Properties

Label 210.3.o.b.61.5
Level 210
Weight 3
Character 210.61
Analytic conductor 5.722
Analytic rank 0
Dimension 16
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) \(=\) \( 210 = 2 \cdot 3 \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 210.o (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.72208555157\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} + \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2^{8}\cdot 7 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 61.5
Root \(-2.10711 + 3.64962i\) of \(x^{16} + 92 x^{14} - 112 x^{13} + 5846 x^{12} - 7728 x^{11} + 197216 x^{10} - 298200 x^{9} + 4836403 x^{8} - 6808704 x^{7} + 64376800 x^{6} - 91953512 x^{5} + 595763862 x^{4} - 630430976 x^{3} + 1087013404 x^{2} + 294123256 x + 101626561\)
Character \(\chi\) \(=\) 210.61
Dual form 210.3.o.b.31.5

$q$-expansion

\(f(q)\) \(=\) \(q+(0.707107 - 1.22474i) q^{2} +(-1.50000 + 0.866025i) q^{3} +(-1.00000 - 1.73205i) q^{4} +(-1.93649 - 1.11803i) q^{5} +2.44949i q^{6} +(-5.26304 + 4.61524i) q^{7} -2.82843 q^{8} +(1.50000 - 2.59808i) q^{9} +O(q^{10})\) \(q+(0.707107 - 1.22474i) q^{2} +(-1.50000 + 0.866025i) q^{3} +(-1.00000 - 1.73205i) q^{4} +(-1.93649 - 1.11803i) q^{5} +2.44949i q^{6} +(-5.26304 + 4.61524i) q^{7} -2.82843 q^{8} +(1.50000 - 2.59808i) q^{9} +(-2.73861 + 1.58114i) q^{10} +(5.41099 + 9.37211i) q^{11} +(3.00000 + 1.73205i) q^{12} +19.2715i q^{13} +(1.93096 + 9.70935i) q^{14} +3.87298 q^{15} +(-2.00000 + 3.46410i) q^{16} +(-8.89730 + 5.13686i) q^{17} +(-2.12132 - 3.67423i) q^{18} +(-18.0756 - 10.4359i) q^{19} +4.47214i q^{20} +(3.89764 - 11.4808i) q^{21} +15.3046 q^{22} +(-10.5373 + 18.2511i) q^{23} +(4.24264 - 2.44949i) q^{24} +(2.50000 + 4.33013i) q^{25} +(23.6026 + 13.6270i) q^{26} +5.19615i q^{27} +(13.2569 + 4.50061i) q^{28} +19.0888 q^{29} +(2.73861 - 4.74342i) q^{30} +(-34.6556 + 20.0084i) q^{31} +(2.82843 + 4.89898i) q^{32} +(-16.2330 - 9.37211i) q^{33} +14.5292i q^{34} +(15.3518 - 3.05312i) q^{35} -6.00000 q^{36} +(25.1827 - 43.6177i) q^{37} +(-25.5627 + 14.7586i) q^{38} +(-16.6896 - 28.9072i) q^{39} +(5.47723 + 3.16228i) q^{40} -22.7706i q^{41} +(-11.3050 - 12.8918i) q^{42} -48.4307 q^{43} +(10.8220 - 18.7442i) q^{44} +(-5.80948 + 3.35410i) q^{45} +(14.9020 + 25.8110i) q^{46} +(57.6236 + 33.2690i) q^{47} -6.92820i q^{48} +(6.39913 - 48.5804i) q^{49} +7.07107 q^{50} +(8.89730 - 15.4106i) q^{51} +(33.3792 - 19.2715i) q^{52} +(-2.47531 - 4.28736i) q^{53} +(6.36396 + 3.67423i) q^{54} -24.1987i q^{55} +(14.8861 - 13.0539i) q^{56} +36.1511 q^{57} +(13.4978 - 23.3789i) q^{58} +(-24.4105 + 14.0934i) q^{59} +(-3.87298 - 6.70820i) q^{60} +(-60.6988 - 35.0445i) q^{61} +56.5924i q^{62} +(4.09619 + 20.5966i) q^{63} +8.00000 q^{64} +(21.5462 - 37.3191i) q^{65} +(-22.9569 + 13.2542i) q^{66} +(-9.65287 - 16.7193i) q^{67} +(17.7946 + 10.2737i) q^{68} -36.5023i q^{69} +(7.11609 - 20.9609i) q^{70} +49.4968 q^{71} +(-4.24264 + 7.34847i) q^{72} +(-115.159 + 66.4872i) q^{73} +(-35.6137 - 61.6848i) q^{74} +(-7.50000 - 4.33013i) q^{75} +41.7437i q^{76} +(-71.7328 - 24.3527i) q^{77} -47.2053 q^{78} +(45.0404 - 78.0122i) q^{79} +(7.74597 - 4.47214i) q^{80} +(-4.50000 - 7.79423i) q^{81} +(-27.8882 - 16.1013i) q^{82} +101.045i q^{83} +(-23.7829 + 4.72987i) q^{84} +22.9727 q^{85} +(-34.2456 + 59.3152i) q^{86} +(-28.6332 + 16.5314i) q^{87} +(-15.3046 - 26.5083i) q^{88} +(34.3077 + 19.8075i) q^{89} +9.48683i q^{90} +(-88.9425 - 101.427i) q^{91} +42.1492 q^{92} +(34.6556 - 60.0253i) q^{93} +(81.4920 - 47.0495i) q^{94} +(23.3355 + 40.4182i) q^{95} +(-8.48528 - 4.89898i) q^{96} -68.6944i q^{97} +(-54.9737 - 42.1888i) q^{98} +32.4659 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q - 24q^{3} - 16q^{4} + 4q^{7} + 24q^{9} + O(q^{10}) \) \( 16q - 24q^{3} - 16q^{4} + 4q^{7} + 24q^{9} - 4q^{11} + 48q^{12} + 8q^{14} - 32q^{16} + 12q^{17} - 72q^{19} - 24q^{21} - 48q^{22} - 12q^{23} + 40q^{25} + 32q^{28} + 72q^{29} + 120q^{31} + 12q^{33} - 20q^{35} - 96q^{36} + 44q^{37} - 72q^{38} + 36q^{39} - 24q^{42} - 56q^{43} - 8q^{44} + 8q^{46} - 24q^{47} - 40q^{49} - 12q^{51} - 72q^{52} + 32q^{53} + 16q^{56} + 144q^{57} - 88q^{58} + 132q^{59} + 96q^{61} + 60q^{63} + 128q^{64} + 20q^{65} + 72q^{66} - 164q^{67} - 24q^{68} - 136q^{71} - 348q^{73} - 112q^{74} - 120q^{75} + 96q^{77} + 280q^{79} - 72q^{81} + 264q^{82} - 24q^{84} + 120q^{85} - 88q^{86} - 108q^{87} + 48q^{88} - 300q^{89} - 272q^{91} + 48q^{92} - 120q^{93} + 200q^{95} + 384q^{98} - 24q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/210\mathbb{Z}\right)^\times\).

\(n\) \(31\) \(71\) \(127\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(1\) \(1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.707107 1.22474i 0.353553 0.612372i
\(3\) −1.50000 + 0.866025i −0.500000 + 0.288675i
\(4\) −1.00000 1.73205i −0.250000 0.433013i
\(5\) −1.93649 1.11803i −0.387298 0.223607i
\(6\) 2.44949i 0.408248i
\(7\) −5.26304 + 4.61524i −0.751863 + 0.659320i
\(8\) −2.82843 −0.353553
\(9\) 1.50000 2.59808i 0.166667 0.288675i
\(10\) −2.73861 + 1.58114i −0.273861 + 0.158114i
\(11\) 5.41099 + 9.37211i 0.491908 + 0.852010i 0.999957 0.00931868i \(-0.00296627\pi\)
−0.508049 + 0.861328i \(0.669633\pi\)
\(12\) 3.00000 + 1.73205i 0.250000 + 0.144338i
\(13\) 19.2715i 1.48242i 0.671273 + 0.741211i \(0.265748\pi\)
−0.671273 + 0.741211i \(0.734252\pi\)
\(14\) 1.93096 + 9.70935i 0.137926 + 0.693525i
\(15\) 3.87298 0.258199
\(16\) −2.00000 + 3.46410i −0.125000 + 0.216506i
\(17\) −8.89730 + 5.13686i −0.523371 + 0.302168i −0.738313 0.674459i \(-0.764377\pi\)
0.214942 + 0.976627i \(0.431044\pi\)
\(18\) −2.12132 3.67423i −0.117851 0.204124i
\(19\) −18.0756 10.4359i −0.951346 0.549260i −0.0578471 0.998325i \(-0.518424\pi\)
−0.893499 + 0.449066i \(0.851757\pi\)
\(20\) 4.47214i 0.223607i
\(21\) 3.89764 11.4808i 0.185602 0.546704i
\(22\) 15.3046 0.695663
\(23\) −10.5373 + 18.2511i −0.458143 + 0.793527i −0.998863 0.0476755i \(-0.984819\pi\)
0.540720 + 0.841203i \(0.318152\pi\)
\(24\) 4.24264 2.44949i 0.176777 0.102062i
\(25\) 2.50000 + 4.33013i 0.100000 + 0.173205i
\(26\) 23.6026 + 13.6270i 0.907794 + 0.524115i
\(27\) 5.19615i 0.192450i
\(28\) 13.2569 + 4.50061i 0.473460 + 0.160736i
\(29\) 19.0888 0.658235 0.329118 0.944289i \(-0.393249\pi\)
0.329118 + 0.944289i \(0.393249\pi\)
\(30\) 2.73861 4.74342i 0.0912871 0.158114i
\(31\) −34.6556 + 20.0084i −1.11792 + 0.645434i −0.940870 0.338768i \(-0.889990\pi\)
−0.177054 + 0.984201i \(0.556657\pi\)
\(32\) 2.82843 + 4.89898i 0.0883883 + 0.153093i
\(33\) −16.2330 9.37211i −0.491908 0.284003i
\(34\) 14.5292i 0.427330i
\(35\) 15.3518 3.05312i 0.438624 0.0872319i
\(36\) −6.00000 −0.166667
\(37\) 25.1827 43.6177i 0.680614 1.17886i −0.294180 0.955750i \(-0.595047\pi\)
0.974794 0.223107i \(-0.0716201\pi\)
\(38\) −25.5627 + 14.7586i −0.672703 + 0.388385i
\(39\) −16.6896 28.9072i −0.427938 0.741211i
\(40\) 5.47723 + 3.16228i 0.136931 + 0.0790569i
\(41\) 22.7706i 0.555382i −0.960671 0.277691i \(-0.910431\pi\)
0.960671 0.277691i \(-0.0895691\pi\)
\(42\) −11.3050 12.8918i −0.269166 0.306947i
\(43\) −48.4307 −1.12629 −0.563147 0.826357i \(-0.690410\pi\)
−0.563147 + 0.826357i \(0.690410\pi\)
\(44\) 10.8220 18.7442i 0.245954 0.426005i
\(45\) −5.80948 + 3.35410i −0.129099 + 0.0745356i
\(46\) 14.9020 + 25.8110i 0.323956 + 0.561109i
\(47\) 57.6236 + 33.2690i 1.22603 + 0.707851i 0.966198 0.257802i \(-0.0829982\pi\)
0.259836 + 0.965653i \(0.416332\pi\)
\(48\) 6.92820i 0.144338i
\(49\) 6.39913 48.5804i 0.130595 0.991436i
\(50\) 7.07107 0.141421
\(51\) 8.89730 15.4106i 0.174457 0.302168i
\(52\) 33.3792 19.2715i 0.641907 0.370605i
\(53\) −2.47531 4.28736i −0.0467040 0.0808937i 0.841728 0.539901i \(-0.181538\pi\)
−0.888432 + 0.459008i \(0.848205\pi\)
\(54\) 6.36396 + 3.67423i 0.117851 + 0.0680414i
\(55\) 24.1987i 0.439976i
\(56\) 14.8861 13.0539i 0.265824 0.233105i
\(57\) 36.1511 0.634231
\(58\) 13.4978 23.3789i 0.232721 0.403085i
\(59\) −24.4105 + 14.0934i −0.413737 + 0.238871i −0.692394 0.721520i \(-0.743444\pi\)
0.278657 + 0.960391i \(0.410111\pi\)
\(60\) −3.87298 6.70820i −0.0645497 0.111803i
\(61\) −60.6988 35.0445i −0.995062 0.574499i −0.0882785 0.996096i \(-0.528137\pi\)
−0.906784 + 0.421596i \(0.861470\pi\)
\(62\) 56.5924i 0.912781i
\(63\) 4.09619 + 20.5966i 0.0650188 + 0.326931i
\(64\) 8.00000 0.125000
\(65\) 21.5462 37.3191i 0.331479 0.574139i
\(66\) −22.9569 + 13.2542i −0.347832 + 0.200821i
\(67\) −9.65287 16.7193i −0.144073 0.249541i 0.784954 0.619554i \(-0.212687\pi\)
−0.929027 + 0.370013i \(0.879353\pi\)
\(68\) 17.7946 + 10.2737i 0.261685 + 0.151084i
\(69\) 36.5023i 0.529018i
\(70\) 7.11609 20.9609i 0.101658 0.299442i
\(71\) 49.4968 0.697138 0.348569 0.937283i \(-0.386668\pi\)
0.348569 + 0.937283i \(0.386668\pi\)
\(72\) −4.24264 + 7.34847i −0.0589256 + 0.102062i
\(73\) −115.159 + 66.4872i −1.57752 + 0.910783i −0.582318 + 0.812961i \(0.697854\pi\)
−0.995204 + 0.0978221i \(0.968812\pi\)
\(74\) −35.6137 61.6848i −0.481266 0.833578i
\(75\) −7.50000 4.33013i −0.100000 0.0577350i
\(76\) 41.7437i 0.549260i
\(77\) −71.7328 24.3527i −0.931594 0.316269i
\(78\) −47.2053 −0.605196
\(79\) 45.0404 78.0122i 0.570132 0.987497i −0.426420 0.904525i \(-0.640226\pi\)
0.996552 0.0829717i \(-0.0264411\pi\)
\(80\) 7.74597 4.47214i 0.0968246 0.0559017i
\(81\) −4.50000 7.79423i −0.0555556 0.0962250i
\(82\) −27.8882 16.1013i −0.340100 0.196357i
\(83\) 101.045i 1.21741i 0.793396 + 0.608706i \(0.208311\pi\)
−0.793396 + 0.608706i \(0.791689\pi\)
\(84\) −23.7829 + 4.72987i −0.283130 + 0.0563080i
\(85\) 22.9727 0.270267
\(86\) −34.2456 + 59.3152i −0.398205 + 0.689712i
\(87\) −28.6332 + 16.5314i −0.329118 + 0.190016i
\(88\) −15.3046 26.5083i −0.173916 0.301231i
\(89\) 34.3077 + 19.8075i 0.385479 + 0.222557i 0.680200 0.733027i \(-0.261893\pi\)
−0.294720 + 0.955584i \(0.595226\pi\)
\(90\) 9.48683i 0.105409i
\(91\) −88.9425 101.427i −0.977390 1.11458i
\(92\) 42.1492 0.458143
\(93\) 34.6556 60.0253i 0.372641 0.645434i
\(94\) 81.4920 47.0495i 0.866937 0.500526i
\(95\) 23.3355 + 40.4182i 0.245636 + 0.425455i
\(96\) −8.48528 4.89898i −0.0883883 0.0510310i
\(97\) 68.6944i 0.708190i −0.935210 0.354095i \(-0.884789\pi\)
0.935210 0.354095i \(-0.115211\pi\)
\(98\) −54.9737 42.1888i −0.560956 0.430498i
\(99\) 32.4659 0.327939
\(100\) 5.00000 8.66025i 0.0500000 0.0866025i
\(101\) −6.96199 + 4.01951i −0.0689306 + 0.0397971i −0.534069 0.845441i \(-0.679338\pi\)
0.465139 + 0.885238i \(0.346004\pi\)
\(102\) −12.5827 21.7939i −0.123360 0.213665i
\(103\) 177.158 + 102.282i 1.71998 + 0.993033i 0.918911 + 0.394465i \(0.129070\pi\)
0.801072 + 0.598568i \(0.204263\pi\)
\(104\) 54.5080i 0.524115i
\(105\) −20.3837 + 17.8747i −0.194130 + 0.170236i
\(106\) −7.00124 −0.0660494
\(107\) −82.2769 + 142.508i −0.768943 + 1.33185i 0.169193 + 0.985583i \(0.445884\pi\)
−0.938136 + 0.346266i \(0.887449\pi\)
\(108\) 9.00000 5.19615i 0.0833333 0.0481125i
\(109\) 39.5050 + 68.4247i 0.362432 + 0.627750i 0.988360 0.152130i \(-0.0486133\pi\)
−0.625929 + 0.779880i \(0.715280\pi\)
\(110\) −29.6372 17.1110i −0.269429 0.155555i
\(111\) 87.2354i 0.785905i
\(112\) −5.46158 27.4622i −0.0487641 0.245198i
\(113\) 84.5690 0.748398 0.374199 0.927348i \(-0.377918\pi\)
0.374199 + 0.927348i \(0.377918\pi\)
\(114\) 25.5627 44.2759i 0.224234 0.388385i
\(115\) 40.8108 23.5621i 0.354876 0.204888i
\(116\) −19.0888 33.0628i −0.164559 0.285024i
\(117\) 50.0688 + 28.9072i 0.427938 + 0.247070i
\(118\) 39.8621i 0.337815i
\(119\) 23.1190 68.0987i 0.194277 0.572258i
\(120\) −10.9545 −0.0912871
\(121\) 1.94240 3.36434i 0.0160529 0.0278044i
\(122\) −85.8410 + 49.5603i −0.703615 + 0.406232i
\(123\) 19.7200 + 34.1560i 0.160325 + 0.277691i
\(124\) 69.3113 + 40.0169i 0.558962 + 0.322717i
\(125\) 11.1803i 0.0894427i
\(126\) 28.1221 + 9.54723i 0.223191 + 0.0757717i
\(127\) −101.777 −0.801393 −0.400697 0.916211i \(-0.631232\pi\)
−0.400697 + 0.916211i \(0.631232\pi\)
\(128\) 5.65685 9.79796i 0.0441942 0.0765466i
\(129\) 72.6460 41.9422i 0.563147 0.325133i
\(130\) −30.4709 52.7771i −0.234391 0.405978i
\(131\) 61.2264 + 35.3491i 0.467377 + 0.269840i 0.715141 0.698980i \(-0.246362\pi\)
−0.247764 + 0.968820i \(0.579696\pi\)
\(132\) 37.4884i 0.284003i
\(133\) 143.297 28.4984i 1.07742 0.214273i
\(134\) −27.3024 −0.203750
\(135\) 5.80948 10.0623i 0.0430331 0.0745356i
\(136\) 25.1654 14.5292i 0.185039 0.106833i
\(137\) 58.9138 + 102.042i 0.430027 + 0.744829i 0.996875 0.0789932i \(-0.0251705\pi\)
−0.566848 + 0.823823i \(0.691837\pi\)
\(138\) −44.7060 25.8110i −0.323956 0.187036i
\(139\) 158.507i 1.14034i 0.821528 + 0.570168i \(0.193122\pi\)
−0.821528 + 0.570168i \(0.806878\pi\)
\(140\) −20.6400 23.5370i −0.147428 0.168122i
\(141\) −115.247 −0.817356
\(142\) 34.9995 60.6209i 0.246475 0.426908i
\(143\) −180.614 + 104.278i −1.26304 + 0.729215i
\(144\) 6.00000 + 10.3923i 0.0416667 + 0.0721688i
\(145\) −36.9653 21.3419i −0.254933 0.147186i
\(146\) 188.054i 1.28804i
\(147\) 32.4731 + 78.4123i 0.220906 + 0.533417i
\(148\) −100.731 −0.680614
\(149\) 147.948 256.254i 0.992940 1.71982i 0.393747 0.919219i \(-0.371179\pi\)
0.599193 0.800604i \(-0.295488\pi\)
\(150\) −10.6066 + 6.12372i −0.0707107 + 0.0408248i
\(151\) 62.6478 + 108.509i 0.414886 + 0.718604i 0.995417 0.0956344i \(-0.0304880\pi\)
−0.580530 + 0.814239i \(0.697155\pi\)
\(152\) 51.1254 + 29.5173i 0.336352 + 0.194193i
\(153\) 30.8212i 0.201445i
\(154\) −80.5486 + 70.6343i −0.523043 + 0.458665i
\(155\) 89.4805 0.577293
\(156\) −33.3792 + 57.8144i −0.213969 + 0.370605i
\(157\) 4.61909 2.66684i 0.0294210 0.0169862i −0.485217 0.874394i \(-0.661260\pi\)
0.514638 + 0.857407i \(0.327926\pi\)
\(158\) −63.6967 110.326i −0.403144 0.698266i
\(159\) 7.42593 + 4.28736i 0.0467040 + 0.0269646i
\(160\) 12.6491i 0.0790569i
\(161\) −28.7752 144.689i −0.178728 0.898686i
\(162\) −12.7279 −0.0785674
\(163\) −119.623 + 207.193i −0.733883 + 1.27112i 0.221329 + 0.975199i \(0.428961\pi\)
−0.955212 + 0.295923i \(0.904373\pi\)
\(164\) −39.4399 + 22.7706i −0.240487 + 0.138845i
\(165\) 20.9567 + 36.2980i 0.127010 + 0.219988i
\(166\) 123.754 + 71.4497i 0.745509 + 0.430420i
\(167\) 310.440i 1.85892i −0.368918 0.929462i \(-0.620272\pi\)
0.368918 0.929462i \(-0.379728\pi\)
\(168\) −11.0242 + 32.4726i −0.0656202 + 0.193289i
\(169\) −202.390 −1.19757
\(170\) 16.2442 28.1357i 0.0955540 0.165504i
\(171\) −54.2267 + 31.3078i −0.317115 + 0.183087i
\(172\) 48.4307 + 83.8844i 0.281574 + 0.487700i
\(173\) 78.7285 + 45.4539i 0.455078 + 0.262739i 0.709972 0.704230i \(-0.248707\pi\)
−0.254894 + 0.966969i \(0.582041\pi\)
\(174\) 46.7579i 0.268723i
\(175\) −33.1422 11.2515i −0.189384 0.0642944i
\(176\) −43.2879 −0.245954
\(177\) 24.4105 42.2802i 0.137912 0.238871i
\(178\) 48.5184 28.0121i 0.272575 0.157371i
\(179\) 121.577 + 210.577i 0.679200 + 1.17641i 0.975222 + 0.221228i \(0.0710066\pi\)
−0.296022 + 0.955181i \(0.595660\pi\)
\(180\) 11.6190 + 6.70820i 0.0645497 + 0.0372678i
\(181\) 245.993i 1.35907i 0.733641 + 0.679537i \(0.237819\pi\)
−0.733641 + 0.679537i \(0.762181\pi\)
\(182\) −187.113 + 37.2125i −1.02810 + 0.204464i
\(183\) 121.398 0.663375
\(184\) 29.8040 51.6220i 0.161978 0.280554i
\(185\) −97.5322 + 56.3102i −0.527201 + 0.304380i
\(186\) −49.0105 84.8886i −0.263497 0.456390i
\(187\) −96.2864 55.5910i −0.514901 0.297278i
\(188\) 133.076i 0.707851i
\(189\) −23.9815 27.3475i −0.126886 0.144696i
\(190\) 66.0027 0.347382
\(191\) 20.6108 35.6989i 0.107910 0.186905i −0.807014 0.590533i \(-0.798918\pi\)
0.914923 + 0.403628i \(0.132251\pi\)
\(192\) −12.0000 + 6.92820i −0.0625000 + 0.0360844i
\(193\) 94.8727 + 164.324i 0.491568 + 0.851422i 0.999953 0.00970872i \(-0.00309043\pi\)
−0.508384 + 0.861130i \(0.669757\pi\)
\(194\) −84.1331 48.5743i −0.433676 0.250383i
\(195\) 74.6381i 0.382760i
\(196\) −90.5428 + 37.4967i −0.461953 + 0.191310i
\(197\) −362.318 −1.83918 −0.919589 0.392882i \(-0.871478\pi\)
−0.919589 + 0.392882i \(0.871478\pi\)
\(198\) 22.9569 39.7625i 0.115944 0.200821i
\(199\) −33.4433 + 19.3085i −0.168057 + 0.0970278i −0.581669 0.813425i \(-0.697600\pi\)
0.413612 + 0.910453i \(0.364267\pi\)
\(200\) −7.07107 12.2474i −0.0353553 0.0612372i
\(201\) 28.9586 + 16.7193i 0.144073 + 0.0831804i
\(202\) 11.3689i 0.0562816i
\(203\) −100.465 + 88.0995i −0.494902 + 0.433987i
\(204\) −35.5892 −0.174457
\(205\) −25.4584 + 44.0952i −0.124187 + 0.215098i
\(206\) 250.540 144.649i 1.21621 0.702180i
\(207\) 31.6119 + 54.7534i 0.152714 + 0.264509i
\(208\) −66.7584 38.5430i −0.320954 0.185303i
\(209\) 225.875i 1.08074i
\(210\) 7.47858 + 37.6041i 0.0356123 + 0.179067i
\(211\) −136.551 −0.647163 −0.323581 0.946200i \(-0.604887\pi\)
−0.323581 + 0.946200i \(0.604887\pi\)
\(212\) −4.95062 + 8.57473i −0.0233520 + 0.0404468i
\(213\) −74.2452 + 42.8655i −0.348569 + 0.201246i
\(214\) 116.357 + 201.537i 0.543725 + 0.941760i
\(215\) 93.7856 + 54.1471i 0.436212 + 0.251847i
\(216\) 14.6969i 0.0680414i
\(217\) 90.0502 265.249i 0.414978 1.22235i
\(218\) 111.737 0.512556
\(219\) 115.159 199.461i 0.525841 0.910783i
\(220\) −41.9133 + 24.1987i −0.190515 + 0.109994i
\(221\) −98.9949 171.464i −0.447941 0.775856i
\(222\) 106.841 + 61.6848i 0.481266 + 0.277859i
\(223\) 154.949i 0.694839i −0.937710 0.347419i \(-0.887058\pi\)
0.937710 0.347419i \(-0.112942\pi\)
\(224\) −37.4961 12.7296i −0.167393 0.0568288i
\(225\) 15.0000 0.0666667
\(226\) 59.7993 103.575i 0.264599 0.458299i
\(227\) 19.3590 11.1769i 0.0852818 0.0492375i −0.456753 0.889594i \(-0.650988\pi\)
0.542034 + 0.840356i \(0.317654\pi\)
\(228\) −36.1511 62.6156i −0.158558 0.274630i
\(229\) 25.9105 + 14.9594i 0.113146 + 0.0653250i 0.555505 0.831513i \(-0.312525\pi\)
−0.442359 + 0.896838i \(0.645858\pi\)
\(230\) 66.6437i 0.289755i
\(231\) 128.689 25.5933i 0.557096 0.110793i
\(232\) −53.9913 −0.232721
\(233\) 126.541 219.176i 0.543095 0.940669i −0.455629 0.890170i \(-0.650586\pi\)
0.998724 0.0504987i \(-0.0160811\pi\)
\(234\) 70.8079 40.8810i 0.302598 0.174705i
\(235\) −74.3917 128.850i −0.316561 0.548299i
\(236\) 48.8209 + 28.1868i 0.206868 + 0.119436i
\(237\) 156.024i 0.658331i
\(238\) −67.0559 76.4679i −0.281747 0.321294i
\(239\) 121.009 0.506315 0.253158 0.967425i \(-0.418531\pi\)
0.253158 + 0.967425i \(0.418531\pi\)
\(240\) −7.74597 + 13.4164i −0.0322749 + 0.0559017i
\(241\) 249.755 144.196i 1.03633 0.598323i 0.117536 0.993069i \(-0.462501\pi\)
0.918791 + 0.394745i \(0.129167\pi\)
\(242\) −2.74697 4.75789i −0.0113511 0.0196607i
\(243\) 13.5000 + 7.79423i 0.0555556 + 0.0320750i
\(244\) 140.178i 0.574499i
\(245\) −66.7064 + 86.9210i −0.272271 + 0.354780i
\(246\) 55.7765 0.226734
\(247\) 201.116 348.343i 0.814234 1.41030i
\(248\) 98.0209 56.5924i 0.395246 0.228195i
\(249\) −87.5076 151.568i −0.351436 0.608706i
\(250\) −13.6931 7.90569i −0.0547723 0.0316228i
\(251\) 422.260i 1.68231i −0.540795 0.841155i \(-0.681876\pi\)
0.540795 0.841155i \(-0.318124\pi\)
\(252\) 31.5782 27.6914i 0.125310 0.109887i
\(253\) −228.069 −0.901457
\(254\) −71.9672 + 124.651i −0.283335 + 0.490751i
\(255\) −34.4591 + 19.8950i −0.135134 + 0.0780195i
\(256\) −8.00000 13.8564i −0.0312500 0.0541266i
\(257\) 64.5077 + 37.2435i 0.251003 + 0.144916i 0.620223 0.784425i \(-0.287042\pi\)
−0.369221 + 0.929342i \(0.620375\pi\)
\(258\) 118.630i 0.459808i
\(259\) 68.7687 + 345.786i 0.265516 + 1.33508i
\(260\) −86.1847 −0.331479
\(261\) 28.6332 49.5942i 0.109706 0.190016i
\(262\) 86.5872 49.9911i 0.330486 0.190806i
\(263\) −156.637 271.304i −0.595579 1.03157i −0.993465 0.114139i \(-0.963589\pi\)
0.397885 0.917435i \(-0.369744\pi\)
\(264\) 45.9138 + 26.5083i 0.173916 + 0.100410i
\(265\) 11.0699i 0.0417733i
\(266\) 66.4229 195.653i 0.249710 0.735539i
\(267\) −68.6153 −0.256986
\(268\) −19.3057 + 33.4385i −0.0720363 + 0.124771i
\(269\) −138.011 + 79.6809i −0.513053 + 0.296211i −0.734088 0.679055i \(-0.762390\pi\)
0.221035 + 0.975266i \(0.429057\pi\)
\(270\) −8.21584 14.2302i −0.0304290 0.0527046i
\(271\) −163.041 94.1320i −0.601629 0.347350i 0.168053 0.985778i \(-0.446252\pi\)
−0.769682 + 0.638427i \(0.779585\pi\)
\(272\) 41.0949i 0.151084i
\(273\) 221.252 + 75.1133i 0.810446 + 0.275140i
\(274\) 166.633 0.608151
\(275\) −27.0549 + 46.8605i −0.0983816 + 0.170402i
\(276\) −63.2238 + 36.5023i −0.229072 + 0.132255i
\(277\) −3.52372 6.10326i −0.0127210 0.0220334i 0.859595 0.510976i \(-0.170716\pi\)
−0.872316 + 0.488943i \(0.837383\pi\)
\(278\) 194.130 + 112.081i 0.698311 + 0.403170i
\(279\) 120.051i 0.430289i
\(280\) −43.4215 + 8.63552i −0.155077 + 0.0308411i
\(281\) 198.386 0.705998 0.352999 0.935624i \(-0.385162\pi\)
0.352999 + 0.935624i \(0.385162\pi\)
\(282\) −81.4920 + 141.148i −0.288979 + 0.500526i
\(283\) −163.790 + 94.5641i −0.578763 + 0.334149i −0.760641 0.649172i \(-0.775115\pi\)
0.181879 + 0.983321i \(0.441782\pi\)
\(284\) −49.4968 85.7309i −0.174284 0.301869i
\(285\) −70.0064 40.4182i −0.245636 0.141818i
\(286\) 294.942i 1.03127i
\(287\) 105.092 + 119.843i 0.366174 + 0.417571i
\(288\) 16.9706 0.0589256
\(289\) −91.7253 + 158.873i −0.317389 + 0.549733i
\(290\) −52.2769 + 30.1821i −0.180265 + 0.104076i
\(291\) 59.4911 + 103.042i 0.204437 + 0.354095i
\(292\) 230.318 + 132.974i 0.788761 + 0.455391i
\(293\) 486.090i 1.65901i −0.558499 0.829505i \(-0.688622\pi\)
0.558499 0.829505i \(-0.311378\pi\)
\(294\) 118.997 + 15.6746i 0.404752 + 0.0533150i
\(295\) 63.0276 0.213653
\(296\) −71.2274 + 123.370i −0.240633 + 0.416789i
\(297\) −48.6989 + 28.1163i −0.163969 + 0.0946678i
\(298\) −209.230 362.397i −0.702115 1.21610i
\(299\) −351.726 203.069i −1.17634 0.679161i
\(300\) 17.3205i 0.0577350i
\(301\) 254.892 223.519i 0.846818 0.742588i
\(302\) 177.195 0.586738
\(303\) 6.96199 12.0585i 0.0229769 0.0397971i
\(304\) 72.3023 41.7437i 0.237836 0.137315i
\(305\) 78.3618 + 135.727i 0.256924 + 0.445005i
\(306\) 37.7481 + 21.7939i 0.123360 + 0.0712217i
\(307\) 427.589i 1.39280i −0.717655 0.696399i \(-0.754784\pi\)
0.717655 0.696399i \(-0.245216\pi\)
\(308\) 29.5526 + 148.598i 0.0959499 + 0.482460i
\(309\) −354.317 −1.14666
\(310\) 63.2723 109.591i 0.204104 0.353519i
\(311\) −311.852 + 180.048i −1.00274 + 0.578931i −0.909057 0.416671i \(-0.863197\pi\)
−0.0936811 + 0.995602i \(0.529863\pi\)
\(312\) 47.2053 + 81.7620i 0.151299 + 0.262058i
\(313\) 505.696 + 291.964i 1.61564 + 0.932792i 0.988029 + 0.154267i \(0.0493016\pi\)
0.627614 + 0.778525i \(0.284032\pi\)
\(314\) 7.54295i 0.0240221i
\(315\) 15.0955 44.4649i 0.0479222 0.141158i
\(316\) −180.162 −0.570132
\(317\) −180.700 + 312.982i −0.570032 + 0.987324i 0.426530 + 0.904473i \(0.359736\pi\)
−0.996562 + 0.0828508i \(0.973597\pi\)
\(318\) 10.5019 6.06325i 0.0330247 0.0190668i
\(319\) 103.289 + 178.902i 0.323791 + 0.560823i
\(320\) −15.4919 8.94427i −0.0484123 0.0279508i
\(321\) 285.016i 0.887899i
\(322\) −197.554 67.0680i −0.613521 0.208286i
\(323\) 214.432 0.663875
\(324\) −9.00000 + 15.5885i −0.0277778 + 0.0481125i
\(325\) −83.4479 + 48.1787i −0.256763 + 0.148242i
\(326\) 169.172 + 293.015i 0.518934 + 0.898819i
\(327\) −118.515 68.4247i −0.362432 0.209250i
\(328\) 64.4051i 0.196357i
\(329\) −456.819 + 90.8507i −1.38851 + 0.276142i
\(330\) 59.2744 0.179619
\(331\) −147.993 + 256.331i −0.447108 + 0.774415i −0.998196 0.0600326i \(-0.980880\pi\)
0.551088 + 0.834447i \(0.314213\pi\)
\(332\) 175.015 101.045i 0.527154 0.304353i
\(333\) −75.5481 130.853i −0.226871 0.392952i
\(334\) −380.210 219.514i −1.13835 0.657229i
\(335\) 43.1689i 0.128863i
\(336\) 31.9753 + 36.4634i 0.0951646 + 0.108522i
\(337\) −22.0162 −0.0653300 −0.0326650 0.999466i \(-0.510399\pi\)
−0.0326650 + 0.999466i \(0.510399\pi\)
\(338\) −143.111 + 247.876i −0.423406 + 0.733361i
\(339\) −126.854 + 73.2389i −0.374199 + 0.216044i
\(340\) −22.9727 39.7899i −0.0675669 0.117029i
\(341\) −375.043 216.531i −1.09983 0.634988i
\(342\) 88.5519i 0.258924i
\(343\) 190.531 + 285.214i 0.555484 + 0.831527i
\(344\) 136.983 0.398205
\(345\) −40.8108 + 70.6863i −0.118292 + 0.204888i
\(346\) 111.339 64.2815i 0.321789 0.185785i
\(347\) 141.953 + 245.870i 0.409086 + 0.708559i 0.994788 0.101969i \(-0.0325141\pi\)
−0.585701 + 0.810527i \(0.699181\pi\)
\(348\) 57.2665 + 33.0628i 0.164559 + 0.0950080i
\(349\) 317.175i 0.908811i 0.890795 + 0.454406i \(0.150148\pi\)
−0.890795 + 0.454406i \(0.849852\pi\)
\(350\) −37.2153 + 32.6347i −0.106329 + 0.0932419i
\(351\) −100.138 −0.285292
\(352\) −30.6092 + 53.0166i −0.0869579 + 0.150615i
\(353\) −101.275 + 58.4712i −0.286898 + 0.165641i −0.636542 0.771242i \(-0.719636\pi\)
0.349644 + 0.936883i \(0.386303\pi\)
\(354\) −34.5216 59.7932i −0.0975187 0.168907i
\(355\) −95.8501 55.3391i −0.270000 0.155885i
\(356\) 79.2302i 0.222557i
\(357\) 24.2967 + 122.170i 0.0680579 + 0.342212i
\(358\) 343.871 0.960534
\(359\) −116.793 + 202.291i −0.325329 + 0.563486i −0.981579 0.191058i \(-0.938808\pi\)
0.656250 + 0.754543i \(0.272142\pi\)
\(360\) 16.4317 9.48683i 0.0456435 0.0263523i
\(361\) 37.3175 + 64.6359i 0.103373 + 0.179047i
\(362\) 301.278 + 173.943i 0.832260 + 0.480505i
\(363\) 6.72867i 0.0185363i
\(364\) −86.7334 + 255.479i −0.238279 + 0.701866i
\(365\) 297.340 0.814629
\(366\) 85.8410 148.681i 0.234538 0.406232i
\(367\) 443.469 256.037i 1.20836 0.697648i 0.245960 0.969280i \(-0.420897\pi\)
0.962401 + 0.271632i \(0.0875634\pi\)
\(368\) −42.1492 73.0045i −0.114536 0.198382i
\(369\) −59.1599 34.1560i −0.160325 0.0925636i
\(370\) 159.269i 0.430458i
\(371\) 32.8149 + 11.1404i 0.0884498 + 0.0300280i
\(372\) −138.623 −0.372641
\(373\) 278.204 481.863i 0.745854 1.29186i −0.203941 0.978983i \(-0.565375\pi\)
0.949795 0.312874i \(-0.101292\pi\)
\(374\) −136.170 + 78.6175i −0.364090 + 0.210207i
\(375\) 9.68246 + 16.7705i 0.0258199 + 0.0447214i
\(376\) −162.984 94.0989i −0.433468 0.250263i
\(377\) 367.870i 0.975782i
\(378\) −50.4512 + 10.0336i −0.133469 + 0.0265438i
\(379\) −536.301 −1.41504 −0.707521 0.706692i \(-0.750187\pi\)
−0.707521 + 0.706692i \(0.750187\pi\)
\(380\) 46.6709 80.8364i 0.122818 0.212727i
\(381\) 152.665 88.1414i 0.400697 0.231342i
\(382\) −29.1480 50.4859i −0.0763038 0.132162i
\(383\) 25.4184 + 14.6753i 0.0663666 + 0.0383168i 0.532816 0.846231i \(-0.321134\pi\)
−0.466450 + 0.884548i \(0.654467\pi\)
\(384\) 19.5959i 0.0510310i
\(385\) 111.683 + 127.359i 0.290085 + 0.330801i
\(386\) 268.341 0.695183
\(387\) −72.6460 + 125.827i −0.187716 + 0.325133i
\(388\) −118.982 + 68.6944i −0.306655 + 0.177047i
\(389\) 349.242 + 604.905i 0.897795 + 1.55503i 0.830307 + 0.557306i \(0.188165\pi\)
0.0674875 + 0.997720i \(0.478502\pi\)
\(390\) 91.4126 + 52.7771i 0.234391 + 0.135326i
\(391\) 216.514i 0.553745i
\(392\) −18.0995 + 137.406i −0.0461721 + 0.350526i
\(393\) −122.453 −0.311585
\(394\) −256.198 + 443.747i −0.650248 + 1.12626i
\(395\) −174.441 + 100.713i −0.441622 + 0.254971i
\(396\) −32.4659 56.2326i −0.0819847 0.142002i
\(397\) −177.270 102.347i −0.446525 0.257801i 0.259837 0.965653i \(-0.416331\pi\)
−0.706361 + 0.707851i \(0.749665\pi\)
\(398\) 54.6127i 0.137218i
\(399\) −190.265 + 166.846i −0.476854 + 0.418161i
\(400\) −20.0000 −0.0500000
\(401\) −214.984 + 372.363i −0.536119 + 0.928585i 0.462989 + 0.886364i \(0.346777\pi\)
−0.999108 + 0.0422215i \(0.986556\pi\)
\(402\) 40.9537 23.6446i 0.101875 0.0588174i
\(403\) −385.592 667.865i −0.956805 1.65723i
\(404\) 13.9240 + 8.03902i 0.0344653 + 0.0198986i
\(405\) 20.1246i 0.0496904i
\(406\) 36.8598 + 185.340i 0.0907876 + 0.456502i
\(407\) 545.053 1.33920
\(408\) −25.1654 + 43.5877i −0.0616798 + 0.106833i
\(409\) 15.3567 8.86618i 0.0375469 0.0216777i −0.481109 0.876661i \(-0.659766\pi\)
0.518656 + 0.854983i \(0.326433\pi\)
\(410\) 36.0035 + 62.3600i 0.0878135 + 0.152097i
\(411\) −176.741 102.042i −0.430027 0.248276i
\(412\) 409.129i 0.993033i
\(413\) 63.4289 186.834i 0.153581 0.452383i
\(414\) 89.4119 0.215971
\(415\) 112.972 195.673i 0.272221 0.471501i
\(416\) −94.4106 + 54.5080i −0.226948 + 0.131029i
\(417\) −137.271 237.760i −0.329187 0.570168i
\(418\) −276.639 159.718i −0.661816 0.382100i
\(419\) 440.768i 1.05195i 0.850499 + 0.525977i \(0.176300\pi\)
−0.850499 + 0.525977i \(0.823700\pi\)
\(420\) 51.3436 + 17.4308i 0.122247 + 0.0415019i
\(421\) −143.012 −0.339696 −0.169848 0.985470i \(-0.554328\pi\)
−0.169848 + 0.985470i \(0.554328\pi\)
\(422\) −96.5564 + 167.241i −0.228807 + 0.396305i
\(423\) 172.871 99.8070i 0.408678 0.235950i
\(424\) 7.00124 + 12.1265i 0.0165123 + 0.0286002i
\(425\) −44.4865 25.6843i −0.104674 0.0604336i
\(426\) 121.242i 0.284605i
\(427\) 481.199 95.6991i 1.12693 0.224120i
\(428\) 329.108 0.768943
\(429\) 180.614 312.833i 0.421012 0.729215i
\(430\) 132.633 76.5756i 0.308448 0.178083i
\(431\) 391.608 + 678.285i 0.908604 + 1.57375i 0.816005 + 0.578045i \(0.196184\pi\)
0.0925988 + 0.995704i \(0.470483\pi\)
\(432\) −18.0000 10.3923i −0.0416667 0.0240563i
\(433\) 286.669i 0.662053i 0.943622 + 0.331026i \(0.107395\pi\)
−0.943622 + 0.331026i \(0.892605\pi\)
\(434\) −261.188 297.848i −0.601815 0.686286i
\(435\) 73.9307 0.169956
\(436\) 79.0101 136.849i 0.181216 0.313875i
\(437\) 380.935 219.933i 0.871705 0.503279i
\(438\) −162.860 282.081i −0.371826 0.644021i
\(439\) −295.016 170.328i −0.672018 0.387990i 0.124823 0.992179i \(-0.460164\pi\)
−0.796841 + 0.604189i \(0.793497\pi\)
\(440\) 68.4442i 0.155555i
\(441\) −116.617 89.4960i −0.264437 0.202939i
\(442\) −280.000 −0.633484
\(443\) −197.629 + 342.304i −0.446116 + 0.772696i −0.998129 0.0611396i \(-0.980527\pi\)
0.552013 + 0.833835i \(0.313860\pi\)
\(444\) 151.096 87.2354i 0.340307 0.196476i
\(445\) −44.2910 76.7143i −0.0995304 0.172392i
\(446\) −189.773 109.566i −0.425500 0.245663i
\(447\) 512.507i 1.14655i
\(448\) −42.1043 + 36.9219i −0.0939828 + 0.0824150i
\(449\) 665.078 1.48124 0.740621 0.671923i \(-0.234531\pi\)
0.740621 + 0.671923i \(0.234531\pi\)
\(450\) 10.6066 18.3712i 0.0235702 0.0408248i
\(451\) 213.409 123.212i 0.473190 0.273197i
\(452\) −84.5690 146.478i −0.187100 0.324066i
\(453\) −187.944 108.509i −0.414886 0.239535i
\(454\) 31.6131i 0.0696323i
\(455\) 58.8381 + 295.852i 0.129314 + 0.650225i
\(456\) −102.251 −0.224234
\(457\) −255.468 + 442.484i −0.559012 + 0.968236i 0.438568 + 0.898698i \(0.355486\pi\)
−0.997579 + 0.0695382i \(0.977847\pi\)
\(458\) 36.6429 21.1558i 0.0800064 0.0461917i
\(459\) −26.6919 46.2317i −0.0581523 0.100723i
\(460\) −81.6215 47.1242i −0.177438 0.102444i
\(461\) 174.303i 0.378097i −0.981968 0.189049i \(-0.939460\pi\)
0.981968 0.189049i \(-0.0605404\pi\)
\(462\) 59.6518 175.709i 0.129116 0.380322i
\(463\) 755.187 1.63107 0.815537 0.578705i \(-0.196442\pi\)
0.815537 + 0.578705i \(0.196442\pi\)
\(464\) −38.1776 + 66.1256i −0.0822794 + 0.142512i
\(465\) −134.221 + 77.4924i −0.288647 + 0.166650i
\(466\) −178.956 309.961i −0.384026 0.665153i
\(467\) −490.666 283.286i −1.05068 0.606609i −0.127839 0.991795i \(-0.540804\pi\)
−0.922839 + 0.385186i \(0.874137\pi\)
\(468\) 115.629i 0.247070i
\(469\) 127.967 + 43.4438i 0.272850 + 0.0926307i
\(470\) −210.412 −0.447684
\(471\) −4.61909 + 8.00051i −0.00980699 + 0.0169862i
\(472\) 69.0432 39.8621i 0.146278 0.0844537i
\(473\) −262.058 453.897i −0.554033 0.959614i
\(474\) 191.090 + 110.326i 0.403144 + 0.232755i
\(475\) 104.359i 0.219704i
\(476\) −141.069 + 28.0554i −0.296364 + 0.0589399i
\(477\) −14.8519 −0.0311360
\(478\) 85.5665 148.206i 0.179009 0.310053i
\(479\) 445.286 257.086i 0.929615 0.536714i 0.0429255 0.999078i \(-0.486332\pi\)
0.886690 + 0.462365i \(0.152999\pi\)
\(480\) 10.9545 + 18.9737i 0.0228218 + 0.0395285i
\(481\) 840.578 + 485.308i 1.74756 + 1.00896i
\(482\) 407.848i 0.846157i
\(483\) 168.467 + 192.113i 0.348792 + 0.397749i
\(484\) −7.76960 −0.0160529
\(485\) −76.8027 + 133.026i −0.158356 + 0.274281i
\(486\) 19.0919 11.0227i 0.0392837 0.0226805i
\(487\) −163.663 283.473i −0.336064 0.582081i 0.647624 0.761960i \(-0.275763\pi\)
−0.983689 + 0.179879i \(0.942429\pi\)
\(488\) 171.682 + 99.1207i 0.351808 + 0.203116i
\(489\) 414.386i 0.847415i
\(490\) 59.2875 + 143.161i 0.120995 + 0.292165i
\(491\) −41.8889 −0.0853134 −0.0426567 0.999090i \(-0.513582\pi\)
−0.0426567 + 0.999090i \(0.513582\pi\)
\(492\) 39.4399 68.3119i 0.0801624 0.138845i
\(493\) −169.839 + 98.0566i −0.344501 + 0.198898i
\(494\) −284.421 492.631i −0.575751 0.997229i
\(495\) −62.8700 36.2980i −0.127010 0.0733293i
\(496\) 160.068i 0.322717i
\(497\) −260.503 + 228.439i −0.524152 + 0.459637i
\(498\) −247.509 −0.497006
\(499\) −207.685 + 359.721i −0.416203 + 0.720885i −0.995554 0.0941936i \(-0.969973\pi\)
0.579351 + 0.815078i \(0.303306\pi\)
\(500\) −19.3649 + 11.1803i −0.0387298 + 0.0223607i
\(501\) 268.849 + 465.660i 0.536625 + 0.929462i
\(502\) −517.160 298.583i −1.03020 0.594786i
\(503\) 51.7604i 0.102903i −0.998675 0.0514517i \(-0.983615\pi\)
0.998675 0.0514517i \(-0.0163848\pi\)
\(504\) −11.5858 58.2561i −0.0229876 0.115587i
\(505\) 17.9758 0.0355956
\(506\) −161.269 + 279.326i −0.318713 + 0.552028i
\(507\) 303.585 175.275i 0.598786 0.345709i
\(508\) 101.777 + 176.283i 0.200348 + 0.347014i
\(509\) 136.916 + 79.0486i 0.268991 + 0.155302i 0.628429 0.777867i \(-0.283698\pi\)
−0.359438 + 0.933169i \(0.617032\pi\)
\(510\) 56.2715i 0.110336i
\(511\) 299.233 881.411i 0.585583 1.72488i
\(512\) −22.6274 −0.0441942
\(513\) 54.2267 93.9234i 0.105705 0.183087i
\(514\) 91.2276 52.6703i 0.177486 0.102471i
\(515\) −228.710 396.138i −0.444098 0.769200i
\(516\) −145.292 83.8844i −0.281574 0.162567i
\(517\) 720.073i 1.39279i
\(518\) 472.126 + 160.283i 0.911441 + 0.309428i
\(519\) −157.457 −0.303385
\(520\) −60.9418 + 105.554i −0.117196 + 0.202989i
\(521\) 306.214 176.793i 0.587744 0.339334i −0.176461 0.984308i \(-0.556465\pi\)
0.764205 + 0.644974i \(0.223132\pi\)
\(522\) −40.4935 70.1368i −0.0775737 0.134362i
\(523\) −103.534 59.7756i −0.197962 0.114294i 0.397742 0.917497i \(-0.369794\pi\)
−0.595705 + 0.803204i \(0.703127\pi\)
\(524\) 141.396i 0.269840i
\(525\) 59.4574 11.8247i 0.113252 0.0225232i
\(526\) −443.037 −0.842277
\(527\) 205.561 356.042i 0.390059 0.675602i
\(528\) 64.9319 37.4884i 0.122977 0.0710008i
\(529\) 42.4308 + 73.4924i 0.0802095 + 0.138927i
\(530\) 13.5578 + 7.82762i 0.0255808 + 0.0147691i
\(531\) 84.5604i 0.159247i
\(532\) −192.657 219.699i −0.362138 0.412968i
\(533\) 438.824 0.823309
\(534\) −48.5184 + 84.0363i −0.0908584 + 0.157371i
\(535\) 318.657 183.977i 0.595621 0.343882i
\(536\) 27.3024 + 47.2892i 0.0509374 + 0.0882261i
\(537\) −364.731 210.577i −0.679200 0.392136i
\(538\) 225.372i 0.418906i
\(539\) 489.926 202.894i 0.908954 0.376427i
\(540\) −23.2379 −0.0430331
\(541\) −272.691 + 472.315i −0.504051 + 0.873041i 0.495938 + 0.868358i \(0.334824\pi\)
−0.999989 + 0.00468349i \(0.998509\pi\)
\(542\) −230.575 + 133.123i −0.425416 + 0.245614i
\(543\) −213.036 368.989i −0.392331 0.679537i
\(544\) −50.3307 29.0585i −0.0925197 0.0534163i
\(545\) 176.672i 0.324169i
\(546\) 248.443 217.864i 0.455024 0.399018i
\(547\) −117.783 −0.215325 −0.107663 0.994188i \(-0.534337\pi\)
−0.107663 + 0.994188i \(0.534337\pi\)
\(548\) 117.828 204.083i 0.215014 0.372415i
\(549\) −182.096 + 105.133i −0.331687 + 0.191500i
\(550\) 38.2615 + 66.2708i 0.0695663 + 0.120492i
\(551\) −345.041 199.210i −0.626209 0.361542i
\(552\) 103.244i 0.187036i
\(553\) 122.996 + 618.454i 0.222416 + 1.11836i
\(554\) −9.96659 −0.0179902
\(555\) 97.5322 168.931i 0.175734 0.304380i
\(556\) 274.542 158.507i 0.493780 0.285084i
\(557\) 307.744 + 533.028i 0.552503 + 0.956963i 0.998093 + 0.0617258i \(0.0196604\pi\)
−0.445590 + 0.895237i \(0.647006\pi\)
\(558\) 147.031 + 84.8886i 0.263497 + 0.152130i
\(559\) 933.330i 1.66964i
\(560\) −20.1273 + 59.2865i −0.0359417 + 0.105869i
\(561\) 192.573 0.343267
\(562\) 140.280 242.972i 0.249608 0.432334i
\(563\) −415.047 + 239.628i −0.737207 + 0.425626i −0.821053 0.570852i \(-0.806613\pi\)
0.0838462 + 0.996479i \(0.473280\pi\)
\(564\) 115.247 + 199.614i 0.204339 + 0.353925i
\(565\) −163.767 94.5510i −0.289853 0.167347i
\(566\) 267.468i 0.472558i
\(567\) 59.6559 + 20.2527i 0.105213 + 0.0357191i
\(568\) −139.998 −0.246475
\(569\) 228.674 396.074i 0.401887 0.696088i −0.592067 0.805889i \(-0.701688\pi\)
0.993954 + 0.109800i \(0.0350212\pi\)
\(570\) −99.0040 + 57.1600i −0.173691 + 0.100281i
\(571\) −186.601 323.203i −0.326797 0.566029i 0.655077 0.755562i \(-0.272636\pi\)
−0.981874 + 0.189532i \(0.939303\pi\)
\(572\) 361.229 + 208.555i 0.631519 + 0.364607i
\(573\) 71.3978i 0.124604i
\(574\) 221.088 43.9692i 0.385171 0.0766014i
\(575\) −105.373 −0.183257
\(576\) 12.0000 20.7846i 0.0208333 0.0360844i
\(577\) −772.108 + 445.777i −1.33814 + 0.772577i −0.986532 0.163569i \(-0.947699\pi\)
−0.351611 + 0.936146i \(0.614366\pi\)
\(578\) 129.719 + 224.680i 0.224428 + 0.388720i
\(579\) −284.618 164.324i −0.491568 0.283807i
\(580\) 85.3678i 0.147186i
\(581\) −466.347 531.804i −0.802663 0.915326i
\(582\) 168.266 0.289117
\(583\) 26.7878 46.3978i 0.0459481 0.0795845i
\(584\) 325.719 188.054i 0.557738 0.322010i
\(585\) −64.6385 111.957i −0.110493 0.191380i
\(586\) −595.336 343.718i −1.01593 0.586549i
\(587\) 786.758i 1.34030i −0.742224 0.670151i \(-0.766229\pi\)
0.742224 0.670151i \(-0.233771\pi\)
\(588\) 103.341 134.657i 0.175750 0.229009i
\(589\) 835.227 1.41804
\(590\) 44.5672 77.1927i 0.0755377 0.130835i
\(591\) 543.477 313.777i 0.919589 0.530925i
\(592\) 100.731 + 174.471i 0.170153 + 0.294714i
\(593\) −541.571 312.676i −0.913273 0.527278i −0.0317903 0.999495i \(-0.510121\pi\)
−0.881483 + 0.472216i \(0.843454\pi\)
\(594\) 79.5250i 0.133880i
\(595\) −120.906 + 106.025i −0.203204 + 0.178193i
\(596\) −591.792 −0.992940
\(597\) 33.4433 57.9256i 0.0560190 0.0970278i
\(598\) −497.416 + 287.183i −0.831799 + 0.480240i
\(599\) −75.2476 130.333i −0.125622 0.217584i 0.796354 0.604831i \(-0.206759\pi\)
−0.921976 + 0.387247i \(0.873426\pi\)
\(600\) 21.2132 + 12.2474i 0.0353553 + 0.0204124i
\(601\) 521.601i 0.867888i 0.900940 + 0.433944i \(0.142878\pi\)
−0.900940 + 0.433944i \(0.857122\pi\)
\(602\) −93.5177 470.230i −0.155345 0.781113i
\(603\) −57.9172 −0.0960485
\(604\) 125.296 217.019i 0.207443 0.359302i
\(605\) −7.52288 + 4.34334i −0.0124345 + 0.00717907i
\(606\) −9.84575 17.0533i −0.0162471 0.0281408i
\(607\) −603.404 348.375i −0.994075 0.573930i −0.0875852 0.996157i \(-0.527915\pi\)
−0.906490 + 0.422228i \(0.861248\pi\)
\(608\) 118.069i 0.194193i
\(609\) 74.4014 219.155i 0.122170 0.359860i
\(610\) 221.641 0.363345
\(611\) −641.143 + 1110.49i −1.04933 + 1.81750i
\(612\) 53.3838 30.8212i 0.0872285 0.0503614i
\(613\) −27.1244 46.9809i −0.0442487 0.0766410i 0.843053 0.537831i \(-0.180756\pi\)
−0.887302 + 0.461190i \(0.847423\pi\)
\(614\) −523.687 302.351i −0.852911 0.492428i
\(615\) 88.1903i 0.143399i
\(616\) 202.891 + 68.8800i 0.329368 + 0.111818i
\(617\) −969.852 −1.57188 −0.785941 0.618301i \(-0.787821\pi\)
−0.785941 + 0.618301i \(0.787821\pi\)
\(618\) −250.540 + 433.947i −0.405404 + 0.702180i
\(619\) −111.240 + 64.2247i −0.179710 + 0.103756i −0.587156 0.809474i \(-0.699753\pi\)
0.407446 + 0.913229i \(0.366419\pi\)
\(620\) −89.4805 154.985i −0.144323 0.249975i
\(621\) −94.8357 54.7534i −0.152714 0.0881697i
\(622\) 509.252i 0.818733i
\(623\) −271.979 + 54.0903i −0.436564 + 0.0868223i
\(624\) 133.517 0.213969
\(625\) −12.5000 + 21.6506i −0.0200000 + 0.0346410i
\(626\) 715.163 412.899i 1.14243 0.659584i
\(627\) 195.613 + 338.812i 0.311983 + 0.540371i
\(628\) −9.23819 5.33367i −0.0147105 0.00849311i
\(629\) 517.440i 0.822639i
\(630\) −43.7840 49.9296i −0.0694984 0.0792533i
\(631\) 115.457 0.182975 0.0914877 0.995806i \(-0.470838\pi\)
0.0914877 + 0.995806i \(0.470838\pi\)
\(632\) −127.393 + 220.652i −0.201572 + 0.349133i
\(633\) 204.827 118.257i 0.323581 0.186820i
\(634\) 255.549 + 442.623i 0.403073 + 0.698144i
\(635\) 197.090 + 113.790i 0.310378 + 0.179197i
\(636\) 17.1495i 0.0269646i
\(637\) 936.215 + 123.321i 1.46973 + 0.193596i
\(638\) 292.146 0.457910
\(639\) 74.2452 128.596i 0.116190 0.201246i
\(640\) −21.9089 + 12.6491i −0.0342327 + 0.0197642i
\(641\) 476.249 + 824.887i 0.742978 + 1.28688i 0.951134 + 0.308780i \(0.0999206\pi\)
−0.208156 + 0.978096i \(0.566746\pi\)
\(642\) −349.072 201.537i −0.543725 0.313920i
\(643\) 253.254i 0.393863i −0.980417 0.196931i \(-0.936902\pi\)
0.980417 0.196931i \(-0.0630976\pi\)
\(644\) −221.833 + 194.529i −0.344461 + 0.302063i
\(645\) −187.571 −0.290808
\(646\) 151.626 262.624i 0.234715 0.406539i
\(647\) 870.161 502.388i 1.34492 0.776488i 0.357393 0.933954i \(-0.383666\pi\)
0.987524 + 0.157466i \(0.0503324\pi\)
\(648\) 12.7279 + 22.0454i 0.0196419 + 0.0340207i
\(649\) −264.170 152.518i −0.407041 0.235005i
\(650\) 136.270i 0.209646i
\(651\) 94.6373 + 475.860i 0.145372 + 0.730967i
\(652\) 478.492 0.733883
\(653\) −532.797 + 922.831i −0.815922 + 1.41322i 0.0927422 + 0.995690i \(0.470437\pi\)
−0.908664 + 0.417528i \(0.862897\pi\)
\(654\) −167.606 + 96.7672i −0.256278 + 0.147962i
\(655\) −79.0429 136.906i −0.120676 0.209017i
\(656\) 78.8798 + 45.5413i 0.120244 + 0.0694227i
\(657\) 398.923i 0.607189i
\(658\) −211.751 + 623.728i −0.321810 + 0.947915i
\(659\) 432.265 0.655941 0.327970 0.944688i \(-0.393635\pi\)
0.327970 + 0.944688i \(0.393635\pi\)
\(660\) 41.9133 72.5960i 0.0635051 0.109994i
\(661\) 327.626 189.155i 0.495652 0.286165i −0.231264 0.972891i \(-0.574286\pi\)
0.726916 + 0.686726i \(0.240953\pi\)
\(662\) 209.294 + 362.507i 0.316153 + 0.547594i
\(663\) 296.985 + 171.464i 0.447941 + 0.258619i
\(664\) 285.799i 0.430420i
\(665\) −309.355 105.024i −0.465196 0.157931i
\(666\) −213.682 −0.320844
\(667\) −201.144 + 348.392i −0.301566 + 0.522328i
\(668\) −537.698 + 310.440i −0.804937 + 0.464731i
\(669\) 134.190 + 232.424i 0.200583 + 0.347419i
\(670\) 52.8709 + 30.5251i 0.0789119 + 0.0455598i
\(671\) 758.501i 1.13040i
\(672\) 67.2683 13.3781i 0.100102 0.0199079i
\(673\) −689.666 −1.02476 −0.512382 0.858758i \(-0.671237\pi\)
−0.512382 + 0.858758i \(0.671237\pi\)
\(674\) −15.5678 + 26.9642i −0.0230976 + 0.0400063i
\(675\) −22.5000 + 12.9904i −0.0333333 + 0.0192450i
\(676\) 202.390 + 350.549i 0.299393 + 0.518564i
\(677\) 328.663 + 189.754i 0.485470 + 0.280286i 0.722693 0.691169i \(-0.242904\pi\)
−0.237223 + 0.971455i \(0.576237\pi\)
\(678\) 207.151i 0.305532i
\(679\) 317.041 + 361.541i 0.466924 + 0.532461i
\(680\) −64.9767 −0.0955540
\(681\) −19.3590 + 33.5307i −0.0284273 + 0.0492375i
\(682\) −530.390 + 306.221i −0.777698 + 0.449004i
\(683\) −373.753 647.360i −0.547223 0.947818i −0.998463 0.0554159i \(-0.982352\pi\)
0.451240 0.892403i \(-0.350982\pi\)
\(684\) 108.453 + 62.6156i 0.158558 + 0.0915433i
\(685\) 263.470i 0.384628i
\(686\) 484.040 31.6754i 0.705598 0.0461740i
\(687\) −51.8209 −0.0754308
\(688\) 96.8613 167.769i 0.140787 0.243850i
\(689\) 82.6238 47.7029i 0.119918 0.0692350i
\(690\) 57.7151 + 99.9656i 0.0836451 + 0.144878i
\(691\) 771.026 + 445.152i 1.11581 + 0.644214i 0.940328 0.340268i \(-0.110518\pi\)
0.175483 + 0.984482i \(0.443851\pi\)
\(692\) 181.816i 0.262739i
\(693\) −170.869 + 149.838i −0.246565 + 0.216217i
\(694\) 401.504 0.578536
\(695\) 177.216 306.947i 0.254987 0.441650i
\(696\) 80.9870 46.7579i 0.116361 0.0671808i
\(697\) 116.970 + 202.597i 0.167819 + 0.290670i
\(698\) 388.459 + 224.277i 0.556531 + 0.321313i
\(699\) 438.352i 0.627112i
\(700\) 13.6540 + 68.6554i 0.0195057 + 0.0980792i
\(701\) −650.703 −0.928250 −0.464125 0.885770i \(-0.653631\pi\)
−0.464125 + 0.885770i \(0.653631\pi\)
\(702\) −70.8079 + 122.643i −0.100866 + 0.174705i
\(703\) −910.384 + 525.610i −1.29500 + 0.747667i
\(704\) 43.2879 + 74.9769i 0.0614885 + 0.106501i
\(705\) 223.175 + 128.850i 0.316561 + 0.182766i
\(706\) 165.382i 0.234251i
\(707\) 18.0902 53.2861i 0.0255873 0.0753693i
\(708\) −97.6419 −0.137912
\(709\) 196.427 340.222i 0.277048 0.479862i −0.693602 0.720359i \(-0.743977\pi\)
0.970650 + 0.240497i \(0.0773105\pi\)
\(710\) −135.553 + 78.2613i −0.190919 + 0.110227i
\(711\) −135.121 234.037i −0.190044 0.329166i
\(712\) −97.0368 56.0242i −0.136288 0.0786857i
\(713\) 843.339i 1.18280i
\(714\) 166.807 + 56.6298i 0.233623 + 0.0793134i
\(715\) 466.344 0.652230
\(716\) 243.154 421.155i 0.339600 0.588205i
\(717\) −181.514 + 104.797i −0.253158 + 0.146161i
\(718\) 165.170 + 286.083i 0.230042 + 0.398444i
\(719\) 899.919 + 519.569i 1.25163 + 0.722627i 0.971432 0.237317i \(-0.0762679\pi\)
0.280194 + 0.959943i \(0.409601\pi\)
\(720\) 26.8328i 0.0372678i
\(721\) −1404.45 + 279.312i −1.94792 + 0.387395i
\(722\) 105.550 0.146191
\(723\) −249.755 + 432.588i −0.345442 + 0.598323i
\(724\) 426.072 245.993i 0.588497 0.339769i
\(725\) 47.7220 + 82.6570i 0.0658235 + 0.114010i
\(726\) 8.24091 + 4.75789i 0.0113511 + 0.00655357i
\(727\) 610.568i 0.839846i 0.907560 + 0.419923i \(0.137943\pi\)
−0.907560 + 0.419923i \(0.862057\pi\)
\(728\) 251.567 + 286.877i 0.345559 + 0.394062i
\(729\) −27.0000 −0.0370370
\(730\) 210.251 364.165i 0.288015 0.498856i
\(731\) 430.902 248.781i 0.589469 0.340330i
\(732\) −121.398 210.267i −0.165844 0.287250i
\(733\) 934.574 + 539.576i 1.27500 + 0.736121i 0.975924 0.218109i \(-0.0699889\pi\)
0.299074 + 0.954230i \(0.403322\pi\)
\(734\) 724.181i 0.986623i
\(735\) 24.7837 188.151i 0.0337194 0.255988i
\(736\) −119.216 −0.161978
\(737\) 104.463 180.935i 0.141741 0.245503i
\(738\) −83.6647 + 48.3038i −0.113367 + 0.0654523i
\(739\) −378.082 654.857i −0.511613 0.886139i −0.999909 0.0134615i \(-0.995715\pi\)
0.488297 0.872678i \(-0.337618\pi\)
\(740\) 195.064 + 112.620i 0.263601 + 0.152190i
\(741\) 696.686i 0.940197i
\(742\) 36.8478 32.3124i 0.0496601 0.0435477i
\(743\) 963.993 1.29743 0.648717 0.761030i \(-0.275306\pi\)
0.648717 + 0.761030i \(0.275306\pi\)
\(744\) −98.0209 + 169.777i −0.131749 + 0.228195i
\(745\) −573.001 + 330.822i −0.769128 + 0.444056i
\(746\) −393.439 681.457i −0.527398 0.913481i
\(747\) 262.523 + 151.568i 0.351436 + 0.202902i
\(748\) 222.364i 0.297278i
\(749\) −224.681 1129.75i −0.299975 1.50835i
\(750\) 27.3861 0.0365148
\(751\) −416.806 + 721.929i −0.555001 + 0.961290i 0.442902 + 0.896570i \(0.353949\pi\)
−0.997903 + 0.0647203i \(0.979384\pi\)
\(752\) −230.494 + 133.076i −0.306508 + 0.176963i
\(753\) 365.688 + 633.389i 0.485641 + 0.841155i
\(754\) 450.547 + 260.123i 0.597542 + 0.344991i
\(755\) 280.170i 0.371086i
\(756\) −23.3859 + 68.8847i −0.0309337 + 0.0911173i
\(757\) −744.966 −0.984103 −0.492051 0.870566i \(-0.663753\pi\)
−0.492051 + 0.870566i \(0.663753\pi\)
\(758\) −379.222 + 656.832i −0.500293 + 0.866533i
\(759\) 342.103 197.513i 0.450729 0.260228i
\(760\) −66.0027 114.320i −0.0868456 0.150421i
\(761\) −64.1518 37.0381i −0.0842993 0.0486702i 0.457258 0.889334i \(-0.348832\pi\)
−0.541557 + 0.840664i \(0.682165\pi\)
\(762\) 249.302i 0.327167i
\(763\) −523.713 177.797i −0.686387 0.233023i
\(764\) −82.4431 −0.107910
\(765\) 34.4591 59.6849i 0.0450446 0.0780195i
\(766\) 35.9471 20.7540i 0.0469283 0.0270941i
\(767\) −271.601 470.426i −0.354108 0.613332i
\(768\) 24.0000 + 13.8564i 0.0312500 + 0.0180422i
\(769\) 961.553i 1.25039i −0.780467 0.625197i \(-0.785019\pi\)
0.780467 0.625197i \(-0.214981\pi\)
\(770\) 234.953 46.7267i 0.305134 0.0606840i