Properties

Label 1050.3.q.e.199.16
Level $1050$
Weight $3$
Character 1050.199
Analytic conductor $28.610$
Analytic rank $0$
Dimension $32$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 1050.q (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(28.6104277578\)
Analytic rank: \(0\)
Dimension: \(32\)
Relative dimension: \(16\) over \(\Q(\zeta_{6})\)
Twist minimal: no (minimal twist has level 210)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 199.16
Character \(\chi\) \(=\) 1050.199
Dual form 1050.3.q.e.649.16

$q$-expansion

\(f(q)\) \(=\) \(q+(1.22474 - 0.707107i) q^{2} +(0.866025 - 1.50000i) q^{3} +(1.00000 - 1.73205i) q^{4} -2.44949i q^{6} +(-4.61524 + 5.26304i) q^{7} -2.82843i q^{8} +(-1.50000 - 2.59808i) q^{9} +O(q^{10})\) \(q+(1.22474 - 0.707107i) q^{2} +(0.866025 - 1.50000i) q^{3} +(1.00000 - 1.73205i) q^{4} -2.44949i q^{6} +(-4.61524 + 5.26304i) q^{7} -2.82843i q^{8} +(-1.50000 - 2.59808i) q^{9} +(5.41099 - 9.37211i) q^{11} +(-1.73205 - 3.00000i) q^{12} +19.2715 q^{13} +(-1.93096 + 9.70935i) q^{14} +(-2.00000 - 3.46410i) q^{16} +(-5.13686 + 8.89730i) q^{17} +(-3.67423 - 2.12132i) q^{18} +(18.0756 - 10.4359i) q^{19} +(3.89764 + 11.4808i) q^{21} -15.3046i q^{22} +(18.2511 - 10.5373i) q^{23} +(-4.24264 - 2.44949i) q^{24} +(23.6026 - 13.6270i) q^{26} -5.19615 q^{27} +(4.50061 + 13.2569i) q^{28} -19.0888 q^{29} +(-34.6556 - 20.0084i) q^{31} +(-4.89898 - 2.82843i) q^{32} +(-9.37211 - 16.2330i) q^{33} +14.5292i q^{34} -6.00000 q^{36} +(43.6177 - 25.1827i) q^{37} +(14.7586 - 25.5627i) q^{38} +(16.6896 - 28.9072i) q^{39} +22.7706i q^{41} +(12.8918 + 11.3050i) q^{42} -48.4307i q^{43} +(-10.8220 - 18.7442i) q^{44} +(14.9020 - 25.8110i) q^{46} +(-33.2690 - 57.6236i) q^{47} -6.92820 q^{48} +(-6.39913 - 48.5804i) q^{49} +(8.89730 + 15.4106i) q^{51} +(19.2715 - 33.3792i) q^{52} +(-4.28736 - 2.47531i) q^{53} +(-6.36396 + 3.67423i) q^{54} +(14.8861 + 13.0539i) q^{56} -36.1511i q^{57} +(-23.3789 + 13.4978i) q^{58} +(24.4105 + 14.0934i) q^{59} +(-60.6988 + 35.0445i) q^{61} -56.5924 q^{62} +(20.5966 + 4.09619i) q^{63} -8.00000 q^{64} +(-22.9569 - 13.2542i) q^{66} +(16.7193 + 9.65287i) q^{67} +(10.2737 + 17.7946i) q^{68} -36.5023i q^{69} +49.4968 q^{71} +(-7.34847 + 4.24264i) q^{72} +(66.4872 - 115.159i) q^{73} +(35.6137 - 61.6848i) q^{74} -41.7437i q^{76} +(24.3527 + 71.7328i) q^{77} -47.2053i q^{78} +(-45.0404 - 78.0122i) q^{79} +(-4.50000 + 7.79423i) q^{81} +(16.1013 + 27.8882i) q^{82} +101.045 q^{83} +(23.7829 + 4.72987i) q^{84} +(-34.2456 - 59.3152i) q^{86} +(-16.5314 + 28.6332i) q^{87} +(-26.5083 - 15.3046i) q^{88} +(-34.3077 + 19.8075i) q^{89} +(-88.9425 + 101.427i) q^{91} -42.1492i q^{92} +(-60.0253 + 34.6556i) q^{93} +(-81.4920 - 47.0495i) q^{94} +(-8.48528 + 4.89898i) q^{96} +68.6944 q^{97} +(-42.1888 - 54.9737i) q^{98} -32.4659 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32 q + 32 q^{4} - 48 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 32 q + 32 q^{4} - 48 q^{9} - 8 q^{11} - 16 q^{14} - 64 q^{16} + 144 q^{19} - 48 q^{21} - 144 q^{29} + 240 q^{31} - 192 q^{36} - 72 q^{39} + 16 q^{44} + 16 q^{46} + 80 q^{49} - 24 q^{51} + 32 q^{56} - 264 q^{59} + 192 q^{61} - 256 q^{64} + 144 q^{66} - 272 q^{71} + 224 q^{74} - 560 q^{79} - 144 q^{81} + 48 q^{84} - 176 q^{86} + 600 q^{89} - 544 q^{91} + 48 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(451\) \(701\)
\(\chi(n)\) \(-1\) \(e\left(\frac{1}{6}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.22474 0.707107i 0.612372 0.353553i
\(3\) 0.866025 1.50000i 0.288675 0.500000i
\(4\) 1.00000 1.73205i 0.250000 0.433013i
\(5\) 0 0
\(6\) 2.44949i 0.408248i
\(7\) −4.61524 + 5.26304i −0.659320 + 0.751863i
\(8\) 2.82843i 0.353553i
\(9\) −1.50000 2.59808i −0.166667 0.288675i
\(10\) 0 0
\(11\) 5.41099 9.37211i 0.491908 0.852010i −0.508049 0.861328i \(-0.669633\pi\)
0.999957 + 0.00931868i \(0.00296627\pi\)
\(12\) −1.73205 3.00000i −0.144338 0.250000i
\(13\) 19.2715 1.48242 0.741211 0.671273i \(-0.234252\pi\)
0.741211 + 0.671273i \(0.234252\pi\)
\(14\) −1.93096 + 9.70935i −0.137926 + 0.693525i
\(15\) 0 0
\(16\) −2.00000 3.46410i −0.125000 0.216506i
\(17\) −5.13686 + 8.89730i −0.302168 + 0.523371i −0.976627 0.214942i \(-0.931044\pi\)
0.674459 + 0.738313i \(0.264377\pi\)
\(18\) −3.67423 2.12132i −0.204124 0.117851i
\(19\) 18.0756 10.4359i 0.951346 0.549260i 0.0578471 0.998325i \(-0.481576\pi\)
0.893499 + 0.449066i \(0.148243\pi\)
\(20\) 0 0
\(21\) 3.89764 + 11.4808i 0.185602 + 0.546704i
\(22\) 15.3046i 0.695663i
\(23\) 18.2511 10.5373i 0.793527 0.458143i −0.0476755 0.998863i \(-0.515181\pi\)
0.841203 + 0.540720i \(0.181848\pi\)
\(24\) −4.24264 2.44949i −0.176777 0.102062i
\(25\) 0 0
\(26\) 23.6026 13.6270i 0.907794 0.524115i
\(27\) −5.19615 −0.192450
\(28\) 4.50061 + 13.2569i 0.160736 + 0.473460i
\(29\) −19.0888 −0.658235 −0.329118 0.944289i \(-0.606751\pi\)
−0.329118 + 0.944289i \(0.606751\pi\)
\(30\) 0 0
\(31\) −34.6556 20.0084i −1.11792 0.645434i −0.177054 0.984201i \(-0.556657\pi\)
−0.940870 + 0.338768i \(0.889990\pi\)
\(32\) −4.89898 2.82843i −0.153093 0.0883883i
\(33\) −9.37211 16.2330i −0.284003 0.491908i
\(34\) 14.5292i 0.427330i
\(35\) 0 0
\(36\) −6.00000 −0.166667
\(37\) 43.6177 25.1827i 1.17886 0.680614i 0.223107 0.974794i \(-0.428380\pi\)
0.955750 + 0.294180i \(0.0950466\pi\)
\(38\) 14.7586 25.5627i 0.388385 0.672703i
\(39\) 16.6896 28.9072i 0.427938 0.741211i
\(40\) 0 0
\(41\) 22.7706i 0.555382i 0.960671 + 0.277691i \(0.0895691\pi\)
−0.960671 + 0.277691i \(0.910431\pi\)
\(42\) 12.8918 + 11.3050i 0.306947 + 0.269166i
\(43\) 48.4307i 1.12629i −0.826357 0.563147i \(-0.809590\pi\)
0.826357 0.563147i \(-0.190410\pi\)
\(44\) −10.8220 18.7442i −0.245954 0.426005i
\(45\) 0 0
\(46\) 14.9020 25.8110i 0.323956 0.561109i
\(47\) −33.2690 57.6236i −0.707851 1.22603i −0.965653 0.259836i \(-0.916332\pi\)
0.257802 0.966198i \(-0.417002\pi\)
\(48\) −6.92820 −0.144338
\(49\) −6.39913 48.5804i −0.130595 0.991436i
\(50\) 0 0
\(51\) 8.89730 + 15.4106i 0.174457 + 0.302168i
\(52\) 19.2715 33.3792i 0.370605 0.641907i
\(53\) −4.28736 2.47531i −0.0808937 0.0467040i 0.459008 0.888432i \(-0.348205\pi\)
−0.539901 + 0.841728i \(0.681538\pi\)
\(54\) −6.36396 + 3.67423i −0.117851 + 0.0680414i
\(55\) 0 0
\(56\) 14.8861 + 13.0539i 0.265824 + 0.233105i
\(57\) 36.1511i 0.634231i
\(58\) −23.3789 + 13.4978i −0.403085 + 0.232721i
\(59\) 24.4105 + 14.0934i 0.413737 + 0.238871i 0.692394 0.721520i \(-0.256556\pi\)
−0.278657 + 0.960391i \(0.589889\pi\)
\(60\) 0 0
\(61\) −60.6988 + 35.0445i −0.995062 + 0.574499i −0.906784 0.421596i \(-0.861470\pi\)
−0.0882785 + 0.996096i \(0.528137\pi\)
\(62\) −56.5924 −0.912781
\(63\) 20.5966 + 4.09619i 0.326931 + 0.0650188i
\(64\) −8.00000 −0.125000
\(65\) 0 0
\(66\) −22.9569 13.2542i −0.347832 0.200821i
\(67\) 16.7193 + 9.65287i 0.249541 + 0.144073i 0.619554 0.784954i \(-0.287313\pi\)
−0.370013 + 0.929027i \(0.620647\pi\)
\(68\) 10.2737 + 17.7946i 0.151084 + 0.261685i
\(69\) 36.5023i 0.529018i
\(70\) 0 0
\(71\) 49.4968 0.697138 0.348569 0.937283i \(-0.386668\pi\)
0.348569 + 0.937283i \(0.386668\pi\)
\(72\) −7.34847 + 4.24264i −0.102062 + 0.0589256i
\(73\) 66.4872 115.159i 0.910783 1.57752i 0.0978221 0.995204i \(-0.468812\pi\)
0.812961 0.582318i \(-0.197854\pi\)
\(74\) 35.6137 61.6848i 0.481266 0.833578i
\(75\) 0 0
\(76\) 41.7437i 0.549260i
\(77\) 24.3527 + 71.7328i 0.316269 + 0.931594i
\(78\) 47.2053i 0.605196i
\(79\) −45.0404 78.0122i −0.570132 0.987497i −0.996552 0.0829717i \(-0.973559\pi\)
0.426420 0.904525i \(-0.359774\pi\)
\(80\) 0 0
\(81\) −4.50000 + 7.79423i −0.0555556 + 0.0962250i
\(82\) 16.1013 + 27.8882i 0.196357 + 0.340100i
\(83\) 101.045 1.21741 0.608706 0.793396i \(-0.291689\pi\)
0.608706 + 0.793396i \(0.291689\pi\)
\(84\) 23.7829 + 4.72987i 0.283130 + 0.0563080i
\(85\) 0 0
\(86\) −34.2456 59.3152i −0.398205 0.689712i
\(87\) −16.5314 + 28.6332i −0.190016 + 0.329118i
\(88\) −26.5083 15.3046i −0.301231 0.173916i
\(89\) −34.3077 + 19.8075i −0.385479 + 0.222557i −0.680200 0.733027i \(-0.738107\pi\)
0.294720 + 0.955584i \(0.404774\pi\)
\(90\) 0 0
\(91\) −88.9425 + 101.427i −0.977390 + 1.11458i
\(92\) 42.1492i 0.458143i
\(93\) −60.0253 + 34.6556i −0.645434 + 0.372641i
\(94\) −81.4920 47.0495i −0.866937 0.500526i
\(95\) 0 0
\(96\) −8.48528 + 4.89898i −0.0883883 + 0.0510310i
\(97\) 68.6944 0.708190 0.354095 0.935210i \(-0.384789\pi\)
0.354095 + 0.935210i \(0.384789\pi\)
\(98\) −42.1888 54.9737i −0.430498 0.560956i
\(99\) −32.4659 −0.327939
\(100\) 0 0
\(101\) −6.96199 4.01951i −0.0689306 0.0397971i 0.465139 0.885238i \(-0.346004\pi\)
−0.534069 + 0.845441i \(0.679338\pi\)
\(102\) 21.7939 + 12.5827i 0.213665 + 0.123360i
\(103\) 102.282 + 177.158i 0.993033 + 1.71998i 0.598568 + 0.801072i \(0.295737\pi\)
0.394465 + 0.918911i \(0.370930\pi\)
\(104\) 54.5080i 0.524115i
\(105\) 0 0
\(106\) −7.00124 −0.0660494
\(107\) −142.508 + 82.2769i −1.33185 + 0.768943i −0.985583 0.169193i \(-0.945884\pi\)
−0.346266 + 0.938136i \(0.612551\pi\)
\(108\) −5.19615 + 9.00000i −0.0481125 + 0.0833333i
\(109\) −39.5050 + 68.4247i −0.362432 + 0.627750i −0.988360 0.152130i \(-0.951387\pi\)
0.625929 + 0.779880i \(0.284720\pi\)
\(110\) 0 0
\(111\) 87.2354i 0.785905i
\(112\) 27.4622 + 5.46158i 0.245198 + 0.0487641i
\(113\) 84.5690i 0.748398i 0.927348 + 0.374199i \(0.122082\pi\)
−0.927348 + 0.374199i \(0.877918\pi\)
\(114\) −25.5627 44.2759i −0.224234 0.388385i
\(115\) 0 0
\(116\) −19.0888 + 33.0628i −0.164559 + 0.285024i
\(117\) −28.9072 50.0688i −0.247070 0.427938i
\(118\) 39.8621 0.337815
\(119\) −23.1190 68.0987i −0.194277 0.572258i
\(120\) 0 0
\(121\) 1.94240 + 3.36434i 0.0160529 + 0.0278044i
\(122\) −49.5603 + 85.8410i −0.406232 + 0.703615i
\(123\) 34.1560 + 19.7200i 0.277691 + 0.160325i
\(124\) −69.3113 + 40.0169i −0.558962 + 0.322717i
\(125\) 0 0
\(126\) 28.1221 9.54723i 0.223191 0.0757717i
\(127\) 101.777i 0.801393i 0.916211 + 0.400697i \(0.131232\pi\)
−0.916211 + 0.400697i \(0.868768\pi\)
\(128\) −9.79796 + 5.65685i −0.0765466 + 0.0441942i
\(129\) −72.6460 41.9422i −0.563147 0.325133i
\(130\) 0 0
\(131\) 61.2264 35.3491i 0.467377 0.269840i −0.247764 0.968820i \(-0.579696\pi\)
0.715141 + 0.698980i \(0.246362\pi\)
\(132\) −37.4884 −0.284003
\(133\) −28.4984 + 143.297i −0.214273 + 1.07742i
\(134\) 27.3024 0.203750
\(135\) 0 0
\(136\) 25.1654 + 14.5292i 0.185039 + 0.106833i
\(137\) −102.042 58.9138i −0.744829 0.430027i 0.0789932 0.996875i \(-0.474829\pi\)
−0.823823 + 0.566848i \(0.808163\pi\)
\(138\) −25.8110 44.7060i −0.187036 0.323956i
\(139\) 158.507i 1.14034i 0.821528 + 0.570168i \(0.193122\pi\)
−0.821528 + 0.570168i \(0.806878\pi\)
\(140\) 0 0
\(141\) −115.247 −0.817356
\(142\) 60.6209 34.9995i 0.426908 0.246475i
\(143\) 104.278 180.614i 0.729215 1.26304i
\(144\) −6.00000 + 10.3923i −0.0416667 + 0.0721688i
\(145\) 0 0
\(146\) 188.054i 1.28804i
\(147\) −78.4123 32.4731i −0.533417 0.220906i
\(148\) 100.731i 0.680614i
\(149\) −147.948 256.254i −0.992940 1.71982i −0.599193 0.800604i \(-0.704512\pi\)
−0.393747 0.919219i \(-0.628821\pi\)
\(150\) 0 0
\(151\) 62.6478 108.509i 0.414886 0.718604i −0.580530 0.814239i \(-0.697155\pi\)
0.995417 + 0.0956344i \(0.0304880\pi\)
\(152\) −29.5173 51.1254i −0.194193 0.336352i
\(153\) 30.8212 0.201445
\(154\) 80.5486 + 70.6343i 0.523043 + 0.458665i
\(155\) 0 0
\(156\) −33.3792 57.8144i −0.213969 0.370605i
\(157\) 2.66684 4.61909i 0.0169862 0.0294210i −0.857407 0.514638i \(-0.827926\pi\)
0.874394 + 0.485217i \(0.161260\pi\)
\(158\) −110.326 63.6967i −0.698266 0.403144i
\(159\) −7.42593 + 4.28736i −0.0467040 + 0.0269646i
\(160\) 0 0
\(161\) −28.7752 + 144.689i −0.178728 + 0.898686i
\(162\) 12.7279i 0.0785674i
\(163\) 207.193 119.623i 1.27112 0.733883i 0.295923 0.955212i \(-0.404373\pi\)
0.975199 + 0.221329i \(0.0710394\pi\)
\(164\) 39.4399 + 22.7706i 0.240487 + 0.138845i
\(165\) 0 0
\(166\) 123.754 71.4497i 0.745509 0.430420i
\(167\) 310.440 1.85892 0.929462 0.368918i \(-0.120272\pi\)
0.929462 + 0.368918i \(0.120272\pi\)
\(168\) 32.4726 11.0242i 0.193289 0.0656202i
\(169\) 202.390 1.19757
\(170\) 0 0
\(171\) −54.2267 31.3078i −0.317115 0.183087i
\(172\) −83.8844 48.4307i −0.487700 0.281574i
\(173\) 45.4539 + 78.7285i 0.262739 + 0.455078i 0.966969 0.254894i \(-0.0820407\pi\)
−0.704230 + 0.709972i \(0.748707\pi\)
\(174\) 46.7579i 0.268723i
\(175\) 0 0
\(176\) −43.2879 −0.245954
\(177\) 42.2802 24.4105i 0.238871 0.137912i
\(178\) −28.0121 + 48.5184i −0.157371 + 0.272575i
\(179\) −121.577 + 210.577i −0.679200 + 1.17641i 0.296022 + 0.955181i \(0.404340\pi\)
−0.975222 + 0.221228i \(0.928993\pi\)
\(180\) 0 0
\(181\) 245.993i 1.35907i −0.733641 0.679537i \(-0.762181\pi\)
0.733641 0.679537i \(-0.237819\pi\)
\(182\) −37.2125 + 187.113i −0.204464 + 1.02810i
\(183\) 121.398i 0.663375i
\(184\) −29.8040 51.6220i −0.161978 0.280554i
\(185\) 0 0
\(186\) −49.0105 + 84.8886i −0.263497 + 0.456390i
\(187\) 55.5910 + 96.2864i 0.297278 + 0.514901i
\(188\) −133.076 −0.707851
\(189\) 23.9815 27.3475i 0.126886 0.144696i
\(190\) 0 0
\(191\) 20.6108 + 35.6989i 0.107910 + 0.186905i 0.914923 0.403628i \(-0.132251\pi\)
−0.807014 + 0.590533i \(0.798918\pi\)
\(192\) −6.92820 + 12.0000i −0.0360844 + 0.0625000i
\(193\) 164.324 + 94.8727i 0.851422 + 0.491568i 0.861130 0.508384i \(-0.169757\pi\)
−0.00970872 + 0.999953i \(0.503090\pi\)
\(194\) 84.1331 48.5743i 0.433676 0.250383i
\(195\) 0 0
\(196\) −90.5428 37.4967i −0.461953 0.191310i
\(197\) 362.318i 1.83918i 0.392882 + 0.919589i \(0.371478\pi\)
−0.392882 + 0.919589i \(0.628522\pi\)
\(198\) −39.7625 + 22.9569i −0.200821 + 0.115944i
\(199\) 33.4433 + 19.3085i 0.168057 + 0.0970278i 0.581669 0.813425i \(-0.302400\pi\)
−0.413612 + 0.910453i \(0.635733\pi\)
\(200\) 0 0
\(201\) 28.9586 16.7193i 0.144073 0.0831804i
\(202\) −11.3689 −0.0562816
\(203\) 88.0995 100.465i 0.433987 0.494902i
\(204\) 35.5892 0.174457
\(205\) 0 0
\(206\) 250.540 + 144.649i 1.21621 + 0.702180i
\(207\) −54.7534 31.6119i −0.264509 0.152714i
\(208\) −38.5430 66.7584i −0.185303 0.320954i
\(209\) 225.875i 1.08074i
\(210\) 0 0
\(211\) −136.551 −0.647163 −0.323581 0.946200i \(-0.604887\pi\)
−0.323581 + 0.946200i \(0.604887\pi\)
\(212\) −8.57473 + 4.95062i −0.0404468 + 0.0233520i
\(213\) 42.8655 74.2452i 0.201246 0.348569i
\(214\) −116.357 + 201.537i −0.543725 + 0.941760i
\(215\) 0 0
\(216\) 14.6969i 0.0680414i
\(217\) 265.249 90.0502i 1.22235 0.414978i
\(218\) 111.737i 0.512556i
\(219\) −115.159 199.461i −0.525841 0.910783i
\(220\) 0 0
\(221\) −98.9949 + 171.464i −0.447941 + 0.775856i
\(222\) −61.6848 106.841i −0.277859 0.481266i
\(223\) −154.949 −0.694839 −0.347419 0.937710i \(-0.612942\pi\)
−0.347419 + 0.937710i \(0.612942\pi\)
\(224\) 37.4961 12.7296i 0.167393 0.0568288i
\(225\) 0 0
\(226\) 59.7993 + 103.575i 0.264599 + 0.458299i
\(227\) 11.1769 19.3590i 0.0492375 0.0852818i −0.840356 0.542034i \(-0.817654\pi\)
0.889594 + 0.456753i \(0.150988\pi\)
\(228\) −62.6156 36.1511i −0.274630 0.158558i
\(229\) −25.9105 + 14.9594i −0.113146 + 0.0653250i −0.555505 0.831513i \(-0.687475\pi\)
0.442359 + 0.896838i \(0.354142\pi\)
\(230\) 0 0
\(231\) 128.689 + 25.5933i 0.557096 + 0.110793i
\(232\) 53.9913i 0.232721i
\(233\) −219.176 + 126.541i −0.940669 + 0.543095i −0.890170 0.455629i \(-0.849414\pi\)
−0.0504987 + 0.998724i \(0.516081\pi\)
\(234\) −70.8079 40.8810i −0.302598 0.174705i
\(235\) 0 0
\(236\) 48.8209 28.1868i 0.206868 0.119436i
\(237\) −156.024 −0.658331
\(238\) −76.4679 67.0559i −0.321294 0.281747i
\(239\) −121.009 −0.506315 −0.253158 0.967425i \(-0.581469\pi\)
−0.253158 + 0.967425i \(0.581469\pi\)
\(240\) 0 0
\(241\) 249.755 + 144.196i 1.03633 + 0.598323i 0.918791 0.394745i \(-0.129167\pi\)
0.117536 + 0.993069i \(0.462501\pi\)
\(242\) 4.75789 + 2.74697i 0.0196607 + 0.0113511i
\(243\) 7.79423 + 13.5000i 0.0320750 + 0.0555556i
\(244\) 140.178i 0.574499i
\(245\) 0 0
\(246\) 55.7765 0.226734
\(247\) 348.343 201.116i 1.41030 0.814234i
\(248\) −56.5924 + 98.0209i −0.228195 + 0.395246i
\(249\) 87.5076 151.568i 0.351436 0.608706i
\(250\) 0 0
\(251\) 422.260i 1.68231i 0.540795 + 0.841155i \(0.318124\pi\)
−0.540795 + 0.841155i \(0.681876\pi\)
\(252\) 27.6914 31.5782i 0.109887 0.125310i
\(253\) 228.069i 0.901457i
\(254\) 71.9672 + 124.651i 0.283335 + 0.490751i
\(255\) 0 0
\(256\) −8.00000 + 13.8564i −0.0312500 + 0.0541266i
\(257\) −37.2435 64.5077i −0.144916 0.251003i 0.784425 0.620223i \(-0.212958\pi\)
−0.929342 + 0.369221i \(0.879625\pi\)
\(258\) −118.630 −0.459808
\(259\) −68.7687 + 345.786i −0.265516 + 1.33508i
\(260\) 0 0
\(261\) 28.6332 + 49.5942i 0.109706 + 0.190016i
\(262\) 49.9911 86.5872i 0.190806 0.330486i
\(263\) −271.304 156.637i −1.03157 0.595579i −0.114139 0.993465i \(-0.536411\pi\)
−0.917435 + 0.397885i \(0.869744\pi\)
\(264\) −45.9138 + 26.5083i −0.173916 + 0.100410i
\(265\) 0 0
\(266\) 66.4229 + 195.653i 0.249710 + 0.735539i
\(267\) 68.6153i 0.256986i
\(268\) 33.4385 19.3057i 0.124771 0.0720363i
\(269\) 138.011 + 79.6809i 0.513053 + 0.296211i 0.734088 0.679055i \(-0.237610\pi\)
−0.221035 + 0.975266i \(0.570943\pi\)
\(270\) 0 0
\(271\) −163.041 + 94.1320i −0.601629 + 0.347350i −0.769682 0.638427i \(-0.779585\pi\)
0.168053 + 0.985778i \(0.446252\pi\)
\(272\) 41.0949 0.151084
\(273\) 75.1133 + 221.252i 0.275140 + 0.810446i
\(274\) −166.633 −0.608151
\(275\) 0 0
\(276\) −63.2238 36.5023i −0.229072 0.132255i
\(277\) 6.10326 + 3.52372i 0.0220334 + 0.0127210i 0.510976 0.859595i \(-0.329284\pi\)
−0.488943 + 0.872316i \(0.662617\pi\)
\(278\) 112.081 + 194.130i 0.403170 + 0.698311i
\(279\) 120.051i 0.430289i
\(280\) 0 0
\(281\) 198.386 0.705998 0.352999 0.935624i \(-0.385162\pi\)
0.352999 + 0.935624i \(0.385162\pi\)
\(282\) −141.148 + 81.4920i −0.500526 + 0.288979i
\(283\) 94.5641 163.790i 0.334149 0.578763i −0.649172 0.760641i \(-0.724885\pi\)
0.983321 + 0.181879i \(0.0582179\pi\)
\(284\) 49.4968 85.7309i 0.174284 0.301869i
\(285\) 0 0
\(286\) 294.942i 1.03127i
\(287\) −119.843 105.092i −0.417571 0.366174i
\(288\) 16.9706i 0.0589256i
\(289\) 91.7253 + 158.873i 0.317389 + 0.549733i
\(290\) 0 0
\(291\) 59.4911 103.042i 0.204437 0.354095i
\(292\) −132.974 230.318i −0.455391 0.788761i
\(293\) −486.090 −1.65901 −0.829505 0.558499i \(-0.811378\pi\)
−0.829505 + 0.558499i \(0.811378\pi\)
\(294\) −118.997 + 15.6746i −0.404752 + 0.0533150i
\(295\) 0 0
\(296\) −71.2274 123.370i −0.240633 0.416789i
\(297\) −28.1163 + 48.6989i −0.0946678 + 0.163969i
\(298\) −362.397 209.230i −1.21610 0.702115i
\(299\) 351.726 203.069i 1.17634 0.679161i
\(300\) 0 0
\(301\) 254.892 + 223.519i 0.846818 + 0.742588i
\(302\) 177.195i 0.586738i
\(303\) −12.0585 + 6.96199i −0.0397971 + 0.0229769i
\(304\) −72.3023 41.7437i −0.237836 0.137315i
\(305\) 0 0
\(306\) 37.7481 21.7939i 0.123360 0.0712217i
\(307\) 427.589 1.39280 0.696399 0.717655i \(-0.254784\pi\)
0.696399 + 0.717655i \(0.254784\pi\)
\(308\) 148.598 + 29.5526i 0.482460 + 0.0959499i
\(309\) 354.317 1.14666
\(310\) 0 0
\(311\) −311.852 180.048i −1.00274 0.578931i −0.0936811 0.995602i \(-0.529863\pi\)
−0.909057 + 0.416671i \(0.863197\pi\)
\(312\) −81.7620 47.2053i −0.262058 0.151299i
\(313\) 291.964 + 505.696i 0.932792 + 1.61564i 0.778525 + 0.627614i \(0.215968\pi\)
0.154267 + 0.988029i \(0.450698\pi\)
\(314\) 7.54295i 0.0240221i
\(315\) 0 0
\(316\) −180.162 −0.570132
\(317\) −312.982 + 180.700i −0.987324 + 0.570032i −0.904473 0.426530i \(-0.859736\pi\)
−0.0828508 + 0.996562i \(0.526403\pi\)
\(318\) −6.06325 + 10.5019i −0.0190668 + 0.0330247i
\(319\) −103.289 + 178.902i −0.323791 + 0.560823i
\(320\) 0 0
\(321\) 285.016i 0.887899i
\(322\) 67.0680 + 197.554i 0.208286 + 0.613521i
\(323\) 214.432i 0.663875i
\(324\) 9.00000 + 15.5885i 0.0277778 + 0.0481125i
\(325\) 0 0
\(326\) 169.172 293.015i 0.518934 0.898819i
\(327\) 68.4247 + 118.515i 0.209250 + 0.362432i
\(328\) 64.4051 0.196357
\(329\) 456.819 + 90.8507i 1.38851 + 0.276142i
\(330\) 0 0
\(331\) −147.993 256.331i −0.447108 0.774415i 0.551088 0.834447i \(-0.314213\pi\)
−0.998196 + 0.0600326i \(0.980880\pi\)
\(332\) 101.045 175.015i 0.304353 0.527154i
\(333\) −130.853 75.5481i −0.392952 0.226871i
\(334\) 380.210 219.514i 1.13835 0.657229i
\(335\) 0 0
\(336\) 31.9753 36.4634i 0.0951646 0.108522i
\(337\) 22.0162i 0.0653300i 0.999466 + 0.0326650i \(0.0103994\pi\)
−0.999466 + 0.0326650i \(0.989601\pi\)
\(338\) 247.876 143.111i 0.733361 0.423406i
\(339\) 126.854 + 73.2389i 0.374199 + 0.216044i
\(340\) 0 0
\(341\) −375.043 + 216.531i −1.09983 + 0.634988i
\(342\) −88.5519 −0.258924
\(343\) 285.214 + 190.531i 0.831527 + 0.555484i
\(344\) −136.983 −0.398205
\(345\) 0 0
\(346\) 111.339 + 64.2815i 0.321789 + 0.185785i
\(347\) −245.870 141.953i −0.708559 0.409086i 0.101969 0.994788i \(-0.467486\pi\)
−0.810527 + 0.585701i \(0.800819\pi\)
\(348\) 33.0628 + 57.2665i 0.0950080 + 0.164559i
\(349\) 317.175i 0.908811i 0.890795 + 0.454406i \(0.150148\pi\)
−0.890795 + 0.454406i \(0.849852\pi\)
\(350\) 0 0
\(351\) −100.138 −0.285292
\(352\) −53.0166 + 30.6092i −0.150615 + 0.0869579i
\(353\) 58.4712 101.275i 0.165641 0.286898i −0.771242 0.636542i \(-0.780364\pi\)
0.936883 + 0.349644i \(0.113697\pi\)
\(354\) 34.5216 59.7932i 0.0975187 0.168907i
\(355\) 0 0
\(356\) 79.2302i 0.222557i
\(357\) −122.170 24.2967i −0.342212 0.0680579i
\(358\) 343.871i 0.960534i
\(359\) 116.793 + 202.291i 0.325329 + 0.563486i 0.981579 0.191058i \(-0.0611918\pi\)
−0.656250 + 0.754543i \(0.727858\pi\)
\(360\) 0 0
\(361\) 37.3175 64.6359i 0.103373 0.179047i
\(362\) −173.943 301.278i −0.480505 0.832260i
\(363\) 6.72867 0.0185363
\(364\) 86.7334 + 255.479i 0.238279 + 0.701866i
\(365\) 0 0
\(366\) 85.8410 + 148.681i 0.234538 + 0.406232i
\(367\) 256.037 443.469i 0.697648 1.20836i −0.271632 0.962401i \(-0.587563\pi\)
0.969280 0.245960i \(-0.0791033\pi\)
\(368\) −73.0045 42.1492i −0.198382 0.114536i
\(369\) 59.1599 34.1560i 0.160325 0.0925636i
\(370\) 0 0
\(371\) 32.8149 11.1404i 0.0884498 0.0300280i
\(372\) 138.623i 0.372641i
\(373\) −481.863 + 278.204i −1.29186 + 0.745854i −0.978983 0.203941i \(-0.934625\pi\)
−0.312874 + 0.949795i \(0.601292\pi\)
\(374\) 136.170 + 78.6175i 0.364090 + 0.210207i
\(375\) 0 0
\(376\) −162.984 + 94.0989i −0.433468 + 0.250263i
\(377\) −367.870 −0.975782
\(378\) 10.0336 50.4512i 0.0265438 0.133469i
\(379\) 536.301 1.41504 0.707521 0.706692i \(-0.249813\pi\)
0.707521 + 0.706692i \(0.249813\pi\)
\(380\) 0 0
\(381\) 152.665 + 88.1414i 0.400697 + 0.231342i
\(382\) 50.4859 + 29.1480i 0.132162 + 0.0763038i
\(383\) 14.6753 + 25.4184i 0.0383168 + 0.0663666i 0.884548 0.466450i \(-0.154467\pi\)
−0.846231 + 0.532816i \(0.821134\pi\)
\(384\) 19.5959i 0.0510310i
\(385\) 0 0
\(386\) 268.341 0.695183
\(387\) −125.827 + 72.6460i −0.325133 + 0.187716i
\(388\) 68.6944 118.982i 0.177047 0.306655i
\(389\) −349.242 + 604.905i −0.897795 + 1.55503i −0.0674875 + 0.997720i \(0.521498\pi\)
−0.830307 + 0.557306i \(0.811835\pi\)
\(390\) 0 0
\(391\) 216.514i 0.553745i
\(392\) −137.406 + 18.0995i −0.350526 + 0.0461721i
\(393\) 122.453i 0.311585i
\(394\) 256.198 + 443.747i 0.650248 + 1.12626i
\(395\) 0 0
\(396\) −32.4659 + 56.2326i −0.0819847 + 0.142002i
\(397\) 102.347 + 177.270i 0.257801 + 0.446525i 0.965653 0.259837i \(-0.0836687\pi\)
−0.707851 + 0.706361i \(0.750335\pi\)
\(398\) 54.6127 0.137218
\(399\) 190.265 + 166.846i 0.476854 + 0.418161i
\(400\) 0 0
\(401\) −214.984 372.363i −0.536119 0.928585i −0.999108 0.0422215i \(-0.986556\pi\)
0.462989 0.886364i \(-0.346777\pi\)
\(402\) 23.6446 40.9537i 0.0588174 0.101875i
\(403\) −667.865 385.592i −1.65723 0.956805i
\(404\) −13.9240 + 8.03902i −0.0344653 + 0.0198986i
\(405\) 0 0
\(406\) 36.8598 185.340i 0.0907876 0.456502i
\(407\) 545.053i 1.33920i
\(408\) 43.5877 25.1654i 0.106833 0.0616798i
\(409\) −15.3567 8.86618i −0.0375469 0.0216777i 0.481109 0.876661i \(-0.340234\pi\)
−0.518656 + 0.854983i \(0.673567\pi\)
\(410\) 0 0
\(411\) −176.741 + 102.042i −0.430027 + 0.248276i
\(412\) 409.129 0.993033
\(413\) −186.834 + 63.4289i −0.452383 + 0.153581i
\(414\) −89.4119 −0.215971
\(415\) 0 0
\(416\) −94.4106 54.5080i −0.226948 0.131029i
\(417\) 237.760 + 137.271i 0.570168 + 0.329187i
\(418\) −159.718 276.639i −0.382100 0.661816i
\(419\) 440.768i 1.05195i 0.850499 + 0.525977i \(0.176300\pi\)
−0.850499 + 0.525977i \(0.823700\pi\)
\(420\) 0 0
\(421\) −143.012 −0.339696 −0.169848 0.985470i \(-0.554328\pi\)
−0.169848 + 0.985470i \(0.554328\pi\)
\(422\) −167.241 + 96.5564i −0.396305 + 0.228807i
\(423\) −99.8070 + 172.871i −0.235950 + 0.408678i
\(424\) −7.00124 + 12.1265i −0.0165123 + 0.0286002i
\(425\) 0 0
\(426\) 121.242i 0.284605i
\(427\) 95.6991 481.199i 0.224120 1.12693i
\(428\) 329.108i 0.768943i
\(429\) −180.614 312.833i −0.421012 0.729215i
\(430\) 0 0
\(431\) 391.608 678.285i 0.908604 1.57375i 0.0925988 0.995704i \(-0.470483\pi\)
0.816005 0.578045i \(-0.196184\pi\)
\(432\) 10.3923 + 18.0000i 0.0240563 + 0.0416667i
\(433\) 286.669 0.662053 0.331026 0.943622i \(-0.392605\pi\)
0.331026 + 0.943622i \(0.392605\pi\)
\(434\) 261.188 297.848i 0.601815 0.686286i
\(435\) 0 0
\(436\) 79.0101 + 136.849i 0.181216 + 0.313875i
\(437\) 219.933 380.935i 0.503279 0.871705i
\(438\) −282.081 162.860i −0.644021 0.371826i
\(439\) 295.016 170.328i 0.672018 0.387990i −0.124823 0.992179i \(-0.539836\pi\)
0.796841 + 0.604189i \(0.206503\pi\)
\(440\) 0 0
\(441\) −116.617 + 89.4960i −0.264437 + 0.202939i
\(442\) 280.000i 0.633484i
\(443\) 342.304 197.629i 0.772696 0.446116i −0.0611396 0.998129i \(-0.519473\pi\)
0.833835 + 0.552013i \(0.186140\pi\)
\(444\) −151.096 87.2354i −0.340307 0.196476i
\(445\) 0 0
\(446\) −189.773 + 109.566i −0.425500 + 0.245663i
\(447\) −512.507 −1.14655
\(448\) 36.9219 42.1043i 0.0824150 0.0939828i
\(449\) −665.078 −1.48124 −0.740621 0.671923i \(-0.765469\pi\)
−0.740621 + 0.671923i \(0.765469\pi\)
\(450\) 0 0
\(451\) 213.409 + 123.212i 0.473190 + 0.273197i
\(452\) 146.478 + 84.5690i 0.324066 + 0.187100i
\(453\) −108.509 187.944i −0.239535 0.414886i
\(454\) 31.6131i 0.0696323i
\(455\) 0 0
\(456\) −102.251 −0.224234
\(457\) −442.484 + 255.468i −0.968236 + 0.559012i −0.898698 0.438568i \(-0.855486\pi\)
−0.0695382 + 0.997579i \(0.522153\pi\)
\(458\) −21.1558 + 36.6429i −0.0461917 + 0.0800064i
\(459\) 26.6919 46.2317i 0.0581523 0.100723i
\(460\) 0 0
\(461\) 174.303i 0.378097i 0.981968 + 0.189049i \(0.0605404\pi\)
−0.981968 + 0.189049i \(0.939460\pi\)
\(462\) 175.709 59.6518i 0.380322 0.129116i
\(463\) 755.187i 1.63107i 0.578705 + 0.815537i \(0.303558\pi\)
−0.578705 + 0.815537i \(0.696442\pi\)
\(464\) 38.1776 + 66.1256i 0.0822794 + 0.142512i
\(465\) 0 0
\(466\) −178.956 + 309.961i −0.384026 + 0.665153i
\(467\) 283.286 + 490.666i 0.606609 + 1.05068i 0.991795 + 0.127839i \(0.0408039\pi\)
−0.385186 + 0.922839i \(0.625863\pi\)
\(468\) −115.629 −0.247070
\(469\) −127.967 + 43.4438i −0.272850 + 0.0926307i
\(470\) 0 0
\(471\) −4.61909 8.00051i −0.00980699 0.0169862i
\(472\) 39.8621 69.0432i 0.0844537 0.146278i
\(473\) −453.897 262.058i −0.959614 0.554033i
\(474\) −191.090 + 110.326i −0.403144 + 0.232755i
\(475\) 0 0
\(476\) −141.069 28.0554i −0.296364 0.0589399i
\(477\) 14.8519i 0.0311360i
\(478\) −148.206 + 85.5665i −0.310053 + 0.179009i
\(479\) −445.286 257.086i −0.929615 0.536714i −0.0429255 0.999078i \(-0.513668\pi\)
−0.886690 + 0.462365i \(0.847001\pi\)
\(480\) 0 0
\(481\) 840.578 485.308i 1.74756 1.00896i
\(482\) 407.848 0.846157
\(483\) 192.113 + 168.467i 0.397749 + 0.348792i
\(484\) 7.76960 0.0160529
\(485\) 0 0
\(486\) 19.0919 + 11.0227i 0.0392837 + 0.0226805i
\(487\) 283.473 + 163.663i 0.582081 + 0.336064i 0.761960 0.647624i \(-0.224237\pi\)
−0.179879 + 0.983689i \(0.557571\pi\)
\(488\) 99.1207 + 171.682i 0.203116 + 0.351808i
\(489\) 414.386i 0.847415i
\(490\) 0 0
\(491\) −41.8889 −0.0853134 −0.0426567 0.999090i \(-0.513582\pi\)
−0.0426567 + 0.999090i \(0.513582\pi\)
\(492\) 68.3119 39.4399i 0.138845 0.0801624i
\(493\) 98.0566 169.839i 0.198898 0.344501i
\(494\) 284.421 492.631i 0.575751 0.997229i
\(495\) 0 0
\(496\) 160.068i 0.322717i
\(497\) −228.439 + 260.503i −0.459637 + 0.524152i
\(498\) 247.509i 0.497006i
\(499\) 207.685 + 359.721i 0.416203 + 0.720885i 0.995554 0.0941936i \(-0.0300273\pi\)
−0.579351 + 0.815078i \(0.696694\pi\)
\(500\) 0 0
\(501\) 268.849 465.660i 0.536625 0.929462i
\(502\) 298.583 + 517.160i 0.594786 + 1.03020i
\(503\) −51.7604 −0.102903 −0.0514517 0.998675i \(-0.516385\pi\)
−0.0514517 + 0.998675i \(0.516385\pi\)
\(504\) 11.5858 58.2561i 0.0229876 0.115587i
\(505\) 0 0
\(506\) −161.269 279.326i −0.318713 0.552028i
\(507\) 175.275 303.585i 0.345709 0.598786i
\(508\) 176.283 + 101.777i 0.347014 + 0.200348i
\(509\) −136.916 + 79.0486i −0.268991 + 0.155302i −0.628429 0.777867i \(-0.716302\pi\)
0.359438 + 0.933169i \(0.382968\pi\)
\(510\) 0 0
\(511\) 299.233 + 881.411i 0.585583 + 1.72488i
\(512\) 22.6274i 0.0441942i
\(513\) −93.9234 + 54.2267i −0.183087 + 0.105705i
\(514\) −91.2276 52.6703i −0.177486 0.102471i
\(515\) 0 0
\(516\) −145.292 + 83.8844i −0.281574 + 0.162567i
\(517\) −720.073 −1.39279
\(518\) 160.283 + 472.126i 0.309428 + 0.911441i
\(519\) 157.457 0.303385
\(520\) 0 0
\(521\) 306.214 + 176.793i 0.587744 + 0.339334i 0.764205 0.644974i \(-0.223132\pi\)
−0.176461 + 0.984308i \(0.556465\pi\)
\(522\) 70.1368 + 40.4935i 0.134362 + 0.0775737i
\(523\) −59.7756 103.534i −0.114294 0.197962i 0.803204 0.595705i \(-0.203127\pi\)
−0.917497 + 0.397742i \(0.869794\pi\)
\(524\) 141.396i 0.269840i
\(525\) 0 0
\(526\) −443.037 −0.842277
\(527\) 356.042 205.561i 0.675602 0.390059i
\(528\) −37.4884 + 64.9319i −0.0710008 + 0.122977i
\(529\) −42.4308 + 73.4924i −0.0802095 + 0.138927i
\(530\) 0 0
\(531\) 84.5604i 0.159247i
\(532\) 219.699 + 192.657i 0.412968 + 0.362138i
\(533\) 438.824i 0.823309i
\(534\) 48.5184 + 84.0363i 0.0908584 + 0.157371i
\(535\) 0 0
\(536\) 27.3024 47.2892i 0.0509374 0.0882261i
\(537\) 210.577 + 364.731i 0.392136 + 0.679200i
\(538\) 225.372 0.418906
\(539\) −489.926 202.894i −0.908954 0.376427i
\(540\) 0 0
\(541\) −272.691 472.315i −0.504051 0.873041i −0.999989 0.00468349i \(-0.998509\pi\)
0.495938 0.868358i \(-0.334824\pi\)
\(542\) −133.123 + 230.575i −0.245614 + 0.425416i
\(543\) −368.989 213.036i −0.679537 0.392331i
\(544\) 50.3307 29.0585i 0.0925197 0.0534163i
\(545\) 0 0
\(546\) 248.443 + 217.864i 0.455024 + 0.399018i
\(547\) 117.783i 0.215325i 0.994188 + 0.107663i \(0.0343366\pi\)
−0.994188 + 0.107663i \(0.965663\pi\)
\(548\) −204.083 + 117.828i −0.372415 + 0.215014i
\(549\) 182.096 + 105.133i 0.331687 + 0.191500i
\(550\) 0 0
\(551\) −345.041 + 199.210i −0.626209 + 0.361542i
\(552\) −103.244 −0.187036
\(553\) 618.454 + 122.996i 1.11836 + 0.222416i
\(554\) 9.96659 0.0179902
\(555\) 0 0
\(556\) 274.542 + 158.507i 0.493780 + 0.285084i
\(557\) −533.028 307.744i −0.956963 0.552503i −0.0617258 0.998093i \(-0.519660\pi\)
−0.895237 + 0.445590i \(0.852994\pi\)
\(558\) 84.8886 + 147.031i 0.152130 + 0.263497i
\(559\) 933.330i 1.66964i
\(560\) 0 0
\(561\) 192.573 0.343267
\(562\) 242.972 140.280i 0.432334 0.249608i
\(563\) 239.628 415.047i 0.425626 0.737207i −0.570852 0.821053i \(-0.693387\pi\)
0.996479 + 0.0838462i \(0.0267205\pi\)
\(564\) −115.247 + 199.614i −0.204339 + 0.353925i
\(565\) 0 0
\(566\) 267.468i 0.472558i
\(567\) −20.2527 59.6559i −0.0357191 0.105213i
\(568\) 139.998i 0.246475i
\(569\) −228.674 396.074i −0.401887 0.696088i 0.592067 0.805889i \(-0.298312\pi\)
−0.993954 + 0.109800i \(0.964979\pi\)
\(570\) 0 0
\(571\) −186.601 + 323.203i −0.326797 + 0.566029i −0.981874 0.189532i \(-0.939303\pi\)
0.655077 + 0.755562i \(0.272636\pi\)
\(572\) −208.555 361.229i −0.364607 0.631519i
\(573\) 71.3978 0.124604
\(574\) −221.088 43.9692i −0.385171 0.0766014i
\(575\) 0 0
\(576\) 12.0000 + 20.7846i 0.0208333 + 0.0360844i
\(577\) −445.777 + 772.108i −0.772577 + 1.33814i 0.163569 + 0.986532i \(0.447699\pi\)
−0.936146 + 0.351611i \(0.885634\pi\)
\(578\) 224.680 + 129.719i 0.388720 + 0.224428i
\(579\) 284.618 164.324i 0.491568 0.283807i
\(580\) 0 0
\(581\) −466.347 + 531.804i −0.802663 + 0.915326i
\(582\) 168.266i 0.289117i
\(583\) −46.3978 + 26.7878i −0.0795845 + 0.0459481i
\(584\) −325.719 188.054i −0.557738 0.322010i
\(585\) 0 0
\(586\) −595.336 + 343.718i −1.01593 + 0.586549i
\(587\) 786.758 1.34030 0.670151 0.742224i \(-0.266229\pi\)
0.670151 + 0.742224i \(0.266229\pi\)
\(588\) −134.657 + 103.341i −0.229009 + 0.175750i
\(589\) −835.227 −1.41804
\(590\) 0 0
\(591\) 543.477 + 313.777i 0.919589 + 0.530925i
\(592\) −174.471 100.731i −0.294714 0.170153i
\(593\) −312.676 541.571i −0.527278 0.913273i −0.999495 0.0317903i \(-0.989879\pi\)
0.472216 0.881483i \(-0.343454\pi\)
\(594\) 79.5250i 0.133880i
\(595\) 0 0
\(596\) −591.792 −0.992940
\(597\) 57.9256 33.4433i 0.0970278 0.0560190i
\(598\) 287.183 497.416i 0.480240 0.831799i
\(599\) 75.2476 130.333i 0.125622 0.217584i −0.796354 0.604831i \(-0.793241\pi\)
0.921976 + 0.387247i \(0.126574\pi\)
\(600\) 0 0
\(601\) 521.601i 0.867888i −0.900940 0.433944i \(-0.857122\pi\)
0.900940 0.433944i \(-0.142878\pi\)
\(602\) 470.230 + 93.5177i 0.781113 + 0.155345i
\(603\) 57.9172i 0.0960485i
\(604\) −125.296 217.019i −0.207443 0.359302i
\(605\) 0 0
\(606\) −9.84575 + 17.0533i −0.0162471 + 0.0281408i
\(607\) 348.375 + 603.404i 0.573930 + 0.994075i 0.996157 + 0.0875852i \(0.0279150\pi\)
−0.422228 + 0.906490i \(0.638752\pi\)
\(608\) −118.069 −0.194193
\(609\) −74.4014 219.155i −0.122170 0.359860i
\(610\) 0 0
\(611\) −641.143 1110.49i −1.04933 1.81750i
\(612\) 30.8212 53.3838i 0.0503614 0.0872285i
\(613\) −46.9809 27.1244i −0.0766410 0.0442487i 0.461190 0.887302i \(-0.347423\pi\)
−0.537831 + 0.843053i \(0.680756\pi\)
\(614\) 523.687 302.351i 0.852911 0.492428i
\(615\) 0 0
\(616\) 202.891 68.8800i 0.329368 0.111818i
\(617\) 969.852i 1.57188i 0.618301 + 0.785941i \(0.287821\pi\)
−0.618301 + 0.785941i \(0.712179\pi\)
\(618\) 433.947 250.540i 0.702180 0.405404i
\(619\) 111.240 + 64.2247i 0.179710 + 0.103756i 0.587156 0.809474i \(-0.300247\pi\)
−0.407446 + 0.913229i \(0.633581\pi\)
\(620\) 0 0
\(621\) −94.8357 + 54.7534i −0.152714 + 0.0881697i
\(622\) −509.252 −0.818733
\(623\) 54.0903 271.979i 0.0868223 0.436564i
\(624\) −133.517 −0.213969
\(625\) 0 0
\(626\) 715.163 + 412.899i 1.14243 + 0.659584i
\(627\) −338.812 195.613i −0.540371 0.311983i
\(628\) −5.33367 9.23819i −0.00849311 0.0147105i
\(629\) 517.440i 0.822639i
\(630\) 0 0
\(631\) 115.457 0.182975 0.0914877 0.995806i \(-0.470838\pi\)
0.0914877 + 0.995806i \(0.470838\pi\)
\(632\) −220.652 + 127.393i −0.349133 + 0.201572i
\(633\) −118.257 + 204.827i −0.186820 + 0.323581i
\(634\) −255.549 + 442.623i −0.403073 + 0.698144i
\(635\) 0 0
\(636\) 17.1495i 0.0269646i
\(637\) −123.321 936.215i −0.193596 1.46973i
\(638\) 292.146i 0.457910i
\(639\) −74.2452 128.596i −0.116190 0.201246i
\(640\) 0 0
\(641\) 476.249 824.887i 0.742978 1.28688i −0.208156 0.978096i \(-0.566746\pi\)
0.951134 0.308780i \(-0.0999206\pi\)
\(642\) 201.537 + 349.072i 0.313920 + 0.543725i
\(643\) −253.254 −0.393863 −0.196931 0.980417i \(-0.563098\pi\)
−0.196931 + 0.980417i \(0.563098\pi\)
\(644\) 221.833 + 194.529i 0.344461 + 0.302063i
\(645\) 0 0
\(646\) 151.626 + 262.624i 0.234715 + 0.406539i
\(647\) 502.388 870.161i 0.776488 1.34492i −0.157466 0.987524i \(-0.550332\pi\)
0.933954 0.357393i \(-0.116334\pi\)
\(648\) 22.0454 + 12.7279i 0.0340207 + 0.0196419i
\(649\) 264.170 152.518i 0.407041 0.235005i
\(650\) 0 0
\(651\) 94.6373 475.860i 0.145372 0.730967i
\(652\) 478.492i 0.733883i
\(653\) 922.831 532.797i 1.41322 0.815922i 0.417528 0.908664i \(-0.362897\pi\)
0.995690 + 0.0927422i \(0.0295632\pi\)
\(654\) 167.606 + 96.7672i 0.256278 + 0.147962i
\(655\) 0 0
\(656\) 78.8798 45.5413i 0.120244 0.0694227i
\(657\) −398.923 −0.607189
\(658\) 623.728 211.751i 0.947915 0.321810i
\(659\) −432.265 −0.655941 −0.327970 0.944688i \(-0.606365\pi\)
−0.327970 + 0.944688i \(0.606365\pi\)
\(660\) 0 0
\(661\) 327.626 + 189.155i 0.495652 + 0.286165i 0.726916 0.686726i \(-0.240953\pi\)
−0.231264 + 0.972891i \(0.574286\pi\)
\(662\) −362.507 209.294i −0.547594 0.316153i
\(663\) 171.464 + 296.985i 0.258619 + 0.447941i
\(664\) 285.799i 0.430420i
\(665\) 0 0
\(666\) −213.682 −0.320844
\(667\) −348.392 + 201.144i −0.522328 + 0.301566i
\(668\) 310.440 537.698i 0.464731 0.804937i
\(669\) −134.190 + 232.424i −0.200583 + 0.347419i
\(670\) 0 0
\(671\) 758.501i 1.13040i
\(672\) 13.3781 67.2683i 0.0199079 0.100102i
\(673\) 689.666i 1.02476i −0.858758 0.512382i \(-0.828763\pi\)
0.858758 0.512382i \(-0.171237\pi\)
\(674\) 15.5678 + 26.9642i 0.0230976 + 0.0400063i
\(675\) 0 0
\(676\) 202.390 350.549i 0.299393 0.518564i
\(677\) −189.754 328.663i −0.280286 0.485470i 0.691169 0.722693i \(-0.257096\pi\)
−0.971455 + 0.237223i \(0.923763\pi\)
\(678\) 207.151 0.305532
\(679\) −317.041 + 361.541i −0.466924 + 0.532461i
\(680\) 0 0
\(681\) −19.3590 33.5307i −0.0284273 0.0492375i
\(682\) −306.221 + 530.390i −0.449004 + 0.777698i
\(683\) −647.360 373.753i −0.947818 0.547223i −0.0554159 0.998463i \(-0.517648\pi\)
−0.892403 + 0.451240i \(0.850982\pi\)
\(684\) −108.453 + 62.6156i −0.158558 + 0.0915433i
\(685\) 0 0
\(686\) 484.040 + 31.6754i 0.705598 + 0.0461740i
\(687\) 51.8209i 0.0754308i
\(688\) −167.769 + 96.8613i −0.243850 + 0.140787i
\(689\) −82.6238 47.7029i −0.119918 0.0692350i
\(690\) 0 0
\(691\) 771.026 445.152i 1.11581 0.644214i 0.175483 0.984482i \(-0.443851\pi\)
0.940328 + 0.340268i \(0.110518\pi\)
\(692\) 181.816 0.262739
\(693\) 149.838 170.869i 0.216217 0.246565i
\(694\) −401.504 −0.578536
\(695\) 0 0
\(696\) 80.9870 + 46.7579i 0.116361 + 0.0671808i
\(697\) −202.597 116.970i −0.290670 0.167819i
\(698\) 224.277 + 388.459i 0.321313 + 0.556531i
\(699\) 438.352i 0.627112i
\(700\) 0 0
\(701\) −650.703 −0.928250 −0.464125 0.885770i \(-0.653631\pi\)
−0.464125 + 0.885770i \(0.653631\pi\)
\(702\) −122.643 + 70.8079i −0.174705 + 0.100866i
\(703\) 525.610 910.384i 0.747667 1.29500i
\(704\) −43.2879 + 74.9769i −0.0614885 + 0.106501i
\(705\) 0 0
\(706\) 165.382i 0.234251i
\(707\) 53.2861 18.0902i 0.0753693 0.0255873i
\(708\) 97.6419i 0.137912i
\(709\) −196.427 340.222i −0.277048 0.479862i 0.693602 0.720359i \(-0.256023\pi\)
−0.970650 + 0.240497i \(0.922690\pi\)
\(710\) 0 0
\(711\) −135.121 + 234.037i −0.190044 + 0.329166i
\(712\) 56.0242 + 97.0368i 0.0786857 + 0.136288i
\(713\) −843.339 −1.18280
\(714\) −166.807 + 56.6298i −0.233623 + 0.0793134i
\(715\) 0 0
\(716\) 243.154 + 421.155i 0.339600 + 0.588205i
\(717\) −104.797 + 181.514i −0.146161 + 0.253158i
\(718\) 286.083 + 165.170i 0.398444 + 0.230042i
\(719\) −899.919 + 519.569i −1.25163 + 0.722627i −0.971432 0.237317i \(-0.923732\pi\)
−0.280194 + 0.959943i \(0.590399\pi\)
\(720\) 0 0
\(721\) −1404.45 279.312i −1.94792 0.387395i
\(722\) 105.550i 0.146191i
\(723\) 432.588 249.755i 0.598323 0.345442i
\(724\) −426.072 245.993i −0.588497 0.339769i
\(725\) 0 0
\(726\) 8.24091 4.75789i 0.0113511 0.00655357i
\(727\) −610.568 −0.839846 −0.419923 0.907560i \(-0.637943\pi\)
−0.419923 + 0.907560i \(0.637943\pi\)
\(728\) 286.877 + 251.567i 0.394062 + 0.345559i
\(729\) 27.0000 0.0370370
\(730\) 0 0
\(731\) 430.902 + 248.781i 0.589469 + 0.340330i
\(732\) 210.267 + 121.398i 0.287250 + 0.165844i
\(733\) 539.576 + 934.574i 0.736121 + 1.27500i 0.954230 + 0.299074i \(0.0966777\pi\)
−0.218109 + 0.975924i \(0.569989\pi\)
\(734\) 724.181i 0.986623i
\(735\) 0 0
\(736\) −119.216 −0.161978
\(737\) 180.935 104.463i 0.245503 0.141741i
\(738\) 48.3038 83.6647i 0.0654523 0.113367i
\(739\) 378.082 654.857i 0.511613 0.886139i −0.488297 0.872678i \(-0.662382\pi\)
0.999909 0.0134615i \(-0.00428507\pi\)
\(740\) 0 0
\(741\) 696.686i 0.940197i
\(742\) 32.3124 36.8478i 0.0435477 0.0496601i
\(743\) 963.993i 1.29743i 0.761030 + 0.648717i \(0.224694\pi\)
−0.761030 + 0.648717i \(0.775306\pi\)
\(744\) 98.0209 + 169.777i 0.131749 + 0.228195i
\(745\) 0 0
\(746\) −393.439 + 681.457i −0.527398 + 0.913481i
\(747\) −151.568 262.523i −0.202902 0.351436i
\(748\) 222.364 0.297278
\(749\) 224.681 1129.75i 0.299975 1.50835i
\(750\) 0 0
\(751\) −416.806 721.929i −0.555001 0.961290i −0.997903 0.0647203i \(-0.979384\pi\)
0.442902 0.896570i \(-0.353949\pi\)
\(752\) −133.076 + 230.494i −0.176963 + 0.306508i
\(753\) 633.389 + 365.688i 0.841155 + 0.485641i
\(754\) −450.547 + 260.123i −0.597542 + 0.344991i
\(755\) 0 0
\(756\) −23.3859 68.8847i −0.0309337 0.0911173i
\(757\) 744.966i 0.984103i 0.870566 + 0.492051i \(0.163753\pi\)
−0.870566 + 0.492051i \(0.836247\pi\)
\(758\) 656.832 379.222i 0.866533 0.500293i
\(759\) −342.103 197.513i −0.450729 0.260228i
\(760\) 0 0
\(761\) −64.1518 + 37.0381i −0.0842993 + 0.0486702i −0.541557 0.840664i \(-0.682165\pi\)
0.457258 + 0.889334i \(0.348832\pi\)
\(762\) 249.302 0.327167
\(763\) −177.797 523.713i −0.233023 0.686387i
\(764\) 82.4431 0.107910
\(765\) 0 0
\(766\) 35.9471 + 20.7540i 0.0469283 + 0.0270941i
\(767\) 470.426 + 271.601i 0.613332 + 0.354108i
\(768\) 13.8564 + 24.0000i 0.0180422 + 0.0312500i
\(769\) 961.553i 1.25039i −0.780467 0.625197i \(-0.785019\pi\)
0.780467 0.625197i \(-0.214981\pi\)
\(770\) 0 0
\(771\) −129.015 −0.167335
\(772\) 328.649 189.745i 0.425711 0.245784i
\(773\) 687.723 1191.17i 0.889680 1.54097i 0.0494271 0.998778i \(-0.484260\pi\)
0.840253 0.542194i \(-0.182406\pi\)
\(774\) −102.737 + 177.946i −0.132735 + 0.229904i
\(775\) 0 0
\(776\) 194.297i 0.250383i
\(777\) 459.123 + 402.612i 0.590892 + 0.518163i
\(778\) 987.806i 1.26967i
\(779\) 237.633 + 411.592i 0.305049 + 0.528360i
\(780\) 0 0
\(781\) 267.826 463.889i 0.342928 0.593968i
\(782\) 153.099 + 265.175i 0.195779 + 0.339098i
\(783\) 99.1884 0.126677