Properties

Label 105.3.n.a.31.4
Level 105
Weight 3
Character 105.31
Analytic conductor 2.861
Analytic rank 0
Dimension 8
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) \(=\) \( 105 = 3 \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 105.n (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.86104277578\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{6})\)
Coefficient field: 8.0.523596960000.16
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 31.4
Root \(1.76021 + 3.04878i\) of \(x^{8} - 2 x^{7} + 13 x^{6} - 2 x^{5} + 91 x^{4} - 50 x^{3} + 190 x^{2} + 100 x + 100\)
Character \(\chi\) \(=\) 105.31
Dual form 105.3.n.a.61.4

$q$-expansion

\(f(q)\) \(=\) \(q+(1.76021 + 3.04878i) q^{2} +(-1.50000 - 0.866025i) q^{3} +(-4.19671 + 7.26891i) q^{4} +(-1.93649 + 1.11803i) q^{5} -6.09756i q^{6} +(0.244004 + 6.99575i) q^{7} -15.4667 q^{8} +(1.50000 + 2.59808i) q^{9} +O(q^{10})\) \(q+(1.76021 + 3.04878i) q^{2} +(-1.50000 - 0.866025i) q^{3} +(-4.19671 + 7.26891i) q^{4} +(-1.93649 + 1.11803i) q^{5} -6.09756i q^{6} +(0.244004 + 6.99575i) q^{7} -15.4667 q^{8} +(1.50000 + 2.59808i) q^{9} +(-6.81728 - 3.93596i) q^{10} +(-1.29685 + 2.24621i) q^{11} +(12.5901 - 7.26891i) q^{12} -11.5763i q^{13} +(-20.8990 + 13.0579i) q^{14} +3.87298 q^{15} +(-10.4379 - 18.0789i) q^{16} +(20.0957 + 11.6023i) q^{17} +(-5.28064 + 9.14634i) q^{18} +(25.9538 - 14.9844i) q^{19} -18.7682i q^{20} +(5.69249 - 10.7049i) q^{21} -9.13094 q^{22} +(17.5542 + 30.4048i) q^{23} +(23.2000 + 13.3945i) q^{24} +(2.50000 - 4.33013i) q^{25} +(35.2936 - 20.3768i) q^{26} -5.19615i q^{27} +(-51.8754 - 27.5854i) q^{28} -24.4905 q^{29} +(6.81728 + 11.8079i) q^{30} +(-32.4355 - 18.7266i) q^{31} +(5.81233 - 10.0673i) q^{32} +(3.89055 - 2.24621i) q^{33} +81.6898i q^{34} +(-8.29399 - 13.2744i) q^{35} -25.1802 q^{36} +(-12.8743 - 22.2990i) q^{37} +(91.3685 + 52.7516i) q^{38} +(-10.0254 + 17.3645i) q^{39} +(29.9511 - 17.2923i) q^{40} -3.71113i q^{41} +(42.6570 - 1.48783i) q^{42} +74.2225 q^{43} +(-10.8850 - 18.8534i) q^{44} +(-5.80948 - 3.35410i) q^{45} +(-61.7983 + 107.038i) q^{46} +(2.92646 - 1.68959i) q^{47} +36.1578i q^{48} +(-48.8809 + 3.41398i) q^{49} +17.6021 q^{50} +(-20.0957 - 34.8068i) q^{51} +(84.1471 + 48.5823i) q^{52} +(20.0193 - 34.6744i) q^{53} +(15.8419 - 9.14634i) q^{54} -5.79969i q^{55} +(-3.77394 - 108.201i) q^{56} -51.9076 q^{57} +(-43.1085 - 74.6661i) q^{58} +(-42.7180 - 24.6632i) q^{59} +(-16.2538 + 28.1524i) q^{60} +(-0.765094 + 0.441727i) q^{61} -131.852i q^{62} +(-17.8095 + 11.1276i) q^{63} -42.5790 q^{64} +(12.9427 + 22.4174i) q^{65} +(13.6964 + 7.90763i) q^{66} +(32.5272 - 56.3388i) q^{67} +(-168.671 + 97.3825i) q^{68} -60.8096i q^{69} +(25.8715 - 48.6523i) q^{70} +86.0786 q^{71} +(-23.2000 - 40.1836i) q^{72} +(-53.3274 - 30.7886i) q^{73} +(45.3231 - 78.5019i) q^{74} +(-7.50000 + 4.33013i) q^{75} +251.541i q^{76} +(-16.0304 - 8.52436i) q^{77} -70.5872 q^{78} +(-13.7718 - 23.8534i) q^{79} +(40.4256 + 23.3397i) q^{80} +(-4.50000 + 7.79423i) q^{81} +(11.3144 - 6.53239i) q^{82} +131.445i q^{83} +(53.9235 + 86.3036i) q^{84} -51.8869 q^{85} +(130.648 + 226.288i) q^{86} +(36.7357 + 21.2094i) q^{87} +(20.0580 - 34.7415i) q^{88} +(-56.5108 + 32.6265i) q^{89} -23.6157i q^{90} +(80.9849 - 2.82467i) q^{91} -294.679 q^{92} +(32.4355 + 56.1799i) q^{93} +(10.3024 + 5.94809i) q^{94} +(-33.5062 + 58.0345i) q^{95} +(-17.4370 + 10.0673i) q^{96} -42.2375i q^{97} +(-96.4494 - 143.018i) q^{98} -7.78111 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q + 2q^{2} - 12q^{3} - 6q^{4} - 16q^{7} - 32q^{8} + 12q^{9} + O(q^{10}) \) \( 8q + 2q^{2} - 12q^{3} - 6q^{4} - 16q^{7} - 32q^{8} + 12q^{9} + 20q^{11} + 18q^{12} - 16q^{14} - 2q^{16} - 18q^{17} - 6q^{18} + 48q^{21} - 16q^{22} + 62q^{23} + 48q^{24} + 20q^{25} + 120q^{26} - 120q^{28} - 100q^{29} - 126q^{31} + 36q^{32} - 60q^{33} - 36q^{36} - 80q^{37} + 114q^{38} - 12q^{39} + 90q^{40} + 90q^{42} + 352q^{43} - 18q^{44} - 82q^{46} - 72q^{47} + 38q^{49} + 20q^{50} + 18q^{51} - 48q^{52} - 76q^{53} + 18q^{54} + 196q^{56} - 40q^{58} - 54q^{59} - 60q^{60} - 396q^{61} - 96q^{63} - 4q^{64} - 60q^{65} + 24q^{66} + 184q^{67} - 312q^{68} + 164q^{71} - 48q^{72} + 348q^{73} - 140q^{74} - 60q^{75} + 152q^{77} - 240q^{78} - 206q^{79} - 36q^{81} + 204q^{82} + 132q^{84} - 60q^{85} + 178q^{86} + 150q^{87} + 124q^{88} + 282q^{89} - 114q^{91} - 288q^{92} + 126q^{93} + 30q^{94} - 120q^{95} - 108q^{96} - 592q^{98} + 120q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/105\mathbb{Z}\right)^\times\).

\(n\) \(22\) \(31\) \(71\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{6}\right)\) \(1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.76021 + 3.04878i 0.880107 + 1.52439i 0.851221 + 0.524807i \(0.175863\pi\)
0.0288858 + 0.999583i \(0.490804\pi\)
\(3\) −1.50000 0.866025i −0.500000 0.288675i
\(4\) −4.19671 + 7.26891i −1.04918 + 1.81723i
\(5\) −1.93649 + 1.11803i −0.387298 + 0.223607i
\(6\) 6.09756i 1.01626i
\(7\) 0.244004 + 6.99575i 0.0348577 + 0.999392i
\(8\) −15.4667 −1.93334
\(9\) 1.50000 + 2.59808i 0.166667 + 0.288675i
\(10\) −6.81728 3.93596i −0.681728 0.393596i
\(11\) −1.29685 + 2.24621i −0.117896 + 0.204201i −0.918934 0.394412i \(-0.870948\pi\)
0.801038 + 0.598614i \(0.204281\pi\)
\(12\) 12.5901 7.26891i 1.04918 0.605742i
\(13\) 11.5763i 0.890485i −0.895410 0.445242i \(-0.853117\pi\)
0.895410 0.445242i \(-0.146883\pi\)
\(14\) −20.8990 + 13.0579i −1.49278 + 0.932709i
\(15\) 3.87298 0.258199
\(16\) −10.4379 18.0789i −0.652366 1.12993i
\(17\) 20.0957 + 11.6023i 1.18210 + 0.682486i 0.956499 0.291734i \(-0.0942323\pi\)
0.225600 + 0.974220i \(0.427566\pi\)
\(18\) −5.28064 + 9.14634i −0.293369 + 0.508130i
\(19\) 25.9538 14.9844i 1.36599 0.788654i 0.375576 0.926791i \(-0.377445\pi\)
0.990413 + 0.138137i \(0.0441115\pi\)
\(20\) 18.7682i 0.938412i
\(21\) 5.69249 10.7049i 0.271071 0.509759i
\(22\) −9.13094 −0.415043
\(23\) 17.5542 + 30.4048i 0.763226 + 1.32195i 0.941179 + 0.337908i \(0.109719\pi\)
−0.177953 + 0.984039i \(0.556947\pi\)
\(24\) 23.2000 + 13.3945i 0.966668 + 0.558106i
\(25\) 2.50000 4.33013i 0.100000 0.173205i
\(26\) 35.2936 20.3768i 1.35745 0.783722i
\(27\) 5.19615i 0.192450i
\(28\) −51.8754 27.5854i −1.85269 0.985194i
\(29\) −24.4905 −0.844499 −0.422250 0.906480i \(-0.638759\pi\)
−0.422250 + 0.906480i \(0.638759\pi\)
\(30\) 6.81728 + 11.8079i 0.227243 + 0.393596i
\(31\) −32.4355 18.7266i −1.04631 0.604085i −0.124693 0.992195i \(-0.539795\pi\)
−0.921613 + 0.388110i \(0.873128\pi\)
\(32\) 5.81233 10.0673i 0.181635 0.314602i
\(33\) 3.89055 2.24621i 0.117896 0.0680670i
\(34\) 81.6898i 2.40264i
\(35\) −8.29399 13.2744i −0.236971 0.379269i
\(36\) −25.1802 −0.699451
\(37\) −12.8743 22.2990i −0.347954 0.602675i 0.637932 0.770093i \(-0.279790\pi\)
−0.985886 + 0.167418i \(0.946457\pi\)
\(38\) 91.3685 + 52.7516i 2.40443 + 1.38820i
\(39\) −10.0254 + 17.3645i −0.257061 + 0.445242i
\(40\) 29.9511 17.2923i 0.748778 0.432307i
\(41\) 3.71113i 0.0905155i −0.998975 0.0452577i \(-0.985589\pi\)
0.998975 0.0452577i \(-0.0144109\pi\)
\(42\) 42.6570 1.48783i 1.01564 0.0354245i
\(43\) 74.2225 1.72611 0.863053 0.505114i \(-0.168549\pi\)
0.863053 + 0.505114i \(0.168549\pi\)
\(44\) −10.8850 18.8534i −0.247386 0.428486i
\(45\) −5.80948 3.35410i −0.129099 0.0745356i
\(46\) −61.7983 + 107.038i −1.34344 + 2.32691i
\(47\) 2.92646 1.68959i 0.0622652 0.0359488i −0.468544 0.883440i \(-0.655221\pi\)
0.530809 + 0.847491i \(0.321888\pi\)
\(48\) 36.1578i 0.753287i
\(49\) −48.8809 + 3.41398i −0.997570 + 0.0696731i
\(50\) 17.6021 0.352043
\(51\) −20.0957 34.8068i −0.394033 0.682486i
\(52\) 84.1471 + 48.5823i 1.61821 + 0.934276i
\(53\) 20.0193 34.6744i 0.377722 0.654234i −0.613008 0.790076i \(-0.710041\pi\)
0.990730 + 0.135843i \(0.0433741\pi\)
\(54\) 15.8419 9.14634i 0.293369 0.169377i
\(55\) 5.79969i 0.105449i
\(56\) −3.77394 108.201i −0.0673917 1.93216i
\(57\) −51.9076 −0.910660
\(58\) −43.1085 74.6661i −0.743250 1.28735i
\(59\) −42.7180 24.6632i −0.724033 0.418021i 0.0922022 0.995740i \(-0.470609\pi\)
−0.816235 + 0.577720i \(0.803943\pi\)
\(60\) −16.2538 + 28.1524i −0.270896 + 0.469206i
\(61\) −0.765094 + 0.441727i −0.0125425 + 0.00724143i −0.506258 0.862382i \(-0.668972\pi\)
0.493716 + 0.869623i \(0.335638\pi\)
\(62\) 131.852i 2.12664i
\(63\) −17.8095 + 11.1276i −0.282690 + 0.176628i
\(64\) −42.5790 −0.665297
\(65\) 12.9427 + 22.4174i 0.199118 + 0.344883i
\(66\) 13.6964 + 7.90763i 0.207521 + 0.119813i
\(67\) 32.5272 56.3388i 0.485481 0.840877i −0.514380 0.857562i \(-0.671978\pi\)
0.999861 + 0.0166850i \(0.00531125\pi\)
\(68\) −168.671 + 97.3825i −2.48046 + 1.43210i
\(69\) 60.8096i 0.881298i
\(70\) 25.8715 48.6523i 0.369593 0.695033i
\(71\) 86.0786 1.21237 0.606187 0.795322i \(-0.292698\pi\)
0.606187 + 0.795322i \(0.292698\pi\)
\(72\) −23.2000 40.1836i −0.322223 0.558106i
\(73\) −53.3274 30.7886i −0.730512 0.421761i 0.0880974 0.996112i \(-0.471921\pi\)
−0.818609 + 0.574350i \(0.805255\pi\)
\(74\) 45.3231 78.5019i 0.612474 1.06084i
\(75\) −7.50000 + 4.33013i −0.100000 + 0.0577350i
\(76\) 251.541i 3.30975i
\(77\) −16.0304 8.52436i −0.208187 0.110706i
\(78\) −70.5872 −0.904964
\(79\) −13.7718 23.8534i −0.174326 0.301942i 0.765602 0.643315i \(-0.222441\pi\)
−0.939928 + 0.341373i \(0.889108\pi\)
\(80\) 40.4256 + 23.3397i 0.505320 + 0.291747i
\(81\) −4.50000 + 7.79423i −0.0555556 + 0.0962250i
\(82\) 11.3144 6.53239i 0.137981 0.0796633i
\(83\) 131.445i 1.58367i 0.610732 + 0.791837i \(0.290875\pi\)
−0.610732 + 0.791837i \(0.709125\pi\)
\(84\) 53.9235 + 86.3036i 0.641946 + 1.02742i
\(85\) −51.8869 −0.610434
\(86\) 130.648 + 226.288i 1.51916 + 2.63126i
\(87\) 36.7357 + 21.2094i 0.422250 + 0.243786i
\(88\) 20.0580 34.7415i 0.227932 0.394789i
\(89\) −56.5108 + 32.6265i −0.634953 + 0.366590i −0.782668 0.622440i \(-0.786142\pi\)
0.147715 + 0.989030i \(0.452808\pi\)
\(90\) 23.6157i 0.262397i
\(91\) 80.9849 2.82467i 0.889944 0.0310403i
\(92\) −294.679 −3.20304
\(93\) 32.4355 + 56.1799i 0.348769 + 0.604085i
\(94\) 10.3024 + 5.94809i 0.109600 + 0.0632776i
\(95\) −33.5062 + 58.0345i −0.352697 + 0.610889i
\(96\) −17.4370 + 10.0673i −0.181635 + 0.104867i
\(97\) 42.2375i 0.435438i −0.976011 0.217719i \(-0.930138\pi\)
0.976011 0.217719i \(-0.0698616\pi\)
\(98\) −96.4494 143.018i −0.984177 1.45937i
\(99\) −7.78111 −0.0785970
\(100\) 20.9835 + 36.3445i 0.209835 + 0.363445i
\(101\) −129.874 74.9830i −1.28589 0.742406i −0.307968 0.951397i \(-0.599649\pi\)
−0.977918 + 0.208991i \(0.932982\pi\)
\(102\) 70.7454 122.535i 0.693583 1.20132i
\(103\) 120.964 69.8388i 1.17441 0.678047i 0.219697 0.975568i \(-0.429493\pi\)
0.954715 + 0.297521i \(0.0961599\pi\)
\(104\) 179.047i 1.72161i
\(105\) 0.945024 + 27.0944i 0.00900023 + 0.258042i
\(106\) 140.953 1.32974
\(107\) 90.6198 + 156.958i 0.846914 + 1.46690i 0.883949 + 0.467584i \(0.154875\pi\)
−0.0370350 + 0.999314i \(0.511791\pi\)
\(108\) 37.7703 + 21.8067i 0.349725 + 0.201914i
\(109\) 36.9049 63.9212i 0.338577 0.586433i −0.645588 0.763686i \(-0.723388\pi\)
0.984165 + 0.177253i \(0.0567211\pi\)
\(110\) 17.6820 10.2087i 0.160745 0.0928064i
\(111\) 44.5979i 0.401783i
\(112\) 123.928 77.4319i 1.10650 0.691356i
\(113\) 7.38562 0.0653595 0.0326797 0.999466i \(-0.489596\pi\)
0.0326797 + 0.999466i \(0.489596\pi\)
\(114\) −91.3685 158.255i −0.801478 1.38820i
\(115\) −67.9872 39.2524i −0.591193 0.341325i
\(116\) 102.779 178.019i 0.886029 1.53465i
\(117\) 30.0761 17.3645i 0.257061 0.148414i
\(118\) 173.650i 1.47161i
\(119\) −76.2630 + 143.415i −0.640866 + 1.20517i
\(120\) −59.9022 −0.499185
\(121\) 57.1364 + 98.9631i 0.472201 + 0.817877i
\(122\) −2.69346 1.55507i −0.0220775 0.0127465i
\(123\) −3.21394 + 5.56670i −0.0261296 + 0.0452577i
\(124\) 272.244 157.180i 2.19552 1.26758i
\(125\) 11.1803i 0.0894427i
\(126\) −65.2740 34.7103i −0.518047 0.275478i
\(127\) −208.640 −1.64283 −0.821416 0.570329i \(-0.806816\pi\)
−0.821416 + 0.570329i \(0.806816\pi\)
\(128\) −98.1975 170.083i −0.767168 1.32877i
\(129\) −111.334 64.2786i −0.863053 0.498284i
\(130\) −45.5638 + 78.9189i −0.350491 + 0.607068i
\(131\) 94.8997 54.7904i 0.724425 0.418247i −0.0919540 0.995763i \(-0.529311\pi\)
0.816379 + 0.577516i \(0.195978\pi\)
\(132\) 37.7068i 0.285657i
\(133\) 111.160 + 177.910i 0.835790 + 1.33767i
\(134\) 229.019 1.70910
\(135\) 5.80948 + 10.0623i 0.0430331 + 0.0745356i
\(136\) −310.814 179.448i −2.28540 1.31947i
\(137\) 88.7262 153.678i 0.647637 1.12174i −0.336049 0.941844i \(-0.609091\pi\)
0.983686 0.179895i \(-0.0575758\pi\)
\(138\) 185.395 107.038i 1.34344 0.775636i
\(139\) 169.894i 1.22226i 0.791532 + 0.611128i \(0.209284\pi\)
−0.791532 + 0.611128i \(0.790716\pi\)
\(140\) 131.298 4.57953i 0.937842 0.0327109i
\(141\) −5.85293 −0.0415101
\(142\) 151.517 + 262.435i 1.06702 + 1.84813i
\(143\) 26.0028 + 15.0127i 0.181838 + 0.104984i
\(144\) 31.3136 54.2367i 0.217455 0.376644i
\(145\) 47.4256 27.3812i 0.327073 0.188836i
\(146\) 216.778i 1.48478i
\(147\) 76.2780 + 37.2111i 0.518898 + 0.253137i
\(148\) 216.119 1.46026
\(149\) −42.6928 73.9461i −0.286529 0.496283i 0.686450 0.727177i \(-0.259168\pi\)
−0.972979 + 0.230894i \(0.925835\pi\)
\(150\) −26.4032 15.2439i −0.176021 0.101626i
\(151\) 68.9977 119.507i 0.456938 0.791440i −0.541859 0.840469i \(-0.682279\pi\)
0.998797 + 0.0490293i \(0.0156128\pi\)
\(152\) −401.419 + 231.760i −2.64092 + 1.52473i
\(153\) 69.6135i 0.454990i
\(154\) −2.22799 63.8777i −0.0144675 0.414791i
\(155\) 83.7481 0.540310
\(156\) −84.1471 145.747i −0.539404 0.934276i
\(157\) 5.94674 + 3.43335i 0.0378773 + 0.0218685i 0.518819 0.854884i \(-0.326372\pi\)
−0.480942 + 0.876753i \(0.659705\pi\)
\(158\) 48.4825 83.9742i 0.306851 0.531482i
\(159\) −60.0578 + 34.6744i −0.377722 + 0.218078i
\(160\) 25.9935i 0.162460i
\(161\) −208.421 + 130.224i −1.29454 + 0.808843i
\(162\) −31.6838 −0.195579
\(163\) 138.363 + 239.652i 0.848854 + 1.47026i 0.882231 + 0.470816i \(0.156040\pi\)
−0.0333772 + 0.999443i \(0.510626\pi\)
\(164\) 26.9759 + 15.5745i 0.164487 + 0.0949667i
\(165\) −5.02268 + 8.69954i −0.0304405 + 0.0527245i
\(166\) −400.747 + 231.371i −2.41414 + 1.39380i
\(167\) 42.3799i 0.253772i 0.991917 + 0.126886i \(0.0404982\pi\)
−0.991917 + 0.126886i \(0.959502\pi\)
\(168\) −88.0439 + 165.570i −0.524071 + 0.985535i
\(169\) 34.9892 0.207036
\(170\) −91.3320 158.192i −0.537247 0.930539i
\(171\) 77.8614 + 44.9533i 0.455330 + 0.262885i
\(172\) −311.490 + 539.517i −1.81099 + 3.13673i
\(173\) 25.5999 14.7801i 0.147976 0.0854342i −0.424184 0.905576i \(-0.639439\pi\)
0.572160 + 0.820142i \(0.306106\pi\)
\(174\) 149.332i 0.858231i
\(175\) 30.9025 + 16.4328i 0.176586 + 0.0939017i
\(176\) 54.1454 0.307644
\(177\) 42.7180 + 73.9897i 0.241344 + 0.418021i
\(178\) −198.942 114.859i −1.11765 0.645277i
\(179\) 74.3408 128.762i 0.415312 0.719341i −0.580149 0.814510i \(-0.697006\pi\)
0.995461 + 0.0951690i \(0.0303392\pi\)
\(180\) 48.7613 28.1524i 0.270896 0.156402i
\(181\) 257.302i 1.42156i −0.703414 0.710780i \(-0.748342\pi\)
0.703414 0.710780i \(-0.251658\pi\)
\(182\) 151.163 + 241.933i 0.830563 + 1.32930i
\(183\) 1.53019 0.00836168
\(184\) −271.505 470.261i −1.47557 2.55577i
\(185\) 49.8620 + 28.7878i 0.269524 + 0.155610i
\(186\) −114.187 + 197.777i −0.613908 + 1.06332i
\(187\) −52.1223 + 30.0928i −0.278729 + 0.160924i
\(188\) 28.3629i 0.150867i
\(189\) 36.3510 1.26788i 0.192333 0.00670837i
\(190\) −235.912 −1.24164
\(191\) −60.8021 105.312i −0.318336 0.551373i 0.661805 0.749676i \(-0.269791\pi\)
−0.980141 + 0.198302i \(0.936457\pi\)
\(192\) 63.8685 + 36.8745i 0.332649 + 0.192055i
\(193\) −121.266 + 210.039i −0.628323 + 1.08829i 0.359566 + 0.933120i \(0.382925\pi\)
−0.987888 + 0.155167i \(0.950408\pi\)
\(194\) 128.773 74.3470i 0.663777 0.383232i
\(195\) 44.8348i 0.229922i
\(196\) 180.323 369.638i 0.920015 1.88591i
\(197\) −98.9929 −0.502502 −0.251251 0.967922i \(-0.580842\pi\)
−0.251251 + 0.967922i \(0.580842\pi\)
\(198\) −13.6964 23.7229i −0.0691738 0.119813i
\(199\) 68.2115 + 39.3819i 0.342772 + 0.197899i 0.661497 0.749948i \(-0.269921\pi\)
−0.318725 + 0.947847i \(0.603255\pi\)
\(200\) −38.6667 + 66.9727i −0.193334 + 0.334864i
\(201\) −97.5816 + 56.3388i −0.485481 + 0.280292i
\(202\) 527.945i 2.61359i
\(203\) −5.97578 171.329i −0.0294373 0.843986i
\(204\) 337.343 1.65364
\(205\) 4.14917 + 7.18658i 0.0202399 + 0.0350565i
\(206\) 425.846 + 245.863i 2.06722 + 1.19351i
\(207\) −52.6626 + 91.2143i −0.254409 + 0.440649i
\(208\) −209.287 + 120.832i −1.00619 + 0.580922i
\(209\) 77.7303i 0.371915i
\(210\) −80.9414 + 50.5731i −0.385435 + 0.240824i
\(211\) −107.144 −0.507790 −0.253895 0.967232i \(-0.581712\pi\)
−0.253895 + 0.967232i \(0.581712\pi\)
\(212\) 168.030 + 291.036i 0.792594 + 1.37281i
\(213\) −129.118 74.5462i −0.606187 0.349982i
\(214\) −319.020 + 552.559i −1.49075 + 2.58205i
\(215\) −143.731 + 82.9833i −0.668518 + 0.385969i
\(216\) 80.3673i 0.372071i
\(217\) 123.092 231.480i 0.567246 1.06673i
\(218\) 259.842 1.19194
\(219\) 53.3274 + 92.3657i 0.243504 + 0.421761i
\(220\) 42.1574 + 24.3396i 0.191625 + 0.110635i
\(221\) 134.311 232.634i 0.607743 1.05264i
\(222\) −135.969 + 78.5019i −0.612474 + 0.353612i
\(223\) 8.72021i 0.0391041i 0.999809 + 0.0195520i \(0.00622400\pi\)
−0.999809 + 0.0195520i \(0.993776\pi\)
\(224\) 71.8462 + 38.2051i 0.320742 + 0.170559i
\(225\) 15.0000 0.0666667
\(226\) 13.0003 + 22.5171i 0.0575233 + 0.0996333i
\(227\) −219.123 126.511i −0.965299 0.557316i −0.0674992 0.997719i \(-0.521502\pi\)
−0.897800 + 0.440404i \(0.854835\pi\)
\(228\) 217.841 377.312i 0.955443 1.65488i
\(229\) 125.988 72.7394i 0.550167 0.317639i −0.199022 0.979995i \(-0.563777\pi\)
0.749189 + 0.662356i \(0.230443\pi\)
\(230\) 276.370i 1.20161i
\(231\) 16.6632 + 26.6692i 0.0721352 + 0.115451i
\(232\) 378.787 1.63270
\(233\) −128.758 223.015i −0.552609 0.957146i −0.998085 0.0618526i \(-0.980299\pi\)
0.445477 0.895294i \(-0.353034\pi\)
\(234\) 105.881 + 61.1303i 0.452482 + 0.261241i
\(235\) −3.77805 + 6.54377i −0.0160768 + 0.0278458i
\(236\) 358.549 207.009i 1.51928 0.877155i
\(237\) 47.7068i 0.201295i
\(238\) −571.481 + 19.9326i −2.40118 + 0.0837506i
\(239\) −128.682 −0.538418 −0.269209 0.963082i \(-0.586762\pi\)
−0.269209 + 0.963082i \(0.586762\pi\)
\(240\) −40.4256 70.0192i −0.168440 0.291747i
\(241\) −8.02227 4.63166i −0.0332874 0.0192185i 0.483264 0.875475i \(-0.339451\pi\)
−0.516551 + 0.856256i \(0.672784\pi\)
\(242\) −201.144 + 348.392i −0.831175 + 1.43964i
\(243\) 13.5000 7.79423i 0.0555556 0.0320750i
\(244\) 7.41519i 0.0303901i
\(245\) 90.8406 61.2617i 0.370778 0.250048i
\(246\) −22.6289 −0.0919872
\(247\) −173.464 300.449i −0.702285 1.21639i
\(248\) 501.670 + 289.639i 2.02286 + 1.16790i
\(249\) 113.835 197.167i 0.457167 0.791837i
\(250\) −34.0864 + 19.6798i −0.136346 + 0.0787192i
\(251\) 29.9212i 0.119208i 0.998222 + 0.0596040i \(0.0189838\pi\)
−0.998222 + 0.0596040i \(0.981016\pi\)
\(252\) −6.14408 176.155i −0.0243813 0.699026i
\(253\) −91.0608 −0.359924
\(254\) −367.251 636.097i −1.44587 2.50432i
\(255\) 77.8303 + 44.9353i 0.305217 + 0.176217i
\(256\) 260.539 451.267i 1.01773 1.76276i
\(257\) 83.7338 48.3438i 0.325813 0.188108i −0.328168 0.944619i \(-0.606431\pi\)
0.653980 + 0.756511i \(0.273098\pi\)
\(258\) 452.576i 1.75417i
\(259\) 152.857 95.5065i 0.590180 0.368751i
\(260\) −217.267 −0.835642
\(261\) −36.7357 63.6281i −0.140750 0.243786i
\(262\) 334.088 + 192.886i 1.27514 + 0.736204i
\(263\) −32.1231 + 55.6388i −0.122141 + 0.211554i −0.920612 0.390479i \(-0.872309\pi\)
0.798471 + 0.602034i \(0.205643\pi\)
\(264\) −60.1740 + 34.7415i −0.227932 + 0.131596i
\(265\) 89.5289i 0.337845i
\(266\) −346.743 + 652.062i −1.30354 + 2.45136i
\(267\) 113.022 0.423302
\(268\) 273.014 + 472.875i 1.01871 + 1.76446i
\(269\) −171.096 98.7823i −0.636044 0.367220i 0.147045 0.989130i \(-0.453024\pi\)
−0.783089 + 0.621910i \(0.786357\pi\)
\(270\) −20.4518 + 35.4236i −0.0757475 + 0.131199i
\(271\) −133.483 + 77.0667i −0.492559 + 0.284379i −0.725635 0.688080i \(-0.758454\pi\)
0.233077 + 0.972458i \(0.425121\pi\)
\(272\) 484.410i 1.78092i
\(273\) −123.924 65.8980i −0.453932 0.241385i
\(274\) 624.708 2.27996
\(275\) 6.48426 + 11.2311i 0.0235791 + 0.0408402i
\(276\) 442.019 + 255.200i 1.60152 + 0.924637i
\(277\) −169.602 + 293.758i −0.612280 + 1.06050i 0.378575 + 0.925570i \(0.376414\pi\)
−0.990855 + 0.134929i \(0.956919\pi\)
\(278\) −517.968 + 299.049i −1.86320 + 1.07572i
\(279\) 112.360i 0.402724i
\(280\) 128.281 + 205.311i 0.458145 + 0.733253i
\(281\) −111.976 −0.398492 −0.199246 0.979949i \(-0.563849\pi\)
−0.199246 + 0.979949i \(0.563849\pi\)
\(282\) −10.3024 17.8443i −0.0365333 0.0632776i
\(283\) −56.6453 32.7042i −0.200160 0.115563i 0.396570 0.918004i \(-0.370200\pi\)
−0.596730 + 0.802442i \(0.703534\pi\)
\(284\) −361.246 + 625.697i −1.27199 + 2.20316i
\(285\) 100.519 58.0345i 0.352697 0.203630i
\(286\) 105.703i 0.369589i
\(287\) 25.9622 0.905532i 0.0904605 0.00315516i
\(288\) 34.8740 0.121090
\(289\) 124.725 + 216.029i 0.431573 + 0.747507i
\(290\) 166.958 + 96.3935i 0.575719 + 0.332391i
\(291\) −36.5787 + 63.3562i −0.125700 + 0.217719i
\(292\) 447.599 258.421i 1.53287 0.885004i
\(293\) 100.992i 0.344681i 0.985037 + 0.172341i \(0.0551330\pi\)
−0.985037 + 0.172341i \(0.944867\pi\)
\(294\) 20.8170 + 298.054i 0.0708060 + 1.01379i
\(295\) 110.297 0.373889
\(296\) 199.123 + 344.891i 0.672713 + 1.16517i
\(297\) 11.6717 + 6.73864i 0.0392985 + 0.0226890i
\(298\) 150.297 260.322i 0.504352 0.873564i
\(299\) 351.975 203.213i 1.17717 0.679642i
\(300\) 72.6891i 0.242297i
\(301\) 18.1106 + 519.242i 0.0601681 + 1.72506i
\(302\) 485.802 1.60862
\(303\) 129.874 + 224.949i 0.428628 + 0.742406i
\(304\) −541.804 312.811i −1.78225 1.02898i
\(305\) 0.987732 1.71080i 0.00323846 0.00560918i
\(306\) −212.236 + 122.535i −0.693583 + 0.400440i
\(307\) 400.388i 1.30420i −0.758135 0.652098i \(-0.773889\pi\)
0.758135 0.652098i \(-0.226111\pi\)
\(308\) 129.237 80.7490i 0.419602 0.262172i
\(309\) −241.929 −0.782941
\(310\) 147.415 + 255.330i 0.475531 + 0.823644i
\(311\) −31.1758 17.9993i −0.100244 0.0578757i 0.449040 0.893512i \(-0.351766\pi\)
−0.549284 + 0.835636i \(0.685099\pi\)
\(312\) 155.059 268.571i 0.496985 0.860803i
\(313\) −99.1558 + 57.2476i −0.316792 + 0.182900i −0.649962 0.759967i \(-0.725215\pi\)
0.333170 + 0.942867i \(0.391882\pi\)
\(314\) 24.1737i 0.0769864i
\(315\) 22.0469 41.4600i 0.0699902 0.131619i
\(316\) 231.184 0.731596
\(317\) −2.01608 3.49195i −0.00635987 0.0110156i 0.862828 0.505498i \(-0.168691\pi\)
−0.869188 + 0.494482i \(0.835358\pi\)
\(318\) −211.429 122.069i −0.664872 0.383864i
\(319\) 31.7605 55.0108i 0.0995627 0.172448i
\(320\) 82.4539 47.6048i 0.257669 0.148765i
\(321\) 313.916i 0.977932i
\(322\) −763.888 406.208i −2.37232 1.26151i
\(323\) 695.413 2.15298
\(324\) −37.7703 65.4202i −0.116575 0.201914i
\(325\) −50.1269 28.9408i −0.154237 0.0890485i
\(326\) −487.098 + 843.678i −1.49417 + 2.58797i
\(327\) −110.715 + 63.9212i −0.338577 + 0.195478i
\(328\) 57.3989i 0.174997i
\(329\) 12.5340 + 20.0605i 0.0380974 + 0.0609742i
\(330\) −35.3640 −0.107164
\(331\) −253.691 439.406i −0.766439 1.32751i −0.939482 0.342598i \(-0.888693\pi\)
0.173043 0.984914i \(-0.444640\pi\)
\(332\) −955.461 551.636i −2.87790 1.66155i
\(333\) 38.6229 66.8969i 0.115985 0.200892i
\(334\) −129.207 + 74.5976i −0.386847 + 0.223346i
\(335\) 145.466i 0.434227i
\(336\) −252.951 + 8.82265i −0.752829 + 0.0262579i
\(337\) −264.279 −0.784210 −0.392105 0.919921i \(-0.628253\pi\)
−0.392105 + 0.919921i \(0.628253\pi\)
\(338\) 61.5884 + 106.674i 0.182214 + 0.315604i
\(339\) −11.0784 6.39614i −0.0326797 0.0188677i
\(340\) 217.754 377.161i 0.640453 1.10930i
\(341\) 84.1280 48.5713i 0.246710 0.142438i
\(342\) 316.510i 0.925467i
\(343\) −35.8105 341.126i −0.104404 0.994535i
\(344\) −1147.98 −3.33714
\(345\) 67.9872 + 117.757i 0.197064 + 0.341325i
\(346\) 90.1226 + 52.0323i 0.260470 + 0.150382i
\(347\) 117.234 203.055i 0.337849 0.585172i −0.646179 0.763186i \(-0.723634\pi\)
0.984028 + 0.178014i \(0.0569673\pi\)
\(348\) −308.338 + 178.019i −0.886029 + 0.511549i
\(349\) 54.2133i 0.155339i −0.996979 0.0776695i \(-0.975252\pi\)
0.996979 0.0776695i \(-0.0247479\pi\)
\(350\) 4.29499 + 123.140i 0.0122714 + 0.351829i
\(351\) −60.1522 −0.171374
\(352\) 15.0755 + 26.1115i 0.0428280 + 0.0741803i
\(353\) −451.914 260.913i −1.28021 0.739129i −0.303322 0.952888i \(-0.598096\pi\)
−0.976886 + 0.213759i \(0.931429\pi\)
\(354\) −150.385 + 260.475i −0.424818 + 0.735806i
\(355\) −166.690 + 96.2388i −0.469551 + 0.271095i
\(356\) 547.696i 1.53847i
\(357\) 238.596 149.077i 0.668336 0.417584i
\(358\) 523.423 1.46208
\(359\) 233.973 + 405.253i 0.651735 + 1.12884i 0.982702 + 0.185196i \(0.0592919\pi\)
−0.330967 + 0.943642i \(0.607375\pi\)
\(360\) 89.8533 + 51.8768i 0.249593 + 0.144102i
\(361\) 268.566 465.171i 0.743951 1.28856i
\(362\) 784.458 452.907i 2.16701 1.25112i
\(363\) 197.926i 0.545251i
\(364\) −319.337 + 600.526i −0.877301 + 1.64980i
\(365\) 137.691 0.377235
\(366\) 2.69346 + 4.66520i 0.00735917 + 0.0127465i
\(367\) −149.151 86.1123i −0.406406 0.234638i 0.282839 0.959168i \(-0.408724\pi\)
−0.689244 + 0.724529i \(0.742057\pi\)
\(368\) 366.456 634.721i 0.995806 1.72479i
\(369\) 9.64181 5.56670i 0.0261296 0.0150859i
\(370\) 202.691i 0.547814i
\(371\) 247.458 + 131.589i 0.667003 + 0.354687i
\(372\) −544.489 −1.46368
\(373\) 230.486 + 399.213i 0.617924 + 1.07028i 0.989864 + 0.142019i \(0.0453593\pi\)
−0.371940 + 0.928257i \(0.621307\pi\)
\(374\) −183.493 105.940i −0.490622 0.283261i
\(375\) 9.68246 16.7705i 0.0258199 0.0447214i
\(376\) −45.2627 + 26.1324i −0.120379 + 0.0695011i
\(377\) 283.509i 0.752014i
\(378\) 67.8510 + 108.594i 0.179500 + 0.287287i
\(379\) 444.638 1.17319 0.586594 0.809881i \(-0.300468\pi\)
0.586594 + 0.809881i \(0.300468\pi\)
\(380\) −281.231 487.107i −0.740083 1.28186i
\(381\) 312.960 + 180.687i 0.821416 + 0.474245i
\(382\) 214.049 370.744i 0.560339 0.970535i
\(383\) −458.528 + 264.731i −1.19720 + 0.691205i −0.959930 0.280239i \(-0.909586\pi\)
−0.237271 + 0.971443i \(0.576253\pi\)
\(384\) 340.166i 0.885849i
\(385\) 40.5732 1.41515i 0.105385 0.00367571i
\(386\) −853.818 −2.21196
\(387\) 111.334 + 192.836i 0.287684 + 0.498284i
\(388\) 307.020 + 177.258i 0.791290 + 0.456851i
\(389\) −97.7554 + 169.317i −0.251299 + 0.435263i −0.963884 0.266323i \(-0.914191\pi\)
0.712585 + 0.701586i \(0.247524\pi\)
\(390\) 136.692 78.9189i 0.350491 0.202356i
\(391\) 814.674i 2.08356i
\(392\) 756.026 52.8030i 1.92864 0.134701i
\(393\) −189.799 −0.482950
\(394\) −174.249 301.808i −0.442256 0.766009i
\(395\) 53.3378 + 30.7946i 0.135032 + 0.0779610i
\(396\) 32.6550 56.5601i 0.0824622 0.142829i
\(397\) 25.3358 14.6276i 0.0638181 0.0368454i −0.467751 0.883860i \(-0.654936\pi\)
0.531570 + 0.847015i \(0.321602\pi\)
\(398\) 277.283i 0.696690i
\(399\) −12.6657 363.132i −0.0317435 0.910106i
\(400\) −104.379 −0.260946
\(401\) −105.396 182.551i −0.262833 0.455241i 0.704160 0.710041i \(-0.251324\pi\)
−0.966994 + 0.254800i \(0.917990\pi\)
\(402\) −343.529 198.337i −0.854550 0.493375i
\(403\) −216.785 + 375.483i −0.537929 + 0.931720i
\(404\) 1090.09 629.363i 2.69824 1.55783i
\(405\) 20.1246i 0.0496904i
\(406\) 511.826 319.795i 1.26066 0.787672i
\(407\) 66.7843 0.164089
\(408\) 310.814 + 538.345i 0.761799 + 1.31947i
\(409\) 281.014 + 162.244i 0.687077 + 0.396684i 0.802516 0.596631i \(-0.203494\pi\)
−0.115439 + 0.993315i \(0.536828\pi\)
\(410\) −14.6069 + 25.2998i −0.0356265 + 0.0617069i
\(411\) −266.179 + 153.678i −0.647637 + 0.373913i
\(412\) 1172.37i 2.84556i
\(413\) 162.114 304.862i 0.392529 0.738164i
\(414\) −370.790 −0.895628
\(415\) −146.960 254.542i −0.354120 0.613355i
\(416\) −116.542 67.2853i −0.280148 0.161744i
\(417\) 147.132 254.841i 0.352835 0.611128i
\(418\) −236.983 + 136.822i −0.566944 + 0.327325i
\(419\) 693.958i 1.65622i 0.560563 + 0.828112i \(0.310585\pi\)
−0.560563 + 0.828112i \(0.689415\pi\)
\(420\) −200.913 106.838i −0.478364 0.254376i
\(421\) −341.554 −0.811292 −0.405646 0.914030i \(-0.632953\pi\)
−0.405646 + 0.914030i \(0.632953\pi\)
\(422\) −188.596 326.657i −0.446909 0.774070i
\(423\) 8.77939 + 5.06878i 0.0207551 + 0.0119829i
\(424\) −309.632 + 536.298i −0.730264 + 1.26485i
\(425\) 100.478 58.0113i 0.236420 0.136497i
\(426\) 524.869i 1.23209i
\(427\) −3.27690 5.24462i −0.00767423 0.0122825i
\(428\) −1521.22 −3.55425
\(429\) −26.0028 45.0382i −0.0606127 0.104984i
\(430\) −505.996 292.137i −1.17673 0.679388i
\(431\) 205.726 356.328i 0.477323 0.826748i −0.522339 0.852738i \(-0.674941\pi\)
0.999662 + 0.0259902i \(0.00827387\pi\)
\(432\) −93.9407 + 54.2367i −0.217455 + 0.125548i
\(433\) 443.458i 1.02415i 0.858940 + 0.512077i \(0.171124\pi\)
−0.858940 + 0.512077i \(0.828876\pi\)
\(434\) 922.400 32.1723i 2.12535 0.0741298i
\(435\) −94.8512 −0.218049
\(436\) 309.758 + 536.517i 0.710454 + 1.23054i
\(437\) 911.197 + 526.080i 2.08512 + 1.20384i
\(438\) −187.735 + 325.167i −0.428619 + 0.742390i
\(439\) −268.002 + 154.731i −0.610484 + 0.352463i −0.773155 0.634217i \(-0.781322\pi\)
0.162671 + 0.986680i \(0.447989\pi\)
\(440\) 89.7021i 0.203868i
\(441\) −82.1912 121.875i −0.186375 0.276361i
\(442\) 945.666 2.13952
\(443\) −409.330 708.981i −0.923996 1.60041i −0.793167 0.609004i \(-0.791569\pi\)
−0.130829 0.991405i \(-0.541764\pi\)
\(444\) −324.178 187.164i −0.730131 0.421541i
\(445\) 72.9552 126.362i 0.163944 0.283960i
\(446\) −26.5860 + 15.3494i −0.0596099 + 0.0344158i
\(447\) 147.892i 0.330855i
\(448\) −10.3895 297.872i −0.0231908 0.664893i
\(449\) 315.756 0.703243 0.351621 0.936142i \(-0.385630\pi\)
0.351621 + 0.936142i \(0.385630\pi\)
\(450\) 26.4032 + 45.7317i 0.0586738 + 0.101626i
\(451\) 8.33600 + 4.81279i 0.0184834 + 0.0106714i
\(452\) −30.9953 + 53.6854i −0.0685736 + 0.118773i
\(453\) −206.993 + 119.507i −0.456938 + 0.263813i
\(454\) 890.743i 1.96199i
\(455\) −153.668 + 96.0138i −0.337733 + 0.211019i
\(456\) 802.839 1.76061
\(457\) 93.6533 + 162.212i 0.204931 + 0.354950i 0.950111 0.311913i \(-0.100970\pi\)
−0.745180 + 0.666863i \(0.767636\pi\)
\(458\) 443.533 + 256.074i 0.968412 + 0.559113i
\(459\) 60.2871 104.420i 0.131344 0.227495i
\(460\) 570.644 329.462i 1.24053 0.716221i
\(461\) 8.27599i 0.0179523i 0.999960 + 0.00897613i \(0.00285723\pi\)
−0.999960 + 0.00897613i \(0.997143\pi\)
\(462\) −51.9778 + 97.7461i −0.112506 + 0.211572i
\(463\) −472.925 −1.02144 −0.510718 0.859748i \(-0.670620\pi\)
−0.510718 + 0.859748i \(0.670620\pi\)
\(464\) 255.628 + 442.761i 0.550922 + 0.954226i
\(465\) −125.622 72.5280i −0.270155 0.155974i
\(466\) 453.283 785.108i 0.972709 1.68478i
\(467\) −620.865 + 358.456i −1.32948 + 0.767573i −0.985218 0.171303i \(-0.945202\pi\)
−0.344257 + 0.938876i \(0.611869\pi\)
\(468\) 291.494i 0.622851i
\(469\) 402.069 + 213.805i 0.857289 + 0.455875i
\(470\) −26.6007 −0.0565972
\(471\) −5.94674 10.3001i −0.0126258 0.0218685i
\(472\) 660.705 + 381.458i 1.39980 + 0.808174i
\(473\) −96.2556 + 166.720i −0.203500 + 0.352473i
\(474\) −145.448 + 83.9742i −0.306851 + 0.177161i
\(475\) 149.844i 0.315462i
\(476\) −722.420 1156.22i −1.51769 2.42904i
\(477\) 120.116 0.251815
\(478\) −226.508 392.323i −0.473866 0.820759i
\(479\) 178.320 + 102.953i 0.372276 + 0.214933i 0.674452 0.738319i \(-0.264380\pi\)
−0.302177 + 0.953252i \(0.597713\pi\)
\(480\) 22.5111 38.9903i 0.0468981 0.0812298i
\(481\) −258.140 + 149.037i −0.536673 + 0.309848i
\(482\) 32.6108i 0.0676573i
\(483\) 425.408 14.8378i 0.880762 0.0307201i
\(484\) −959.138 −1.98169
\(485\) 47.2230 + 81.7926i 0.0973669 + 0.168644i
\(486\) 47.5258 + 27.4390i 0.0977897 + 0.0564589i
\(487\) −161.439 + 279.621i −0.331498 + 0.574171i −0.982806 0.184643i \(-0.940887\pi\)
0.651308 + 0.758813i \(0.274221\pi\)
\(488\) 11.8335 6.83205i 0.0242489 0.0140001i
\(489\) 479.304i 0.980172i
\(490\) 346.672 + 169.119i 0.707494 + 0.345141i
\(491\) 272.380 0.554745 0.277372 0.960763i \(-0.410536\pi\)
0.277372 + 0.960763i \(0.410536\pi\)
\(492\) −26.9759 46.7236i −0.0548290 0.0949667i
\(493\) −492.153 284.145i −0.998282 0.576359i
\(494\) 610.669 1057.71i 1.23617 2.14111i
\(495\) 15.0680 8.69954i 0.0304405 0.0175748i
\(496\) 781.864i 1.57634i
\(497\) 21.0035 + 602.184i 0.0422606 + 1.21164i
\(498\) 801.494 1.60943
\(499\) −264.597 458.296i −0.530255 0.918429i −0.999377 0.0352954i \(-0.988763\pi\)
0.469122 0.883134i \(-0.344571\pi\)
\(500\) −81.2689 46.9206i −0.162538 0.0938412i
\(501\) 36.7020 63.5698i 0.0732576 0.126886i
\(502\) −91.2231 + 52.6677i −0.181719 + 0.104916i
\(503\) 204.695i 0.406948i 0.979080 + 0.203474i \(0.0652232\pi\)
−0.979080 + 0.203474i \(0.934777\pi\)
\(504\) 275.454 172.106i 0.546535 0.341481i
\(505\) 335.334 0.664028
\(506\) −160.286 277.624i −0.316772 0.548665i
\(507\) −52.4837 30.3015i −0.103518 0.0597663i
\(508\) 875.599 1516.58i 1.72362 2.98540i
\(509\) −473.892 + 273.602i −0.931026 + 0.537528i −0.887136 0.461508i \(-0.847309\pi\)
−0.0438903 + 0.999036i \(0.513975\pi\)
\(510\) 316.383i 0.620359i
\(511\) 202.377 380.577i 0.396041 0.744770i
\(512\) 1048.84 2.04851
\(513\) −77.8614 134.860i −0.151777 0.262885i
\(514\) 294.779 + 170.191i 0.573500 + 0.331110i
\(515\) −156.164 + 270.485i −0.303232 + 0.525213i
\(516\) 934.470 539.517i 1.81099 1.04558i
\(517\) 8.76461i 0.0169528i
\(518\) 560.238 + 297.914i 1.08154 + 0.575124i
\(519\) −51.1998 −0.0986509
\(520\) −200.181 346.723i −0.384963 0.666775i
\(521\) 30.1482 + 17.4061i 0.0578660 + 0.0334090i 0.528654 0.848837i \(-0.322697\pi\)
−0.470788 + 0.882246i \(0.656030\pi\)
\(522\) 129.325 223.998i 0.247750 0.429115i
\(523\) 720.290 415.860i 1.37723 0.795143i 0.385403 0.922748i \(-0.374062\pi\)
0.991825 + 0.127606i \(0.0407292\pi\)
\(524\) 919.756i 1.75526i
\(525\) −32.1225 51.4115i −0.0611857 0.0979267i
\(526\) −226.174 −0.429989
\(527\) −434.543 752.650i −0.824559 1.42818i
\(528\) −81.2180 46.8913i −0.153822 0.0888092i
\(529\) −351.800 + 609.336i −0.665029 + 1.15186i
\(530\) −272.954 + 157.590i −0.515007 + 0.297340i
\(531\) 147.979i 0.278680i
\(532\) −1759.72 + 61.3770i −3.30774 + 0.115370i
\(533\) −42.9612 −0.0806027
\(534\) 198.942 + 344.578i 0.372551 + 0.645277i
\(535\) −350.969 202.632i −0.656017 0.378751i
\(536\) −503.088 + 871.374i −0.938597 + 1.62570i
\(537\) −223.022 + 128.762i −0.415312 + 0.239780i
\(538\) 695.512i 1.29277i
\(539\) 55.7228 114.224i 0.103382 0.211919i
\(540\) −97.5226 −0.180597
\(541\) 112.177 + 194.296i 0.207351 + 0.359143i 0.950879 0.309562i \(-0.100182\pi\)
−0.743528 + 0.668705i \(0.766849\pi\)
\(542\) −469.919 271.308i −0.867008 0.500568i
\(543\) −222.830 + 385.954i −0.410369 + 0.710780i
\(544\) 233.606 134.872i 0.429422 0.247927i
\(545\) 165.044i 0.302833i
\(546\) −17.2236 493.810i −0.0315450 0.904414i
\(547\) −456.739 −0.834989 −0.417495 0.908679i \(-0.637092\pi\)
−0.417495 + 0.908679i \(0.637092\pi\)
\(548\) 744.716 + 1289.89i 1.35897 + 2.35381i
\(549\) −2.29528 1.32518i −0.00418084 0.00241381i
\(550\) −22.8274 + 39.5381i −0.0415043 + 0.0718875i
\(551\) −635.621 + 366.976i −1.15358 + 0.666018i
\(552\) 940.522i 1.70384i
\(553\) 163.512 102.164i 0.295682 0.184745i
\(554\) −1194.14 −2.15549
\(555\) −49.8620 86.3635i −0.0898414 0.155610i
\(556\) −1234.94 712.994i −2.22112 1.28236i
\(557\) 388.525 672.945i 0.697532 1.20816i −0.271788 0.962357i \(-0.587615\pi\)
0.969320 0.245803i \(-0.0790516\pi\)
\(558\) 342.561 197.777i 0.613908 0.354440i
\(559\) 859.223i 1.53707i
\(560\) −153.415 + 288.502i −0.273955 + 0.515183i
\(561\) 104.245 0.185819
\(562\) −197.102 341.391i −0.350716 0.607457i
\(563\) −72.2428 41.7094i −0.128318 0.0740842i 0.434467 0.900688i \(-0.356937\pi\)
−0.562785 + 0.826603i \(0.690270\pi\)
\(564\) 24.5630 42.5444i 0.0435514 0.0754333i
\(565\) −14.3022 + 8.25738i −0.0253136 + 0.0146148i
\(566\) 230.265i 0.406829i
\(567\) −55.6245 29.5790i −0.0981031 0.0521676i
\(568\) −1331.35 −2.34393
\(569\) 111.671 + 193.421i 0.196259 + 0.339931i 0.947313 0.320311i \(-0.103787\pi\)
−0.751053 + 0.660241i \(0.770454\pi\)
\(570\) 353.869 + 204.306i 0.620822 + 0.358432i
\(571\) −88.3631 + 153.049i −0.154751 + 0.268037i −0.932969 0.359958i \(-0.882791\pi\)
0.778217 + 0.627995i \(0.216124\pi\)
\(572\) −218.252 + 126.008i −0.381560 + 0.220294i
\(573\) 210.625i 0.367582i
\(574\) 48.4597 + 77.5590i 0.0844246 + 0.135120i
\(575\) 175.542 0.305291
\(576\) −63.8685 110.624i −0.110883 0.192055i
\(577\) 780.812 + 450.802i 1.35323 + 0.781286i 0.988700 0.149907i \(-0.0478975\pi\)
0.364527 + 0.931193i \(0.381231\pi\)
\(578\) −439.084 + 760.516i −0.759661 + 1.31577i
\(579\) 363.799 210.039i 0.628323 0.362762i
\(580\) 459.643i 0.792488i
\(581\) −919.556 + 32.0731i −1.58271 + 0.0552033i
\(582\) −257.546 −0.442518
\(583\) 51.9240 + 89.9351i 0.0890635 + 0.154263i
\(584\) 824.798 + 476.197i 1.41233 + 0.815406i
\(585\) −38.8281 + 67.2523i −0.0663728 + 0.114961i
\(586\) −307.901 + 177.767i −0.525429 + 0.303356i
\(587\) 163.544i 0.278610i 0.990250 + 0.139305i \(0.0444868\pi\)
−0.990250 + 0.139305i \(0.955513\pi\)
\(588\) −590.601 + 398.293i −1.00442 + 0.677370i
\(589\) −1122.43 −1.90566
\(590\) 194.147 + 336.272i 0.329062 + 0.569953i
\(591\) 148.489 + 85.7304i 0.251251 + 0.145060i
\(592\) −268.760 + 465.507i −0.453987 + 0.786329i
\(593\) 1004.47 579.932i 1.69388 0.977964i 0.742554 0.669786i \(-0.233614\pi\)
0.951329 0.308177i \(-0.0997190\pi\)
\(594\) 47.4458i 0.0798750i
\(595\) −12.6606 362.987i −0.0212783 0.610063i
\(596\) 716.677 1.20248
\(597\) −68.2115 118.146i −0.114257 0.197899i
\(598\) 1239.10 + 715.396i 2.07208 + 1.19631i
\(599\) −16.3990 + 28.4039i −0.0273773 + 0.0474188i −0.879389 0.476103i \(-0.842049\pi\)
0.852012 + 0.523522i \(0.175382\pi\)
\(600\) 116.000 66.9727i 0.193334 0.111621i
\(601\) 796.834i 1.32585i 0.748687 + 0.662924i \(0.230685\pi\)
−0.748687 + 0.662924i \(0.769315\pi\)
\(602\) −1551.18 + 969.192i −2.57670 + 1.60995i
\(603\) 195.163 0.323654
\(604\) 579.126 + 1003.08i 0.958817 + 1.66072i
\(605\) −221.288 127.761i −0.365766 0.211175i
\(606\) −457.214 + 791.917i −0.754478 + 1.30679i
\(607\) −453.877 + 262.046i −0.747739 + 0.431707i −0.824876 0.565313i \(-0.808755\pi\)
0.0771375 + 0.997020i \(0.475422\pi\)
\(608\) 348.378i 0.572990i
\(609\) −139.412 + 262.169i −0.228919 + 0.430491i
\(610\) 6.95448 0.0114008
\(611\) −19.5593 33.8776i −0.0320119 0.0554462i
\(612\) −506.014 292.147i −0.826821 0.477365i
\(613\) 126.866 219.738i 0.206959 0.358463i −0.743796 0.668406i \(-0.766977\pi\)
0.950755 + 0.309944i \(0.100310\pi\)
\(614\) 1220.69 704.769i 1.98810 1.14783i
\(615\) 14.3732i 0.0233710i
\(616\) 247.937 + 131.844i 0.402495 + 0.214032i
\(617\) 620.813 1.00618 0.503090 0.864234i \(-0.332196\pi\)
0.503090 + 0.864234i \(0.332196\pi\)
\(618\) −425.846 737.588i −0.689072 1.19351i
\(619\) 555.643 + 320.801i 0.897647 + 0.518257i 0.876436 0.481519i \(-0.159915\pi\)
0.0212107 + 0.999775i \(0.493248\pi\)
\(620\) −351.466 + 608.757i −0.566881 + 0.981866i
\(621\) 157.988 91.2143i 0.254409 0.146883i
\(622\) 126.731i 0.203747i
\(623\) −242.036 387.374i −0.388501 0.621789i
\(624\) 418.573 0.670791
\(625\) −12.5000 21.6506i −0.0200000 0.0346410i
\(626\) −349.071 201.536i −0.557621 0.321943i
\(627\) 67.3164 116.595i 0.107363 0.185958i
\(628\) −49.9134 + 28.8175i −0.0794800 + 0.0458878i
\(629\) 597.484i 0.949896i
\(630\) 165.210 5.76234i 0.262238 0.00914657i
\(631\) −166.338 −0.263610 −0.131805 0.991276i \(-0.542077\pi\)
−0.131805 + 0.991276i \(0.542077\pi\)
\(632\) 213.004 + 368.933i 0.337031 + 0.583755i
\(633\) 160.715 + 92.7891i 0.253895 + 0.146586i
\(634\) 7.09746 12.2932i 0.0111947 0.0193899i
\(635\) 404.029 233.266i 0.636266 0.367348i
\(636\) 582.073i 0.915209i
\(637\) 39.5213 + 565.860i 0.0620429 + 0.888321i
\(638\) 223.621 0.350503
\(639\) 129.118 + 223.639i 0.202062 + 0.349982i
\(640\) 380.317 + 219.576i 0.594246 + 0.343088i
\(641\) −68.5302 + 118.698i −0.106911 + 0.185176i −0.914518 0.404546i \(-0.867429\pi\)
0.807606 + 0.589722i \(0.200763\pi\)
\(642\) 957.061 552.559i 1.49075 0.860685i
\(643\) 812.010i 1.26285i −0.775438 0.631423i \(-0.782471\pi\)
0.775438 0.631423i \(-0.217529\pi\)
\(644\) −71.9030 2061.50i −0.111651 3.20109i
\(645\) 287.463 0.445679
\(646\) 1224.08 + 2120.16i 1.89485 + 3.28198i
\(647\) −197.709 114.148i −0.305579 0.176426i 0.339368 0.940654i \(-0.389787\pi\)
−0.644946 + 0.764228i \(0.723120\pi\)
\(648\) 69.6001 120.551i 0.107408 0.186035i
\(649\) 110.798 63.9691i 0.170721 0.0985656i
\(650\) 203.768i 0.313489i
\(651\) −385.106 + 240.619i −0.591561 + 0.369614i
\(652\) −2322.68 −3.56239
\(653\) 435.557 + 754.406i 0.667009 + 1.15529i 0.978736 + 0.205122i \(0.0657590\pi\)
−0.311728 + 0.950171i \(0.600908\pi\)
\(654\) −389.763 225.030i −0.595968 0.344082i
\(655\) −122.515 + 212.202i −0.187046 + 0.323973i
\(656\) −67.0932 + 38.7363i −0.102276 + 0.0590492i
\(657\) 184.731i 0.281174i
\(658\) −39.0975 + 73.5243i −0.0594187 + 0.111739i
\(659\) −677.945 −1.02875 −0.514374 0.857566i \(-0.671976\pi\)
−0.514374 + 0.857566i \(0.671976\pi\)
\(660\) −42.1574 73.0188i −0.0638749 0.110635i
\(661\) 608.681 + 351.422i 0.920849 + 0.531652i 0.883906 0.467665i \(-0.154905\pi\)
0.0369430 + 0.999317i \(0.488238\pi\)
\(662\) 893.102 1546.90i 1.34910 2.33670i
\(663\) −402.934 + 232.634i −0.607743 + 0.350881i
\(664\) 2033.02i 3.06177i
\(665\) −414.170 220.240i −0.622812 0.331188i
\(666\) 271.939 0.408316
\(667\) −429.911 744.628i −0.644544 1.11638i
\(668\) −308.055 177.856i −0.461161 0.266251i
\(669\) 7.55192 13.0803i 0.0112884 0.0195520i
\(670\) −443.494 + 256.051i −0.661932 + 0.382166i
\(671\) 2.29142i 0.00341493i
\(672\) −74.6827 119.528i −0.111135 0.177870i
\(673\) 612.283 0.909782 0.454891 0.890547i \(-0.349678\pi\)
0.454891 + 0.890547i \(0.349678\pi\)
\(674\) −465.187 805.727i −0.690188 1.19544i
\(675\) −22.5000 12.9904i −0.0333333 0.0192450i
\(676\) −146.839 + 254.333i −0.217218 + 0.376232i
\(677\) −5.01270 + 2.89408i −0.00740428 + 0.00427487i −0.503698 0.863880i \(-0.668027\pi\)
0.496293 + 0.868155i \(0.334694\pi\)
\(678\) 45.0343i 0.0664222i
\(679\) 295.483 10.3061i 0.435173 0.0151784i
\(680\) 802.518 1.18017
\(681\) 219.123 + 379.532i 0.321766 + 0.557316i
\(682\) 296.167 + 170.992i 0.434262 + 0.250721i
\(683\) 58.3832 101.123i 0.0854806 0.148057i −0.820115 0.572198i \(-0.806091\pi\)
0.905596 + 0.424142i \(0.139424\pi\)
\(684\) −653.523 + 377.312i −0.955443 + 0.551625i
\(685\) 396.796i 0.579264i
\(686\) 976.982 709.632i 1.42417 1.03445i
\(687\) −251.977 −0.366778
\(688\) −774.724 1341.86i −1.12605 1.95038i
\(689\) −401.401 231.749i −0.582585 0.336356i
\(690\) −239.344 + 414.556i −0.346875 + 0.600805i
\(691\) 820.541 473.740i 1.18747 0.685585i 0.229738 0.973252i \(-0.426213\pi\)
0.957730 + 0.287667i \(0.0928796\pi\)
\(692\) 248.111i 0.358542i
\(693\) −1.89862 54.4346i −0.00273971 0.0785493i
\(694\) 825.425 1.18937
\(695\) −189.947 328.998i −0.273305 0.473378i
\(696\) −568.180 328.039i −0.816350 0.471320i
\(697\) 43.0575 74.5778i 0.0617755 0.106998i
\(698\) 165.284 95.4270i 0.236797 0.136715i
\(699\) 446.030i 0.638097i
\(700\) −249.137 + 155.664i −0.355910 + 0.222377i
\(701\) 1168.56 1.66700 0.833498 0.552523i \(-0.186335\pi\)
0.833498 + 0.552523i \(0.186335\pi\)
\(702\) −105.881 183.391i −0.150827 0.261241i
\(703\) −668.275 385.829i −0.950604 0.548832i
\(704\) 55.2187 95.6415i 0.0784356 0.135854i
\(705\) 11.3341 6.54377i 0.0160768 0.00928194i
\(706\) 1837.05i 2.60205i
\(707\) 492.872 926.865i 0.697132 1.31098i
\(708\) −717.099 −1.01285
\(709\) −334.781 579.857i −0.472187 0.817852i 0.527306 0.849675i \(-0.323202\pi\)
−0.999494 + 0.0318230i \(0.989869\pi\)
\(710\) −586.822 338.802i −0.826509 0.477185i
\(711\) 41.3153 71.5602i 0.0581087 0.100647i
\(712\) 874.035 504.625i 1.22758 0.708742i
\(713\) 1314.93i 1.84422i
\(714\) 874.484 + 465.018i 1.22477 + 0.651286i
\(715\) −67.1390 −0.0939008
\(716\) 623.973 + 1080.75i 0.871471 + 1.50943i
\(717\) 193.023 + 111.442i 0.269209 + 0.155428i
\(718\) −823.685 + 1426.66i −1.14719 + 1.98700i
\(719\) −805.983 + 465.334i −1.12098 + 0.647196i −0.941650 0.336593i \(-0.890725\pi\)
−0.179327 + 0.983790i \(0.557392\pi\)
\(720\) 140.038i 0.194498i
\(721\) 518.091 + 829.195i 0.718572 + 1.15006i
\(722\) 1890.94 2.61903
\(723\) 8.02227 + 13.8950i 0.0110958 + 0.0192185i
\(724\) 1870.31 + 1079.82i 2.58330 + 1.49147i
\(725\) −61.2262 + 106.047i −0.0844499 + 0.146272i
\(726\) 603.433 348.392i 0.831175 0.479879i
\(727\) 290.932i 0.400182i 0.979777 + 0.200091i \(0.0641238\pi\)
−0.979777 + 0.200091i \(0.935876\pi\)
\(728\) −1252.57 + 43.6882i −1.72056 + 0.0600113i
\(729\) −27.0000 −0.0370370
\(730\) 242.365 + 419.789i 0.332007 + 0.575053i
\(731\) 1491.55 + 861.149i 2.04043 + 1.17804i
\(732\) −6.42174 + 11.1228i −0.00877288 + 0.0151951i
\(733\) −0.836082 + 0.482712i −0.00114063 + 0.000658543i −0.500570 0.865696i \(-0.666876\pi\)
0.499430 + 0.866354i \(0.333543\pi\)
\(734\) 606.304i 0.826027i
\(735\) −189.315 + 13.2223i −0.257571 + 0.0179895i
\(736\) 408.124 0.554516
\(737\) 84.3659 + 146.126i 0.114472 + 0.198271i
\(738\) 33.9433 + 19.5972i 0.0459936 + 0.0265544i
\(739\) 49.9365 86.4925i 0.0675731 0.117040i −0.830259 0.557377i \(-0.811808\pi\)
0.897832 + 0.440337i \(0.145141\pi\)
\(740\) −418.512 + 241.628i −0.565557 + 0.326525i
\(741\) 600.898i 0.810929i
\(742\) 34.3931 + 986.070i 0.0463518 + 1.32894i
\(743\) 890.635 1.19870 0.599351 0.800486i \(-0.295425\pi\)
0.599351 + 0.800486i \(0.295425\pi\)
\(744\) −501.670 868.917i −0.674287 1.16790i
\(745\) 165.349 + 95.4640i 0.221944 + 0.128140i
\(746\) −811.408 + 1405.40i −1.08768 + 1.88391i
\(747\) −341.504 + 197.167i −0.457167 + 0.263946i
\(748\) 505.162i 0.675351i
\(749\) −1075.93 + 672.251i −1.43648 + 0.897532i
\(750\) 68.1728 0.0908971
\(751\) −310.537 537.867i −0.413499 0.716200i 0.581771 0.813353i \(-0.302360\pi\)
−0.995270 + 0.0971521i \(0.969027\pi\)
\(752\) −61.0920 35.2715i −0.0812393 0.0469035i
\(753\) 25.9125 44.8818i 0.0344124 0.0596040i
\(754\) −864.357 + 499.037i −1.14636 + 0.661853i
\(755\) 308.567i 0.408698i
\(756\) −143.338 + 269.553i −0.189601 + 0.356551i
\(757\) 675.637 0.892519 0.446259 0.894904i \(-0.352756\pi\)
0.446259 + 0.894904i \(0.352756\pi\)
\(758\) 782.658 + 1355.60i 1.03253 + 1.78840i
\(759\) 136.591 + 78.8609i 0.179962 + 0.103901i
\(760\) 518.230 897.601i 0.681882 1.18105i
\(761\) 549.336 317.159i 0.721861 0.416766i −0.0935765 0.995612i \(-0.529830\pi\)
0.815437 + 0.578846i \(0.196497\pi\)
\(762\) 1272.19i 1.66954i
\(763\) 456.181 + 242.580i 0.597878 + 0.317930i
\(764\) 1020.67 1.33596
\(765\) −77.8303 134.806i −0.101739 0.176217i
\(766\) −1614.22 931.967i −2.10733 1.21667i
\(767\) −285.509 + 494.516i −0.372241 + 0.644741i
\(768\) −781.618 + 451.267i −1.01773 + 0.587587i
\(769\) 17.8434i 0.0232033i −0.999933 0.0116017i \(-0.996307\pi\)
0.999933 0.0116017i \(-0.00369301\pi\)
\(770\) 75.7320 + 121.208i 0.0983532 + 0.157413i
\(771\) −167.468 −0.217208
\(772\) −1017.84 1762.95i −1.31844 2.28361i
\(773\) −223.935 129.289i −0.289697 0.167256i 0.348108 0.937454i \(-0.386824\pi\)
−0.637805 + 0.770198i \(0.720157\pi\)
\(774\) −391.943 + 678.865i −0.506386 + 0.877086i
\(775\) −162.178 + 93.6332i −0.209261 + 0.120817i
\(776\) 653.274i