Properties

Label 882.2.h.m.79.1
Level $882$
Weight $2$
Character 882.79
Analytic conductor $7.043$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 882 = 2 \cdot 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 882.h (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(7.04280545828\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\sqrt{-3}, \sqrt{-11})\)
Defining polynomial: \(x^{4} - x^{3} - 2 x^{2} - 3 x + 9\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 126)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 79.1
Root \(1.68614 + 0.396143i\) of defining polynomial
Character \(\chi\) \(=\) 882.79
Dual form 882.2.h.m.67.1

$q$-expansion

\(f(q)\) \(=\) \(q+(0.500000 + 0.866025i) q^{2} +(-1.68614 - 0.396143i) q^{3} +(-0.500000 + 0.866025i) q^{4} -1.37228 q^{5} +(-0.500000 - 1.65831i) q^{6} -1.00000 q^{8} +(2.68614 + 1.33591i) q^{9} +O(q^{10})\) \(q+(0.500000 + 0.866025i) q^{2} +(-1.68614 - 0.396143i) q^{3} +(-0.500000 + 0.866025i) q^{4} -1.37228 q^{5} +(-0.500000 - 1.65831i) q^{6} -1.00000 q^{8} +(2.68614 + 1.33591i) q^{9} +(-0.686141 - 1.18843i) q^{10} +4.37228 q^{11} +(1.18614 - 1.26217i) q^{12} +(-1.00000 - 1.73205i) q^{13} +(2.31386 + 0.543620i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(2.18614 + 3.78651i) q^{17} +(0.186141 + 2.99422i) q^{18} +(-2.50000 + 4.33013i) q^{19} +(0.686141 - 1.18843i) q^{20} +(2.18614 + 3.78651i) q^{22} -7.37228 q^{23} +(1.68614 + 0.396143i) q^{24} -3.11684 q^{25} +(1.00000 - 1.73205i) q^{26} +(-4.00000 - 3.31662i) q^{27} +(-1.37228 + 2.37686i) q^{29} +(0.686141 + 2.27567i) q^{30} +(-1.00000 + 1.73205i) q^{31} +(0.500000 - 0.866025i) q^{32} +(-7.37228 - 1.73205i) q^{33} +(-2.18614 + 3.78651i) q^{34} +(-2.50000 + 1.65831i) q^{36} +(-1.00000 + 1.73205i) q^{37} -5.00000 q^{38} +(1.00000 + 3.31662i) q^{39} +1.37228 q^{40} +(-5.18614 - 8.98266i) q^{41} +(-4.55842 + 7.89542i) q^{43} +(-2.18614 + 3.78651i) q^{44} +(-3.68614 - 1.83324i) q^{45} +(-3.68614 - 6.38458i) q^{46} +(0.500000 + 1.65831i) q^{48} +(-1.55842 - 2.69927i) q^{50} +(-2.18614 - 7.25061i) q^{51} +2.00000 q^{52} +(-1.37228 - 2.37686i) q^{53} +(0.872281 - 5.12241i) q^{54} -6.00000 q^{55} +(5.93070 - 6.31084i) q^{57} -2.74456 q^{58} +(-3.55842 + 6.16337i) q^{59} +(-1.62772 + 1.73205i) q^{60} +(7.05842 + 12.2255i) q^{61} -2.00000 q^{62} +1.00000 q^{64} +(1.37228 + 2.37686i) q^{65} +(-2.18614 - 7.25061i) q^{66} +(-7.55842 + 13.0916i) q^{67} -4.37228 q^{68} +(12.4307 + 2.92048i) q^{69} +10.1168 q^{71} +(-2.68614 - 1.33591i) q^{72} +(2.55842 + 4.43132i) q^{73} -2.00000 q^{74} +(5.25544 + 1.23472i) q^{75} +(-2.50000 - 4.33013i) q^{76} +(-2.37228 + 2.52434i) q^{78} +(-6.05842 - 10.4935i) q^{79} +(0.686141 + 1.18843i) q^{80} +(5.43070 + 7.17687i) q^{81} +(5.18614 - 8.98266i) q^{82} +(2.74456 - 4.75372i) q^{83} +(-3.00000 - 5.19615i) q^{85} -9.11684 q^{86} +(3.25544 - 3.46410i) q^{87} -4.37228 q^{88} +(-1.62772 + 2.81929i) q^{89} +(-0.255437 - 4.10891i) q^{90} +(3.68614 - 6.38458i) q^{92} +(2.37228 - 2.52434i) q^{93} +(3.43070 - 5.94215i) q^{95} +(-1.18614 + 1.26217i) q^{96} +(-4.55842 + 7.89542i) q^{97} +(11.7446 + 5.84096i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q + 2q^{2} - q^{3} - 2q^{4} + 6q^{5} - 2q^{6} - 4q^{8} + 5q^{9} + O(q^{10}) \) \( 4q + 2q^{2} - q^{3} - 2q^{4} + 6q^{5} - 2q^{6} - 4q^{8} + 5q^{9} + 3q^{10} + 6q^{11} - q^{12} - 4q^{13} + 15q^{15} - 2q^{16} + 3q^{17} - 5q^{18} - 10q^{19} - 3q^{20} + 3q^{22} - 18q^{23} + q^{24} + 22q^{25} + 4q^{26} - 16q^{27} + 6q^{29} - 3q^{30} - 4q^{31} + 2q^{32} - 18q^{33} - 3q^{34} - 10q^{36} - 4q^{37} - 20q^{38} + 4q^{39} - 6q^{40} - 15q^{41} - q^{43} - 3q^{44} - 9q^{45} - 9q^{46} + 2q^{48} + 11q^{50} - 3q^{51} + 8q^{52} + 6q^{53} - 8q^{54} - 24q^{55} - 5q^{57} + 12q^{58} + 3q^{59} - 18q^{60} + 11q^{61} - 8q^{62} + 4q^{64} - 6q^{65} - 3q^{66} - 13q^{67} - 6q^{68} + 21q^{69} + 6q^{71} - 5q^{72} - 7q^{73} - 8q^{74} + 44q^{75} - 10q^{76} + 2q^{78} - 7q^{79} - 3q^{80} - 7q^{81} + 15q^{82} - 12q^{83} - 12q^{85} - 2q^{86} + 36q^{87} - 6q^{88} - 18q^{89} - 24q^{90} + 9q^{92} - 2q^{93} - 15q^{95} + q^{96} - q^{97} + 24q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/882\mathbb{Z}\right)^\times\).

\(n\) \(199\) \(785\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\)

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
\(3\) −1.68614 0.396143i −0.973494 0.228714i
\(4\) −0.500000 + 0.866025i −0.250000 + 0.433013i
\(5\) −1.37228 −0.613703 −0.306851 0.951757i \(-0.599275\pi\)
−0.306851 + 0.951757i \(0.599275\pi\)
\(6\) −0.500000 1.65831i −0.204124 0.677003i
\(7\) 0 0
\(8\) −1.00000 −0.353553
\(9\) 2.68614 + 1.33591i 0.895380 + 0.445302i
\(10\) −0.686141 1.18843i −0.216977 0.375815i
\(11\) 4.37228 1.31829 0.659146 0.752015i \(-0.270918\pi\)
0.659146 + 0.752015i \(0.270918\pi\)
\(12\) 1.18614 1.26217i 0.342409 0.364357i
\(13\) −1.00000 1.73205i −0.277350 0.480384i 0.693375 0.720577i \(-0.256123\pi\)
−0.970725 + 0.240192i \(0.922790\pi\)
\(14\) 0 0
\(15\) 2.31386 + 0.543620i 0.597436 + 0.140362i
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) 2.18614 + 3.78651i 0.530217 + 0.918363i 0.999379 + 0.0352504i \(0.0112229\pi\)
−0.469162 + 0.883112i \(0.655444\pi\)
\(18\) 0.186141 + 2.99422i 0.0438738 + 0.705744i
\(19\) −2.50000 + 4.33013i −0.573539 + 0.993399i 0.422659 + 0.906289i \(0.361097\pi\)
−0.996199 + 0.0871106i \(0.972237\pi\)
\(20\) 0.686141 1.18843i 0.153426 0.265741i
\(21\) 0 0
\(22\) 2.18614 + 3.78651i 0.466087 + 0.807286i
\(23\) −7.37228 −1.53723 −0.768613 0.639713i \(-0.779053\pi\)
−0.768613 + 0.639713i \(0.779053\pi\)
\(24\) 1.68614 + 0.396143i 0.344182 + 0.0808625i
\(25\) −3.11684 −0.623369
\(26\) 1.00000 1.73205i 0.196116 0.339683i
\(27\) −4.00000 3.31662i −0.769800 0.638285i
\(28\) 0 0
\(29\) −1.37228 + 2.37686i −0.254826 + 0.441372i −0.964848 0.262807i \(-0.915352\pi\)
0.710022 + 0.704179i \(0.248685\pi\)
\(30\) 0.686141 + 2.27567i 0.125272 + 0.415479i
\(31\) −1.00000 + 1.73205i −0.179605 + 0.311086i −0.941745 0.336327i \(-0.890815\pi\)
0.762140 + 0.647412i \(0.224149\pi\)
\(32\) 0.500000 0.866025i 0.0883883 0.153093i
\(33\) −7.37228 1.73205i −1.28335 0.301511i
\(34\) −2.18614 + 3.78651i −0.374920 + 0.649381i
\(35\) 0 0
\(36\) −2.50000 + 1.65831i −0.416667 + 0.276385i
\(37\) −1.00000 + 1.73205i −0.164399 + 0.284747i −0.936442 0.350823i \(-0.885902\pi\)
0.772043 + 0.635571i \(0.219235\pi\)
\(38\) −5.00000 −0.811107
\(39\) 1.00000 + 3.31662i 0.160128 + 0.531085i
\(40\) 1.37228 0.216977
\(41\) −5.18614 8.98266i −0.809939 1.40286i −0.912906 0.408171i \(-0.866167\pi\)
0.102966 0.994685i \(-0.467167\pi\)
\(42\) 0 0
\(43\) −4.55842 + 7.89542i −0.695153 + 1.20404i 0.274976 + 0.961451i \(0.411330\pi\)
−0.970129 + 0.242589i \(0.922003\pi\)
\(44\) −2.18614 + 3.78651i −0.329573 + 0.570837i
\(45\) −3.68614 1.83324i −0.549497 0.273283i
\(46\) −3.68614 6.38458i −0.543492 0.941355i
\(47\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(48\) 0.500000 + 1.65831i 0.0721688 + 0.239357i
\(49\) 0 0
\(50\) −1.55842 2.69927i −0.220394 0.381734i
\(51\) −2.18614 7.25061i −0.306121 1.01529i
\(52\) 2.00000 0.277350
\(53\) −1.37228 2.37686i −0.188497 0.326487i 0.756252 0.654280i \(-0.227028\pi\)
−0.944749 + 0.327793i \(0.893695\pi\)
\(54\) 0.872281 5.12241i 0.118702 0.697072i
\(55\) −6.00000 −0.809040
\(56\) 0 0
\(57\) 5.93070 6.31084i 0.785541 0.835892i
\(58\) −2.74456 −0.360379
\(59\) −3.55842 + 6.16337i −0.463267 + 0.802402i −0.999121 0.0419083i \(-0.986656\pi\)
0.535854 + 0.844310i \(0.319990\pi\)
\(60\) −1.62772 + 1.73205i −0.210138 + 0.223607i
\(61\) 7.05842 + 12.2255i 0.903738 + 1.56532i 0.822602 + 0.568618i \(0.192522\pi\)
0.0811364 + 0.996703i \(0.474145\pi\)
\(62\) −2.00000 −0.254000
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) 1.37228 + 2.37686i 0.170211 + 0.294813i
\(66\) −2.18614 7.25061i −0.269095 0.892488i
\(67\) −7.55842 + 13.0916i −0.923408 + 1.59939i −0.129307 + 0.991605i \(0.541275\pi\)
−0.794101 + 0.607785i \(0.792058\pi\)
\(68\) −4.37228 −0.530217
\(69\) 12.4307 + 2.92048i 1.49648 + 0.351585i
\(70\) 0 0
\(71\) 10.1168 1.20065 0.600324 0.799757i \(-0.295038\pi\)
0.600324 + 0.799757i \(0.295038\pi\)
\(72\) −2.68614 1.33591i −0.316565 0.157438i
\(73\) 2.55842 + 4.43132i 0.299441 + 0.518646i 0.976008 0.217734i \(-0.0698666\pi\)
−0.676567 + 0.736381i \(0.736533\pi\)
\(74\) −2.00000 −0.232495
\(75\) 5.25544 + 1.23472i 0.606846 + 0.142573i
\(76\) −2.50000 4.33013i −0.286770 0.496700i
\(77\) 0 0
\(78\) −2.37228 + 2.52434i −0.268608 + 0.285825i
\(79\) −6.05842 10.4935i −0.681626 1.18061i −0.974485 0.224455i \(-0.927940\pi\)
0.292859 0.956156i \(-0.405393\pi\)
\(80\) 0.686141 + 1.18843i 0.0767129 + 0.132871i
\(81\) 5.43070 + 7.17687i 0.603411 + 0.797430i
\(82\) 5.18614 8.98266i 0.572713 0.991969i
\(83\) 2.74456 4.75372i 0.301255 0.521789i −0.675166 0.737666i \(-0.735928\pi\)
0.976420 + 0.215877i \(0.0692612\pi\)
\(84\) 0 0
\(85\) −3.00000 5.19615i −0.325396 0.563602i
\(86\) −9.11684 −0.983095
\(87\) 3.25544 3.46410i 0.349020 0.371391i
\(88\) −4.37228 −0.466087
\(89\) −1.62772 + 2.81929i −0.172538 + 0.298844i −0.939306 0.343079i \(-0.888530\pi\)
0.766769 + 0.641924i \(0.221863\pi\)
\(90\) −0.255437 4.10891i −0.0269255 0.433117i
\(91\) 0 0
\(92\) 3.68614 6.38458i 0.384307 0.665639i
\(93\) 2.37228 2.52434i 0.245994 0.261762i
\(94\) 0 0
\(95\) 3.43070 5.94215i 0.351983 0.609652i
\(96\) −1.18614 + 1.26217i −0.121060 + 0.128820i
\(97\) −4.55842 + 7.89542i −0.462838 + 0.801658i −0.999101 0.0423924i \(-0.986502\pi\)
0.536263 + 0.844051i \(0.319835\pi\)
\(98\) 0 0
\(99\) 11.7446 + 5.84096i 1.18037 + 0.587039i
\(100\) 1.55842 2.69927i 0.155842 0.269927i
\(101\) 7.37228 0.733569 0.366785 0.930306i \(-0.380459\pi\)
0.366785 + 0.930306i \(0.380459\pi\)
\(102\) 5.18614 5.51856i 0.513504 0.546419i
\(103\) −10.0000 −0.985329 −0.492665 0.870219i \(-0.663977\pi\)
−0.492665 + 0.870219i \(0.663977\pi\)
\(104\) 1.00000 + 1.73205i 0.0980581 + 0.169842i
\(105\) 0 0
\(106\) 1.37228 2.37686i 0.133288 0.230861i
\(107\) 0.813859 1.40965i 0.0786788 0.136276i −0.824001 0.566588i \(-0.808263\pi\)
0.902680 + 0.430312i \(0.141597\pi\)
\(108\) 4.87228 1.80579i 0.468835 0.173762i
\(109\) −7.00000 12.1244i −0.670478 1.16130i −0.977769 0.209687i \(-0.932756\pi\)
0.307290 0.951616i \(-0.400578\pi\)
\(110\) −3.00000 5.19615i −0.286039 0.495434i
\(111\) 2.37228 2.52434i 0.225167 0.239600i
\(112\) 0 0
\(113\) −0.686141 1.18843i −0.0645467 0.111798i 0.831946 0.554856i \(-0.187227\pi\)
−0.896493 + 0.443058i \(0.853893\pi\)
\(114\) 8.43070 + 1.98072i 0.789608 + 0.185511i
\(115\) 10.1168 0.943401
\(116\) −1.37228 2.37686i −0.127413 0.220686i
\(117\) −0.372281 5.98844i −0.0344174 0.553631i
\(118\) −7.11684 −0.655159
\(119\) 0 0
\(120\) −2.31386 0.543620i −0.211225 0.0496255i
\(121\) 8.11684 0.737895
\(122\) −7.05842 + 12.2255i −0.639040 + 1.10685i
\(123\) 5.18614 + 17.2005i 0.467619 + 1.55092i
\(124\) −1.00000 1.73205i −0.0898027 0.155543i
\(125\) 11.1386 0.996266
\(126\) 0 0
\(127\) −14.1168 −1.25267 −0.626334 0.779555i \(-0.715445\pi\)
−0.626334 + 0.779555i \(0.715445\pi\)
\(128\) 0.500000 + 0.866025i 0.0441942 + 0.0765466i
\(129\) 10.8139 11.5070i 0.952107 1.01313i
\(130\) −1.37228 + 2.37686i −0.120357 + 0.208464i
\(131\) −7.37228 −0.644119 −0.322060 0.946719i \(-0.604375\pi\)
−0.322060 + 0.946719i \(0.604375\pi\)
\(132\) 5.18614 5.51856i 0.451396 0.480329i
\(133\) 0 0
\(134\) −15.1168 −1.30590
\(135\) 5.48913 + 4.55134i 0.472429 + 0.391717i
\(136\) −2.18614 3.78651i −0.187460 0.324690i
\(137\) 16.3723 1.39878 0.699389 0.714741i \(-0.253455\pi\)
0.699389 + 0.714741i \(0.253455\pi\)
\(138\) 3.68614 + 12.2255i 0.313785 + 1.04071i
\(139\) 10.6168 + 18.3889i 0.900509 + 1.55973i 0.826835 + 0.562445i \(0.190139\pi\)
0.0736742 + 0.997282i \(0.476528\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 5.05842 + 8.76144i 0.424493 + 0.735244i
\(143\) −4.37228 7.57301i −0.365629 0.633287i
\(144\) −0.186141 2.99422i −0.0155117 0.249518i
\(145\) 1.88316 3.26172i 0.156388 0.270871i
\(146\) −2.55842 + 4.43132i −0.211737 + 0.366738i
\(147\) 0 0
\(148\) −1.00000 1.73205i −0.0821995 0.142374i
\(149\) 14.7446 1.20792 0.603961 0.797014i \(-0.293588\pi\)
0.603961 + 0.797014i \(0.293588\pi\)
\(150\) 1.55842 + 5.16870i 0.127245 + 0.422023i
\(151\) −8.11684 −0.660539 −0.330270 0.943887i \(-0.607140\pi\)
−0.330270 + 0.943887i \(0.607140\pi\)
\(152\) 2.50000 4.33013i 0.202777 0.351220i
\(153\) 0.813859 + 13.0916i 0.0657966 + 1.05839i
\(154\) 0 0
\(155\) 1.37228 2.37686i 0.110224 0.190914i
\(156\) −3.37228 0.792287i −0.269999 0.0634337i
\(157\) 4.05842 7.02939i 0.323897 0.561007i −0.657391 0.753549i \(-0.728340\pi\)
0.981289 + 0.192543i \(0.0616734\pi\)
\(158\) 6.05842 10.4935i 0.481982 0.834818i
\(159\) 1.37228 + 4.55134i 0.108829 + 0.360945i
\(160\) −0.686141 + 1.18843i −0.0542442 + 0.0939537i
\(161\) 0 0
\(162\) −3.50000 + 8.29156i −0.274986 + 0.651447i
\(163\) −8.11684 + 14.0588i −0.635760 + 1.10117i 0.350593 + 0.936528i \(0.385980\pi\)
−0.986354 + 0.164641i \(0.947353\pi\)
\(164\) 10.3723 0.809939
\(165\) 10.1168 + 2.37686i 0.787595 + 0.185038i
\(166\) 5.48913 0.426039
\(167\) −8.74456 15.1460i −0.676675 1.17203i −0.975976 0.217876i \(-0.930087\pi\)
0.299302 0.954158i \(-0.403246\pi\)
\(168\) 0 0
\(169\) 4.50000 7.79423i 0.346154 0.599556i
\(170\) 3.00000 5.19615i 0.230089 0.398527i
\(171\) −12.5000 + 8.29156i −0.955899 + 0.634072i
\(172\) −4.55842 7.89542i −0.347576 0.602020i
\(173\) 3.00000 + 5.19615i 0.228086 + 0.395056i 0.957241 0.289292i \(-0.0934200\pi\)
−0.729155 + 0.684349i \(0.760087\pi\)
\(174\) 4.62772 + 1.08724i 0.350826 + 0.0824235i
\(175\) 0 0
\(176\) −2.18614 3.78651i −0.164787 0.285419i
\(177\) 8.44158 8.98266i 0.634508 0.675178i
\(178\) −3.25544 −0.244005
\(179\) −7.37228 12.7692i −0.551030 0.954412i −0.998201 0.0599635i \(-0.980902\pi\)
0.447170 0.894449i \(-0.352432\pi\)
\(180\) 3.43070 2.27567i 0.255710 0.169619i
\(181\) 18.1168 1.34661 0.673307 0.739363i \(-0.264873\pi\)
0.673307 + 0.739363i \(0.264873\pi\)
\(182\) 0 0
\(183\) −7.05842 23.4101i −0.521774 1.73053i
\(184\) 7.37228 0.543492
\(185\) 1.37228 2.37686i 0.100892 0.174750i
\(186\) 3.37228 + 0.792287i 0.247268 + 0.0580933i
\(187\) 9.55842 + 16.5557i 0.698981 + 1.21067i
\(188\) 0 0
\(189\) 0 0
\(190\) 6.86141 0.497779
\(191\) 0.941578 + 1.63086i 0.0681302 + 0.118005i 0.898078 0.439836i \(-0.144963\pi\)
−0.829948 + 0.557841i \(0.811630\pi\)
\(192\) −1.68614 0.396143i −0.121687 0.0285892i
\(193\) 3.50000 6.06218i 0.251936 0.436365i −0.712123 0.702055i \(-0.752266\pi\)
0.964059 + 0.265689i \(0.0855996\pi\)
\(194\) −9.11684 −0.654551
\(195\) −1.37228 4.55134i −0.0982711 0.325928i
\(196\) 0 0
\(197\) −6.00000 −0.427482 −0.213741 0.976890i \(-0.568565\pi\)
−0.213741 + 0.976890i \(0.568565\pi\)
\(198\) 0.813859 + 13.0916i 0.0578385 + 0.930377i
\(199\) 5.00000 + 8.66025i 0.354441 + 0.613909i 0.987022 0.160585i \(-0.0513380\pi\)
−0.632581 + 0.774494i \(0.718005\pi\)
\(200\) 3.11684 0.220394
\(201\) 17.9307 19.0800i 1.26473 1.34580i
\(202\) 3.68614 + 6.38458i 0.259356 + 0.449218i
\(203\) 0 0
\(204\) 7.37228 + 1.73205i 0.516163 + 0.121268i
\(205\) 7.11684 + 12.3267i 0.497062 + 0.860937i
\(206\) −5.00000 8.66025i −0.348367 0.603388i
\(207\) −19.8030 9.84868i −1.37640 0.684531i
\(208\) −1.00000 + 1.73205i −0.0693375 + 0.120096i
\(209\) −10.9307 + 18.9325i −0.756093 + 1.30959i
\(210\) 0 0
\(211\) 8.00000 + 13.8564i 0.550743 + 0.953914i 0.998221 + 0.0596196i \(0.0189888\pi\)
−0.447478 + 0.894295i \(0.647678\pi\)
\(212\) 2.74456 0.188497
\(213\) −17.0584 4.00772i −1.16882 0.274605i
\(214\) 1.62772 0.111269
\(215\) 6.25544 10.8347i 0.426617 0.738923i
\(216\) 4.00000 + 3.31662i 0.272166 + 0.225668i
\(217\) 0 0
\(218\) 7.00000 12.1244i 0.474100 0.821165i
\(219\) −2.55842 8.48533i −0.172882 0.573385i
\(220\) 3.00000 5.19615i 0.202260 0.350325i
\(221\) 4.37228 7.57301i 0.294111 0.509416i
\(222\) 3.37228 + 0.792287i 0.226333 + 0.0531748i
\(223\) 2.00000 3.46410i 0.133930 0.231973i −0.791258 0.611482i \(-0.790574\pi\)
0.925188 + 0.379509i \(0.123907\pi\)
\(224\) 0 0
\(225\) −8.37228 4.16381i −0.558152 0.277588i
\(226\) 0.686141 1.18843i 0.0456414 0.0790532i
\(227\) −23.7446 −1.57598 −0.787991 0.615687i \(-0.788879\pi\)
−0.787991 + 0.615687i \(0.788879\pi\)
\(228\) 2.50000 + 8.29156i 0.165567 + 0.549122i
\(229\) −20.1168 −1.32936 −0.664679 0.747129i \(-0.731432\pi\)
−0.664679 + 0.747129i \(0.731432\pi\)
\(230\) 5.05842 + 8.76144i 0.333542 + 0.577713i
\(231\) 0 0
\(232\) 1.37228 2.37686i 0.0900947 0.156049i
\(233\) 5.87228 10.1711i 0.384706 0.666330i −0.607022 0.794685i \(-0.707636\pi\)
0.991728 + 0.128354i \(0.0409695\pi\)
\(234\) 5.00000 3.31662i 0.326860 0.216815i
\(235\) 0 0
\(236\) −3.55842 6.16337i −0.231634 0.401201i
\(237\) 6.05842 + 20.0935i 0.393537 + 1.30521i
\(238\) 0 0
\(239\) 9.43070 + 16.3345i 0.610021 + 1.05659i 0.991236 + 0.132102i \(0.0421725\pi\)
−0.381215 + 0.924487i \(0.624494\pi\)
\(240\) −0.686141 2.27567i −0.0442902 0.146894i
\(241\) 0.883156 0.0568891 0.0284445 0.999595i \(-0.490945\pi\)
0.0284445 + 0.999595i \(0.490945\pi\)
\(242\) 4.05842 + 7.02939i 0.260885 + 0.451867i
\(243\) −6.31386 14.2525i −0.405034 0.914302i
\(244\) −14.1168 −0.903738
\(245\) 0 0
\(246\) −12.3030 + 13.0916i −0.784410 + 0.834688i
\(247\) 10.0000 0.636285
\(248\) 1.00000 1.73205i 0.0635001 0.109985i
\(249\) −6.51087 + 6.92820i −0.412610 + 0.439057i
\(250\) 5.56930 + 9.64630i 0.352233 + 0.610086i
\(251\) −9.00000 −0.568075 −0.284037 0.958813i \(-0.591674\pi\)
−0.284037 + 0.958813i \(0.591674\pi\)
\(252\) 0 0
\(253\) −32.2337 −2.02651
\(254\) −7.05842 12.2255i −0.442885 0.767099i
\(255\) 3.00000 + 9.94987i 0.187867 + 0.623085i
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) 21.8614 1.36368 0.681839 0.731503i \(-0.261181\pi\)
0.681839 + 0.731503i \(0.261181\pi\)
\(258\) 15.3723 + 3.61158i 0.957036 + 0.224847i
\(259\) 0 0
\(260\) −2.74456 −0.170211
\(261\) −6.86141 + 4.55134i −0.424710 + 0.281721i
\(262\) −3.68614 6.38458i −0.227731 0.394441i
\(263\) 13.3723 0.824570 0.412285 0.911055i \(-0.364731\pi\)
0.412285 + 0.911055i \(0.364731\pi\)
\(264\) 7.37228 + 1.73205i 0.453733 + 0.106600i
\(265\) 1.88316 + 3.26172i 0.115681 + 0.200366i
\(266\) 0 0
\(267\) 3.86141 4.10891i 0.236314 0.251461i
\(268\) −7.55842 13.0916i −0.461704 0.799695i
\(269\) 3.68614 + 6.38458i 0.224748 + 0.389275i 0.956244 0.292571i \(-0.0945108\pi\)
−0.731496 + 0.681846i \(0.761177\pi\)
\(270\) −1.19702 + 7.02939i −0.0728480 + 0.427795i
\(271\) 9.11684 15.7908i 0.553809 0.959225i −0.444186 0.895934i \(-0.646507\pi\)
0.997995 0.0632906i \(-0.0201595\pi\)
\(272\) 2.18614 3.78651i 0.132554 0.229591i
\(273\) 0 0
\(274\) 8.18614 + 14.1788i 0.494543 + 0.856573i
\(275\) −13.6277 −0.821782
\(276\) −8.74456 + 9.30506i −0.526361 + 0.560099i
\(277\) 22.2337 1.33589 0.667946 0.744209i \(-0.267174\pi\)
0.667946 + 0.744209i \(0.267174\pi\)
\(278\) −10.6168 + 18.3889i −0.636756 + 1.10289i
\(279\) −5.00000 + 3.31662i −0.299342 + 0.198561i
\(280\) 0 0
\(281\) −5.31386 + 9.20387i −0.316998 + 0.549057i −0.979860 0.199685i \(-0.936008\pi\)
0.662862 + 0.748742i \(0.269342\pi\)
\(282\) 0 0
\(283\) −4.94158 + 8.55906i −0.293746 + 0.508784i −0.974692 0.223550i \(-0.928235\pi\)
0.680946 + 0.732333i \(0.261569\pi\)
\(284\) −5.05842 + 8.76144i −0.300162 + 0.519896i
\(285\) −8.13859 + 8.66025i −0.482089 + 0.512989i
\(286\) 4.37228 7.57301i 0.258538 0.447802i
\(287\) 0 0
\(288\) 2.50000 1.65831i 0.147314 0.0977170i
\(289\) −1.05842 + 1.83324i −0.0622601 + 0.107838i
\(290\) 3.76631 0.221165
\(291\) 10.8139 11.5070i 0.633920 0.674552i
\(292\) −5.11684 −0.299441
\(293\) 2.31386 + 4.00772i 0.135177 + 0.234134i 0.925665 0.378344i \(-0.123506\pi\)
−0.790488 + 0.612478i \(0.790173\pi\)
\(294\) 0 0
\(295\) 4.88316 8.45787i 0.284308 0.492436i
\(296\) 1.00000 1.73205i 0.0581238 0.100673i
\(297\) −17.4891 14.5012i −1.01482 0.841446i
\(298\) 7.37228 + 12.7692i 0.427065 + 0.739698i
\(299\) 7.37228 + 12.7692i 0.426350 + 0.738460i
\(300\) −3.69702 + 3.93398i −0.213447 + 0.227129i
\(301\) 0 0
\(302\) −4.05842 7.02939i −0.233536 0.404496i
\(303\) −12.4307 2.92048i −0.714125 0.167777i
\(304\) 5.00000 0.286770
\(305\) −9.68614 16.7769i −0.554627 0.960642i
\(306\) −10.9307 + 7.25061i −0.624867 + 0.414490i
\(307\) −13.0000 −0.741949 −0.370975 0.928643i \(-0.620976\pi\)
−0.370975 + 0.928643i \(0.620976\pi\)
\(308\) 0 0
\(309\) 16.8614 + 3.96143i 0.959212 + 0.225358i
\(310\) 2.74456 0.155881
\(311\) 13.1168 22.7190i 0.743788 1.28828i −0.206971 0.978347i \(-0.566361\pi\)
0.950759 0.309931i \(-0.100306\pi\)
\(312\) −1.00000 3.31662i −0.0566139 0.187767i
\(313\) 1.44158 + 2.49689i 0.0814828 + 0.141132i 0.903887 0.427771i \(-0.140701\pi\)
−0.822404 + 0.568904i \(0.807368\pi\)
\(314\) 8.11684 0.458060
\(315\) 0 0
\(316\) 12.1168 0.681626
\(317\) 3.00000 + 5.19615i 0.168497 + 0.291845i 0.937892 0.346929i \(-0.112775\pi\)
−0.769395 + 0.638774i \(0.779442\pi\)
\(318\) −3.25544 + 3.46410i −0.182556 + 0.194257i
\(319\) −6.00000 + 10.3923i −0.335936 + 0.581857i
\(320\) −1.37228 −0.0767129
\(321\) −1.93070 + 2.05446i −0.107761 + 0.114669i
\(322\) 0 0
\(323\) −21.8614 −1.21640
\(324\) −8.93070 + 1.11469i −0.496150 + 0.0619273i
\(325\) 3.11684 + 5.39853i 0.172891 + 0.299457i
\(326\) −16.2337 −0.899101
\(327\) 7.00000 + 23.2164i 0.387101 + 1.28387i
\(328\) 5.18614 + 8.98266i 0.286357 + 0.495984i
\(329\) 0 0
\(330\) 3.00000 + 9.94987i 0.165145 + 0.547723i
\(331\) 6.11684 + 10.5947i 0.336212 + 0.582337i 0.983717 0.179725i \(-0.0575207\pi\)
−0.647505 + 0.762061i \(0.724187\pi\)
\(332\) 2.74456 + 4.75372i 0.150627 + 0.260894i
\(333\) −5.00000 + 3.31662i −0.273998 + 0.181750i
\(334\) 8.74456 15.1460i 0.478481 0.828754i
\(335\) 10.3723 17.9653i 0.566698 0.981550i
\(336\) 0 0
\(337\) −4.55842 7.89542i −0.248313 0.430091i 0.714745 0.699385i \(-0.246543\pi\)
−0.963058 + 0.269294i \(0.913210\pi\)
\(338\) 9.00000 0.489535
\(339\) 0.686141 + 2.27567i 0.0372660 + 0.123597i
\(340\) 6.00000 0.325396
\(341\) −4.37228 + 7.57301i −0.236772 + 0.410102i
\(342\) −13.4307 6.67954i −0.726249 0.361188i
\(343\) 0 0
\(344\) 4.55842 7.89542i 0.245774 0.425692i
\(345\) −17.0584 4.00772i −0.918395 0.215768i
\(346\) −3.00000 + 5.19615i −0.161281 + 0.279347i
\(347\) −3.55842 + 6.16337i −0.191026 + 0.330867i −0.945591 0.325359i \(-0.894515\pi\)
0.754564 + 0.656226i \(0.227848\pi\)
\(348\) 1.37228 + 4.55134i 0.0735620 + 0.243978i
\(349\) 11.0000 19.0526i 0.588817 1.01986i −0.405571 0.914063i \(-0.632927\pi\)
0.994388 0.105797i \(-0.0337393\pi\)
\(350\) 0 0
\(351\) −1.74456 + 10.2448i −0.0931179 + 0.546828i
\(352\) 2.18614 3.78651i 0.116522 0.201821i
\(353\) −7.62772 −0.405983 −0.202991 0.979181i \(-0.565066\pi\)
−0.202991 + 0.979181i \(0.565066\pi\)
\(354\) 12.0000 + 2.81929i 0.637793 + 0.149844i
\(355\) −13.8832 −0.736841
\(356\) −1.62772 2.81929i −0.0862689 0.149422i
\(357\) 0 0
\(358\) 7.37228 12.7692i 0.389637 0.674871i
\(359\) 3.43070 5.94215i 0.181066 0.313615i −0.761178 0.648543i \(-0.775379\pi\)
0.942244 + 0.334928i \(0.108712\pi\)
\(360\) 3.68614 + 1.83324i 0.194277 + 0.0966203i
\(361\) −3.00000 5.19615i −0.157895 0.273482i
\(362\) 9.05842 + 15.6896i 0.476100 + 0.824630i
\(363\) −13.6861 3.21543i −0.718336 0.168767i
\(364\) 0 0
\(365\) −3.51087 6.08101i −0.183768 0.318295i
\(366\) 16.7446 17.8178i 0.875252 0.931353i
\(367\) 22.2337 1.16059 0.580295 0.814407i \(-0.302937\pi\)
0.580295 + 0.814407i \(0.302937\pi\)
\(368\) 3.68614 + 6.38458i 0.192153 + 0.332819i
\(369\) −1.93070 31.0569i −0.100508 1.61676i
\(370\) 2.74456 0.142683
\(371\) 0 0
\(372\) 1.00000 + 3.31662i 0.0518476 + 0.171959i
\(373\) −10.0000 −0.517780 −0.258890 0.965907i \(-0.583357\pi\)
−0.258890 + 0.965907i \(0.583357\pi\)
\(374\) −9.55842 + 16.5557i −0.494254 + 0.856073i
\(375\) −18.7812 4.41248i −0.969859 0.227860i
\(376\) 0 0
\(377\) 5.48913 0.282704
\(378\) 0 0
\(379\) 9.11684 0.468301 0.234150 0.972200i \(-0.424769\pi\)
0.234150 + 0.972200i \(0.424769\pi\)
\(380\) 3.43070 + 5.94215i 0.175991 + 0.304826i
\(381\) 23.8030 + 5.59230i 1.21946 + 0.286502i
\(382\) −0.941578 + 1.63086i −0.0481753 + 0.0834421i
\(383\) −21.2554 −1.08610 −0.543051 0.839700i \(-0.682731\pi\)
−0.543051 + 0.839700i \(0.682731\pi\)
\(384\) −0.500000 1.65831i −0.0255155 0.0846254i
\(385\) 0 0
\(386\) 7.00000 0.356291
\(387\) −22.7921 + 15.1186i −1.15859 + 0.768520i
\(388\) −4.55842 7.89542i −0.231419 0.400829i
\(389\) −34.9783 −1.77347 −0.886734 0.462280i \(-0.847031\pi\)
−0.886734 + 0.462280i \(0.847031\pi\)
\(390\) 3.25544 3.46410i 0.164845 0.175412i
\(391\) −16.1168 27.9152i −0.815064 1.41173i
\(392\) 0 0
\(393\) 12.4307 + 2.92048i 0.627046 + 0.147319i
\(394\) −3.00000 5.19615i −0.151138 0.261778i
\(395\) 8.31386 + 14.4000i 0.418316 + 0.724544i
\(396\) −10.9307 + 7.25061i −0.549289 + 0.364357i
\(397\) 11.0000 19.0526i 0.552074 0.956221i −0.446051 0.895008i \(-0.647170\pi\)
0.998125 0.0612128i \(-0.0194968\pi\)
\(398\) −5.00000 + 8.66025i −0.250627 + 0.434099i
\(399\) 0 0
\(400\) 1.55842 + 2.69927i 0.0779211 + 0.134963i
\(401\) −0.255437 −0.0127559 −0.00637797 0.999980i \(-0.502030\pi\)
−0.00637797 + 0.999980i \(0.502030\pi\)
\(402\) 25.4891 + 5.98844i 1.27128 + 0.298676i
\(403\) 4.00000 0.199254
\(404\) −3.68614 + 6.38458i −0.183392 + 0.317645i
\(405\) −7.45245 9.84868i −0.370315 0.489385i
\(406\) 0 0
\(407\) −4.37228 + 7.57301i −0.216726 + 0.375380i
\(408\) 2.18614 + 7.25061i 0.108230 + 0.358959i
\(409\) −14.6753 + 25.4183i −0.725645 + 1.25685i 0.233063 + 0.972462i \(0.425125\pi\)
−0.958708 + 0.284393i \(0.908208\pi\)
\(410\) −7.11684 + 12.3267i −0.351476 + 0.608774i
\(411\) −27.6060 6.48577i −1.36170 0.319920i
\(412\) 5.00000 8.66025i 0.246332 0.426660i
\(413\) 0 0
\(414\) −1.37228 22.0742i −0.0674439 1.08489i
\(415\) −3.76631 + 6.52344i −0.184881 + 0.320223i
\(416\) −2.00000 −0.0980581
\(417\) −10.6168 35.2121i −0.519909 1.72434i
\(418\) −21.8614 −1.06928
\(419\) −13.8030 23.9075i −0.674320 1.16796i −0.976667 0.214759i \(-0.931104\pi\)
0.302347 0.953198i \(-0.402230\pi\)
\(420\) 0 0
\(421\) 0.116844 0.202380i 0.00569463 0.00986338i −0.863164 0.504924i \(-0.831521\pi\)
0.868859 + 0.495060i \(0.164854\pi\)
\(422\) −8.00000 + 13.8564i −0.389434 + 0.674519i
\(423\) 0 0
\(424\) 1.37228 + 2.37686i 0.0666439 + 0.115431i
\(425\) −6.81386 11.8020i −0.330521 0.572479i
\(426\) −5.05842 16.7769i −0.245081 0.812843i
\(427\) 0 0
\(428\) 0.813859 + 1.40965i 0.0393394 + 0.0681378i
\(429\) 4.37228 + 14.5012i 0.211096 + 0.700125i
\(430\) 12.5109 0.603328
\(431\) 14.7446 + 25.5383i 0.710221 + 1.23014i 0.964774 + 0.263079i \(0.0847381\pi\)
−0.254554 + 0.967059i \(0.581929\pi\)
\(432\) −0.872281 + 5.12241i −0.0419677 + 0.246452i
\(433\) −2.88316 −0.138556 −0.0692778 0.997597i \(-0.522069\pi\)
−0.0692778 + 0.997597i \(0.522069\pi\)
\(434\) 0 0
\(435\) −4.46738 + 4.75372i −0.214194 + 0.227924i
\(436\) 14.0000 0.670478
\(437\) 18.4307 31.9229i 0.881660 1.52708i
\(438\) 6.06930 6.45832i 0.290002 0.308591i
\(439\) −4.00000 6.92820i −0.190910 0.330665i 0.754642 0.656136i \(-0.227810\pi\)
−0.945552 + 0.325471i \(0.894477\pi\)
\(440\) 6.00000 0.286039
\(441\) 0 0
\(442\) 8.74456 0.415936
\(443\) 11.4416 + 19.8174i 0.543606 + 0.941553i 0.998693 + 0.0511061i \(0.0162747\pi\)
−0.455087 + 0.890447i \(0.650392\pi\)
\(444\) 1.00000 + 3.31662i 0.0474579 + 0.157400i
\(445\) 2.23369 3.86886i 0.105887 0.183402i
\(446\) 4.00000 0.189405
\(447\) −24.8614 5.84096i −1.17590 0.276268i
\(448\) 0 0
\(449\) 33.0000 1.55737 0.778683 0.627417i \(-0.215888\pi\)
0.778683 + 0.627417i \(0.215888\pi\)
\(450\) −0.580171 9.33252i −0.0273495 0.439939i
\(451\) −22.6753 39.2747i −1.06774 1.84937i
\(452\) 1.37228 0.0645467
\(453\) 13.6861 + 3.21543i 0.643031 + 0.151074i
\(454\) −11.8723 20.5634i −0.557194 0.965088i
\(455\) 0 0
\(456\) −5.93070 + 6.31084i −0.277731 + 0.295532i
\(457\) −16.7337 28.9836i −0.782769 1.35580i −0.930323 0.366742i \(-0.880473\pi\)
0.147554 0.989054i \(-0.452860\pi\)
\(458\) −10.0584 17.4217i −0.469999 0.814062i
\(459\) 3.81386 22.3966i 0.178016 1.04539i
\(460\) −5.05842 + 8.76144i −0.235850 + 0.408504i
\(461\) −15.4307 + 26.7268i −0.718680 + 1.24479i 0.242844 + 0.970065i \(0.421920\pi\)
−0.961523 + 0.274724i \(0.911414\pi\)
\(462\) 0 0
\(463\) 2.94158 + 5.09496i 0.136707 + 0.236783i 0.926248 0.376914i \(-0.123015\pi\)
−0.789541 + 0.613697i \(0.789682\pi\)
\(464\) 2.74456 0.127413
\(465\) −3.25544 + 3.46410i −0.150967 + 0.160644i
\(466\) 11.7446 0.544056
\(467\) 15.0475 26.0631i 0.696317 1.20606i −0.273417 0.961896i \(-0.588154\pi\)
0.969735 0.244162i \(-0.0785127\pi\)
\(468\) 5.37228 + 2.67181i 0.248334 + 0.123505i
\(469\) 0 0
\(470\) 0 0
\(471\) −9.62772 + 10.2448i −0.443622 + 0.472057i
\(472\) 3.55842 6.16337i 0.163790 0.283692i
\(473\) −19.9307 + 34.5210i −0.916415 + 1.58728i
\(474\) −14.3723 + 15.2935i −0.660141 + 0.702454i
\(475\) 7.79211 13.4963i 0.357527 0.619254i
\(476\) 0 0
\(477\) −0.510875 8.21782i −0.0233913 0.376268i
\(478\) −9.43070 + 16.3345i −0.431350 + 0.747121i
\(479\) 21.2554 0.971186 0.485593 0.874185i \(-0.338604\pi\)
0.485593 + 0.874185i \(0.338604\pi\)
\(480\) 1.62772 1.73205i 0.0742949 0.0790569i
\(481\) 4.00000 0.182384
\(482\) 0.441578 + 0.764836i 0.0201133 + 0.0348373i
\(483\) 0 0
\(484\) −4.05842 + 7.02939i −0.184474 + 0.319518i
\(485\) 6.25544 10.8347i 0.284045 0.491980i
\(486\) 9.18614 12.5942i 0.416692 0.571286i
\(487\) 8.17527 + 14.1600i 0.370457 + 0.641650i 0.989636 0.143600i \(-0.0458679\pi\)
−0.619179 + 0.785250i \(0.712535\pi\)
\(488\) −7.05842 12.2255i −0.319520 0.553424i
\(489\) 19.2554 20.4897i 0.870761 0.926574i
\(490\) 0 0
\(491\) 9.81386 + 16.9981i 0.442893 + 0.767114i 0.997903 0.0647303i \(-0.0206187\pi\)
−0.555010 + 0.831844i \(0.687285\pi\)
\(492\) −17.4891 4.10891i −0.788471 0.185244i
\(493\) −12.0000 −0.540453
\(494\) 5.00000 + 8.66025i 0.224961 + 0.389643i
\(495\) −16.1168 8.01544i −0.724398 0.360267i
\(496\) 2.00000 0.0898027
\(497\) 0 0
\(498\) −9.25544 2.17448i −0.414746 0.0974408i
\(499\) 0.883156 0.0395355 0.0197677 0.999805i \(-0.493707\pi\)
0.0197677 + 0.999805i \(0.493707\pi\)
\(500\) −5.56930 + 9.64630i −0.249067 + 0.431396i
\(501\) 8.74456 + 29.0024i 0.390678 + 1.29573i
\(502\) −4.50000 7.79423i −0.200845 0.347873i
\(503\) 2.23369 0.0995952 0.0497976 0.998759i \(-0.484142\pi\)
0.0497976 + 0.998759i \(0.484142\pi\)
\(504\) 0 0
\(505\) −10.1168 −0.450194
\(506\) −16.1168 27.9152i −0.716481 1.24098i
\(507\) −10.6753 + 11.3595i −0.474105 + 0.504494i
\(508\) 7.05842 12.2255i 0.313167 0.542421i
\(509\) 16.9783 0.752548 0.376274 0.926508i \(-0.377205\pi\)
0.376274 + 0.926508i \(0.377205\pi\)
\(510\) −7.11684 + 7.57301i −0.315139 + 0.335339i
\(511\) 0 0
\(512\) −1.00000 −0.0441942
\(513\) 24.3614 9.02895i 1.07558 0.398638i
\(514\) 10.9307 + 18.9325i 0.482133 + 0.835078i
\(515\) 13.7228 0.604699
\(516\) 4.55842 + 15.1186i 0.200673 + 0.665558i
\(517\) 0 0
\(518\) 0 0
\(519\) −3.00000 9.94987i −0.131685 0.436751i
\(520\) −1.37228 2.37686i −0.0601785 0.104232i
\(521\) −1.93070 3.34408i −0.0845856 0.146507i 0.820629 0.571461i \(-0.193623\pi\)
−0.905215 + 0.424955i \(0.860290\pi\)
\(522\) −7.37228 3.66648i −0.322676 0.160478i
\(523\) 8.94158 15.4873i 0.390988 0.677211i −0.601592 0.798803i \(-0.705467\pi\)
0.992580 + 0.121592i \(0.0388001\pi\)
\(524\) 3.68614 6.38458i 0.161030 0.278912i
\(525\) 0 0
\(526\) 6.68614 + 11.5807i 0.291530 + 0.504944i
\(527\) −8.74456 −0.380919
\(528\) 2.18614 + 7.25061i 0.0951396 + 0.315542i
\(529\) 31.3505 1.36307
\(530\) −1.88316 + 3.26172i −0.0817991 + 0.141680i
\(531\) −17.7921 + 11.8020i −0.772112 + 0.512161i
\(532\) 0 0
\(533\) −10.3723 + 17.9653i −0.449273 + 0.778164i
\(534\) 5.48913 + 1.28962i 0.237538 + 0.0558073i
\(535\) −1.11684 + 1.93443i −0.0482854 + 0.0836327i
\(536\) 7.55842 13.0916i 0.326474 0.565470i
\(537\) 7.37228 + 24.4511i 0.318137 + 1.05514i
\(538\) −3.68614 + 6.38458i −0.158921 + 0.275259i
\(539\) 0 0
\(540\) −6.68614 + 2.47805i −0.287726 + 0.106638i
\(541\) −14.1168 + 24.4511i −0.606931 + 1.05123i 0.384813 + 0.922995i \(0.374266\pi\)
−0.991743 + 0.128240i \(0.959067\pi\)
\(542\) 18.2337 0.783204
\(543\) −30.5475 7.17687i −1.31092 0.307989i
\(544\) 4.37228 0.187460
\(545\) 9.60597 + 16.6380i 0.411475 + 0.712695i
\(546\) 0 0
\(547\) −0.441578 + 0.764836i −0.0188805 + 0.0327020i −0.875311 0.483560i \(-0.839344\pi\)
0.856431 + 0.516262i \(0.172677\pi\)
\(548\) −8.18614 + 14.1788i −0.349695 + 0.605689i
\(549\) 2.62772 + 42.2689i 0.112148 + 1.80399i
\(550\) −6.81386 11.8020i −0.290544 0.503237i
\(551\) −6.86141 11.8843i −0.292306 0.506288i
\(552\) −12.4307 2.92048i −0.529086 0.124304i
\(553\) 0 0
\(554\) 11.1168 + 19.2549i 0.472309 + 0.818064i
\(555\) −3.25544 + 3.46410i −0.138186 + 0.147043i
\(556\) −21.2337 −0.900509
\(557\) −3.25544 5.63858i −0.137937 0.238914i 0.788778 0.614678i \(-0.210714\pi\)
−0.926716 + 0.375763i \(0.877381\pi\)
\(558\) −5.37228 2.67181i −0.227427 0.113107i
\(559\) 18.2337 0.771203
\(560\) 0 0
\(561\) −9.55842 31.7017i −0.403557 1.33845i
\(562\) −10.6277 −0.448303
\(563\) −1.50000 + 2.59808i −0.0632175 + 0.109496i −0.895902 0.444252i \(-0.853470\pi\)
0.832684 + 0.553748i \(0.186803\pi\)
\(564\) 0 0
\(565\) 0.941578 + 1.63086i 0.0396125 + 0.0686108i
\(566\) −9.88316 −0.415420
\(567\) 0 0
\(568\) −10.1168 −0.424493
\(569\) 0.558422 + 0.967215i 0.0234103 + 0.0405478i 0.877493 0.479589i \(-0.159214\pi\)
−0.854083 + 0.520137i \(0.825881\pi\)
\(570\) −11.5693 2.71810i −0.484585 0.113849i
\(571\) −14.6753 + 25.4183i −0.614141 + 1.06372i 0.376394 + 0.926460i \(0.377164\pi\)
−0.990535 + 0.137263i \(0.956169\pi\)
\(572\) 8.74456 0.365629
\(573\) −0.941578 3.12286i −0.0393350 0.130459i
\(574\) 0 0
\(575\) 22.9783 0.958259
\(576\) 2.68614 + 1.33591i 0.111923 + 0.0556628i
\(577\) −13.5584 23.4839i −0.564444 0.977647i −0.997101 0.0760878i \(-0.975757\pi\)
0.432657 0.901559i \(-0.357576\pi\)
\(578\) −2.11684 −0.0880491
\(579\) −8.30298 + 8.83518i −0.345060 + 0.367178i
\(580\) 1.88316 + 3.26172i 0.0781938 + 0.135436i
\(581\) 0 0
\(582\) 15.3723 + 3.61158i 0.637202 + 0.149705i
\(583\) −6.00000 10.3923i −0.248495 0.430405i
\(584\) −2.55842 4.43132i −0.105868 0.183369i
\(585\) 0.510875 + 8.21782i 0.0211221 + 0.339765i
\(586\) −2.31386 + 4.00772i −0.0955846 + 0.165557i
\(587\) 4.24456 7.35180i 0.175192 0.303441i −0.765036 0.643988i \(-0.777279\pi\)
0.940228 + 0.340547i \(0.110612\pi\)
\(588\) 0 0
\(589\) −5.00000 8.66025i −0.206021 0.356840i
\(590\) 9.76631 0.402073
\(591\) 10.1168 + 2.37686i 0.416151 + 0.0977710i
\(592\) 2.00000 0.0821995
\(593\) −1.62772 + 2.81929i −0.0668424 + 0.115774i −0.897510 0.440995i \(-0.854626\pi\)
0.830667 + 0.556769i \(0.187959\pi\)
\(594\) 3.81386 22.3966i 0.156485 0.918945i
\(595\) 0 0
\(596\) −7.37228 + 12.7692i −0.301980 + 0.523045i
\(597\) −5.00000 16.5831i −0.204636 0.678702i
\(598\) −7.37228 + 12.7692i −0.301475 + 0.522170i
\(599\) −12.0000 + 20.7846i −0.490307 + 0.849236i −0.999938 0.0111569i \(-0.996449\pi\)
0.509631 + 0.860393i \(0.329782\pi\)
\(600\) −5.25544 1.23472i −0.214552 0.0504071i
\(601\) −3.44158 + 5.96099i −0.140385 + 0.243154i −0.927642 0.373472i \(-0.878167\pi\)
0.787257 + 0.616625i \(0.211501\pi\)
\(602\) 0 0
\(603\) −37.7921 + 25.0684i −1.53901 + 1.02087i
\(604\) 4.05842 7.02939i 0.165135 0.286022i
\(605\) −11.1386 −0.452848
\(606\) −3.68614 12.2255i −0.149739 0.496629i
\(607\) −12.2337 −0.496550 −0.248275 0.968690i \(-0.579864\pi\)
−0.248275 + 0.968690i \(0.579864\pi\)
\(608\) 2.50000 + 4.33013i 0.101388 + 0.175610i
\(609\) 0 0
\(610\) 9.68614 16.7769i 0.392180 0.679276i
\(611\) 0 0
\(612\) −11.7446 5.84096i −0.474746 0.236107i
\(613\) 0.883156 + 1.52967i 0.0356703 + 0.0617828i 0.883309 0.468790i \(-0.155310\pi\)
−0.847639 + 0.530573i \(0.821977\pi\)
\(614\) −6.50000 11.2583i −0.262319 0.454349i
\(615\) −7.11684 23.6039i −0.286979 0.951801i
\(616\) 0 0
\(617\) 4.93070 + 8.54023i 0.198503 + 0.343817i 0.948043 0.318142i \(-0.103059\pi\)
−0.749540 + 0.661959i \(0.769725\pi\)
\(618\) 5.00000 + 16.5831i 0.201129 + 0.667071i
\(619\) −23.4674 −0.943233 −0.471617 0.881804i \(-0.656329\pi\)
−0.471617 + 0.881804i \(0.656329\pi\)
\(620\) 1.37228 + 2.37686i 0.0551121 + 0.0954570i
\(621\) 29.4891 + 24.4511i 1.18336 + 0.981188i
\(622\) 26.2337 1.05188
\(623\) 0 0
\(624\) 2.37228 2.52434i 0.0949673 0.101054i
\(625\) 0.298936 0.0119574
\(626\) −1.44158 + 2.49689i −0.0576170 + 0.0997956i
\(627\) 25.9307 27.5928i 1.03557 1.10195i
\(628\) 4.05842 + 7.02939i 0.161949 + 0.280503i
\(629\) −8.74456 −0.348669
\(630\) 0 0
\(631\) 14.3505 0.571286 0.285643 0.958336i \(-0.407793\pi\)
0.285643 + 0.958336i \(0.407793\pi\)
\(632\) 6.05842 + 10.4935i 0.240991 + 0.417409i
\(633\) −8.00000 26.5330i −0.317971 1.05459i
\(634\) −3.00000 + 5.19615i −0.119145 + 0.206366i
\(635\) 19.3723 0.768766
\(636\) −4.62772 1.08724i −0.183501 0.0431119i
\(637\) 0 0
\(638\) −12.0000 −0.475085
\(639\) 27.1753 + 13.5152i 1.07504 + 0.534652i
\(640\) −0.686141 1.18843i −0.0271221 0.0469768i
\(641\) −46.2119 −1.82526 −0.912631 0.408785i \(-0.865953\pi\)
−0.912631 + 0.408785i \(0.865953\pi\)
\(642\) −2.74456 0.644810i −0.108319 0.0254486i
\(643\) 12.6753 + 21.9542i 0.499864 + 0.865789i 1.00000 0.000157386i \(-5.00974e-5\pi\)
−0.500136 + 0.865947i \(0.666717\pi\)
\(644\) 0 0
\(645\) −14.8397 + 15.7908i −0.584311 + 0.621764i
\(646\) −10.9307 18.9325i −0.430063 0.744891i
\(647\) 8.74456 + 15.1460i 0.343784 + 0.595452i 0.985132 0.171798i \(-0.0549578\pi\)
−0.641348 + 0.767250i \(0.721624\pi\)
\(648\) −5.43070 7.17687i −0.213338 0.281934i
\(649\) −15.5584 + 26.9480i −0.610721 + 1.05780i
\(650\) −3.11684 + 5.39853i −0.122253 + 0.211748i
\(651\) 0 0
\(652\) −8.11684 14.0588i −0.317880 0.550585i
\(653\) −15.2554 −0.596991 −0.298496 0.954411i \(-0.596485\pi\)
−0.298496 + 0.954411i \(0.596485\pi\)
\(654\) −16.6060 + 17.6704i −0.649345 + 0.690966i
\(655\) 10.1168 0.395298
\(656\) −5.18614 + 8.98266i −0.202485 + 0.350714i
\(657\) 0.952453 + 15.3210i 0.0371587 + 0.597727i
\(658\) 0 0
\(659\) 4.62772 8.01544i 0.180270 0.312237i −0.761702 0.647927i \(-0.775636\pi\)
0.941973 + 0.335690i \(0.108969\pi\)
\(660\) −7.11684 + 7.57301i −0.277023 + 0.294779i
\(661\) −4.94158 + 8.55906i −0.192205 + 0.332909i −0.945981 0.324223i \(-0.894897\pi\)
0.753776 + 0.657132i \(0.228231\pi\)
\(662\) −6.11684 + 10.5947i −0.237738 + 0.411774i
\(663\) −10.3723 + 11.0371i −0.402826 + 0.428646i
\(664\) −2.74456 + 4.75372i −0.106510 + 0.184480i
\(665\) 0 0
\(666\) −5.37228 2.67181i −0.208172 0.103531i
\(667\) 10.1168 17.5229i 0.391726 0.678489i
\(668\) 17.4891 0.676675
\(669\) −4.74456 + 5.04868i −0.183435 + 0.195193i
\(670\) 20.7446 0.801432
\(671\) 30.8614 + 53.4535i 1.19139 + 2.06355i
\(672\) 0 0
\(673\) 10.0584 17.4217i 0.387724 0.671557i −0.604419 0.796666i \(-0.706595\pi\)
0.992143 + 0.125109i \(0.0399281\pi\)
\(674\) 4.55842 7.89542i 0.175584 0.304120i
\(675\) 12.4674 + 10.3374i 0.479870 + 0.397887i
\(676\) 4.50000 + 7.79423i 0.173077 + 0.299778i
\(677\) 17.2337 + 29.8496i 0.662344 + 1.14721i 0.979998 + 0.199007i \(0.0637718\pi\)
−0.317654 + 0.948207i \(0.602895\pi\)
\(678\) −1.62772 + 1.73205i −0.0625122 + 0.0665190i
\(679\) 0 0
\(680\) 3.00000 + 5.19615i 0.115045 + 0.199263i
\(681\) 40.0367 + 9.40625i 1.53421 + 0.360448i
\(682\) −8.74456 −0.334847
\(683\) 22.4198 + 38.8323i 0.857871 + 1.48588i 0.873956 + 0.486005i \(0.161546\pi\)
−0.0160849 + 0.999871i \(0.505120\pi\)
\(684\) −0.930703 14.9711i −0.0355863 0.572434i
\(685\) −22.4674 −0.858434
\(686\) 0 0
\(687\) 33.9198 + 7.96916i 1.29412 + 0.304042i
\(688\) 9.11684 0.347576
\(689\) −2.74456 + 4.75372i −0.104560 + 0.181102i
\(690\) −5.05842 16.7769i −0.192571 0.638685i
\(691\) 2.94158 + 5.09496i 0.111903 + 0.193822i 0.916537 0.399949i \(-0.130972\pi\)
−0.804635 + 0.593770i \(0.797639\pi\)
\(692\) −6.00000 −0.228086
\(693\) 0 0
\(694\) −7.11684 −0.270152
\(695\) −14.5693 25.2348i −0.552645 0.957209i
\(696\) −3.25544 + 3.46410i −0.123397 + 0.131306i
\(697\) 22.6753 39.2747i 0.858887 1.48764i
\(698\) 22.0000 0.832712
\(699\) −13.9307 + 14.8236i −0.526908 + 0.560681i
\(700\) 0 0
\(701\) −3.76631 −0.142252 −0.0711258 0.997467i \(-0.522659\pi\)
−0.0711258 + 0.997467i \(0.522659\pi\)
\(702\) −9.74456 + 3.61158i −0.367785 + 0.136310i
\(703\) −5.00000 8.66025i −0.188579 0.326628i
\(704\) 4.37228 0.164787
\(705\) 0 0
\(706\) −3.81386 6.60580i −0.143536 0.248612i
\(707\) 0 0
\(708\) 3.55842 + 11.8020i 0.133734 + 0.443544i
\(709\) −22.0000 38.1051i −0.826227 1.43107i −0.900978 0.433865i \(-0.857149\pi\)
0.0747503 0.997202i \(-0.476184\pi\)
\(710\) −6.94158 12.0232i −0.260513 0.451221i
\(711\) −2.25544 36.2805i −0.0845855 1.36062i
\(712\) 1.62772 2.81929i 0.0610013 0.105657i
\(713\) 7.37228 12.7692i 0.276094 0.478209i
\(714\) 0 0
\(715\) 6.00000 + 10.3923i 0.224387 + 0.388650i
\(716\) 14.7446 0.551030
\(717\) −9.43070 31.2781i −0.352196 1.16810i
\(718\) 6.86141 0.256065
\(719\) 4.37228 7.57301i 0.163059 0.282426i −0.772906 0.634521i \(-0.781197\pi\)
0.935964 + 0.352095i \(0.114531\pi\)
\(720\) 0.255437 + 4.10891i 0.00951959 + 0.153130i
\(721\) 0 0
\(722\) 3.00000 5.19615i 0.111648 0.193381i
\(723\) −1.48913 0.349857i −0.0553812 0.0130113i
\(724\) −9.05842 + 15.6896i −0.336654 + 0.583101i
\(725\) 4.27719 7.40830i 0.158851 0.275138i
\(726\) −4.05842 13.4603i −0.150622 0.499557i
\(727\) 0.883156 1.52967i 0.0327544 0.0567324i −0.849183 0.528098i \(-0.822905\pi\)
0.881938 + 0.471366i \(0.156239\pi\)
\(728\) 0 0
\(729\) 5.00000 + 26.5330i 0.185185 + 0.982704i
\(730\) 3.51087 6.08101i 0.129943 0.225068i
\(731\) −39.8614 −1.47433
\(732\) 23.8030 + 5.59230i 0.879784 + 0.206697i
\(733\) −23.8832 −0.882144 −0.441072 0.897472i \(-0.645402\pi\)
−0.441072 + 0.897472i \(0.645402\pi\)
\(734\) 11.1168 + 19.2549i 0.410330 + 0.710713i
\(735\) 0 0
\(736\) −3.68614 + 6.38458i −0.135873 + 0.235339i
\(737\) −33.0475 + 57.2400i −1.21732 + 2.10846i
\(738\) 25.9307 17.2005i 0.954522 0.633159i
\(739\) −4.55842 7.89542i −0.167684 0.290438i 0.769921 0.638139i \(-0.220296\pi\)
−0.937605 + 0.347702i \(0.886962\pi\)
\(740\) 1.37228 + 2.37686i 0.0504461 + 0.0873751i
\(741\) −16.8614 3.96143i −0.619419 0.145527i
\(742\) 0 0
\(743\) −21.8614 37.8651i −0.802017 1.38913i −0.918286 0.395917i \(-0.870427\pi\)
0.116269 0.993218i \(-0.462906\pi\)
\(744\) −2.37228 + 2.52434i −0.0869721 + 0.0925467i
\(745\) −20.2337 −0.741305
\(746\) −5.00000 8.66025i −0.183063 0.317074i
\(747\) 13.7228 9.10268i 0.502091 0.333050i
\(748\) −19.1168 −0.698981
\(749\) 0 0
\(750\) −5.56930 18.4713i −0.203362 0.674475i
\(751\) 0.116844 0.00426370 0.00213185 0.999998i \(-0.499321\pi\)
0.00213185 + 0.999998i \(0.499321\pi\)
\(752\) 0 0
\(753\) 15.1753 + 3.56529i 0.553017 + 0.129926i
\(754\) 2.74456 + 4.75372i 0.0999511 + 0.173120i
\(755\) 11.1386 0.405375
\(756\) 0 0
\(757\) 11.7663 0.427654 0.213827 0.976872i \(-0.431407\pi\)
0.213827 + 0.976872i \(0.431407\pi\)
\(758\) 4.55842 + 7.89542i 0.165569 + 0.286775i
\(759\) 54.3505 + 12.7692i 1.97280 + 0.463491i
\(760\) −3.43070 + 5.94215i −0.124445 + 0.215545i
\(761\) 12.5109 0.453519 0.226759 0.973951i \(-0.427187\pi\)
0.226759 + 0.973951i \(0.427187\pi\)
\(762\) 7.05842 + 23.4101i 0.255700 + 0.848060i
\(763\) 0 0
\(764\) −1.88316 −0.0681302
\(765\) −1.11684 17.9653i −0.0403796 0.649537i
\(766\) −10.6277 18.4077i −0.383995 0.665099i
\(767\) 14.2337 0.513949
\(768\) 1.18614 1.26217i 0.0428012 0.0455446i
\(769\) 5.00000 + 8.66025i 0.180305 + 0.312297i 0.941984 0.335657i \(-0.108958\pi\)
−0.761680 + 0.647954i \(0.775625\pi\)
\(770\) 0 0
\(771\) −36.8614 8.66025i −1.32753 0.311891i
\(772\) 3.50000 + 6.06218i 0.125968 + 0.218183i
\(773\) 5.56930 + 9.64630i 0.200314 + 0.346953i 0.948629 0.316389i \(-0.102471\pi\)
−0.748316 + 0.663343i \(0.769137\pi\)
\(774\) −24.4891 12.1793i −0.880243 0.437774i
\(775\) 3.11684 5.39853i 0.111960 0.193921i
\(776\) 4.55842 7.89542i 0.163638 0.283429i
\(777\) 0 0
\(778\) −17.4891 30.2921i −0.627016 1.08602i
\(779\) 51.8614 1.85813
\(780\) 4.62772 + 1.08724i 0.165699 + 0.0389295i
\(781\) 44.2337