Properties

Label 1050.3.q.e.649.16
Level $1050$
Weight $3$
Character 1050.649
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 649.16
Character \(\chi\) \(=\) 1050.649
Dual form 1050.3.q.e.199.16

$q$-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 \(\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(451\) \(701\)
\(\chi(n)\) \(-1\) \(e\left(\frac{5}{6}\right)\) \(1\)

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 0.999957 0.00931868i \(-0.00296627\pi\)
−0.508049 + 0.861328i \(0.669633\pi\)
\(12\) −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 0.674459 0.738313i \(-0.264377\pi\)
−0.976627 + 0.214942i \(0.931044\pi\)
\(18\) −3.67423 + 2.12132i −0.204124 + 0.117851i
\(19\) 18.0756 + 10.4359i 0.951346 + 0.549260i 0.893499 0.449066i \(-0.148243\pi\)
0.0578471 + 0.998325i \(0.481576\pi\)
\(20\) 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 0.841203 0.540720i \(-0.181848\pi\)
−0.0476755 + 0.998863i \(0.515181\pi\)
\(24\) −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 −0.940870 0.338768i \(-0.889990\pi\)
−0.177054 + 0.984201i \(0.556657\pi\)
\(32\) −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 0.955750 0.294180i \(-0.0950466\pi\)
0.223107 + 0.974794i \(0.428380\pi\)
\(38\) 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 \(-0.910431\pi\)
0.960671 0.277691i \(-0.0895691\pi\)
\(42\) 12.8918 11.3050i 0.306947 0.269166i
\(43\) 48.4307i 1.12629i 0.826357 + 0.563147i \(0.190410\pi\)
−0.826357 + 0.563147i \(0.809590\pi\)
\(44\) −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 0.257802 + 0.966198i \(0.417002\pi\)
−0.965653 + 0.259836i \(0.916332\pi\)
\(48\) −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 −0.539901 0.841728i \(-0.681538\pi\)
0.459008 + 0.888432i \(0.348205\pi\)
\(54\) −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 −0.278657 0.960391i \(-0.589889\pi\)
0.692394 + 0.721520i \(0.256556\pi\)
\(60\) 0 0
\(61\) −60.6988 35.0445i −0.995062 0.574499i −0.0882785 0.996096i \(-0.528137\pi\)
−0.906784 + 0.421596i \(0.861470\pi\)
\(62\) −56.5924 −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 −0.370013 0.929027i \(-0.620647\pi\)
0.619554 + 0.784954i \(0.287313\pi\)
\(68\) 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 0.812961 + 0.582318i \(0.197854\pi\)
0.0978221 + 0.995204i \(0.468812\pi\)
\(74\) 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 0.426420 + 0.904525i \(0.359774\pi\)
−0.996552 + 0.0829717i \(0.973559\pi\)
\(80\) 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 0.294720 0.955584i \(-0.404774\pi\)
−0.680200 + 0.733027i \(0.738107\pi\)
\(90\) 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 −0.534069 0.845441i \(-0.679338\pi\)
0.465139 + 0.885238i \(0.346004\pi\)
\(102\) 21.7939 12.5827i 0.213665 0.123360i
\(103\) 102.282 177.158i 0.993033 1.71998i 0.394465 0.918911i \(-0.370930\pi\)
0.598568 0.801072i \(-0.295737\pi\)
\(104\) 54.5080i 0.524115i
\(105\) 0 0
\(106\) −7.00124 −0.0660494
\(107\) −142.508 82.2769i −1.33185 0.768943i −0.346266 0.938136i \(-0.612551\pi\)
−0.985583 + 0.169193i \(0.945884\pi\)
\(108\) −5.19615 9.00000i −0.0481125 0.0833333i
\(109\) −39.5050 68.4247i −0.362432 0.627750i 0.625929 0.779880i \(-0.284720\pi\)
−0.988360 + 0.152130i \(0.951387\pi\)
\(110\) 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 \(-0.877918\pi\)
0.927348 0.374199i \(-0.122082\pi\)
\(114\) −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 \(-0.868768\pi\)
0.916211 0.400697i \(-0.131232\pi\)
\(128\) −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 0.715141 0.698980i \(-0.246362\pi\)
−0.247764 + 0.968820i \(0.579696\pi\)
\(132\) −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 −0.823823 0.566848i \(-0.808163\pi\)
0.0789932 + 0.996875i \(0.474829\pi\)
\(138\) −25.8110 + 44.7060i −0.187036 + 0.323956i
\(139\) 158.507i 1.14034i −0.821528 0.570168i \(-0.806878\pi\)
0.821528 0.570168i \(-0.193122\pi\)
\(140\) 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 −0.393747 + 0.919219i \(0.628821\pi\)
−0.599193 + 0.800604i \(0.704512\pi\)
\(150\) 0 0
\(151\) 62.6478 + 108.509i 0.414886 + 0.718604i 0.995417 0.0956344i \(-0.0304880\pi\)
−0.580530 + 0.814239i \(0.697155\pi\)
\(152\) −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 0.874394 0.485217i \(-0.161260\pi\)
−0.857407 + 0.514638i \(0.827926\pi\)
\(158\) −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 0.975199 0.221329i \(-0.0710394\pi\)
0.295923 + 0.955212i \(0.404373\pi\)
\(164\) 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 −0.704230 0.709972i \(-0.748707\pi\)
0.966969 + 0.254894i \(0.0820407\pi\)
\(174\) 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 −0.975222 0.221228i \(-0.928993\pi\)
0.296022 0.955181i \(-0.404340\pi\)
\(180\) 0 0
\(181\) 245.993i 1.35907i 0.733641 + 0.679537i \(0.237819\pi\)
−0.733641 + 0.679537i \(0.762181\pi\)
\(182\) −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 −0.807014 0.590533i \(-0.798918\pi\)
0.914923 + 0.403628i \(0.132251\pi\)
\(192\) −6.92820 12.0000i −0.0360844 0.0625000i
\(193\) 164.324 94.8727i 0.851422 0.491568i −0.00970872 0.999953i \(-0.503090\pi\)
0.861130 + 0.508384i \(0.169757\pi\)
\(194\) 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 \(-0.628522\pi\)
0.392882 0.919589i \(-0.371478\pi\)
\(198\) −39.7625 22.9569i −0.200821 0.115944i
\(199\) 33.4433 19.3085i 0.168057 0.0970278i −0.413612 0.910453i \(-0.635733\pi\)
0.581669 + 0.813425i \(0.302400\pi\)
\(200\) 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 0.889594 0.456753i \(-0.150988\pi\)
−0.840356 + 0.542034i \(0.817654\pi\)
\(228\) −62.6156 + 36.1511i −0.274630 + 0.158558i
\(229\) −25.9105 14.9594i −0.113146 0.0653250i 0.442359 0.896838i \(-0.354142\pi\)
−0.555505 + 0.831513i \(0.687475\pi\)
\(230\) 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 −0.0504987 0.998724i \(-0.516081\pi\)
−0.890170 + 0.455629i \(0.849414\pi\)
\(234\) −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 0.117536 0.993069i \(-0.462501\pi\)
0.918791 + 0.394745i \(0.129167\pi\)
\(242\) 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 \(-0.681876\pi\)
0.540795 0.841155i \(-0.318124\pi\)
\(252\) 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 −0.929342 0.369221i \(-0.879625\pi\)
0.784425 + 0.620223i \(0.212958\pi\)
\(258\) −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 −0.917435 0.397885i \(-0.869744\pi\)
−0.114139 + 0.993465i \(0.536411\pi\)
\(264\) −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 −0.221035 0.975266i \(-0.570943\pi\)
0.734088 + 0.679055i \(0.237610\pi\)
\(270\) 0 0
\(271\) −163.041 94.1320i −0.601629 0.347350i 0.168053 0.985778i \(-0.446252\pi\)
−0.769682 + 0.638427i \(0.779585\pi\)
\(272\) 41.0949 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 −0.488943 0.872316i \(-0.662617\pi\)
0.510976 + 0.859595i \(0.329284\pi\)
\(278\) 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 0.983321 0.181879i \(-0.0582179\pi\)
−0.649172 + 0.760641i \(0.724885\pi\)
\(284\) 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 −0.909057 0.416671i \(-0.863197\pi\)
−0.0936811 + 0.995602i \(0.529863\pi\)
\(312\) −81.7620 + 47.2053i −0.262058 + 0.151299i
\(313\) 291.964 505.696i 0.932792 1.61564i 0.154267 0.988029i \(-0.450698\pi\)
0.778525 0.627614i \(-0.215968\pi\)
\(314\) 7.54295i 0.0240221i
\(315\) 0 0
\(316\) −180.162 −0.570132
\(317\) −312.982 180.700i −0.987324 0.570032i −0.0828508 0.996562i \(-0.526403\pi\)
−0.904473 + 0.426530i \(0.859736\pi\)
\(318\) −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 −0.998196 0.0600326i \(-0.980880\pi\)
0.551088 + 0.834447i \(0.314213\pi\)
\(332\) 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 \(-0.989601\pi\)
0.999466 0.0326650i \(-0.0103994\pi\)
\(338\) 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 −0.810527 0.585701i \(-0.800819\pi\)
0.101969 + 0.994788i \(0.467486\pi\)
\(348\) 33.0628 57.2665i 0.0950080 0.164559i
\(349\) 317.175i 0.908811i −0.890795 0.454406i \(-0.849852\pi\)
0.890795 0.454406i \(-0.150148\pi\)
\(350\) 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 0.936883 0.349644i \(-0.113697\pi\)
−0.771242 + 0.636542i \(0.780364\pi\)
\(354\) 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 −0.656250 0.754543i \(-0.727858\pi\)
0.981579 + 0.191058i \(0.0611918\pi\)
\(360\) 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 0.969280 + 0.245960i \(0.0791033\pi\)
−0.271632 + 0.962401i \(0.587563\pi\)
\(368\) −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 −0.312874 0.949795i \(-0.601292\pi\)
−0.978983 + 0.203941i \(0.934625\pi\)
\(374\) 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 −0.846231 0.532816i \(-0.821134\pi\)
0.884548 + 0.466450i \(0.154467\pi\)
\(384\) 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 −0.830307 0.557306i \(-0.811835\pi\)
−0.0674875 0.997720i \(-0.521498\pi\)
\(390\) 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 −0.707851 0.706361i \(-0.750335\pi\)
0.965653 + 0.259837i \(0.0836687\pi\)
\(398\) 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 0.462989 + 0.886364i \(0.346777\pi\)
−0.999108 + 0.0422215i \(0.986556\pi\)
\(402\) 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 −0.518656 0.854983i \(-0.673567\pi\)
0.481109 + 0.876661i \(0.340234\pi\)
\(410\) 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 \(-0.823700\pi\)
0.850499 0.525977i \(-0.176300\pi\)
\(420\) 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 0.816005 + 0.578045i \(0.196184\pi\)
0.0925988 + 0.995704i \(0.470483\pi\)
\(432\) 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 0.796841 0.604189i \(-0.206503\pi\)
−0.124823 + 0.992179i \(0.539836\pi\)
\(440\) 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 0.833835 0.552013i \(-0.186140\pi\)
−0.0611396 + 0.998129i \(0.519473\pi\)
\(444\) −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 −0.0695382 0.997579i \(-0.522153\pi\)
−0.898698 + 0.438568i \(0.855486\pi\)
\(458\) −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 \(-0.939460\pi\)
0.981968 0.189049i \(-0.0605404\pi\)
\(462\) 175.709 + 59.6518i 0.380322 + 0.129116i
\(463\) 755.187i 1.63107i −0.578705 0.815537i \(-0.696442\pi\)
0.578705 0.815537i \(-0.303558\pi\)
\(464\) 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 −0.385186 0.922839i \(-0.625863\pi\)
0.991795 0.127839i \(-0.0408039\pi\)
\(468\) −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 −0.886690 0.462365i \(-0.847001\pi\)
−0.0429255 + 0.999078i \(0.513668\pi\)
\(480\) 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 −0.179879 0.983689i \(-0.557571\pi\)
0.761960 + 0.647624i \(0.224237\pi\)
\(488\) 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 −0.579351 0.815078i \(-0.696694\pi\)
0.995554 + 0.0941936i \(0.0300273\pi\)
\(500\) 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 0.359438 0.933169i \(-0.382968\pi\)
−0.628429 + 0.777867i \(0.716302\pi\)
\(510\) 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 −0.176461 0.984308i \(-0.556465\pi\)
0.764205 + 0.644974i \(0.223132\pi\)
\(522\) 70.1368 40.4935i 0.134362 0.0775737i
\(523\) −59.7756 + 103.534i −0.114294 + 0.197962i −0.917497 0.397742i \(-0.869794\pi\)
0.803204 + 0.595705i \(0.203127\pi\)
\(524\) 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 0.495938 + 0.868358i \(0.334824\pi\)
−0.999989 + 0.00468349i \(0.998509\pi\)
\(542\) −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 \(-0.965663\pi\)
0.994188 0.107663i \(-0.0343366\pi\)
\(548\) −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 −0.895237 0.445590i \(-0.852994\pi\)
−0.0617258 + 0.998093i \(0.519660\pi\)
\(558\) 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 0.996479 0.0838462i \(-0.0267205\pi\)
−0.570852 + 0.821053i \(0.693387\pi\)
\(564\) −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 −0.993954 0.109800i \(-0.964979\pi\)
0.592067 + 0.805889i \(0.298312\pi\)
\(570\) 0 0
\(571\) −186.601 323.203i −0.326797 0.566029i 0.655077 0.755562i \(-0.272636\pi\)
−0.981874 + 0.189532i \(0.939303\pi\)
\(572\) −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 −0.936146 0.351611i \(-0.885634\pi\)
0.163569 0.986532i \(-0.447699\pi\)
\(578\) 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 0.472216 + 0.881483i \(0.343454\pi\)
−0.999495 + 0.0317903i \(0.989879\pi\)
\(594\) 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 0.921976 0.387247i \(-0.126574\pi\)
−0.796354 + 0.604831i \(0.793241\pi\)
\(600\) 0 0
\(601\) 521.601i 0.867888i 0.900940 + 0.433944i \(0.142878\pi\)
−0.900940 + 0.433944i \(0.857122\pi\)
\(602\) 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 −0.422228 0.906490i \(-0.638752\pi\)
0.996157 0.0875852i \(-0.0279150\pi\)
\(608\) −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 −0.537831 0.843053i \(-0.680756\pi\)
0.461190 + 0.887302i \(0.347423\pi\)
\(614\) 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 \(-0.712179\pi\)
0.618301 0.785941i \(-0.287821\pi\)
\(618\) 433.947 + 250.540i 0.702180 + 0.405404i
\(619\) 111.240 64.2247i 0.179710 0.103756i −0.407446 0.913229i \(-0.633581\pi\)
0.587156 + 0.809474i \(0.300247\pi\)
\(620\) 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 0.951134 + 0.308780i \(0.0999206\pi\)
−0.208156 + 0.978096i \(0.566746\pi\)
\(642\) 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 0.933954 + 0.357393i \(0.116334\pi\)
−0.157466 + 0.987524i \(0.550332\pi\)
\(648\) 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 0.995690 0.0927422i \(-0.0295632\pi\)
0.417528 + 0.908664i \(0.362897\pi\)
\(654\) 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 −0.231264 0.972891i \(-0.574286\pi\)
0.726916 + 0.686726i \(0.240953\pi\)
\(662\) −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 \(0.171237\pi\)
−0.858758 + 0.512382i \(0.828763\pi\)
\(674\) 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 −0.971455 0.237223i \(-0.923763\pi\)
0.691169 + 0.722693i \(0.257096\pi\)
\(678\) 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 −0.892403 0.451240i \(-0.850982\pi\)
−0.0554159 + 0.998463i \(0.517648\pi\)
\(684\) −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 0.940328 0.340268i \(-0.110518\pi\)
0.175483 + 0.984482i \(0.443851\pi\)
\(692\) 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 −0.970650 0.240497i \(-0.922690\pi\)
0.693602 + 0.720359i \(0.256023\pi\)
\(710\) 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 −0.280194 0.959943i \(-0.590399\pi\)
−0.971432 + 0.237317i \(0.923732\pi\)
\(720\) 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 −0.218109 0.975924i \(-0.569989\pi\)
0.954230 0.299074i \(-0.0966777\pi\)
\(734\) 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 0.999909 + 0.0134615i \(0.00428507\pi\)
−0.488297 + 0.872678i \(0.662382\pi\)
\(740\) 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 \(-0.775306\pi\)
0.761030 0.648717i \(-0.224694\pi\)
\(744\) 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 0.442902 + 0.896570i \(0.353949\pi\)
−0.997903 + 0.0647203i \(0.979384\pi\)
\(752\) −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 \(-0.836247\pi\)
0.870566 0.492051i \(-0.163753\pi\)
\(758\) 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 0.457258 0.889334i \(-0.348832\pi\)
−0.541557 + 0.840664i \(0.682165\pi\)
\(762\) 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 \(0.214981\pi\)
−0.780467 + 0.625197i \(0.785019\pi\)
\(770\) 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 0.840253 + 0.542194i \(0.182406\pi\)
0.0494271 + 0.998778i \(0.484260\pi\)
\(774\) −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