Properties

Label 950.2.e.h.201.1
Level $950$
Weight $2$
Character 950.201
Analytic conductor $7.586$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 950.e (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(7.58578819202\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\sqrt{-3}, \sqrt{17})\)
Defining polynomial: \(x^{4} - x^{3} + 5 x^{2} + 4 x + 16\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 190)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 201.1
Root \(1.28078 - 2.21837i\) of defining polynomial
Character \(\chi\) \(=\) 950.201
Dual form 950.2.e.h.501.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.500000 + 0.866025i) q^{2} +(-1.28078 + 2.21837i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.28078 - 2.21837i) q^{6} -0.438447 q^{7} +1.00000 q^{8} +(-1.78078 - 3.08440i) q^{9} +O(q^{10})\) \(q+(-0.500000 + 0.866025i) q^{2} +(-1.28078 + 2.21837i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.28078 - 2.21837i) q^{6} -0.438447 q^{7} +1.00000 q^{8} +(-1.78078 - 3.08440i) q^{9} +1.00000 q^{11} +2.56155 q^{12} +(-1.00000 - 1.73205i) q^{13} +(0.219224 - 0.379706i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(2.56155 - 4.43674i) q^{17} +3.56155 q^{18} +(-2.50000 - 3.57071i) q^{19} +(0.561553 - 0.972638i) q^{21} +(-0.500000 + 0.866025i) q^{22} +(-2.34233 - 4.05703i) q^{23} +(-1.28078 + 2.21837i) q^{24} +2.00000 q^{26} +1.43845 q^{27} +(0.219224 + 0.379706i) q^{28} +(-1.00000 - 1.73205i) q^{29} +10.2462 q^{31} +(-0.500000 - 0.866025i) q^{32} +(-1.28078 + 2.21837i) q^{33} +(2.56155 + 4.43674i) q^{34} +(-1.78078 + 3.08440i) q^{36} +4.68466 q^{37} +(4.34233 - 0.379706i) q^{38} +5.12311 q^{39} +(3.06155 - 5.30277i) q^{41} +(0.561553 + 0.972638i) q^{42} +(1.56155 - 2.70469i) q^{43} +(-0.500000 - 0.866025i) q^{44} +4.68466 q^{46} +(1.43845 + 2.49146i) q^{47} +(-1.28078 - 2.21837i) q^{48} -6.80776 q^{49} +(6.56155 + 11.3649i) q^{51} +(-1.00000 + 1.73205i) q^{52} +(-3.78078 - 6.54850i) q^{53} +(-0.719224 + 1.24573i) q^{54} -0.438447 q^{56} +(11.1231 - 0.972638i) q^{57} +2.00000 q^{58} +(-7.28078 + 12.6107i) q^{59} +(-2.56155 - 4.43674i) q^{61} +(-5.12311 + 8.87348i) q^{62} +(0.780776 + 1.35234i) q^{63} +1.00000 q^{64} +(-1.28078 - 2.21837i) q^{66} +(4.71922 + 8.17394i) q^{67} -5.12311 q^{68} +12.0000 q^{69} +(-8.12311 + 14.0696i) q^{71} +(-1.78078 - 3.08440i) q^{72} +(-0.842329 + 1.45896i) q^{73} +(-2.34233 + 4.05703i) q^{74} +(-1.84233 + 3.95042i) q^{76} -0.438447 q^{77} +(-2.56155 + 4.43674i) q^{78} +(5.56155 - 9.63289i) q^{79} +(3.50000 - 6.06218i) q^{81} +(3.06155 + 5.30277i) q^{82} +10.8078 q^{83} -1.12311 q^{84} +(1.56155 + 2.70469i) q^{86} +5.12311 q^{87} +1.00000 q^{88} +(1.34233 + 2.32498i) q^{89} +(0.438447 + 0.759413i) q^{91} +(-2.34233 + 4.05703i) q^{92} +(-13.1231 + 22.7299i) q^{93} -2.87689 q^{94} +2.56155 q^{96} +(0.842329 - 1.45896i) q^{97} +(3.40388 - 5.89570i) q^{98} +(-1.78078 - 3.08440i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q - 2q^{2} - q^{3} - 2q^{4} - q^{6} - 10q^{7} + 4q^{8} - 3q^{9} + O(q^{10}) \) \( 4q - 2q^{2} - q^{3} - 2q^{4} - q^{6} - 10q^{7} + 4q^{8} - 3q^{9} + 4q^{11} + 2q^{12} - 4q^{13} + 5q^{14} - 2q^{16} + 2q^{17} + 6q^{18} - 10q^{19} - 6q^{21} - 2q^{22} + 3q^{23} - q^{24} + 8q^{26} + 14q^{27} + 5q^{28} - 4q^{29} + 8q^{31} - 2q^{32} - q^{33} + 2q^{34} - 3q^{36} - 6q^{37} + 5q^{38} + 4q^{39} + 4q^{41} - 6q^{42} - 2q^{43} - 2q^{44} - 6q^{46} + 14q^{47} - q^{48} + 14q^{49} + 18q^{51} - 4q^{52} - 11q^{53} - 7q^{54} - 10q^{56} + 28q^{57} + 8q^{58} - 25q^{59} - 2q^{61} - 4q^{62} - q^{63} + 4q^{64} - q^{66} + 23q^{67} - 4q^{68} + 48q^{69} - 16q^{71} - 3q^{72} + 9q^{73} + 3q^{74} + 5q^{76} - 10q^{77} - 2q^{78} + 14q^{79} + 14q^{81} + 4q^{82} + 2q^{83} + 12q^{84} - 2q^{86} + 4q^{87} + 4q^{88} - 7q^{89} + 10q^{91} + 3q^{92} - 36q^{93} - 28q^{94} + 2q^{96} - 9q^{97} - 7q^{98} - 3q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/950\mathbb{Z}\right)^\times\).

\(n\) \(77\) \(401\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.500000 + 0.866025i −0.353553 + 0.612372i
\(3\) −1.28078 + 2.21837i −0.739457 + 1.28078i 0.213284 + 0.976990i \(0.431584\pi\)
−0.952740 + 0.303786i \(0.901749\pi\)
\(4\) −0.500000 0.866025i −0.250000 0.433013i
\(5\) 0 0
\(6\) −1.28078 2.21837i −0.522875 0.905646i
\(7\) −0.438447 −0.165717 −0.0828587 0.996561i \(-0.526405\pi\)
−0.0828587 + 0.996561i \(0.526405\pi\)
\(8\) 1.00000 0.353553
\(9\) −1.78078 3.08440i −0.593592 1.02813i
\(10\) 0 0
\(11\) 1.00000 0.301511 0.150756 0.988571i \(-0.451829\pi\)
0.150756 + 0.988571i \(0.451829\pi\)
\(12\) 2.56155 0.739457
\(13\) −1.00000 1.73205i −0.277350 0.480384i 0.693375 0.720577i \(-0.256123\pi\)
−0.970725 + 0.240192i \(0.922790\pi\)
\(14\) 0.219224 0.379706i 0.0585900 0.101481i
\(15\) 0 0
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) 2.56155 4.43674i 0.621268 1.07607i −0.367982 0.929833i \(-0.619951\pi\)
0.989250 0.146235i \(-0.0467154\pi\)
\(18\) 3.56155 0.839466
\(19\) −2.50000 3.57071i −0.573539 0.819178i
\(20\) 0 0
\(21\) 0.561553 0.972638i 0.122541 0.212247i
\(22\) −0.500000 + 0.866025i −0.106600 + 0.184637i
\(23\) −2.34233 4.05703i −0.488409 0.845950i 0.511502 0.859282i \(-0.329089\pi\)
−0.999911 + 0.0133324i \(0.995756\pi\)
\(24\) −1.28078 + 2.21837i −0.261437 + 0.452823i
\(25\) 0 0
\(26\) 2.00000 0.392232
\(27\) 1.43845 0.276829
\(28\) 0.219224 + 0.379706i 0.0414294 + 0.0717578i
\(29\) −1.00000 1.73205i −0.185695 0.321634i 0.758115 0.652121i \(-0.226120\pi\)
−0.943811 + 0.330487i \(0.892787\pi\)
\(30\) 0 0
\(31\) 10.2462 1.84027 0.920137 0.391597i \(-0.128077\pi\)
0.920137 + 0.391597i \(0.128077\pi\)
\(32\) −0.500000 0.866025i −0.0883883 0.153093i
\(33\) −1.28078 + 2.21837i −0.222955 + 0.386169i
\(34\) 2.56155 + 4.43674i 0.439303 + 0.760895i
\(35\) 0 0
\(36\) −1.78078 + 3.08440i −0.296796 + 0.514066i
\(37\) 4.68466 0.770153 0.385077 0.922885i \(-0.374175\pi\)
0.385077 + 0.922885i \(0.374175\pi\)
\(38\) 4.34233 0.379706i 0.704419 0.0615965i
\(39\) 5.12311 0.820353
\(40\) 0 0
\(41\) 3.06155 5.30277i 0.478134 0.828153i −0.521552 0.853220i \(-0.674647\pi\)
0.999686 + 0.0250670i \(0.00797991\pi\)
\(42\) 0.561553 + 0.972638i 0.0866495 + 0.150081i
\(43\) 1.56155 2.70469i 0.238135 0.412461i −0.722044 0.691847i \(-0.756797\pi\)
0.960179 + 0.279385i \(0.0901307\pi\)
\(44\) −0.500000 0.866025i −0.0753778 0.130558i
\(45\) 0 0
\(46\) 4.68466 0.690715
\(47\) 1.43845 + 2.49146i 0.209819 + 0.363417i 0.951657 0.307161i \(-0.0993792\pi\)
−0.741838 + 0.670579i \(0.766046\pi\)
\(48\) −1.28078 2.21837i −0.184864 0.320194i
\(49\) −6.80776 −0.972538
\(50\) 0 0
\(51\) 6.56155 + 11.3649i 0.918801 + 1.59141i
\(52\) −1.00000 + 1.73205i −0.138675 + 0.240192i
\(53\) −3.78078 6.54850i −0.519330 0.899505i −0.999748 0.0224656i \(-0.992848\pi\)
0.480418 0.877040i \(-0.340485\pi\)
\(54\) −0.719224 + 1.24573i −0.0978739 + 0.169523i
\(55\) 0 0
\(56\) −0.438447 −0.0585900
\(57\) 11.1231 0.972638i 1.47329 0.128829i
\(58\) 2.00000 0.262613
\(59\) −7.28078 + 12.6107i −0.947876 + 1.64177i −0.197989 + 0.980204i \(0.563441\pi\)
−0.749887 + 0.661566i \(0.769892\pi\)
\(60\) 0 0
\(61\) −2.56155 4.43674i −0.327973 0.568066i 0.654136 0.756377i \(-0.273032\pi\)
−0.982110 + 0.188310i \(0.939699\pi\)
\(62\) −5.12311 + 8.87348i −0.650635 + 1.12693i
\(63\) 0.780776 + 1.35234i 0.0983686 + 0.170379i
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) −1.28078 2.21837i −0.157653 0.273062i
\(67\) 4.71922 + 8.17394i 0.576545 + 0.998605i 0.995872 + 0.0907698i \(0.0289328\pi\)
−0.419327 + 0.907835i \(0.637734\pi\)
\(68\) −5.12311 −0.621268
\(69\) 12.0000 1.44463
\(70\) 0 0
\(71\) −8.12311 + 14.0696i −0.964035 + 1.66976i −0.251850 + 0.967766i \(0.581039\pi\)
−0.712185 + 0.701992i \(0.752294\pi\)
\(72\) −1.78078 3.08440i −0.209867 0.363499i
\(73\) −0.842329 + 1.45896i −0.0985872 + 0.170758i −0.911100 0.412185i \(-0.864766\pi\)
0.812513 + 0.582943i \(0.198099\pi\)
\(74\) −2.34233 + 4.05703i −0.272290 + 0.471621i
\(75\) 0 0
\(76\) −1.84233 + 3.95042i −0.211330 + 0.453144i
\(77\) −0.438447 −0.0499657
\(78\) −2.56155 + 4.43674i −0.290039 + 0.502362i
\(79\) 5.56155 9.63289i 0.625724 1.08379i −0.362677 0.931915i \(-0.618137\pi\)
0.988400 0.151870i \(-0.0485295\pi\)
\(80\) 0 0
\(81\) 3.50000 6.06218i 0.388889 0.673575i
\(82\) 3.06155 + 5.30277i 0.338092 + 0.585592i
\(83\) 10.8078 1.18631 0.593153 0.805090i \(-0.297883\pi\)
0.593153 + 0.805090i \(0.297883\pi\)
\(84\) −1.12311 −0.122541
\(85\) 0 0
\(86\) 1.56155 + 2.70469i 0.168387 + 0.291654i
\(87\) 5.12311 0.549255
\(88\) 1.00000 0.106600
\(89\) 1.34233 + 2.32498i 0.142287 + 0.246448i 0.928357 0.371689i \(-0.121221\pi\)
−0.786071 + 0.618137i \(0.787888\pi\)
\(90\) 0 0
\(91\) 0.438447 + 0.759413i 0.0459618 + 0.0796081i
\(92\) −2.34233 + 4.05703i −0.244205 + 0.422975i
\(93\) −13.1231 + 22.7299i −1.36080 + 2.35698i
\(94\) −2.87689 −0.296729
\(95\) 0 0
\(96\) 2.56155 0.261437
\(97\) 0.842329 1.45896i 0.0855256 0.148135i −0.820089 0.572235i \(-0.806076\pi\)
0.905615 + 0.424101i \(0.139410\pi\)
\(98\) 3.40388 5.89570i 0.343844 0.595555i
\(99\) −1.78078 3.08440i −0.178975 0.309993i
\(100\) 0 0
\(101\) −5.00000 8.66025i −0.497519 0.861727i 0.502477 0.864590i \(-0.332422\pi\)
−0.999996 + 0.00286291i \(0.999089\pi\)
\(102\) −13.1231 −1.29938
\(103\) 5.80776 0.572256 0.286128 0.958191i \(-0.407632\pi\)
0.286128 + 0.958191i \(0.407632\pi\)
\(104\) −1.00000 1.73205i −0.0980581 0.169842i
\(105\) 0 0
\(106\) 7.56155 0.734443
\(107\) −2.24621 −0.217149 −0.108575 0.994088i \(-0.534629\pi\)
−0.108575 + 0.994088i \(0.534629\pi\)
\(108\) −0.719224 1.24573i −0.0692073 0.119871i
\(109\) 7.12311 12.3376i 0.682270 1.18173i −0.292017 0.956413i \(-0.594326\pi\)
0.974286 0.225313i \(-0.0723404\pi\)
\(110\) 0 0
\(111\) −6.00000 + 10.3923i −0.569495 + 0.986394i
\(112\) 0.219224 0.379706i 0.0207147 0.0358789i
\(113\) 16.8078 1.58114 0.790571 0.612371i \(-0.209784\pi\)
0.790571 + 0.612371i \(0.209784\pi\)
\(114\) −4.71922 + 10.1192i −0.441996 + 0.947751i
\(115\) 0 0
\(116\) −1.00000 + 1.73205i −0.0928477 + 0.160817i
\(117\) −3.56155 + 6.16879i −0.329266 + 0.570305i
\(118\) −7.28078 12.6107i −0.670250 1.16091i
\(119\) −1.12311 + 1.94528i −0.102955 + 0.178323i
\(120\) 0 0
\(121\) −10.0000 −0.909091
\(122\) 5.12311 0.463824
\(123\) 7.84233 + 13.5833i 0.707119 + 1.22477i
\(124\) −5.12311 8.87348i −0.460068 0.796862i
\(125\) 0 0
\(126\) −1.56155 −0.139114
\(127\) −7.78078 13.4767i −0.690432 1.19586i −0.971696 0.236233i \(-0.924087\pi\)
0.281264 0.959630i \(-0.409246\pi\)
\(128\) −0.500000 + 0.866025i −0.0441942 + 0.0765466i
\(129\) 4.00000 + 6.92820i 0.352180 + 0.609994i
\(130\) 0 0
\(131\) 8.06155 13.9630i 0.704341 1.21995i −0.262588 0.964908i \(-0.584576\pi\)
0.966929 0.255046i \(-0.0820908\pi\)
\(132\) 2.56155 0.222955
\(133\) 1.09612 + 1.56557i 0.0950455 + 0.135752i
\(134\) −9.43845 −0.815358
\(135\) 0 0
\(136\) 2.56155 4.43674i 0.219651 0.380447i
\(137\) −2.71922 4.70983i −0.232319 0.402388i 0.726171 0.687514i \(-0.241298\pi\)
−0.958490 + 0.285126i \(0.907965\pi\)
\(138\) −6.00000 + 10.3923i −0.510754 + 0.884652i
\(139\) −4.40388 7.62775i −0.373532 0.646977i 0.616574 0.787297i \(-0.288520\pi\)
−0.990106 + 0.140320i \(0.955187\pi\)
\(140\) 0 0
\(141\) −7.36932 −0.620608
\(142\) −8.12311 14.0696i −0.681676 1.18070i
\(143\) −1.00000 1.73205i −0.0836242 0.144841i
\(144\) 3.56155 0.296796
\(145\) 0 0
\(146\) −0.842329 1.45896i −0.0697117 0.120744i
\(147\) 8.71922 15.1021i 0.719149 1.24560i
\(148\) −2.34233 4.05703i −0.192538 0.333486i
\(149\) −8.00000 + 13.8564i −0.655386 + 1.13516i 0.326411 + 0.945228i \(0.394160\pi\)
−0.981797 + 0.189933i \(0.939173\pi\)
\(150\) 0 0
\(151\) 20.4924 1.66765 0.833825 0.552029i \(-0.186146\pi\)
0.833825 + 0.552029i \(0.186146\pi\)
\(152\) −2.50000 3.57071i −0.202777 0.289623i
\(153\) −18.2462 −1.47512
\(154\) 0.219224 0.379706i 0.0176655 0.0305976i
\(155\) 0 0
\(156\) −2.56155 4.43674i −0.205088 0.355223i
\(157\) 1.21922 2.11176i 0.0973046 0.168537i −0.813263 0.581896i \(-0.802311\pi\)
0.910568 + 0.413359i \(0.135645\pi\)
\(158\) 5.56155 + 9.63289i 0.442453 + 0.766352i
\(159\) 19.3693 1.53609
\(160\) 0 0
\(161\) 1.02699 + 1.77879i 0.0809380 + 0.140189i
\(162\) 3.50000 + 6.06218i 0.274986 + 0.476290i
\(163\) −17.0540 −1.33577 −0.667885 0.744264i \(-0.732800\pi\)
−0.667885 + 0.744264i \(0.732800\pi\)
\(164\) −6.12311 −0.478134
\(165\) 0 0
\(166\) −5.40388 + 9.35980i −0.419423 + 0.726461i
\(167\) 0.342329 + 0.592932i 0.0264902 + 0.0458824i 0.878967 0.476883i \(-0.158234\pi\)
−0.852476 + 0.522766i \(0.824900\pi\)
\(168\) 0.561553 0.972638i 0.0433247 0.0750407i
\(169\) 4.50000 7.79423i 0.346154 0.599556i
\(170\) 0 0
\(171\) −6.56155 + 14.0696i −0.501774 + 1.07593i
\(172\) −3.12311 −0.238135
\(173\) −2.90388 + 5.02967i −0.220778 + 0.382399i −0.955044 0.296463i \(-0.904193\pi\)
0.734266 + 0.678861i \(0.237526\pi\)
\(174\) −2.56155 + 4.43674i −0.194191 + 0.336348i
\(175\) 0 0
\(176\) −0.500000 + 0.866025i −0.0376889 + 0.0652791i
\(177\) −18.6501 32.3029i −1.40183 2.42804i
\(178\) −2.68466 −0.201224
\(179\) 11.4924 0.858984 0.429492 0.903071i \(-0.358693\pi\)
0.429492 + 0.903071i \(0.358693\pi\)
\(180\) 0 0
\(181\) −10.6847 18.5064i −0.794184 1.37557i −0.923356 0.383945i \(-0.874565\pi\)
0.129171 0.991622i \(-0.458768\pi\)
\(182\) −0.876894 −0.0649997
\(183\) 13.1231 0.970088
\(184\) −2.34233 4.05703i −0.172679 0.299088i
\(185\) 0 0
\(186\) −13.1231 22.7299i −0.962233 1.66664i
\(187\) 2.56155 4.43674i 0.187319 0.324447i
\(188\) 1.43845 2.49146i 0.104910 0.181709i
\(189\) −0.630683 −0.0458754
\(190\) 0 0
\(191\) −5.36932 −0.388510 −0.194255 0.980951i \(-0.562229\pi\)
−0.194255 + 0.980951i \(0.562229\pi\)
\(192\) −1.28078 + 2.21837i −0.0924321 + 0.160097i
\(193\) 12.8078 22.1837i 0.921923 1.59682i 0.125487 0.992095i \(-0.459951\pi\)
0.796436 0.604722i \(-0.206716\pi\)
\(194\) 0.842329 + 1.45896i 0.0604757 + 0.104747i
\(195\) 0 0
\(196\) 3.40388 + 5.89570i 0.243134 + 0.421121i
\(197\) −14.4384 −1.02870 −0.514348 0.857581i \(-0.671966\pi\)
−0.514348 + 0.857581i \(0.671966\pi\)
\(198\) 3.56155 0.253109
\(199\) 1.43845 + 2.49146i 0.101969 + 0.176615i 0.912496 0.409086i \(-0.134152\pi\)
−0.810527 + 0.585701i \(0.800819\pi\)
\(200\) 0 0
\(201\) −24.1771 −1.70532
\(202\) 10.0000 0.703598
\(203\) 0.438447 + 0.759413i 0.0307730 + 0.0533003i
\(204\) 6.56155 11.3649i 0.459401 0.795705i
\(205\) 0 0
\(206\) −2.90388 + 5.02967i −0.202323 + 0.350434i
\(207\) −8.34233 + 14.4493i −0.579832 + 1.00430i
\(208\) 2.00000 0.138675
\(209\) −2.50000 3.57071i −0.172929 0.246991i
\(210\) 0 0
\(211\) 1.65767 2.87117i 0.114119 0.197659i −0.803308 0.595563i \(-0.796929\pi\)
0.917427 + 0.397904i \(0.130262\pi\)
\(212\) −3.78078 + 6.54850i −0.259665 + 0.449753i
\(213\) −20.8078 36.0401i −1.42572 2.46943i
\(214\) 1.12311 1.94528i 0.0767739 0.132976i
\(215\) 0 0
\(216\) 1.43845 0.0978739
\(217\) −4.49242 −0.304966
\(218\) 7.12311 + 12.3376i 0.482438 + 0.835606i
\(219\) −2.15767 3.73720i −0.145802 0.252536i
\(220\) 0 0
\(221\) −10.2462 −0.689235
\(222\) −6.00000 10.3923i −0.402694 0.697486i
\(223\) 5.65767 9.79937i 0.378866 0.656215i −0.612032 0.790833i \(-0.709648\pi\)
0.990897 + 0.134619i \(0.0429809\pi\)
\(224\) 0.219224 + 0.379706i 0.0146475 + 0.0253702i
\(225\) 0 0
\(226\) −8.40388 + 14.5560i −0.559018 + 0.968247i
\(227\) −19.9309 −1.32286 −0.661429 0.750008i \(-0.730050\pi\)
−0.661429 + 0.750008i \(0.730050\pi\)
\(228\) −6.40388 9.14657i −0.424107 0.605747i
\(229\) 12.8769 0.850929 0.425465 0.904975i \(-0.360111\pi\)
0.425465 + 0.904975i \(0.360111\pi\)
\(230\) 0 0
\(231\) 0.561553 0.972638i 0.0369475 0.0639949i
\(232\) −1.00000 1.73205i −0.0656532 0.113715i
\(233\) 1.15767 2.00514i 0.0758415 0.131361i −0.825610 0.564241i \(-0.809169\pi\)
0.901452 + 0.432879i \(0.142502\pi\)
\(234\) −3.56155 6.16879i −0.232826 0.403266i
\(235\) 0 0
\(236\) 14.5616 0.947876
\(237\) 14.2462 + 24.6752i 0.925391 + 1.60282i
\(238\) −1.12311 1.94528i −0.0728001 0.126094i
\(239\) 18.2462 1.18025 0.590125 0.807312i \(-0.299079\pi\)
0.590125 + 0.807312i \(0.299079\pi\)
\(240\) 0 0
\(241\) 4.28078 + 7.41452i 0.275749 + 0.477611i 0.970324 0.241809i \(-0.0777408\pi\)
−0.694575 + 0.719421i \(0.744407\pi\)
\(242\) 5.00000 8.66025i 0.321412 0.556702i
\(243\) 11.1231 + 19.2658i 0.713548 + 1.23590i
\(244\) −2.56155 + 4.43674i −0.163987 + 0.284033i
\(245\) 0 0
\(246\) −15.6847 −1.00002
\(247\) −3.68466 + 7.90084i −0.234449 + 0.502718i
\(248\) 10.2462 0.650635
\(249\) −13.8423 + 23.9756i −0.877222 + 1.51939i
\(250\) 0 0
\(251\) −12.9654 22.4568i −0.818371 1.41746i −0.906882 0.421385i \(-0.861544\pi\)
0.0885109 0.996075i \(-0.471789\pi\)
\(252\) 0.780776 1.35234i 0.0491843 0.0851897i
\(253\) −2.34233 4.05703i −0.147261 0.255063i
\(254\) 15.5616 0.976419
\(255\) 0 0
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) 6.52699 + 11.3051i 0.407142 + 0.705191i 0.994568 0.104087i \(-0.0331920\pi\)
−0.587426 + 0.809278i \(0.699859\pi\)
\(258\) −8.00000 −0.498058
\(259\) −2.05398 −0.127628
\(260\) 0 0
\(261\) −3.56155 + 6.16879i −0.220455 + 0.381839i
\(262\) 8.06155 + 13.9630i 0.498044 + 0.862638i
\(263\) −1.09612 + 1.89853i −0.0675895 + 0.117068i −0.897840 0.440322i \(-0.854864\pi\)
0.830250 + 0.557391i \(0.188197\pi\)
\(264\) −1.28078 + 2.21837i −0.0788263 + 0.136531i
\(265\) 0 0
\(266\) −1.90388 + 0.166481i −0.116734 + 0.0102076i
\(267\) −6.87689 −0.420859
\(268\) 4.71922 8.17394i 0.288272 0.499303i
\(269\) −2.00000 + 3.46410i −0.121942 + 0.211210i −0.920534 0.390664i \(-0.872246\pi\)
0.798591 + 0.601874i \(0.205579\pi\)
\(270\) 0 0
\(271\) 4.12311 7.14143i 0.250461 0.433811i −0.713192 0.700969i \(-0.752751\pi\)
0.963653 + 0.267158i \(0.0860845\pi\)
\(272\) 2.56155 + 4.43674i 0.155317 + 0.269017i
\(273\) −2.24621 −0.135947
\(274\) 5.43845 0.328549
\(275\) 0 0
\(276\) −6.00000 10.3923i −0.361158 0.625543i
\(277\) −4.24621 −0.255130 −0.127565 0.991830i \(-0.540716\pi\)
−0.127565 + 0.991830i \(0.540716\pi\)
\(278\) 8.80776 0.528255
\(279\) −18.2462 31.6034i −1.09237 1.89204i
\(280\) 0 0
\(281\) −4.18466 7.24804i −0.249636 0.432382i 0.713789 0.700361i \(-0.246978\pi\)
−0.963425 + 0.267979i \(0.913644\pi\)
\(282\) 3.68466 6.38202i 0.219418 0.380043i
\(283\) −9.71922 + 16.8342i −0.577748 + 1.00069i 0.417989 + 0.908452i \(0.362735\pi\)
−0.995737 + 0.0922367i \(0.970598\pi\)
\(284\) 16.2462 0.964035
\(285\) 0 0
\(286\) 2.00000 0.118262
\(287\) −1.34233 + 2.32498i −0.0792352 + 0.137239i
\(288\) −1.78078 + 3.08440i −0.104933 + 0.181750i
\(289\) −4.62311 8.00745i −0.271947 0.471027i
\(290\) 0 0
\(291\) 2.15767 + 3.73720i 0.126485 + 0.219078i
\(292\) 1.68466 0.0985872
\(293\) −23.5616 −1.37648 −0.688240 0.725483i \(-0.741617\pi\)
−0.688240 + 0.725483i \(0.741617\pi\)
\(294\) 8.71922 + 15.1021i 0.508515 + 0.880775i
\(295\) 0 0
\(296\) 4.68466 0.272290
\(297\) 1.43845 0.0834672
\(298\) −8.00000 13.8564i −0.463428 0.802680i
\(299\) −4.68466 + 8.11407i −0.270921 + 0.469249i
\(300\) 0 0
\(301\) −0.684658 + 1.18586i −0.0394631 + 0.0683520i
\(302\) −10.2462 + 17.7470i −0.589603 + 1.02122i
\(303\) 25.6155 1.47157
\(304\) 4.34233 0.379706i 0.249050 0.0217777i
\(305\) 0 0
\(306\) 9.12311 15.8017i 0.521533 0.903322i
\(307\) −11.9654 + 20.7247i −0.682903 + 1.18282i 0.291187 + 0.956666i \(0.405950\pi\)
−0.974091 + 0.226157i \(0.927384\pi\)
\(308\) 0.219224 + 0.379706i 0.0124914 + 0.0216358i
\(309\) −7.43845 + 12.8838i −0.423158 + 0.732932i
\(310\) 0 0
\(311\) 4.00000 0.226819 0.113410 0.993548i \(-0.463823\pi\)
0.113410 + 0.993548i \(0.463823\pi\)
\(312\) 5.12311 0.290039
\(313\) 2.15767 + 3.73720i 0.121959 + 0.211239i 0.920540 0.390648i \(-0.127749\pi\)
−0.798581 + 0.601887i \(0.794416\pi\)
\(314\) 1.21922 + 2.11176i 0.0688048 + 0.119173i
\(315\) 0 0
\(316\) −11.1231 −0.625724
\(317\) 9.34233 + 16.1814i 0.524717 + 0.908837i 0.999586 + 0.0287805i \(0.00916237\pi\)
−0.474868 + 0.880057i \(0.657504\pi\)
\(318\) −9.68466 + 16.7743i −0.543089 + 0.940657i
\(319\) −1.00000 1.73205i −0.0559893 0.0969762i
\(320\) 0 0
\(321\) 2.87689 4.98293i 0.160573 0.278120i
\(322\) −2.05398 −0.114464
\(323\) −22.2462 + 1.94528i −1.23781 + 0.108238i
\(324\) −7.00000 −0.388889
\(325\) 0 0
\(326\) 8.52699 14.7692i 0.472266 0.817989i
\(327\) 18.2462 + 31.6034i 1.00902 + 1.74767i
\(328\) 3.06155 5.30277i 0.169046 0.292796i
\(329\) −0.630683 1.09238i −0.0347707 0.0602246i
\(330\) 0 0
\(331\) 23.4924 1.29126 0.645630 0.763650i \(-0.276595\pi\)
0.645630 + 0.763650i \(0.276595\pi\)
\(332\) −5.40388 9.35980i −0.296577 0.513686i
\(333\) −8.34233 14.4493i −0.457157 0.791819i
\(334\) −0.684658 −0.0374628
\(335\) 0 0
\(336\) 0.561553 + 0.972638i 0.0306352 + 0.0530618i
\(337\) 10.5270 18.2333i 0.573442 0.993230i −0.422767 0.906238i \(-0.638941\pi\)
0.996209 0.0869917i \(-0.0277254\pi\)
\(338\) 4.50000 + 7.79423i 0.244768 + 0.423950i
\(339\) −21.5270 + 37.2858i −1.16919 + 2.02509i
\(340\) 0 0
\(341\) 10.2462 0.554863
\(342\) −8.90388 12.7173i −0.481467 0.687672i
\(343\) 6.05398 0.326884
\(344\) 1.56155 2.70469i 0.0841933 0.145827i
\(345\) 0 0
\(346\) −2.90388 5.02967i −0.156114 0.270397i
\(347\) 0.842329 1.45896i 0.0452186 0.0783209i −0.842530 0.538649i \(-0.818935\pi\)
0.887749 + 0.460328i \(0.152268\pi\)
\(348\) −2.56155 4.43674i −0.137314 0.237834i
\(349\) −14.2462 −0.762582 −0.381291 0.924455i \(-0.624520\pi\)
−0.381291 + 0.924455i \(0.624520\pi\)
\(350\) 0 0
\(351\) −1.43845 2.49146i −0.0767786 0.132984i
\(352\) −0.500000 0.866025i −0.0266501 0.0461593i
\(353\) −24.1771 −1.28682 −0.643408 0.765523i \(-0.722480\pi\)
−0.643408 + 0.765523i \(0.722480\pi\)
\(354\) 37.3002 1.98248
\(355\) 0 0
\(356\) 1.34233 2.32498i 0.0711433 0.123224i
\(357\) −2.87689 4.98293i −0.152261 0.263724i
\(358\) −5.74621 + 9.95273i −0.303697 + 0.526018i
\(359\) −7.56155 + 13.0970i −0.399083 + 0.691233i −0.993613 0.112841i \(-0.964005\pi\)
0.594530 + 0.804074i \(0.297338\pi\)
\(360\) 0 0
\(361\) −6.50000 + 17.8536i −0.342105 + 0.939662i
\(362\) 21.3693 1.12315
\(363\) 12.8078 22.1837i 0.672233 1.16434i
\(364\) 0.438447 0.759413i 0.0229809 0.0398040i
\(365\) 0 0
\(366\) −6.56155 + 11.3649i −0.342978 + 0.594055i
\(367\) −8.87689 15.3752i −0.463370 0.802581i 0.535756 0.844373i \(-0.320027\pi\)
−0.999126 + 0.0417921i \(0.986693\pi\)
\(368\) 4.68466 0.244205
\(369\) −21.8078 −1.13527
\(370\) 0 0
\(371\) 1.65767 + 2.87117i 0.0860620 + 0.149064i
\(372\) 26.2462 1.36080
\(373\) 35.8078 1.85406 0.927028 0.374992i \(-0.122355\pi\)
0.927028 + 0.374992i \(0.122355\pi\)
\(374\) 2.56155 + 4.43674i 0.132455 + 0.229418i
\(375\) 0 0
\(376\) 1.43845 + 2.49146i 0.0741822 + 0.128487i
\(377\) −2.00000 + 3.46410i −0.103005 + 0.178410i
\(378\) 0.315342 0.546188i 0.0162194 0.0280929i
\(379\) −0.492423 −0.0252940 −0.0126470 0.999920i \(-0.504026\pi\)
−0.0126470 + 0.999920i \(0.504026\pi\)
\(380\) 0 0
\(381\) 39.8617 2.04218
\(382\) 2.68466 4.64996i 0.137359 0.237913i
\(383\) 2.56155 4.43674i 0.130889 0.226707i −0.793130 0.609052i \(-0.791550\pi\)
0.924020 + 0.382345i \(0.124883\pi\)
\(384\) −1.28078 2.21837i −0.0653593 0.113206i
\(385\) 0 0
\(386\) 12.8078 + 22.1837i 0.651898 + 1.12912i
\(387\) −11.1231 −0.565419
\(388\) −1.68466 −0.0855256
\(389\) 9.56155 + 16.5611i 0.484790 + 0.839681i 0.999847 0.0174749i \(-0.00556271\pi\)
−0.515057 + 0.857156i \(0.672229\pi\)
\(390\) 0 0
\(391\) −24.0000 −1.21373
\(392\) −6.80776 −0.343844
\(393\) 20.6501 + 35.7670i 1.04166 + 1.80421i
\(394\) 7.21922 12.5041i 0.363699 0.629946i
\(395\) 0 0
\(396\) −1.78078 + 3.08440i −0.0894874 + 0.154997i
\(397\) 14.1501 24.5087i 0.710173 1.23006i −0.254619 0.967041i \(-0.581950\pi\)
0.964792 0.263014i \(-0.0847165\pi\)
\(398\) −2.87689 −0.144206
\(399\) −4.87689 + 0.426450i −0.244150 + 0.0213492i
\(400\) 0 0
\(401\) −13.9654 + 24.1888i −0.697401 + 1.20793i 0.271964 + 0.962307i \(0.412327\pi\)
−0.969365 + 0.245626i \(0.921007\pi\)
\(402\) 12.0885 20.9380i 0.602922 1.04429i
\(403\) −10.2462 17.7470i −0.510400 0.884039i
\(404\) −5.00000 + 8.66025i −0.248759 + 0.430864i
\(405\) 0 0
\(406\) −0.876894 −0.0435195
\(407\) 4.68466 0.232210
\(408\) 6.56155 + 11.3649i 0.324845 + 0.562649i
\(409\) −10.5000 18.1865i −0.519192 0.899266i −0.999751 0.0223042i \(-0.992900\pi\)
0.480560 0.876962i \(-0.340434\pi\)
\(410\) 0 0
\(411\) 13.9309 0.687159
\(412\) −2.90388 5.02967i −0.143064 0.247794i
\(413\) 3.19224 5.52911i 0.157080 0.272070i
\(414\) −8.34233 14.4493i −0.410003 0.710146i
\(415\) 0 0
\(416\) −1.00000 + 1.73205i −0.0490290 + 0.0849208i
\(417\) 22.5616 1.10484
\(418\) 4.34233 0.379706i 0.212390 0.0185720i
\(419\) −17.5616 −0.857938 −0.428969 0.903319i \(-0.641123\pi\)
−0.428969 + 0.903319i \(0.641123\pi\)
\(420\) 0 0
\(421\) −16.2462 + 28.1393i −0.791792 + 1.37142i 0.133065 + 0.991107i \(0.457518\pi\)
−0.924856 + 0.380316i \(0.875815\pi\)
\(422\) 1.65767 + 2.87117i 0.0806942 + 0.139766i
\(423\) 5.12311 8.87348i 0.249094 0.431443i
\(424\) −3.78078 6.54850i −0.183611 0.318023i
\(425\) 0 0
\(426\) 41.6155 2.01628
\(427\) 1.12311 + 1.94528i 0.0543509 + 0.0941385i
\(428\) 1.12311 + 1.94528i 0.0542874 + 0.0940285i
\(429\) 5.12311 0.247346
\(430\) 0 0
\(431\) 3.68466 + 6.38202i 0.177484 + 0.307411i 0.941018 0.338356i \(-0.109871\pi\)
−0.763534 + 0.645767i \(0.776538\pi\)
\(432\) −0.719224 + 1.24573i −0.0346037 + 0.0599353i
\(433\) −18.3693 31.8166i −0.882773 1.52901i −0.848245 0.529604i \(-0.822341\pi\)
−0.0345280 0.999404i \(-0.510993\pi\)
\(434\) 2.24621 3.89055i 0.107822 0.186752i
\(435\) 0 0
\(436\) −14.2462 −0.682270
\(437\) −8.63068 + 18.5064i −0.412862 + 0.885280i
\(438\) 4.31534 0.206195
\(439\) 8.24621 14.2829i 0.393570 0.681684i −0.599347 0.800489i \(-0.704573\pi\)
0.992918 + 0.118806i \(0.0379065\pi\)
\(440\) 0 0
\(441\) 12.1231 + 20.9978i 0.577291 + 0.999897i
\(442\) 5.12311 8.87348i 0.243681 0.422068i
\(443\) 16.9654 + 29.3850i 0.806052 + 1.39612i 0.915578 + 0.402139i \(0.131733\pi\)
−0.109526 + 0.993984i \(0.534933\pi\)
\(444\) 12.0000 0.569495
\(445\) 0 0
\(446\) 5.65767 + 9.79937i 0.267898 + 0.464014i
\(447\) −20.4924 35.4939i −0.969258 1.67880i
\(448\) −0.438447 −0.0207147
\(449\) 29.0000 1.36859 0.684297 0.729203i \(-0.260109\pi\)
0.684297 + 0.729203i \(0.260109\pi\)
\(450\) 0 0
\(451\) 3.06155 5.30277i 0.144163 0.249697i
\(452\) −8.40388 14.5560i −0.395285 0.684654i
\(453\) −26.2462 + 45.4598i −1.23315 + 2.13589i
\(454\) 9.96543 17.2606i 0.467701 0.810082i
\(455\) 0 0
\(456\) 11.1231 0.972638i 0.520887 0.0455479i
\(457\) −7.05398 −0.329971 −0.164986 0.986296i \(-0.552758\pi\)
−0.164986 + 0.986296i \(0.552758\pi\)
\(458\) −6.43845 + 11.1517i −0.300849 + 0.521086i
\(459\) 3.68466 6.38202i 0.171985 0.297887i
\(460\) 0 0
\(461\) 19.4924 33.7619i 0.907853 1.57245i 0.0908110 0.995868i \(-0.471054\pi\)
0.817042 0.576579i \(-0.195613\pi\)
\(462\) 0.561553 + 0.972638i 0.0261258 + 0.0452512i
\(463\) 19.5616 0.909102 0.454551 0.890721i \(-0.349800\pi\)
0.454551 + 0.890721i \(0.349800\pi\)
\(464\) 2.00000 0.0928477
\(465\) 0 0
\(466\) 1.15767 + 2.00514i 0.0536281 + 0.0928865i
\(467\) −16.5616 −0.766377 −0.383189 0.923670i \(-0.625174\pi\)
−0.383189 + 0.923670i \(0.625174\pi\)
\(468\) 7.12311 0.329266
\(469\) −2.06913 3.58384i −0.0955436 0.165486i
\(470\) 0 0
\(471\) 3.12311 + 5.40938i 0.143905 + 0.249251i
\(472\) −7.28078 + 12.6107i −0.335125 + 0.580453i
\(473\) 1.56155 2.70469i 0.0718003 0.124362i
\(474\) −28.4924 −1.30870
\(475\) 0 0
\(476\) 2.24621 0.102955
\(477\) −13.4654 + 23.3228i −0.616540 + 1.06788i
\(478\) −9.12311 + 15.8017i −0.417281 + 0.722752i
\(479\) −14.6847 25.4346i −0.670959 1.16214i −0.977632 0.210321i \(-0.932549\pi\)
0.306673 0.951815i \(-0.400784\pi\)
\(480\) 0 0
\(481\) −4.68466 8.11407i −0.213602 0.369970i
\(482\) −8.56155 −0.389968
\(483\) −5.26137 −0.239400
\(484\) 5.00000 + 8.66025i 0.227273 + 0.393648i
\(485\) 0 0
\(486\) −22.2462 −1.00911
\(487\) 6.93087 0.314068 0.157034 0.987593i \(-0.449807\pi\)
0.157034 + 0.987593i \(0.449807\pi\)
\(488\) −2.56155 4.43674i −0.115956 0.200842i
\(489\) 21.8423 37.8320i 0.987744 1.71082i
\(490\) 0 0
\(491\) 4.58854 7.94759i 0.207078 0.358670i −0.743715 0.668497i \(-0.766938\pi\)
0.950793 + 0.309827i \(0.100271\pi\)
\(492\) 7.84233 13.5833i 0.353560 0.612383i
\(493\) −10.2462 −0.461466
\(494\) −5.00000 7.14143i −0.224961 0.321308i
\(495\) 0 0
\(496\) −5.12311 + 8.87348i −0.230034 + 0.398431i
\(497\) 3.56155 6.16879i 0.159757 0.276708i
\(498\) −13.8423 23.9756i −0.620290 1.07437i
\(499\) −14.5000 + 25.1147i −0.649109 + 1.12429i 0.334227 + 0.942493i \(0.391525\pi\)
−0.983336 + 0.181797i \(0.941809\pi\)
\(500\) 0 0
\(501\) −1.75379 −0.0783535
\(502\) 25.9309 1.15735
\(503\) 13.7116 + 23.7493i 0.611372 + 1.05893i 0.991009 + 0.133792i \(0.0427154\pi\)
−0.379637 + 0.925135i \(0.623951\pi\)
\(504\) 0.780776 + 1.35234i 0.0347785 + 0.0602382i
\(505\) 0 0
\(506\) 4.68466 0.208258
\(507\) 11.5270 + 19.9653i 0.511931 + 0.886691i
\(508\) −7.78078 + 13.4767i −0.345216 + 0.597932i
\(509\) 0.438447 + 0.759413i 0.0194338 + 0.0336604i 0.875579 0.483075i \(-0.160480\pi\)
−0.856145 + 0.516736i \(0.827147\pi\)
\(510\) 0 0
\(511\) 0.369317 0.639676i 0.0163376 0.0282976i
\(512\) 1.00000 0.0441942
\(513\) −3.59612 5.13628i −0.158772 0.226772i
\(514\) −13.0540 −0.575786
\(515\) 0 0
\(516\) 4.00000 6.92820i 0.176090 0.304997i
\(517\) 1.43845 + 2.49146i 0.0632628 + 0.109574i
\(518\) 1.02699 1.77879i 0.0451232 0.0781558i
\(519\) −7.43845 12.8838i −0.326512 0.565535i
\(520\) 0 0
\(521\) −22.8078 −0.999226 −0.499613 0.866249i \(-0.666524\pi\)
−0.499613 + 0.866249i \(0.666524\pi\)
\(522\) −3.56155 6.16879i −0.155885 0.270001i
\(523\) 7.31534 + 12.6705i 0.319878 + 0.554044i 0.980462 0.196707i \(-0.0630249\pi\)
−0.660585 + 0.750752i \(0.729692\pi\)
\(524\) −16.1231 −0.704341
\(525\) 0 0
\(526\) −1.09612 1.89853i −0.0477930 0.0827799i
\(527\) 26.2462 45.4598i 1.14330 1.98026i
\(528\) −1.28078 2.21837i −0.0557386 0.0965422i
\(529\) 0.526988 0.912769i 0.0229125 0.0396856i
\(530\) 0 0
\(531\) 51.8617 2.25061
\(532\) 0.807764 1.73205i 0.0350210 0.0750939i
\(533\) −12.2462 −0.530442
\(534\) 3.43845 5.95557i 0.148796 0.257723i
\(535\) 0 0
\(536\) 4.71922 + 8.17394i 0.203839 + 0.353060i
\(537\) −14.7192 + 25.4944i −0.635181 + 1.10017i
\(538\) −2.00000 3.46410i −0.0862261 0.149348i
\(539\) −6.80776 −0.293231
\(540\) 0 0
\(541\) 14.2462 + 24.6752i 0.612492 + 1.06087i 0.990819 + 0.135196i \(0.0431664\pi\)
−0.378326 + 0.925672i \(0.623500\pi\)
\(542\) 4.12311 + 7.14143i 0.177103 + 0.306751i
\(543\) 54.7386 2.34906
\(544\) −5.12311 −0.219651
\(545\) 0 0
\(546\) 1.12311 1.94528i 0.0480645 0.0832501i
\(547\) −2.43845 4.22351i −0.104260 0.180584i 0.809175 0.587567i \(-0.199914\pi\)
−0.913436 + 0.406983i \(0.866581\pi\)
\(548\) −2.71922 + 4.70983i −0.116159 + 0.201194i
\(549\) −9.12311 + 15.8017i −0.389365 + 0.674399i
\(550\) 0 0
\(551\) −3.68466 + 7.90084i −0.156972 + 0.336587i
\(552\) 12.0000 0.510754
\(553\) −2.43845 + 4.22351i −0.103693 + 0.179602i
\(554\) 2.12311 3.67733i 0.0902021 0.156235i
\(555\) 0 0
\(556\) −4.40388 + 7.62775i −0.186766 + 0.323489i
\(557\) 20.8348 + 36.0868i 0.882797 + 1.52905i 0.848218 + 0.529647i \(0.177676\pi\)
0.0345785 + 0.999402i \(0.488991\pi\)
\(558\) 36.4924 1.54485
\(559\) −6.24621 −0.264187
\(560\) 0 0
\(561\) 6.56155 + 11.3649i 0.277029 + 0.479828i
\(562\) 8.36932 0.353038
\(563\) −21.3002 −0.897696 −0.448848 0.893608i \(-0.648166\pi\)
−0.448848 + 0.893608i \(0.648166\pi\)
\(564\) 3.68466 + 6.38202i 0.155152 + 0.268731i
\(565\) 0 0
\(566\) −9.71922 16.8342i −0.408529 0.707594i
\(567\) −1.53457 + 2.65794i −0.0644457 + 0.111623i
\(568\) −8.12311 + 14.0696i −0.340838 + 0.590349i
\(569\) −11.1771 −0.468568 −0.234284 0.972168i \(-0.575274\pi\)
−0.234284 + 0.972168i \(0.575274\pi\)
\(570\) 0 0
\(571\) −4.80776 −0.201199 −0.100599 0.994927i \(-0.532076\pi\)
−0.100599 + 0.994927i \(0.532076\pi\)
\(572\) −1.00000 + 1.73205i −0.0418121 + 0.0724207i
\(573\) 6.87689 11.9111i 0.287286 0.497595i
\(574\) −1.34233 2.32498i −0.0560277 0.0970429i
\(575\) 0 0
\(576\) −1.78078 3.08440i −0.0741990 0.128516i
\(577\) 16.3153 0.679217 0.339608 0.940567i \(-0.389705\pi\)
0.339608 + 0.940567i \(0.389705\pi\)
\(578\) 9.24621 0.384592
\(579\) 32.8078 + 56.8247i 1.36344 + 2.36155i
\(580\) 0 0
\(581\) −4.73863 −0.196592
\(582\) −4.31534 −0.178877
\(583\) −3.78078 6.54850i −0.156584 0.271211i
\(584\) −0.842329 + 1.45896i −0.0348558 + 0.0603721i
\(585\) 0 0
\(586\) 11.7808 20.4049i 0.486659 0.842919i
\(587\) 13.3693 23.1563i 0.551811 0.955764i −0.446333 0.894867i \(-0.647270\pi\)
0.998144 0.0608975i \(-0.0193963\pi\)
\(588\) −17.4384 −0.719149
\(589\) −25.6155 36.5863i −1.05547 1.50751i
\(590\) 0 0
\(591\) 18.4924 32.0298i 0.760677 1.31753i
\(592\) −2.34233 + 4.05703i −0.0962691 + 0.166743i
\(593\) 12.7732 + 22.1238i 0.524532 + 0.908517i 0.999592 + 0.0285632i \(0.00909317\pi\)
−0.475060 + 0.879954i \(0.657573\pi\)
\(594\) −0.719224 + 1.24573i −0.0295101 + 0.0511130i
\(595\) 0 0
\(596\) 16.0000 0.655386
\(597\) −7.36932 −0.301606
\(598\) −4.68466 8.11407i −0.191570 0.331809i
\(599\) 16.2462 + 28.1393i 0.663802 + 1.14974i 0.979609 + 0.200915i \(0.0643917\pi\)
−0.315806 + 0.948824i \(0.602275\pi\)
\(600\) 0 0
\(601\) −11.6307 −0.474425 −0.237213 0.971458i \(-0.576234\pi\)
−0.237213 + 0.971458i \(0.576234\pi\)
\(602\) −0.684658 1.18586i −0.0279046 0.0483322i
\(603\) 16.8078 29.1119i 0.684465 1.18553i
\(604\) −10.2462 17.7470i −0.416912 0.722113i
\(605\) 0 0
\(606\) −12.8078 + 22.1837i −0.520280 + 0.901151i
\(607\) −10.1922 −0.413690 −0.206845 0.978374i \(-0.566320\pi\)
−0.206845 + 0.978374i \(0.566320\pi\)
\(608\) −1.84233 + 3.95042i −0.0747163 + 0.160211i
\(609\) −2.24621 −0.0910211
\(610\) 0 0
\(611\) 2.87689 4.98293i 0.116387 0.201588i
\(612\) 9.12311 + 15.8017i 0.368780 + 0.638745i
\(613\) 15.3423 26.5737i 0.619671 1.07330i −0.369875 0.929082i \(-0.620599\pi\)
0.989546 0.144220i \(-0.0460672\pi\)
\(614\) −11.9654 20.7247i −0.482886 0.836382i
\(615\) 0 0
\(616\) −0.438447 −0.0176655
\(617\) 3.59612 + 6.22866i 0.144774 + 0.250756i 0.929289 0.369354i \(-0.120421\pi\)
−0.784514 + 0.620111i \(0.787088\pi\)
\(618\) −7.43845 12.8838i −0.299218 0.518261i
\(619\) 26.0540 1.04720 0.523599 0.851965i \(-0.324589\pi\)
0.523599 + 0.851965i \(0.324589\pi\)
\(620\) 0 0
\(621\) −3.36932 5.83583i −0.135206 0.234184i
\(622\) −2.00000 + 3.46410i −0.0801927 + 0.138898i
\(623\) −0.588540 1.01938i −0.0235794 0.0408407i
\(624\) −2.56155 + 4.43674i −0.102544 + 0.177612i
\(625\) 0 0
\(626\) −4.31534 −0.172476
\(627\) 11.1231 0.972638i 0.444214 0.0388434i
\(628\) −2.43845 −0.0973046
\(629\) 12.0000 20.7846i 0.478471 0.828737i
\(630\) 0 0
\(631\) −2.12311 3.67733i −0.0845195 0.146392i 0.820667 0.571407i \(-0.193602\pi\)
−0.905186 + 0.425015i \(0.860269\pi\)
\(632\) 5.56155 9.63289i 0.221227 0.383176i
\(633\) 4.24621 + 7.35465i 0.168772 + 0.292321i
\(634\) −18.6847 −0.742063
\(635\) 0 0
\(636\) −9.68466 16.7743i −0.384022 0.665145i
\(637\) 6.80776 + 11.7914i 0.269733 + 0.467192i
\(638\) 2.00000 0.0791808
\(639\) 57.8617 2.28898
\(640\) 0 0
\(641\) −3.71922 + 6.44188i −0.146900 + 0.254439i −0.930080 0.367356i \(-0.880263\pi\)
0.783180 + 0.621795i \(0.213596\pi\)
\(642\) 2.87689 + 4.98293i 0.113542 + 0.196660i
\(643\) −11.2808 + 19.5389i −0.444870 + 0.770538i −0.998043 0.0625284i \(-0.980084\pi\)
0.553173 + 0.833067i \(0.313417\pi\)
\(644\) 1.02699 1.77879i 0.0404690 0.0700943i
\(645\) 0 0
\(646\) 9.43845 20.2384i 0.371351 0.796270i
\(647\) −3.17708 −0.124904 −0.0624520 0.998048i \(-0.519892\pi\)
−0.0624520 + 0.998048i \(0.519892\pi\)
\(648\) 3.50000 6.06218i 0.137493 0.238145i
\(649\) −7.28078 + 12.6107i −0.285795 + 0.495012i
\(650\) 0 0
\(651\) 5.75379 9.96585i 0.225509 0.390593i
\(652\) 8.52699 + 14.7692i 0.333943 + 0.578406i
\(653\) 5.06913 0.198370 0.0991852 0.995069i \(-0.468376\pi\)
0.0991852 + 0.995069i \(0.468376\pi\)
\(654\) −36.4924 −1.42697
\(655\) 0 0
\(656\) 3.06155 + 5.30277i 0.119534 + 0.207038i
\(657\) 6.00000 0.234082
\(658\) 1.26137 0.0491732
\(659\) −9.46543 16.3946i −0.368721 0.638643i 0.620645 0.784092i \(-0.286871\pi\)
−0.989366 + 0.145448i \(0.953538\pi\)
\(660\) 0 0
\(661\) 19.9309 + 34.5213i 0.775221 + 1.34272i 0.934670 + 0.355516i \(0.115695\pi\)
−0.159449 + 0.987206i \(0.550972\pi\)
\(662\) −11.7462 + 20.3450i −0.456529 + 0.790732i
\(663\) 13.1231 22.7299i 0.509659 0.882756i
\(664\) 10.8078 0.419423
\(665\) 0 0
\(666\) 16.6847 0.646517
\(667\) −4.68466 + 8.11407i −0.181391 + 0.314178i
\(668\) 0.342329 0.592932i 0.0132451 0.0229412i
\(669\) 14.4924 + 25.1016i 0.560309 + 0.970484i
\(670\) 0 0
\(671\) −2.56155 4.43674i −0.0988876 0.171278i
\(672\) −1.12311 −0.0433247
\(673\) −46.1080 −1.77733 −0.888665 0.458556i \(-0.848367\pi\)
−0.888665 + 0.458556i \(0.848367\pi\)
\(674\) 10.5270 + 18.2333i 0.405484 + 0.702320i
\(675\) 0 0
\(676\) −9.00000 −0.346154
\(677\) 23.1771 0.890768 0.445384 0.895340i \(-0.353067\pi\)
0.445384 + 0.895340i \(0.353067\pi\)
\(678\) −21.5270 37.2858i −0.826739 1.43195i
\(679\) −0.369317 + 0.639676i −0.0141731 + 0.0245485i
\(680\) 0 0
\(681\) 25.5270 44.2140i 0.978196 1.69429i
\(682\) −5.12311 + 8.87348i −0.196174 + 0.339783i
\(683\) −28.0000 −1.07139 −0.535695 0.844411i \(-0.679950\pi\)
−0.535695 + 0.844411i \(0.679950\pi\)
\(684\) 15.4654 1.35234i 0.591336 0.0517082i
\(685\) 0 0
\(686\) −3.02699 + 5.24290i −0.115571 + 0.200175i
\(687\) −16.4924 + 28.5657i −0.629225 + 1.08985i
\(688\) 1.56155 + 2.70469i 0.0595336 + 0.103115i
\(689\) −7.56155 + 13.0970i −0.288072 + 0.498956i
\(690\) 0 0
\(691\) −21.0691 −0.801507 −0.400754 0.916186i \(-0.631252\pi\)
−0.400754 + 0.916186i \(0.631252\pi\)
\(692\) 5.80776 0.220778
\(693\) 0.780776 + 1.35234i 0.0296592 + 0.0513713i
\(694\) 0.842329 + 1.45896i 0.0319744 + 0.0553813i
\(695\) 0 0
\(696\) 5.12311 0.194191
\(697\) −15.6847 27.1666i −0.594099 1.02901i
\(698\) 7.12311 12.3376i 0.269614 0.466984i
\(699\) 2.96543 + 5.13628i 0.112163 + 0.194272i
\(700\) 0 0
\(701\) −3.24621 + 5.62260i −0.122608 + 0.212363i −0.920795 0.390046i \(-0.872459\pi\)
0.798188 + 0.602409i \(0.205792\pi\)
\(702\) 2.87689 0.108581
\(703\) −11.7116 16.7276i −0.441713 0.630892i
\(704\) 1.00000 0.0376889
\(705\) 0 0
\(706\) 12.0885 20.9380i 0.454958 0.788011i
\(707\) 2.19224 + 3.79706i 0.0824475 + 0.142803i
\(708\) −18.6501 + 32.3029i −0.700913 + 1.21402i
\(709\) 20.0000 + 34.6410i 0.751116 + 1.30097i 0.947282 + 0.320400i \(0.103817\pi\)
−0.196167 + 0.980571i \(0.562849\pi\)
\(710\) 0 0
\(711\) −39.6155 −1.48570
\(712\) 1.34233 + 2.32498i 0.0503059 + 0.0871324i
\(713\) −24.0000 41.5692i −0.898807 1.55678i
\(714\) 5.75379 0.215330
\(715\) 0 0
\(716\) −5.74621 9.95273i −0.214746 0.371951i
\(717\) −23.3693 + 40.4768i −0.872743 + 1.51164i
\(718\) −7.56155 13.0970i −0.282195 0.488775i
\(719\) −7.43845 + 12.8838i −0.277407 + 0.480483i −0.970740 0.240134i \(-0.922808\pi\)
0.693332 + 0.720618i \(0.256142\pi\)
\(720\) 0 0
\(721\) −2.54640 −0.0948328
\(722\) −12.2116 14.5560i −0.454470 0.541716i
\(723\) −21.9309 −0.815618
\(724\) −10.6847 + 18.5064i −0.397092 + 0.687784i
\(725\) 0 0
\(726\) 12.8078 + 22.1837i 0.475341 + 0.823314i
\(727\) −4.00000 + 6.92820i −0.148352 + 0.256953i −0.930618 0.365991i \(-0.880730\pi\)
0.782267 + 0.622944i \(0.214063\pi\)
\(728\) 0.438447 + 0.759413i 0.0162499 + 0.0281457i
\(729\) −35.9848 −1.33277
\(730\) 0 0
\(731\) −8.00000 13.8564i −0.295891 0.512498i
\(732\) −6.56155 11.3649i −0.242522 0.420060i
\(733\) 26.9309 0.994714 0.497357 0.867546i \(-0.334304\pi\)
0.497357 + 0.867546i \(0.334304\pi\)
\(734\) 17.7538 0.655304
\(735\) 0 0
\(736\) −2.34233 + 4.05703i −0.0863394 + 0.149544i
\(737\) 4.71922 + 8.17394i 0.173835 + 0.301091i
\(738\) 10.9039 18.8861i 0.401377 0.695206i
\(739\) −9.37689 + 16.2413i −0.344935 + 0.597444i −0.985342 0.170591i \(-0.945432\pi\)
0.640407 + 0.768036i \(0.278766\pi\)
\(740\) 0 0
\(741\) −12.8078 18.2931i −0.470505 0.672016i
\(742\) −3.31534 −0.121710
\(743\) −9.21922 + 15.9682i −0.338221 + 0.585815i −0.984098 0.177626i \(-0.943158\pi\)
0.645878 + 0.763441i \(0.276492\pi\)
\(744\) −13.1231 + 22.7299i −0.481116 + 0.833318i
\(745\) 0 0
\(746\) −17.9039 + 31.0104i −0.655508 + 1.13537i
\(747\) −19.2462 33.3354i −0.704182 1.21968i
\(748\) −5.12311 −0.187319
\(749\) 0.984845 0.0359855
\(750\) 0 0
\(751\) 17.4384 + 30.2043i 0.636338 + 1.10217i 0.986230 + 0.165380i \(0.0528849\pi\)
−0.349892 + 0.936790i \(0.613782\pi\)
\(752\) −2.87689 −0.104910
\(753\) 66.4233 2.42060
\(754\) −2.00000 3.46410i −0.0728357 0.126155i
\(755\) 0 0
\(756\) 0.315342 + 0.546188i 0.0114689 + 0.0198647i
\(757\) −9.78078 + 16.9408i −0.355488 + 0.615724i −0.987201 0.159478i \(-0.949019\pi\)
0.631713 + 0.775202i \(0.282352\pi\)
\(758\) 0.246211 0.426450i 0.00894280 0.0154894i
\(759\) 12.0000 0.435572
\(760\) 0 0
\(761\) −51.9848 −1.88445 −0.942225 0.334982i \(-0.891270\pi\)
−0.942225 + 0.334982i \(0.891270\pi\)
\(762\) −19.9309 + 34.5213i −0.722019 + 1.25057i
\(763\) −3.12311 + 5.40938i −0.113064 + 0.195833i
\(764\) 2.68466 + 4.64996i 0.0971275 + 0.168230i
\(765\) 0 0
\(766\) 2.56155 + 4.43674i 0.0925527 + 0.160306i
\(767\) 29.1231 1.05157
\(768\) 2.56155 0.0924321
\(769\) −13.2462 22.9431i −0.477671 0.827350i 0.522002 0.852944i \(-0.325185\pi\)
−0.999672 + 0.0255946i \(0.991852\pi\)
\(770\) 0 0
\(771\) −33.4384 −1.20426
\(772\) −25.6155 −0.921923
\(773\) −7.15009 12.3843i −0.257171 0.445433i 0.708312 0.705900i \(-0.249457\pi\)
−0.965483 + 0.260466i \(0.916124\pi\)
\(774\) 5.56155 9.63289i 0.199906 0.346247i
\(775\) 0 0
\(776\) 0.842329 1.45896i 0.0302379 0.0523735i
\(777\) 2.63068 4.55648i 0.0943752 0.163463i
\(778\) −19.1231 −0.685597
\(779\) −26.5885 + 2.32498i −0.952633 + 0.0833011i
\(780\) 0 0
\(781\) −8.12311 + 14.0696i −0.290668 + 0.503451i
\(782\) 12.0000 20.7846i 0.429119 0.743256i
\(783\) −1.43845 2.49146i −0.0514059 0.0890376i
\(784\) 3.40388 5.89570i 0.121567 0.210561i