Properties

Label 804.2.q.b.193.6
Level 804
Weight 2
Character 804.193
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 193.6
Character \(\chi\) = 804.193
Dual form 804.2.q.b.25.6

$q$-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 \(\left(\mathbb{Z}/804\mathbb{Z}\right)^\times\).

\(n\) \(269\) \(337\) \(403\)
\(\chi(n)\) \(1\) \(e\left(\frac{6}{11}\right)\) \(1\)

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 0.971564 0.236777i \(-0.0760912\pi\)
0.188222 + 0.982126i \(0.439728\pi\)
\(6\) 0 0
\(7\) 0.180977 1.25872i 0.0684028 0.475752i −0.926612 0.376020i \(-0.877292\pi\)
0.995014 0.0997319i \(-0.0317985\pi\)
\(8\) 0 0
\(9\) −0.142315 + 0.989821i −0.0474383 + 0.329940i
\(10\) 0 0
\(11\) 4.04726 + 2.60101i 1.22029 + 0.784235i 0.982352 0.187044i \(-0.0598907\pi\)
0.237942 + 0.971279i \(0.423527\pi\)
\(12\) 0 0
\(13\) −2.03230 4.45011i −0.563658 1.23424i −0.950106 0.311927i \(-0.899026\pi\)
0.386449 0.922311i \(-0.373702\pi\)
\(14\) 0 0
\(15\) 0.438719 + 3.05136i 0.113277 + 0.787857i
\(16\) 0 0
\(17\) 3.53314 1.03742i 0.856911 0.251612i 0.176372 0.984324i \(-0.443564\pi\)
0.680539 + 0.732712i \(0.261746\pi\)
\(18\) 0 0
\(19\) 0.417152 + 2.90136i 0.0957013 + 0.665617i 0.980044 + 0.198779i \(0.0636977\pi\)
−0.884343 + 0.466838i \(0.845393\pi\)
\(20\) 0 0
\(21\) 1.06979 0.687514i 0.233448 0.150028i
\(22\) 0 0
\(23\) −1.78008 2.05432i −0.371172 0.428355i 0.539180 0.842191i \(-0.318734\pi\)
−0.910352 + 0.413836i \(0.864189\pi\)
\(24\) 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 0.641736 + 0.766925i \(0.278214\pi\)
−0.999851 + 0.0172375i \(0.994513\pi\)
\(32\) 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 −0.632988 0.774162i \(-0.718172\pi\)
−0.113960 + 0.993485i \(0.536354\pi\)
\(42\) 0 0
\(43\) 10.2741 3.01674i 1.56678 0.460049i 0.620721 0.784032i \(-0.286840\pi\)
0.946063 + 0.323983i \(0.105022\pi\)
\(44\) 0 0
\(45\) −2.01876 + 2.32977i −0.300939 + 0.347302i
\(46\) 0 0
\(47\) −0.421438 0.486365i −0.0614731 0.0709437i 0.724180 0.689611i \(-0.242218\pi\)
−0.785653 + 0.618667i \(0.787673\pi\)
\(48\) 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 −0.999935 0.0114203i \(-0.996365\pi\)
−0.847373 0.530998i \(-0.821817\pi\)
\(54\) 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 −0.982883 0.184229i \(-0.941021\pi\)
0.782883 + 0.622170i \(0.213749\pi\)
\(60\) 0 0
\(61\) −0.360924 + 0.231952i −0.0462116 + 0.0296984i −0.563543 0.826087i \(-0.690562\pi\)
0.517331 + 0.855785i \(0.326926\pi\)
\(62\) 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 0.789840 0.613313i \(-0.210164\pi\)
0.332874 + 0.942971i \(0.391982\pi\)
\(72\) 0 0
\(73\) −0.916042 + 0.588705i −0.107215 + 0.0689027i −0.593149 0.805092i \(-0.702116\pi\)
0.485935 + 0.873995i \(0.338479\pi\)
\(74\) 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 0.979225 0.202778i \(-0.0649969\pi\)
−0.794505 + 0.607258i \(0.792270\pi\)
\(80\) 0 0
\(81\) −0.959493 0.281733i −0.106610 0.0313036i
\(82\) 0 0
\(83\) −4.80142 3.08568i −0.527024 0.338698i 0.249921 0.968266i \(-0.419595\pi\)
−0.776945 + 0.629568i \(0.783232\pi\)
\(84\) 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 −0.106216 0.994343i \(-0.533874\pi\)
0.999338 0.0363747i \(-0.0115810\pi\)
\(90\) 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 0.897195 + 0.441635i \(0.145601\pi\)
−0.736429 + 0.676515i \(0.763489\pi\)
\(102\) 0 0
\(103\) 3.99109 8.73926i 0.393253 0.861105i −0.604657 0.796486i \(-0.706690\pi\)
0.997910 0.0646185i \(-0.0205830\pi\)
\(104\) 0 0
\(105\) 3.92020 0.382573
\(106\) 0 0
\(107\) 1.67901 1.07903i 0.162316 0.104314i −0.456961 0.889487i \(-0.651062\pi\)
0.619277 + 0.785173i \(0.287426\pi\)
\(108\) 0 0
\(109\) −6.37773 13.9653i −0.610876 1.33763i −0.921973 0.387254i \(-0.873424\pi\)
0.311097 0.950378i \(-0.399304\pi\)
\(110\) 0 0
\(111\) −4.97236 5.73841i −0.471955 0.544666i
\(112\) 0 0
\(113\) 10.4150 6.69331i 0.979760 0.629654i 0.0503616 0.998731i \(-0.483963\pi\)
0.929399 + 0.369077i \(0.120326\pi\)
\(114\) 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 0.539962 + 0.841689i \(0.318439\pi\)
−0.755221 + 0.655470i \(0.772471\pi\)
\(128\) 0 0
\(129\) 9.00800 + 5.78909i 0.793110 + 0.509701i
\(130\) 0 0
\(131\) −7.73740 8.92944i −0.676020 0.780169i 0.309286 0.950969i \(-0.399910\pi\)
−0.985306 + 0.170801i \(0.945365\pi\)
\(132\) 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 −0.799678 0.600429i \(-0.794996\pi\)
−0.480512 0.876988i \(-0.659549\pi\)
\(138\) 0 0
\(139\) 7.20148 + 4.62811i 0.610822 + 0.392551i 0.809165 0.587581i \(-0.199920\pi\)
−0.198344 + 0.980133i \(0.563556\pi\)
\(140\) 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 −0.941319 0.337517i \(-0.890413\pi\)
0.808100 0.589046i \(-0.200496\pi\)
\(150\) 0 0
\(151\) −10.0782 + 2.95922i −0.820150 + 0.240818i −0.664781 0.747039i \(-0.731475\pi\)
−0.155369 + 0.987856i \(0.549657\pi\)
\(152\) 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 −0.999987 0.00507169i \(-0.998386\pi\)
0.137293 0.990530i \(-0.456160\pi\)
\(158\) 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 0.993691 0.112155i \(-0.0357755\pi\)
−0.985037 + 0.172343i \(0.944866\pi\)
\(168\) 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 −0.672846 0.739782i \(-0.734929\pi\)
0.999711 + 0.0240491i \(0.00765580\pi\)
\(174\) 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 −0.863598 0.504181i \(-0.831795\pi\)
0.621952 + 0.783056i \(0.286340\pi\)
\(180\) 0 0
\(181\) −7.78046 8.97913i −0.578317 0.667413i 0.388925 0.921269i \(-0.372846\pi\)
−0.967242 + 0.253856i \(0.918301\pi\)
\(182\) 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 −0.977755 0.209748i \(-0.932736\pi\)
0.346762 + 0.937953i \(0.387281\pi\)
\(192\) 0 0
\(193\) 0.745307 1.63200i 0.0536484 0.117474i −0.880909 0.473285i \(-0.843068\pi\)
0.934558 + 0.355811i \(0.115795\pi\)
\(194\) 0 0
\(195\) 12.6873 8.15360i 0.908553 0.583892i
\(196\) 0 0
\(197\) 2.10277 + 0.617430i 0.149816 + 0.0439900i 0.355781 0.934569i \(-0.384215\pi\)
−0.205965 + 0.978559i \(0.566033\pi\)
\(198\) 0 0
\(199\) −0.277162 + 1.92770i −0.0196475 + 0.136651i −0.997284 0.0736498i \(-0.976535\pi\)
0.977637 + 0.210301i \(0.0674444\pi\)
\(200\) 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 0.0101191 0.999949i \(-0.496779\pi\)
0.988331 0.152324i \(-0.0486756\pi\)
\(212\) 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 −0.605461 0.795875i \(-0.707011\pi\)
0.873940 + 0.486033i \(0.161557\pi\)
\(224\) 0 0
\(225\) −4.32083 + 1.26871i −0.288056 + 0.0845807i
\(226\) 0 0
\(227\) −17.9113 + 5.25922i −1.18881 + 0.349067i −0.815565 0.578666i \(-0.803574\pi\)
−0.373247 + 0.927732i \(0.621756\pi\)
\(228\) 0 0
\(229\) −6.31208 + 13.8215i −0.417114 + 0.913352i 0.578131 + 0.815944i \(0.303782\pi\)
−0.995245 + 0.0974077i \(0.968945\pi\)
\(230\) 0 0
\(231\) 6.11796 0.402532
\(232\) 0 0
\(233\) 13.6117 15.7088i 0.891734 1.02912i −0.107655 0.994188i \(-0.534334\pi\)
0.999390 0.0349282i \(-0.0111202\pi\)
\(234\) 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 −0.253864 0.967240i \(-0.581701\pi\)
0.774374 + 0.632729i \(0.218065\pi\)
\(242\) 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 0.325191 0.945648i \(-0.394571\pi\)
0.784824 + 0.619718i \(0.212753\pi\)
\(252\) 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 0.904219 0.427069i \(-0.140454\pi\)
−0.0128490 + 0.999917i \(0.504090\pi\)
\(258\) 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 0.449850 0.893104i \(-0.351478\pi\)
−0.625522 + 0.780207i \(0.715114\pi\)
\(264\) 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 0.218359 0.975868i \(-0.429930\pi\)
−0.997011 + 0.0772562i \(0.975384\pi\)
\(272\) 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 0.790942 + 0.611892i \(0.209591\pi\)
−0.931293 + 0.364272i \(0.881318\pi\)
\(278\) 0 0
\(279\) −4.03783 2.59496i −0.241739 0.155356i
\(280\) 0 0
\(281\) −9.90941 21.6986i −0.591146 1.29443i −0.934747 0.355313i \(-0.884374\pi\)
0.343601 0.939116i \(-0.388353\pi\)
\(282\) 0 0
\(283\) 1.59471 + 11.0915i 0.0947957 + 0.659318i 0.980710 + 0.195469i \(0.0626230\pi\)
−0.885914 + 0.463849i \(0.846468\pi\)
\(284\) 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 0.923969 0.382468i \(-0.124926\pi\)
−0.894121 + 0.447826i \(0.852198\pi\)
\(294\) 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 −0.868358 0.495938i \(-0.834824\pi\)
0.943458 + 0.331491i \(0.107552\pi\)
\(308\) 0 0
\(309\) 9.21830 2.70674i 0.524410 0.153981i
\(310\) 0 0
\(311\) −1.69351 + 0.497260i −0.0960303 + 0.0281970i −0.329395 0.944192i \(-0.606845\pi\)
0.233364 + 0.972389i \(0.425026\pi\)
\(312\) 0 0
\(313\) −14.5048 + 16.7394i −0.819860 + 0.946169i −0.999293 0.0376013i \(-0.988028\pi\)
0.179433 + 0.983770i \(0.442574\pi\)
\(314\) 0 0
\(315\) 2.56719 + 2.96269i 0.144645 + 0.166929i
\(316\) 0 0
\(317\) 17.9688 + 5.27612i 1.00923 + 0.296336i 0.744238 0.667915i \(-0.232813\pi\)
0.264991 + 0.964251i \(0.414631\pi\)
\(318\) 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 −0.213746 0.976889i \(-0.568567\pi\)
−0.707961 + 0.706252i \(0.750385\pi\)
\(332\) 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 0.515188 + 0.857077i \(0.327722\pi\)
−0.735786 + 0.677214i \(0.763187\pi\)
\(338\) 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 0.709891 + 0.704311i \(0.248744\pi\)
0.0674033 + 0.997726i \(0.478529\pi\)
\(348\) 0 0
\(349\) −2.45689 0.721408i −0.131514 0.0386161i 0.215313 0.976545i \(-0.430923\pi\)
−0.346827 + 0.937929i \(0.612741\pi\)
\(350\) 0 0
\(351\) 4.11559 + 2.64493i 0.219674 + 0.141176i
\(352\) 0 0
\(353\) 14.6377 + 4.29803i 0.779088 + 0.228761i 0.647013 0.762479i \(-0.276018\pi\)
0.132075 + 0.991240i \(0.457836\pi\)
\(354\) 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 −0.203881 0.978996i \(-0.565356\pi\)
0.357769 + 0.933810i \(0.383538\pi\)
\(360\) 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 0.321570 0.946886i \(-0.395790\pi\)
0.891484 0.453052i \(-0.149665\pi\)
\(368\) 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 0.643234 0.765670i \(-0.277592\pi\)
−0.849418 + 0.527721i \(0.823047\pi\)
\(380\) 0 0
\(381\) −14.3397 + 9.21556i −0.734645 + 0.472128i
\(382\) 0 0
\(383\) −2.01495 14.0143i −0.102959 0.716098i −0.974273 0.225371i \(-0.927640\pi\)
0.871314 0.490727i \(-0.163269\pi\)
\(384\) 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 0.994835 0.101510i \(-0.0323674\pi\)
−0.728194 + 0.685371i \(0.759640\pi\)
\(390\) 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 0.821100 0.570785i \(-0.193361\pi\)
−0.178107 + 0.984011i \(0.556997\pi\)
\(398\) 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 0.192072 + 0.981381i \(0.438479\pi\)
−0.460778 + 0.887515i \(0.652430\pi\)
\(410\) 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 0.461395 0.887195i \(-0.347349\pi\)
0.867804 + 0.496907i \(0.165531\pi\)
\(420\) 0 0
\(421\) 4.22583 + 29.3913i 0.205954 + 1.43244i 0.786185 + 0.617991i \(0.212053\pi\)
−0.580231 + 0.814452i \(0.697038\pi\)
\(422\) 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 −0.958400 0.285429i \(-0.907864\pi\)
0.843331 + 0.537394i \(0.180591\pi\)
\(434\) 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 −0.0730823 0.997326i \(-0.523284\pi\)
0.477714 + 0.878515i \(0.341465\pi\)
\(444\) 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 0.154932 0.987925i \(-0.450484\pi\)
−0.999919 + 0.0127581i \(0.995939\pi\)
\(450\) 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 0.989639 + 0.143576i \(0.0458601\pi\)
−0.539569 + 0.841942i \(0.681413\pi\)
\(458\) 0 0
\(459\) −2.41139 + 2.78289i −0.112554 + 0.129894i
\(460\) 0 0
\(461\) −4.96332 + 10.8681i −0.231165 + 0.506180i −0.989296 0.145922i \(-0.953385\pi\)
0.758131 + 0.652102i \(0.226113\pi\)
\(462\) 0 0
\(463\) 32.4444 20.8508i 1.50782 0.969018i 0.514028 0.857773i \(-0.328153\pi\)
0.993793 0.111245i \(-0.0354837\pi\)
\(464\) 0 0
\(465\) −14.1971 4.16864i −0.658374 0.193316i
\(466\) 0 0
\(467\) −5.19324 + 36.1198i −0.240315 + 1.67142i 0.410250 + 0.911973i \(0.365442\pi\)
−0.650564 + 0.759451i \(0.725468\pi\)
\(468\) 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 −0.0305996 + 0.999532i \(0.509742\pi\)
−0.985003 + 0.172536i \(0.944804\pi\)
\(480\) 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 −0.328893 0.944367i \(-0.606676\pi\)
−0.787246 + 0.616639i \(0.788494\pi\)
\(488\) 0 0
\(489\) −15.6479 18.0586i −0.707621 0.816638i
\(490\) 0 0
\(491\) −9.24794 + 10.6727i −0.417354 + 0.481652i −0.925029 0.379897i \(-0.875960\pi\)
0.507675 + 0.861549i \(0.330505\pi\)
\(492\) 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 0.971828 + 0.235691i \(0.0757354\pi\)
−0.866060 + 0.499940i \(0.833355\pi\)
\(504\) 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 −0.270366 0.962758i \(-0.587145\pi\)
0.763441 + 0.645877i \(0.223508\pi\)
\(510\) 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 0.666728 + 0.745301i \(0.267694\pi\)
−0.429745 + 0.902950i \(0.641397\pi\)
\(522\) 0 0
\(523\) 5.04096 + 11.0382i 0.220426 + 0.482665i 0.987247 0.159196i \(-0.0508901\pi\)
−0.766821 + 0.641861i \(0.778163\pi\)
\(524\) 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 0.494360 0.869257i \(-0.335402\pi\)
−0.585340 + 0.810788i \(0.699039\pi\)
\(542\) 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 0.734608 0.678492i \(-0.237366\pi\)
−0.312011 + 0.950078i \(0.601003\pi\)
\(548\) 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 −0.497464 0.867484i \(-0.665735\pi\)
0.582437 + 0.812876i \(0.302099\pi\)
\(558\) 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 −0.715707 0.698401i \(-0.753895\pi\)
0.337972 + 0.941156i \(0.390259\pi\)
\(564\) 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 −0.982896 0.184162i \(-0.941043\pi\)
0.891197 0.453616i \(-0.149866\pi\)
\(570\) 0 0
\(571\) −1.60634 + 1.85382i −0.0672233 + 0.0775799i −0.788365 0.615208i \(-0.789072\pi\)
0.721142 + 0.692788i \(0.243618\pi\)
\(572\) 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 −0.999135 0.0415724i \(-0.986763\pi\)
−0.818051 + 0.575146i \(0.804945\pi\)
\(578\) 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 0.802749 0.596317i \(-0.203370\pi\)
−0.208955 + 0.977925i \(0.567006\pi\)
\(588\) 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 −0.678664 0.734449i \(-0.737441\pi\)
0.823557 + 0.567233i \(0.191986\pi\)
\(594\) 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 −0.194824 0.980838i \(-0.562414\pi\)
−0.694178 + 0.719804i \(0.744232\pi\)
\(600\) 0 0
\(601\) −2.39915 + 16.6864i −0.0978632 + 0.680653i 0.880544 + 0.473965i \(0.157178\pi\)
−0.978407 + 0.206688i \(0.933731\pi\)
\(602\) 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 −0.524542 0.851384i \(-0.675764\pi\)
−0.901566 + 0.432641i \(0.857582\pi\)
\(608\) 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 0.0453636 + 0.998971i \(0.485555\pi\)
−0.995258 + 0.0972665i \(0.968990\pi\)
\(614\) 0 0
\(615\) −6.38350 13.9779i −0.257408 0.563644i
\(616\) 0 0
\(617\) −15.6019 4.58113i −0.628109 0.184429i −0.0478407 0.998855i \(-0.515234\pi\)
−0.580268 + 0.814426i \(0.697052\pi\)
\(618\) 0 0
\(619\) −22.4566 14.4319i −0.902605 0.580069i 0.00495671 0.999988i \(-0.498422\pi\)
−0.907562 + 0.419919i \(0.862059\pi\)
\(620\) 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 −0.996786 0.0801133i \(-0.974472\pi\)
0.713301 + 0.700857i \(0.247199\pi\)
\(632\) 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 −0.590966 0.806697i \(-0.701253\pi\)
0.488301 + 0.872675i \(0.337617\pi\)
\(644\) 0 0
\(645\) 13.7126 + 30.0264i 0.539933 + 1.18229i
\(646\) 0 0
\(647\) −4.46857 5.15700i −0.175678 0.202743i 0.661081 0.750314i \(-0.270098\pi\)
−0.836759 + 0.547572i \(0.815552\pi\)
\(648\) 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 −0.829636 0.558305i \(-0.811452\pi\)
−0.396091 + 0.918211i \(0.629634\pi\)
\(654\) 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 0.489626 0.871933i \(-0.337133\pi\)
−0.589740 + 0.807593i \(0.700770\pi\)
\(660\) 0 0
\(661\) 0.336948 2.34352i 0.0131058 0.0911526i −0.982219 0.187740i \(-0.939884\pi\)
0.995324 + 0.0965876i \(0.0307928\pi\)
\(662\) 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 0.569238 0.822173i \(-0.307238\pi\)
−0.894815 + 0.446436i \(0.852693\pi\)
\(674\) 0 0
\(675\) −3.78837 2.43464i −0.145814 0.0937093i
\(676\) 0 0
\(677\) 4.82467 33.5563i 0.185427 1.28968i −0.658240 0.752808i \(-0.728699\pi\)
0.843667 0.536867i \(-0.180392\pi\)
\(678\) 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 −0.945181 0.326546i \(-0.894115\pi\)
0.372175 0.928163i \(-0.378612\pi\)
\(684\) 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 −0.880242 0.474524i \(-0.842620\pi\)
0.0659768 + 0.997821i \(0.478984\pi\)
\(692\) 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 −0.854041 0.520205i \(-0.825856\pi\)
0.952423 + 0.304780i \(0.0985828\pi\)
\(702\) 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 −0.375113 0.926979i \(-0.622396\pi\)
0.946211 0.323551i \(-0.104877\pi\)
\(710\) 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 −0.0713030 0.997455i \(-0.522716\pi\)
−0.599249 + 0.800563i \(0.704534\pi\)
\(720\) 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 −0.0654035 0.997859i \(-0.520833\pi\)
0.997010 0.0772723i \(-0.0246211\pi\)
\(728\) 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 0.664614 0.747187i \(-0.268596\pi\)
0.155149 + 0.987891i \(0.450414\pi\)
\(734\) 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 0.585865 + 0.810409i \(0.300755\pi\)
−0.790452 + 0.612524i \(0.790154\pi\)
\(740\) 0 0
\(741\) 13.7591 + 4.04004i 0.505454 + 0.148415i
\(742\) 0 0
\(743\) 29.5955 19.0199i 1.08575 0.697771i 0.129874 0.991531i \(-0.458543\pi\)
0.955879 + 0.293760i \(0.0949065\pi\)
\(744\) 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 0.0291521 0.999575i \(-0.490719\pi\)
−0.515887 + 0.856657i \(0.672537\pi\)
\(752\) 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 0.991203 + 0.132348i \(0.0422518\pi\)
−0.0100617 + 0.999949i \(0.503203\pi\)
\(758\) 0 0
\(759\) 8.56392 9.88329i 0.310851 0.358741i
\(760\) 0 0
\(761\) 44.2559 12.9947i 1.60428 0.471058i 0.647544 0.762028i \(-0.275796\pi\)
0.956732 + 0.290970i \(0.0939779\pi\)
\(762\) 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 −0.216787 0.976219i \(-0.569558\pi\)
0.997134 + 0.0756500i \(0.0241032\pi\)
\(770\) 0 0
\(771\) 2.41740 + 16.8134i 0.0870604 + 0.605519i
\(772\) 0 0
\(773\) 0.726752 1.59136i 0.0261394 0.0572374i −0.896112 0.443828i \(-0.853620\pi\)
0.922251 + 0.386591i \(0.126347\pi\)
\(774\) 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