705\) 1.29918 + 1.49934i 0.0489300 + 0.0564682i
\(706\) 0 0
\(707\) 14.4370 0.542959
\(708\) 0 0
\(709\) 15.2067 + 33.2979i 0.571098 + 1.25053i 0.946211 + 0.323551i \(0.104877\pi\)
−0.375113 + 0.926979i \(0.622396\pi\)
\(710\) 0 0
\(711\) −3.79216 1.11348i −0.142217 0.0417587i
\(712\) 0 0
\(713\) 12.5185 + 3.67577i 0.468822 + 0.137659i
\(714\) 0 0
\(715\) 47.5142 + 54.8343i 1.77693 + 2.05069i
\(716\) 0 0
\(717\) 9.63678 11.1214i 0.359892 0.415338i
\(718\) 0 0
\(719\) −17.9803 + 5.27949i −0.670552 + 0.196892i −0.599249 0.800563i \(-0.704534\pi\)
−0.0713030 + 0.997455i \(0.522716\pi\)
\(720\) 0 0
\(721\) −10.2780 + 6.60527i −0.382773 + 0.245993i
\(722\) 0 0
\(723\) 9.21621 2.70612i 0.342755 0.100642i
\(724\) 0 0
\(725\) 1.94791 4.26533i 0.0723436 0.158410i
\(726\) 0 0
\(727\) 25.1188 + 28.9887i 0.931606 + 1.07513i 0.997010 + 0.0772723i \(0.0246211\pi\)
−0.0654035 + 0.997859i \(0.520833\pi\)
\(728\) 0 0
\(729\) 0.415415 + 0.909632i 0.0153857 + 0.0336901i
\(730\) 0 0
\(731\) 33.1701 + 21.3171i 1.22684 + 0.788443i
\(732\) 0 0
\(733\) 22.1942 6.51682i 0.819763 0.240704i 0.155149 0.987891i \(-0.450414\pi\)
0.664614 + 0.747187i \(0.268596\pi\)
\(734\) 0 0
\(735\) −2.36157 16.4250i −0.0871076 0.605847i
\(736\) 0 0
\(737\) −37.7357 11.2592i −1.39001 0.414736i
\(738\) 0 0
\(739\) −5.56160 38.6818i −0.204587 1.42293i −0.790452 0.612524i \(-0.790154\pi\)
0.585865 0.810409i \(-0.300755\pi\)
\(740\) 0 0
\(741\) 13.7591 4.04004i 0.505454 0.148415i
\(742\) 0 0
\(743\) 29.5955 + 19.0199i 1.08575 + 0.697771i 0.955879 0.293760i \(-0.0949065\pi\)
0.129874 + 0.991531i \(0.458543\pi\)
\(744\) 0 0
\(745\) 14.6329 + 32.0415i 0.536106 + 1.17391i
\(746\) 0 0
\(747\) 3.73759 + 4.31341i 0.136751 + 0.157819i
\(748\) 0 0
\(749\) −1.05434 + 2.30868i −0.0385248 + 0.0843575i
\(750\) 0 0
\(751\) −13.3387 + 3.91658i −0.486735 + 0.142918i −0.515887 0.856657i \(-0.672537\pi\)
0.0291521 + 0.999575i \(0.490719\pi\)
\(752\) 0 0
\(753\) 15.4188 9.90907i 0.561893 0.361107i
\(754\) 0 0
\(755\) −31.0683 + 9.12248i −1.13069 + 0.332001i
\(756\) 0 0
\(757\) 26.9948 31.1536i 0.981142 1.13230i −0.0100617 0.999949i \(-0.503203\pi\)
0.991203 0.132348i \(-0.0422518\pi\)
\(758\) 0 0
\(759\) 8.56392 + 9.88329i 0.310851 + 0.358741i
\(760\) 0 0
\(761\) 44.2559 + 12.9947i 1.60428 + 0.471058i 0.956732 0.290970i \(-0.0939779\pi\)
0.647544 + 0.762028i \(0.275796\pi\)
\(762\) 0 0
\(763\) −18.7326 5.50040i −0.678167 0.199128i
\(764\) 0 0
\(765\) −4.71560 10.3257i −0.170493 0.373327i
\(766\) 0 0
\(767\) 18.0917 0.653255
\(768\) 0 0
\(769\) 21.6397 + 24.9735i 0.780347 + 0.900569i 0.997134 0.0756500i \(-0.0241032\pi\)
−0.216787 + 0.976219i \(0.569558\pi\)
\(770\) 0 0
\(771\) 2.41740 16.8134i 0.0870604 0.605519i
\(772\) 0 0
\(773\) 0.726752 + 1.59136i 0.0261394 + 0.0572374i 0.922251 0.386591i \(-0.126347\pi\)
−0.896112 + 0.443828i \(0.853620\pi\)
\(774\) 0 0
\(775\) −21.6146 −0.776419
\(776\) 0 0
\(777\) −8.12294 5.22030i −0.291409 0.187277i
\(778\) 0 0
\(779\) −6.06970 + 13.2908i −0.217469 + 0.476192i
\(780\) 0 0
\(781\) 31.0627 35.8483i 1.11151 1.28275i
\(782\)