Properties

Label 882.2.h.n.79.2
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 79.2
Root \(1.68614 - 0.396143i\) of defining polynomial
Character \(\chi\) \(=\) 882.79
Dual form 882.2.h.n.67.2

$q$-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 \(-0.400725\pi\)
0.306851 + 0.951757i \(0.400725\pi\)
\(6\) 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 0.970725 0.240192i \(-0.0772105\pi\)
−0.693375 + 0.720577i \(0.743877\pi\)
\(14\) 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 \(-0.988777\pi\)
0.469162 0.883112i \(-0.344556\pi\)
\(18\) 0.186141 + 2.99422i 0.0438738 + 0.705744i
\(19\) 2.50000 4.33013i 0.573539 0.993399i −0.422659 0.906289i \(-0.638903\pi\)
0.996199 0.0871106i \(-0.0277634\pi\)
\(20\) −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 −0.762140 0.647412i \(-0.775851\pi\)
0.941745 + 0.336327i \(0.109185\pi\)
\(32\) 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 \(0.133833\pi\)
−0.102966 + 0.994685i \(0.532833\pi\)
\(42\) 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 −0.535854 0.844310i \(-0.680010\pi\)
0.999121 + 0.0419083i \(0.0133437\pi\)
\(60\) −1.62772 + 1.73205i −0.210138 + 0.223607i
\(61\) −7.05842 12.2255i −0.903738 1.56532i −0.822602 0.568618i \(-0.807478\pi\)
−0.0811364 0.996703i \(-0.525855\pi\)
\(62\) 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 0.676567 0.736381i \(-0.263467\pi\)
−0.976008 + 0.217734i \(0.930133\pi\)
\(74\) −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 −0.976420 0.215877i \(-0.930739\pi\)
0.675166 + 0.737666i \(0.264072\pi\)
\(84\) 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 −0.766769 0.641924i \(-0.778137\pi\)
0.939306 + 0.343079i \(0.111470\pi\)
\(90\) 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 −0.536263 0.844051i \(-0.680165\pi\)
0.999101 + 0.0423924i \(0.0134980\pi\)
\(98\) 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 \(-0.619541\pi\)
−0.366785 + 0.930306i \(0.619541\pi\)
\(102\) 5.18614 5.51856i 0.513504 0.546419i
\(103\) 10.0000 0.985329 0.492665 0.870219i \(-0.336023\pi\)
0.492665 + 0.870219i \(0.336023\pi\)
\(104\) −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 \(-0.395625\pi\)
0.322060 + 0.946719i \(0.395625\pi\)
\(132\) −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 \(-0.809861\pi\)
−0.0736742 0.997282i \(-0.523472\pi\)
\(140\) 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 −0.981289 0.192543i \(-0.938327\pi\)
0.657391 + 0.753549i \(0.271660\pi\)
\(158\) 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 \(0.0699129\pi\)
−0.299302 + 0.954158i \(0.596754\pi\)
\(168\) 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 0.729155 0.684349i \(-0.239913\pi\)
−0.957241 + 0.289292i \(0.906580\pi\)
\(174\) −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 \(-0.735127\pi\)
−0.673307 + 0.739363i \(0.735127\pi\)
\(182\) 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 0.632581 0.774494i \(-0.281995\pi\)
−0.987022 + 0.160585i \(0.948662\pi\)
\(200\) 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 −0.925188 0.379509i \(-0.876093\pi\)
0.791258 + 0.611482i \(0.209426\pi\)
\(224\) 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 \(-0.211121\pi\)
0.787991 + 0.615687i \(0.211121\pi\)
\(228\) 2.50000 + 8.29156i 0.165567 + 0.549122i
\(229\) 20.1168 1.32936 0.664679 0.747129i \(-0.268568\pi\)
0.664679 + 0.747129i \(0.268568\pi\)
\(230\) −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 \(-0.509055\pi\)
−0.0284445 + 0.999595i \(0.509055\pi\)
\(242\) 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 \(-0.408326\pi\)
0.284037 + 0.958813i \(0.408326\pi\)
\(252\) 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 \(-0.738819\pi\)
−0.681839 + 0.731503i \(0.738819\pi\)
\(258\) −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 0.731496 0.681846i \(-0.238823\pi\)
−0.956244 + 0.292571i \(0.905489\pi\)
\(270\) −1.19702 + 7.02939i −0.0728480 + 0.427795i
\(271\) −9.11684 + 15.7908i −0.553809 + 0.959225i 0.444186 + 0.895934i \(0.353493\pi\)
−0.997995 + 0.0632906i \(0.979841\pi\)
\(272\) −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 −0.680946 0.732333i \(-0.738431\pi\)
0.974692 + 0.223550i \(0.0717646\pi\)
\(284\) −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 0.790488 0.612478i \(-0.209827\pi\)
−0.925665 + 0.378344i \(0.876494\pi\)
\(294\) 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 \(-0.379024\pi\)
0.370975 + 0.928643i \(0.379024\pi\)
\(308\) 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 \(0.433639\pi\)
−0.950759 + 0.309931i \(0.899694\pi\)
\(312\) −1.00000 3.31662i −0.0566139 0.187767i
\(313\) −1.44158 2.49689i −0.0814828 0.141132i 0.822404 0.568904i \(-0.192632\pi\)
−0.903887 + 0.427771i \(0.859299\pi\)
\(314\) −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 \(0.367073\pi\)
−0.994388 + 0.105797i \(0.966261\pi\)
\(350\) 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 \(-0.434934\pi\)
0.202991 + 0.979181i \(0.434934\pi\)
\(354\) 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 \(-0.697063\pi\)
−0.580295 + 0.814407i \(0.697063\pi\)
\(368\) 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 \(-0.317269\pi\)
0.543051 + 0.839700i \(0.317269\pi\)
\(384\) 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 \(0.352830\pi\)
−0.998125 + 0.0612128i \(0.980503\pi\)
\(398\) 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 \(-0.574875\pi\)
0.958708 0.284393i \(-0.0917919\pi\)
\(410\) −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 \(0.0688964\pi\)
−0.302347 + 0.953198i \(0.597770\pi\)
\(420\) 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 \(-0.477931\pi\)
0.0692778 + 0.997597i \(0.477931\pi\)
\(434\) 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 0.945552 0.325471i \(-0.105523\pi\)
−0.754642 + 0.656136i \(0.772190\pi\)
\(440\) −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 \(-0.578080\pi\)
0.961523 0.274724i \(-0.0885865\pi\)
\(462\) 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 \(0.411846\pi\)
−0.969735 + 0.244162i \(0.921487\pi\)
\(468\) −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 \(-0.661396\pi\)
−0.485593 + 0.874185i \(0.661396\pi\)
\(480\) 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 \(-0.515858\pi\)
−0.0497976 + 0.998759i \(0.515858\pi\)
\(504\) 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 \(-0.622795\pi\)
−0.376274 + 0.926508i \(0.622795\pi\)
\(510\) 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 0.905215 0.424955i \(-0.139710\pi\)
−0.820629 + 0.571461i \(0.806377\pi\)
\(522\) −7.37228 3.66648i −0.322676 0.160478i
\(523\) −8.94158 + 15.4873i −0.390988 + 0.677211i −0.992580 0.121592i \(-0.961200\pi\)
0.601592 + 0.798803i \(0.294533\pi\)
\(524\) −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 −0.832684 0.553748i \(-0.813197\pi\)
0.895902 + 0.444252i \(0.146530\pi\)
\(564\) 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 \(0.0242429\pi\)
−0.432657 + 0.901559i \(0.642424\pi\)
\(578\) −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 −0.940228 0.340547i \(-0.889388\pi\)
0.765036 + 0.643988i \(0.222721\pi\)
\(588\) 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 −0.830667 0.556769i \(-0.812041\pi\)
0.897510 + 0.440995i \(0.145374\pi\)
\(594\) −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 −0.787257 0.616625i \(-0.788499\pi\)
0.927642 + 0.373472i \(0.121833\pi\)
\(602\) 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 \(-0.420136\pi\)
0.248275 + 0.968690i \(0.420136\pi\)
\(608\) −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 \(-0.343671\pi\)
0.471617 + 0.881804i \(0.343671\pi\)
\(620\) 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 0.500136 0.865947i \(-0.333283\pi\)
−1.00000 0.000157386i \(0.999950\pi\)
\(644\) 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 0.641348 0.767250i \(-0.278376\pi\)
−0.985132 + 0.171798i \(0.945042\pi\)
\(648\) −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 −0.753776 0.657132i \(-0.771769\pi\)
0.945981 + 0.324223i \(0.105103\pi\)
\(662\) −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 \(-0.936228\pi\)
0.317654 0.948207i \(-0.397105\pi\)
\(678\) 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 0.804635 0.593770i \(-0.202361\pi\)
−0.916537 + 0.399949i \(0.869028\pi\)
\(692\) 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 −0.935964 0.352095i \(-0.885469\pi\)
0.772906 + 0.634521i \(0.218803\pi\)
\(720\) −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 −0.881938 0.471366i \(-0.843761\pi\)
0.849183 + 0.528098i \(0.177095\pi\)
\(728\) 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 \(-0.354598\pi\)
0.441072 + 0.897472i \(0.354598\pi\)
\(734\) −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 \(-0.572813\pi\)
−0.226759 + 0.973951i \(0.572813\pi\)
\(762\) −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 0.761680 0.647954i \(-0.224375\pi\)
−0.941984 + 0.335657i \(0.891042\pi\)
\(770\) 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 0.748316 0.663343i \(-0.230863\pi\)
−0.948629 + 0.316389i \(0.897529\pi\)
\(774\) −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