Properties

Label 225.4.p.b.32.5
Level $225$
Weight $4$
Character 225.32
Analytic conductor $13.275$
Analytic rank $0$
Dimension $64$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 225 = 3^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 225.p (of order \(12\), degree \(4\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(13.2754297513\)
Analytic rank: \(0\)
Dimension: \(64\)
Relative dimension: \(16\) over \(\Q(\zeta_{12})\)
Twist minimal: no (minimal twist has level 45)
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 32.5
Character \(\chi\) \(=\) 225.32
Dual form 225.4.p.b.218.5

$q$-expansion

\(f(q)\) \(=\) \(q+(-2.15214 - 0.576664i) q^{2} +(-4.75638 - 2.09209i) q^{3} +(-2.62904 - 1.51788i) q^{4} +(9.02996 + 7.24530i) q^{6} +(3.70051 - 13.8105i) q^{7} +(17.3866 + 17.3866i) q^{8} +(18.2463 + 19.9016i) q^{9} +O(q^{10})\) \(q+(-2.15214 - 0.576664i) q^{2} +(-4.75638 - 2.09209i) q^{3} +(-2.62904 - 1.51788i) q^{4} +(9.02996 + 7.24530i) q^{6} +(3.70051 - 13.8105i) q^{7} +(17.3866 + 17.3866i) q^{8} +(18.2463 + 19.9016i) q^{9} +(-35.0788 + 20.2528i) q^{11} +(9.32918 + 12.7198i) q^{12} +(14.4092 + 53.7760i) q^{13} +(-15.9280 + 27.5881i) q^{14} +(-15.2491 - 26.4122i) q^{16} +(-18.3703 + 18.3703i) q^{17} +(-27.7921 - 53.3529i) q^{18} -29.3394i q^{19} +(-46.4938 + 57.9461i) q^{21} +(87.1736 - 23.3581i) q^{22} +(176.622 - 47.3257i) q^{23} +(-46.3228 - 119.071i) q^{24} -124.043i q^{26} +(-45.1505 - 132.832i) q^{27} +(-30.6914 + 30.6914i) q^{28} +(39.7429 + 68.8368i) q^{29} +(62.6702 - 108.548i) q^{31} +(-33.3242 - 124.368i) q^{32} +(209.219 - 22.9418i) q^{33} +(50.1290 - 28.9420i) q^{34} +(-17.7622 - 80.0177i) q^{36} +(-248.921 - 248.921i) q^{37} +(-16.9190 + 63.1425i) q^{38} +(43.9685 - 285.924i) q^{39} +(155.350 + 89.6914i) q^{41} +(133.477 - 97.8968i) q^{42} +(-361.167 - 96.7744i) q^{43} +122.965 q^{44} -407.406 q^{46} +(253.018 + 67.7961i) q^{47} +(17.2737 + 157.529i) q^{48} +(120.011 + 69.2884i) q^{49} +(125.809 - 48.9438i) q^{51} +(43.7429 - 163.251i) q^{52} +(56.9787 + 56.9787i) q^{53} +(20.5705 + 311.910i) q^{54} +(304.456 - 175.778i) q^{56} +(-61.3807 + 139.549i) q^{57} +(-45.8366 - 171.065i) q^{58} +(213.746 - 370.219i) q^{59} +(-400.668 - 693.978i) q^{61} +(-197.471 + 197.471i) q^{62} +(342.371 - 178.344i) q^{63} +530.858i q^{64} +(-463.498 - 71.2751i) q^{66} +(576.627 - 154.507i) q^{67} +(76.1803 - 20.4124i) q^{68} +(-939.091 - 144.410i) q^{69} +655.546i q^{71} +(-28.7792 + 663.260i) q^{72} +(91.3719 - 91.3719i) q^{73} +(392.170 + 679.258i) q^{74} +(-44.5337 + 77.1346i) q^{76} +(149.891 + 559.401i) q^{77} +(-259.509 + 589.994i) q^{78} +(529.437 - 305.671i) q^{79} +(-63.1444 + 726.260i) q^{81} +(-282.613 - 282.613i) q^{82} +(55.3072 - 206.409i) q^{83} +(210.189 - 81.7708i) q^{84} +(721.475 + 416.544i) q^{86} +(-45.0197 - 410.560i) q^{87} +(-962.027 - 257.774i) q^{88} -451.962 q^{89} +795.994 q^{91} +(-536.181 - 143.669i) q^{92} +(-525.175 + 385.183i) q^{93} +(-505.435 - 291.813i) q^{94} +(-101.686 + 661.257i) q^{96} +(-310.669 + 1159.43i) q^{97} +(-218.324 - 218.324i) q^{98} +(-1043.12 - 328.585i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 64 q + 6 q^{2} - 24 q^{6} + 2 q^{7} + O(q^{10}) \) \( 64 q + 6 q^{2} - 24 q^{6} + 2 q^{7} - 36 q^{11} + 138 q^{12} + 2 q^{13} + 316 q^{16} + 480 q^{18} + 480 q^{21} + 34 q^{22} - 306 q^{23} - 180 q^{27} + 232 q^{28} - 4 q^{31} + 1770 q^{32} + 294 q^{33} - 216 q^{36} - 136 q^{37} - 114 q^{38} + 1992 q^{41} - 1698 q^{42} + 2 q^{43} - 952 q^{46} - 3462 q^{47} - 4326 q^{48} - 2496 q^{51} + 242 q^{52} - 7128 q^{56} + 2544 q^{57} - 534 q^{58} + 32 q^{61} + 4038 q^{63} + 2892 q^{66} - 610 q^{67} + 2694 q^{68} + 1854 q^{72} + 8 q^{73} + 1368 q^{76} + 6486 q^{77} - 1434 q^{78} + 3012 q^{81} + 3784 q^{82} - 2814 q^{83} + 12480 q^{86} - 4830 q^{87} + 1338 q^{88} + 992 q^{91} - 13152 q^{92} - 8310 q^{93} - 7932 q^{96} - 358 q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/225\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(127\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{4}\right)\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.15214 0.576664i −0.760896 0.203881i −0.142550 0.989788i \(-0.545530\pi\)
−0.618346 + 0.785906i \(0.712197\pi\)
\(3\) −4.75638 2.09209i −0.915366 0.402623i
\(4\) −2.62904 1.51788i −0.328630 0.189735i
\(5\) 0 0
\(6\) 9.02996 + 7.24530i 0.614411 + 0.492980i
\(7\) 3.70051 13.8105i 0.199809 0.745696i −0.791161 0.611608i \(-0.790523\pi\)
0.990969 0.134088i \(-0.0428104\pi\)
\(8\) 17.3866 + 17.3866i 0.768385 + 0.768385i
\(9\) 18.2463 + 19.9016i 0.675789 + 0.737095i
\(10\) 0 0
\(11\) −35.0788 + 20.2528i −0.961516 + 0.555131i −0.896639 0.442762i \(-0.853999\pi\)
−0.0648764 + 0.997893i \(0.520665\pi\)
\(12\) 9.32918 + 12.7198i 0.224425 + 0.305991i
\(13\) 14.4092 + 53.7760i 0.307416 + 1.14729i 0.930846 + 0.365412i \(0.119072\pi\)
−0.623431 + 0.781879i \(0.714262\pi\)
\(14\) −15.9280 + 27.5881i −0.304067 + 0.526660i
\(15\) 0 0
\(16\) −15.2491 26.4122i −0.238267 0.412690i
\(17\) −18.3703 + 18.3703i −0.262086 + 0.262086i −0.825901 0.563815i \(-0.809333\pi\)
0.563815 + 0.825901i \(0.309333\pi\)
\(18\) −27.7921 53.3529i −0.363925 0.698634i
\(19\) 29.3394i 0.354259i −0.984188 0.177130i \(-0.943319\pi\)
0.984188 0.177130i \(-0.0566812\pi\)
\(20\) 0 0
\(21\) −46.4938 + 57.9461i −0.483132 + 0.602137i
\(22\) 87.1736 23.3581i 0.844794 0.226362i
\(23\) 176.622 47.3257i 1.60123 0.429047i 0.655814 0.754923i \(-0.272326\pi\)
0.945413 + 0.325875i \(0.105659\pi\)
\(24\) −46.3228 119.071i −0.393984 1.01272i
\(25\) 0 0
\(26\) 124.043i 0.935645i
\(27\) −45.1505 132.832i −0.321823 0.946800i
\(28\) −30.6914 + 30.6914i −0.207148 + 0.207148i
\(29\) 39.7429 + 68.8368i 0.254486 + 0.440782i 0.964756 0.263147i \(-0.0847606\pi\)
−0.710270 + 0.703929i \(0.751427\pi\)
\(30\) 0 0
\(31\) 62.6702 108.548i 0.363093 0.628896i −0.625375 0.780324i \(-0.715054\pi\)
0.988468 + 0.151428i \(0.0483873\pi\)
\(32\) −33.3242 124.368i −0.184092 0.687041i
\(33\) 209.219 22.9418i 1.10365 0.121020i
\(34\) 50.1290 28.9420i 0.252854 0.145986i
\(35\) 0 0
\(36\) −17.7622 80.0177i −0.0822323 0.370452i
\(37\) −248.921 248.921i −1.10601 1.10601i −0.993670 0.112342i \(-0.964165\pi\)
−0.112342 0.993670i \(-0.535835\pi\)
\(38\) −16.9190 + 63.1425i −0.0722269 + 0.269554i
\(39\) 43.9685 285.924i 0.180528 1.17396i
\(40\) 0 0
\(41\) 155.350 + 89.6914i 0.591746 + 0.341645i 0.765788 0.643093i \(-0.222349\pi\)
−0.174041 + 0.984738i \(0.555683\pi\)
\(42\) 133.477 97.8968i 0.490378 0.359662i
\(43\) −361.167 96.7744i −1.28087 0.343208i −0.446685 0.894691i \(-0.647395\pi\)
−0.834186 + 0.551483i \(0.814062\pi\)
\(44\) 122.965 0.421311
\(45\) 0 0
\(46\) −407.406 −1.30584
\(47\) 253.018 + 67.7961i 0.785245 + 0.210406i 0.629096 0.777328i \(-0.283425\pi\)
0.156149 + 0.987733i \(0.450092\pi\)
\(48\) 17.2737 + 157.529i 0.0519426 + 0.473694i
\(49\) 120.011 + 69.2884i 0.349886 + 0.202007i
\(50\) 0 0
\(51\) 125.809 48.9438i 0.345426 0.134383i
\(52\) 43.7429 163.251i 0.116655 0.435362i
\(53\) 56.9787 + 56.9787i 0.147672 + 0.147672i 0.777077 0.629405i \(-0.216701\pi\)
−0.629405 + 0.777077i \(0.716701\pi\)
\(54\) 20.5705 + 311.910i 0.0518388 + 0.786030i
\(55\) 0 0
\(56\) 304.456 175.778i 0.726511 0.419451i
\(57\) −61.3807 + 139.549i −0.142633 + 0.324277i
\(58\) −45.8366 171.065i −0.103770 0.387274i
\(59\) 213.746 370.219i 0.471651 0.816923i −0.527823 0.849354i \(-0.676992\pi\)
0.999474 + 0.0324311i \(0.0103250\pi\)
\(60\) 0 0
\(61\) −400.668 693.978i −0.840989 1.45664i −0.889059 0.457792i \(-0.848641\pi\)
0.0480704 0.998844i \(-0.484693\pi\)
\(62\) −197.471 + 197.471i −0.404496 + 0.404496i
\(63\) 342.371 178.344i 0.684677 0.356655i
\(64\) 530.858i 1.03683i
\(65\) 0 0
\(66\) −463.498 71.2751i −0.864434 0.132930i
\(67\) 576.627 154.507i 1.05144 0.281732i 0.308591 0.951195i \(-0.400142\pi\)
0.742845 + 0.669463i \(0.233476\pi\)
\(68\) 76.1803 20.4124i 0.135856 0.0364025i
\(69\) −939.091 144.410i −1.63845 0.251956i
\(70\) 0 0
\(71\) 655.546i 1.09576i 0.836557 + 0.547880i \(0.184565\pi\)
−0.836557 + 0.547880i \(0.815435\pi\)
\(72\) −28.7792 + 663.260i −0.0471064 + 1.08564i
\(73\) 91.3719 91.3719i 0.146497 0.146497i −0.630054 0.776551i \(-0.716967\pi\)
0.776551 + 0.630054i \(0.216967\pi\)
\(74\) 392.170 + 679.258i 0.616065 + 1.06706i
\(75\) 0 0
\(76\) −44.5337 + 77.1346i −0.0672153 + 0.116420i
\(77\) 149.891 + 559.401i 0.221840 + 0.827918i
\(78\) −259.509 + 589.994i −0.376712 + 0.856458i
\(79\) 529.437 305.671i 0.754004 0.435325i −0.0731347 0.997322i \(-0.523300\pi\)
0.827139 + 0.561998i \(0.189967\pi\)
\(80\) 0 0
\(81\) −63.1444 + 726.260i −0.0866179 + 0.996242i
\(82\) −282.613 282.613i −0.380602 0.380602i
\(83\) 55.3072 206.409i 0.0731417 0.272968i −0.919664 0.392707i \(-0.871539\pi\)
0.992806 + 0.119738i \(0.0382055\pi\)
\(84\) 210.189 81.7708i 0.273018 0.106213i
\(85\) 0 0
\(86\) 721.475 + 416.544i 0.904636 + 0.522292i
\(87\) −45.0197 410.560i −0.0554784 0.505938i
\(88\) −962.027 257.774i −1.16537 0.312259i
\(89\) −451.962 −0.538291 −0.269146 0.963100i \(-0.586741\pi\)
−0.269146 + 0.963100i \(0.586741\pi\)
\(90\) 0 0
\(91\) 795.994 0.916954
\(92\) −536.181 143.669i −0.607617 0.162810i
\(93\) −525.175 + 385.183i −0.585571 + 0.429480i
\(94\) −505.435 291.813i −0.554592 0.320194i
\(95\) 0 0
\(96\) −101.686 + 661.257i −0.108107 + 0.703013i
\(97\) −310.669 + 1159.43i −0.325193 + 1.21364i 0.588926 + 0.808187i \(0.299551\pi\)
−0.914118 + 0.405448i \(0.867116\pi\)
\(98\) −218.324 218.324i −0.225042 0.225042i
\(99\) −1043.12 328.585i −1.05897 0.333577i
\(100\) 0 0
\(101\) 919.775 531.032i 0.906149 0.523165i 0.0269588 0.999637i \(-0.491418\pi\)
0.879190 + 0.476471i \(0.158084\pi\)
\(102\) −298.982 + 32.7847i −0.290231 + 0.0318252i
\(103\) 22.8146 + 85.1453i 0.0218251 + 0.0814526i 0.975979 0.217863i \(-0.0699085\pi\)
−0.954154 + 0.299315i \(0.903242\pi\)
\(104\) −684.452 + 1185.51i −0.645347 + 1.11777i
\(105\) 0 0
\(106\) −89.7685 155.484i −0.0822555 0.142471i
\(107\) 422.554 422.554i 0.381774 0.381774i −0.489967 0.871741i \(-0.662991\pi\)
0.871741 + 0.489967i \(0.162991\pi\)
\(108\) −82.9208 + 417.755i −0.0738801 + 0.372208i
\(109\) 1529.73i 1.34424i −0.740444 0.672118i \(-0.765385\pi\)
0.740444 0.672118i \(-0.234615\pi\)
\(110\) 0 0
\(111\) 663.199 + 1704.73i 0.567100 + 1.45771i
\(112\) −421.194 + 112.859i −0.355349 + 0.0952155i
\(113\) 2041.91 547.128i 1.69988 0.455482i 0.726971 0.686668i \(-0.240927\pi\)
0.972910 + 0.231186i \(0.0742607\pi\)
\(114\) 212.573 264.934i 0.174643 0.217661i
\(115\) 0 0
\(116\) 241.300i 0.193139i
\(117\) −807.311 + 1267.98i −0.637914 + 1.00192i
\(118\) −673.504 + 673.504i −0.525433 + 0.525433i
\(119\) 185.723 + 321.683i 0.143069 + 0.247803i
\(120\) 0 0
\(121\) 154.850 268.209i 0.116341 0.201509i
\(122\) 462.102 + 1724.59i 0.342924 + 1.27981i
\(123\) −551.261 751.613i −0.404110 0.550981i
\(124\) −329.525 + 190.251i −0.238647 + 0.137783i
\(125\) 0 0
\(126\) −839.674 + 186.389i −0.593684 + 0.131785i
\(127\) 212.243 + 212.243i 0.148296 + 0.148296i 0.777356 0.629061i \(-0.216560\pi\)
−0.629061 + 0.777356i \(0.716560\pi\)
\(128\) 39.5332 147.540i 0.0272990 0.101881i
\(129\) 1515.39 + 1215.89i 1.03428 + 0.829869i
\(130\) 0 0
\(131\) 285.089 + 164.596i 0.190140 + 0.109777i 0.592048 0.805903i \(-0.298320\pi\)
−0.401908 + 0.915680i \(0.631653\pi\)
\(132\) −584.868 257.254i −0.385654 0.169629i
\(133\) −405.192 108.571i −0.264170 0.0707840i
\(134\) −1330.08 −0.857474
\(135\) 0 0
\(136\) −638.793 −0.402765
\(137\) 1269.01 + 340.030i 0.791378 + 0.212049i 0.631795 0.775136i \(-0.282318\pi\)
0.159583 + 0.987185i \(0.448985\pi\)
\(138\) 1937.78 + 852.330i 1.19532 + 0.525762i
\(139\) 1886.00 + 1088.88i 1.15085 + 0.664446i 0.949095 0.314989i \(-0.102001\pi\)
0.201759 + 0.979435i \(0.435334\pi\)
\(140\) 0 0
\(141\) −1061.62 851.801i −0.634072 0.508756i
\(142\) 378.029 1410.83i 0.223405 0.833759i
\(143\) −1594.57 1594.57i −0.932482 0.932482i
\(144\) 247.404 785.405i 0.143174 0.454517i
\(145\) 0 0
\(146\) −249.336 + 143.954i −0.141337 + 0.0816009i
\(147\) −425.861 580.636i −0.238941 0.325783i
\(148\) 276.593 + 1032.26i 0.153620 + 0.573318i
\(149\) −238.236 + 412.637i −0.130987 + 0.226876i −0.924057 0.382254i \(-0.875148\pi\)
0.793070 + 0.609130i \(0.208481\pi\)
\(150\) 0 0
\(151\) −999.275 1730.80i −0.538542 0.932783i −0.998983 0.0450920i \(-0.985642\pi\)
0.460441 0.887691i \(-0.347691\pi\)
\(152\) 510.112 510.112i 0.272207 0.272207i
\(153\) −700.789 30.4076i −0.370297 0.0160674i
\(154\) 1290.35i 0.675189i
\(155\) 0 0
\(156\) −549.594 + 684.969i −0.282069 + 0.351547i
\(157\) 1403.25 375.998i 0.713320 0.191133i 0.116131 0.993234i \(-0.462951\pi\)
0.597189 + 0.802101i \(0.296284\pi\)
\(158\) −1315.69 + 352.538i −0.662473 + 0.177509i
\(159\) −151.808 390.217i −0.0757178 0.194630i
\(160\) 0 0
\(161\) 2614.36i 1.27976i
\(162\) 554.704 1526.60i 0.269022 0.740377i
\(163\) 1588.23 1588.23i 0.763188 0.763188i −0.213710 0.976897i \(-0.568555\pi\)
0.976897 + 0.213710i \(0.0685547\pi\)
\(164\) −272.281 471.605i −0.129644 0.224550i
\(165\) 0 0
\(166\) −238.058 + 412.328i −0.111306 + 0.192788i
\(167\) −500.820 1869.08i −0.232063 0.866072i −0.979451 0.201684i \(-0.935359\pi\)
0.747387 0.664389i \(-0.231308\pi\)
\(168\) −1815.85 + 199.116i −0.833904 + 0.0914413i
\(169\) −781.573 + 451.241i −0.355746 + 0.205390i
\(170\) 0 0
\(171\) 583.900 535.336i 0.261123 0.239405i
\(172\) 802.631 + 802.631i 0.355814 + 0.355814i
\(173\) 93.5626 349.180i 0.0411181 0.153455i −0.942315 0.334729i \(-0.891355\pi\)
0.983433 + 0.181274i \(0.0580220\pi\)
\(174\) −139.866 + 909.543i −0.0609382 + 0.396278i
\(175\) 0 0
\(176\) 1069.84 + 617.672i 0.458194 + 0.264539i
\(177\) −1791.19 + 1313.73i −0.760645 + 0.557886i
\(178\) 972.686 + 260.630i 0.409583 + 0.109748i
\(179\) 1522.98 0.635937 0.317969 0.948101i \(-0.396999\pi\)
0.317969 + 0.948101i \(0.396999\pi\)
\(180\) 0 0
\(181\) 2025.51 0.831797 0.415898 0.909411i \(-0.363467\pi\)
0.415898 + 0.909411i \(0.363467\pi\)
\(182\) −1713.09 459.021i −0.697707 0.186950i
\(183\) 453.866 + 4139.06i 0.183337 + 1.67196i
\(184\) 3893.68 + 2248.02i 1.56003 + 0.900685i
\(185\) 0 0
\(186\) 1352.37 526.119i 0.533122 0.207403i
\(187\) 272.360 1016.46i 0.106508 0.397491i
\(188\) −562.290 562.290i −0.218134 0.218134i
\(189\) −2001.56 + 132.003i −0.770328 + 0.0508032i
\(190\) 0 0
\(191\) −1086.41 + 627.242i −0.411572 + 0.237621i −0.691465 0.722410i \(-0.743034\pi\)
0.279893 + 0.960031i \(0.409701\pi\)
\(192\) 1110.60 2524.96i 0.417453 0.949081i
\(193\) −751.094 2803.12i −0.280129 1.04546i −0.952326 0.305084i \(-0.901316\pi\)
0.672196 0.740373i \(-0.265351\pi\)
\(194\) 1337.21 2316.11i 0.494876 0.857150i
\(195\) 0 0
\(196\) −210.343 364.324i −0.0766555 0.132771i
\(197\) 1576.77 1576.77i 0.570255 0.570255i −0.361945 0.932200i \(-0.617887\pi\)
0.932200 + 0.361945i \(0.117887\pi\)
\(198\) 2055.46 + 1308.69i 0.737753 + 0.469721i
\(199\) 3635.06i 1.29489i −0.762113 0.647444i \(-0.775838\pi\)
0.762113 0.647444i \(-0.224162\pi\)
\(200\) 0 0
\(201\) −3065.90 471.464i −1.07588 0.165445i
\(202\) −2285.71 + 612.454i −0.796149 + 0.213327i
\(203\) 1097.74 294.138i 0.379538 0.101697i
\(204\) −405.047 62.2867i −0.139015 0.0213772i
\(205\) 0 0
\(206\) 196.401i 0.0664267i
\(207\) 4164.55 + 2651.53i 1.39834 + 0.890310i
\(208\) 1200.61 1200.61i 0.400228 0.400228i
\(209\) 594.205 + 1029.19i 0.196660 + 0.340626i
\(210\) 0 0
\(211\) −870.723 + 1508.14i −0.284090 + 0.492059i −0.972388 0.233369i \(-0.925025\pi\)
0.688298 + 0.725428i \(0.258358\pi\)
\(212\) −63.3126 236.286i −0.0205110 0.0765481i
\(213\) 1371.46 3118.02i 0.441178 1.00302i
\(214\) −1153.07 + 665.724i −0.368327 + 0.212654i
\(215\) 0 0
\(216\) 1524.49 3094.51i 0.480223 0.974790i
\(217\) −1267.19 1267.19i −0.396416 0.396416i
\(218\) −882.142 + 3292.20i −0.274065 + 1.02282i
\(219\) −625.758 + 243.441i −0.193081 + 0.0751152i
\(220\) 0 0
\(221\) −1252.58 723.180i −0.381258 0.220119i
\(222\) −444.239 4051.26i −0.134303 1.22479i
\(223\) 5027.28 + 1347.06i 1.50965 + 0.404509i 0.916318 0.400451i \(-0.131146\pi\)
0.593329 + 0.804960i \(0.297813\pi\)
\(224\) −1840.89 −0.549107
\(225\) 0 0
\(226\) −4709.98 −1.38630
\(227\) −2255.67 604.406i −0.659534 0.176722i −0.0864984 0.996252i \(-0.527568\pi\)
−0.573036 + 0.819530i \(0.694234\pi\)
\(228\) 373.192 273.713i 0.108400 0.0795047i
\(229\) −2860.05 1651.25i −0.825316 0.476496i 0.0269303 0.999637i \(-0.491427\pi\)
−0.852246 + 0.523141i \(0.824760\pi\)
\(230\) 0 0
\(231\) 457.379 2974.31i 0.130274 0.847166i
\(232\) −505.842 + 1887.83i −0.143147 + 0.534233i
\(233\) 1380.71 + 1380.71i 0.388213 + 0.388213i 0.874049 0.485837i \(-0.161485\pi\)
−0.485837 + 0.874049i \(0.661485\pi\)
\(234\) 2468.64 2263.32i 0.689659 0.632299i
\(235\) 0 0
\(236\) −1123.90 + 648.882i −0.309997 + 0.178977i
\(237\) −3157.70 + 346.255i −0.865461 + 0.0949017i
\(238\) −214.200 799.406i −0.0583384 0.217722i
\(239\) 2043.12 3538.78i 0.552963 0.957761i −0.445095 0.895483i \(-0.646830\pi\)
0.998059 0.0622776i \(-0.0198364\pi\)
\(240\) 0 0
\(241\) 2368.28 + 4101.99i 0.633007 + 1.09640i 0.986934 + 0.161127i \(0.0515128\pi\)
−0.353927 + 0.935273i \(0.615154\pi\)
\(242\) −487.926 + 487.926i −0.129608 + 0.129608i
\(243\) 1819.74 3322.27i 0.480397 0.877051i
\(244\) 2432.66i 0.638259i
\(245\) 0 0
\(246\) 752.963 + 1935.47i 0.195151 + 0.501630i
\(247\) 1577.76 422.759i 0.406438 0.108905i
\(248\) 2976.89 797.656i 0.762229 0.204239i
\(249\) −694.890 + 866.054i −0.176855 + 0.220417i
\(250\) 0 0
\(251\) 3435.06i 0.863822i 0.901916 + 0.431911i \(0.142161\pi\)
−0.901916 + 0.431911i \(0.857839\pi\)
\(252\) −1170.81 50.8021i −0.292676 0.0126993i
\(253\) −5237.22 + 5237.22i −1.30143 + 1.30143i
\(254\) −334.384 579.170i −0.0826028 0.143072i
\(255\) 0 0
\(256\) 1953.27 3383.17i 0.476873 0.825968i
\(257\) 614.874 + 2294.74i 0.149240 + 0.556973i 0.999530 + 0.0306577i \(0.00976017\pi\)
−0.850289 + 0.526315i \(0.823573\pi\)
\(258\) −2560.16 3490.63i −0.617786 0.842315i
\(259\) −4358.86 + 2516.59i −1.04574 + 0.603758i
\(260\) 0 0
\(261\) −644.798 + 2046.96i −0.152919 + 0.485456i
\(262\) −518.634 518.634i −0.122295 0.122295i
\(263\) −1733.57 + 6469.78i −0.406451 + 1.51690i 0.394913 + 0.918718i \(0.370775\pi\)
−0.801364 + 0.598177i \(0.795892\pi\)
\(264\) 4036.48 + 3238.72i 0.941015 + 0.755036i
\(265\) 0 0
\(266\) 809.420 + 467.319i 0.186574 + 0.107719i
\(267\) 2149.70 + 945.546i 0.492733 + 0.216728i
\(268\) −1750.50 469.045i −0.398988 0.106909i
\(269\) −3363.52 −0.762370 −0.381185 0.924499i \(-0.624484\pi\)
−0.381185 + 0.924499i \(0.624484\pi\)
\(270\) 0 0
\(271\) 6582.75 1.47555 0.737775 0.675047i \(-0.235877\pi\)
0.737775 + 0.675047i \(0.235877\pi\)
\(272\) 765.330 + 205.070i 0.170606 + 0.0457139i
\(273\) −3786.05 1665.29i −0.839348 0.369187i
\(274\) −2535.00 1463.58i −0.558923 0.322695i
\(275\) 0 0
\(276\) 2249.71 + 1805.09i 0.490640 + 0.393672i
\(277\) −297.389 + 1109.87i −0.0645067 + 0.240742i −0.990650 0.136430i \(-0.956437\pi\)
0.926143 + 0.377173i \(0.123104\pi\)
\(278\) −3431.02 3431.02i −0.740212 0.740212i
\(279\) 3303.77 733.364i 0.708931 0.157367i
\(280\) 0 0
\(281\) −5577.86 + 3220.38i −1.18415 + 0.683672i −0.956972 0.290180i \(-0.906285\pi\)
−0.227183 + 0.973852i \(0.572951\pi\)
\(282\) 1793.54 + 2445.39i 0.378737 + 0.516386i
\(283\) 1473.52 + 5499.24i 0.309511 + 1.15511i 0.928992 + 0.370099i \(0.120676\pi\)
−0.619482 + 0.785011i \(0.712657\pi\)
\(284\) 995.038 1723.46i 0.207904 0.360100i
\(285\) 0 0
\(286\) 2512.21 + 4351.27i 0.519406 + 0.899637i
\(287\) 1813.56 1813.56i 0.372999 0.372999i
\(288\) 1867.07 2932.45i 0.382007 0.599988i
\(289\) 4238.06i 0.862622i
\(290\) 0 0
\(291\) 3903.30 4864.76i 0.786308 0.979990i
\(292\) −378.912 + 101.529i −0.0759388 + 0.0203477i
\(293\) 988.051 264.747i 0.197005 0.0527874i −0.158967 0.987284i \(-0.550816\pi\)
0.355972 + 0.934496i \(0.384150\pi\)
\(294\) 581.679 + 1495.19i 0.115388 + 0.296603i
\(295\) 0 0
\(296\) 8655.78i 1.69969i
\(297\) 4274.05 + 3745.18i 0.835036 + 0.731709i
\(298\) 750.669 750.669i 0.145923 0.145923i
\(299\) 5089.97 + 8816.09i 0.984484 + 1.70518i
\(300\) 0 0
\(301\) −2673.00 + 4629.77i −0.511858 + 0.886564i
\(302\) 1152.49 + 4301.16i 0.219598 + 0.819549i
\(303\) −5485.77 + 601.539i −1.04010 + 0.114051i
\(304\) −774.917 + 447.399i −0.146199 + 0.0844082i
\(305\) 0 0
\(306\) 1490.66 + 469.561i 0.278482 + 0.0877222i
\(307\) −337.059 337.059i −0.0626611 0.0626611i 0.675082 0.737743i \(-0.264108\pi\)
−0.737743 + 0.675082i \(0.764108\pi\)
\(308\) 455.033 1698.21i 0.0841815 0.314170i
\(309\) 69.6167 452.714i 0.0128167 0.0833462i
\(310\) 0 0
\(311\) −4362.60 2518.75i −0.795434 0.459244i 0.0464378 0.998921i \(-0.485213\pi\)
−0.841872 + 0.539677i \(0.818546\pi\)
\(312\) 5735.70 4206.78i 1.04077 0.763340i
\(313\) −4562.05 1222.40i −0.823842 0.220748i −0.177816 0.984064i \(-0.556903\pi\)
−0.646025 + 0.763316i \(0.723570\pi\)
\(314\) −3236.80 −0.581731
\(315\) 0 0
\(316\) −1855.88 −0.330385
\(317\) −9568.96 2563.99i −1.69541 0.454285i −0.723636 0.690182i \(-0.757530\pi\)
−0.971778 + 0.235897i \(0.924197\pi\)
\(318\) 101.687 + 927.343i 0.0179319 + 0.163531i
\(319\) −2788.27 1609.81i −0.489384 0.282546i
\(320\) 0 0
\(321\) −2893.85 + 1125.81i −0.503175 + 0.195752i
\(322\) −1507.61 + 5626.47i −0.260918 + 0.973761i
\(323\) 538.975 + 538.975i 0.0928463 + 0.0928463i
\(324\) 1268.38 1813.52i 0.217487 0.310961i
\(325\) 0 0
\(326\) −4333.96 + 2502.21i −0.736306 + 0.425107i
\(327\) −3200.34 + 7275.99i −0.541221 + 1.23047i
\(328\) 1141.58 + 4260.43i 0.192174 + 0.717204i
\(329\) 1872.59 3243.43i 0.313797 0.543513i
\(330\) 0 0
\(331\) −2314.33 4008.54i −0.384312 0.665648i 0.607362 0.794426i \(-0.292228\pi\)
−0.991673 + 0.128778i \(0.958895\pi\)
\(332\) −458.710 + 458.710i −0.0758282 + 0.0758282i
\(333\) 412.028 9495.82i 0.0678048 1.56267i
\(334\) 4311.33i 0.706304i
\(335\) 0 0
\(336\) 2239.47 + 344.378i 0.363610 + 0.0559147i
\(337\) −908.869 + 243.531i −0.146912 + 0.0393649i −0.331525 0.943446i \(-0.607563\pi\)
0.184614 + 0.982811i \(0.440897\pi\)
\(338\) 1942.27 520.429i 0.312561 0.0837503i
\(339\) −10856.7 1669.51i −1.73940 0.267479i
\(340\) 0 0
\(341\) 5076.98i 0.806258i
\(342\) −1565.34 + 815.403i −0.247497 + 0.128924i
\(343\) 4868.73 4868.73i 0.766433 0.766433i
\(344\) −4596.88 7962.02i −0.720485 1.24792i
\(345\) 0 0
\(346\) −402.719 + 697.531i −0.0625732 + 0.108380i
\(347\) −155.452 580.155i −0.0240493 0.0897532i 0.952858 0.303416i \(-0.0981272\pi\)
−0.976907 + 0.213663i \(0.931461\pi\)
\(348\) −504.821 + 1147.71i −0.0777622 + 0.176793i
\(349\) 8983.64 5186.71i 1.37789 0.795525i 0.385984 0.922505i \(-0.373862\pi\)
0.991905 + 0.126980i \(0.0405285\pi\)
\(350\) 0 0
\(351\) 6492.61 4342.02i 0.987321 0.660285i
\(352\) 3687.77 + 3687.77i 0.558405 + 0.558405i
\(353\) −2450.37 + 9144.89i −0.369461 + 1.37885i 0.491810 + 0.870702i \(0.336335\pi\)
−0.861271 + 0.508145i \(0.830331\pi\)
\(354\) 4612.47 1794.41i 0.692515 0.269412i
\(355\) 0 0
\(356\) 1188.23 + 686.024i 0.176899 + 0.102133i
\(357\) −210.382 1918.59i −0.0311894 0.284434i
\(358\) −3277.66 878.247i −0.483882 0.129656i
\(359\) 6712.05 0.986765 0.493382 0.869813i \(-0.335760\pi\)
0.493382 + 0.869813i \(0.335760\pi\)
\(360\) 0 0
\(361\) 5998.20 0.874500
\(362\) −4359.19 1168.04i −0.632911 0.169588i
\(363\) −1297.64 + 951.742i −0.187627 + 0.137613i
\(364\) −2092.70 1208.22i −0.301339 0.173978i
\(365\) 0 0
\(366\) 1410.06 9169.56i 0.201380 1.30956i
\(367\) 829.995 3097.58i 0.118053 0.440579i −0.881444 0.472288i \(-0.843428\pi\)
0.999497 + 0.0317089i \(0.0100950\pi\)
\(368\) −3943.29 3943.29i −0.558582 0.558582i
\(369\) 1049.57 + 4728.25i 0.148071 + 0.667053i
\(370\) 0 0
\(371\) 997.753 576.053i 0.139625 0.0806123i
\(372\) 1965.37 215.511i 0.273924 0.0300369i
\(373\) −793.369 2960.89i −0.110132 0.411017i 0.888745 0.458402i \(-0.151578\pi\)
−0.998877 + 0.0473850i \(0.984911\pi\)
\(374\) −1172.31 + 2030.50i −0.162082 + 0.280735i
\(375\) 0 0
\(376\) 3220.38 + 5577.86i 0.441698 + 0.765043i
\(377\) −3129.10 + 3129.10i −0.427472 + 0.427472i
\(378\) 4383.75 + 870.138i 0.596497 + 0.118400i
\(379\) 8477.84i 1.14902i 0.818499 + 0.574509i \(0.194807\pi\)
−0.818499 + 0.574509i \(0.805193\pi\)
\(380\) 0 0
\(381\) −565.477 1453.54i −0.0760374 0.195452i
\(382\) 2699.82 723.415i 0.361610 0.0968930i
\(383\) −6497.52 + 1741.00i −0.866860 + 0.232275i −0.664730 0.747084i \(-0.731453\pi\)
−0.202131 + 0.979359i \(0.564787\pi\)
\(384\) −496.702 + 619.049i −0.0660084 + 0.0822675i
\(385\) 0 0
\(386\) 6465.84i 0.852597i
\(387\) −4664.00 8953.56i −0.612621 1.17606i
\(388\) 2576.64 2576.64i 0.337137 0.337137i
\(389\) −2078.63 3600.30i −0.270928 0.469260i 0.698172 0.715930i \(-0.253997\pi\)
−0.969100 + 0.246670i \(0.920664\pi\)
\(390\) 0 0
\(391\) −2375.21 + 4113.99i −0.307211 + 0.532106i
\(392\) 881.892 + 3291.27i 0.113628 + 0.424066i
\(393\) −1011.64 1379.31i −0.129849 0.177041i
\(394\) −4302.70 + 2484.16i −0.550169 + 0.317640i
\(395\) 0 0
\(396\) 2243.66 + 2447.20i 0.284717 + 0.310546i
\(397\) −2587.31 2587.31i −0.327087 0.327087i 0.524391 0.851478i \(-0.324293\pi\)
−0.851478 + 0.524391i \(0.824293\pi\)
\(398\) −2096.21 + 7823.16i −0.264004 + 0.985276i
\(399\) 1700.11 + 1364.10i 0.213313 + 0.171154i
\(400\) 0 0
\(401\) 8012.98 + 4626.29i 0.997878 + 0.576125i 0.907620 0.419794i \(-0.137898\pi\)
0.0902579 + 0.995918i \(0.471231\pi\)
\(402\) 6326.37 + 2782.65i 0.784902 + 0.345239i
\(403\) 6740.30 + 1806.06i 0.833147 + 0.223241i
\(404\) −3224.17 −0.397051
\(405\) 0 0
\(406\) −2532.10 −0.309523
\(407\) 13773.2 + 3690.53i 1.67743 + 0.449466i
\(408\) 3038.34 + 1336.41i 0.368678 + 0.162163i
\(409\) −6326.24 3652.45i −0.764822 0.441570i 0.0662023 0.997806i \(-0.478912\pi\)
−0.831024 + 0.556236i \(0.812245\pi\)
\(410\) 0 0
\(411\) −5324.52 4272.19i −0.639024 0.512729i
\(412\) 69.2596 258.480i 0.00828198 0.0309088i
\(413\) −4321.94 4321.94i −0.514936 0.514936i
\(414\) −7433.65 8108.01i −0.882474 0.962529i
\(415\) 0 0
\(416\) 6207.82 3584.08i 0.731642 0.422414i
\(417\) −6692.50 9124.84i −0.785931 1.07157i
\(418\) −685.313 2557.62i −0.0801908 0.299276i
\(419\) 2581.15 4470.68i 0.300948 0.521257i −0.675403 0.737449i \(-0.736030\pi\)
0.976351 + 0.216192i \(0.0693636\pi\)
\(420\) 0 0
\(421\) 946.112 + 1638.71i 0.109527 + 0.189705i 0.915579 0.402139i \(-0.131733\pi\)
−0.806052 + 0.591845i \(0.798400\pi\)
\(422\) 2743.61 2743.61i 0.316485 0.316485i
\(423\) 3267.40 + 6272.49i 0.375571 + 0.720990i
\(424\) 1981.33i 0.226938i
\(425\) 0 0
\(426\) −4749.63 + 5919.55i −0.540188 + 0.673247i
\(427\) −11066.8 + 2965.35i −1.25424 + 0.336074i
\(428\) −1752.30 + 469.527i −0.197899 + 0.0530268i
\(429\) 4248.40 + 10920.4i 0.478123 + 1.22900i
\(430\) 0 0
\(431\) 12717.6i 1.42132i −0.703538 0.710658i \(-0.748397\pi\)
0.703538 0.710658i \(-0.251603\pi\)
\(432\) −2819.89 + 3218.09i −0.314055 + 0.358404i
\(433\) 4103.64 4103.64i 0.455447 0.455447i −0.441711 0.897158i \(-0.645628\pi\)
0.897158 + 0.441711i \(0.145628\pi\)
\(434\) 1996.42 + 3457.90i 0.220810 + 0.382453i
\(435\) 0 0
\(436\) −2321.95 + 4021.73i −0.255048 + 0.441757i
\(437\) −1388.51 5181.98i −0.151994 0.567249i
\(438\) 1487.10 163.067i 0.162229 0.0177892i
\(439\) 7178.99 4144.79i 0.780488 0.450615i −0.0561151 0.998424i \(-0.517871\pi\)
0.836603 + 0.547809i \(0.184538\pi\)
\(440\) 0 0
\(441\) 810.811 + 3652.67i 0.0875511 + 0.394414i
\(442\) 2278.70 + 2278.70i 0.245219 + 0.245219i
\(443\) 1535.41 5730.24i 0.164672 0.614565i −0.833410 0.552656i \(-0.813614\pi\)
0.998082 0.0619089i \(-0.0197188\pi\)
\(444\) 843.997 5488.47i 0.0902125 0.586647i
\(445\) 0 0
\(446\) −10042.6 5798.10i −1.06621 0.615578i
\(447\) 1996.41 1464.25i 0.211246 0.154936i
\(448\) 7331.41 + 1964.45i 0.773162 + 0.207168i
\(449\) −3855.25 −0.405213 −0.202606 0.979260i \(-0.564941\pi\)
−0.202606 + 0.979260i \(0.564941\pi\)
\(450\) 0 0
\(451\) −7266.00 −0.758631
\(452\) −6198.73 1660.95i −0.645053 0.172841i
\(453\) 1131.95 + 10322.9i 0.117403 + 1.07067i
\(454\) 4505.98 + 2601.53i 0.465807 + 0.268934i
\(455\) 0 0
\(456\) −3493.48 + 1359.08i −0.358766 + 0.139572i
\(457\) 463.264 1728.92i 0.0474192 0.176971i −0.938155 0.346216i \(-0.887466\pi\)
0.985574 + 0.169245i \(0.0541330\pi\)
\(458\) 5203.01 + 5203.01i 0.530831 + 0.530831i
\(459\) 3269.60 + 1610.74i 0.332488 + 0.163798i
\(460\) 0 0
\(461\) −10218.4 + 5899.62i −1.03237 + 0.596036i −0.917661 0.397363i \(-0.869925\pi\)
−0.114704 + 0.993400i \(0.536592\pi\)
\(462\) −2699.52 + 6137.38i −0.271847 + 0.618045i
\(463\) 640.951 + 2392.06i 0.0643359 + 0.240105i 0.990604 0.136760i \(-0.0436689\pi\)
−0.926268 + 0.376865i \(0.877002\pi\)
\(464\) 1212.09 2099.39i 0.121271 0.210047i
\(465\) 0 0
\(466\) −2175.28 3767.69i −0.216240 0.374539i
\(467\) 11085.9 11085.9i 1.09849 1.09849i 0.103901 0.994588i \(-0.466868\pi\)
0.994588 0.103901i \(-0.0331324\pi\)
\(468\) 4047.09 2108.17i 0.399737 0.208227i
\(469\) 8535.26i 0.840344i
\(470\) 0 0
\(471\) −7460.99 1147.33i −0.729903 0.112242i
\(472\) 10153.2 2720.53i 0.990120 0.265302i
\(473\) 14629.3 3919.90i 1.42210 0.381051i
\(474\) 6995.47 + 1075.74i 0.677875 + 0.104241i
\(475\) 0 0
\(476\) 1127.62i 0.108581i
\(477\) −94.3142 + 2173.61i −0.00905314 + 0.208644i
\(478\) −6437.76 + 6437.76i −0.616017 + 0.616017i
\(479\) 4528.18 + 7843.03i 0.431937 + 0.748136i 0.997040 0.0768839i \(-0.0244971\pi\)
−0.565103 + 0.825020i \(0.691164\pi\)
\(480\) 0 0
\(481\) 9799.23 16972.8i 0.928912 1.60892i
\(482\) −2731.41 10193.8i −0.258117 0.963305i
\(483\) −5469.49 + 12434.9i −0.515259 + 1.17144i
\(484\) −814.217 + 470.088i −0.0764666 + 0.0441480i
\(485\) 0 0
\(486\) −5832.17 + 6100.60i −0.544347 + 0.569401i
\(487\) 2327.30 + 2327.30i 0.216551 + 0.216551i 0.807043 0.590492i \(-0.201066\pi\)
−0.590492 + 0.807043i \(0.701066\pi\)
\(488\) 5099.65 19032.1i 0.473053 1.76546i
\(489\) −10876.9 + 4231.50i −1.00587 + 0.391319i
\(490\) 0 0
\(491\) −2623.22 1514.51i −0.241108 0.139204i 0.374578 0.927195i \(-0.377788\pi\)
−0.615686 + 0.787992i \(0.711121\pi\)
\(492\) 308.433 + 2812.77i 0.0282626 + 0.257743i
\(493\) −1994.64 534.463i −0.182220 0.0488256i
\(494\) −3639.34 −0.331461
\(495\) 0 0
\(496\) −3822.65 −0.346052
\(497\) 9053.40 + 2425.85i 0.817104 + 0.218942i
\(498\) 1994.92 1463.15i 0.179507 0.131657i
\(499\) −171.019 98.7379i −0.0153424 0.00885795i 0.492309 0.870420i \(-0.336153\pi\)
−0.507652 + 0.861562i \(0.669486\pi\)
\(500\) 0 0
\(501\) −1528.21 + 9937.84i −0.136278 + 0.886207i
\(502\) 1980.88 7392.73i 0.176117 0.657279i
\(503\) −4650.74 4650.74i −0.412259 0.412259i 0.470266 0.882525i \(-0.344158\pi\)
−0.882525 + 0.470266i \(0.844158\pi\)
\(504\) 9053.45 + 2851.85i 0.800144 + 0.252047i
\(505\) 0 0
\(506\) 14291.3 8251.10i 1.25559 0.724914i
\(507\) 4661.50 511.154i 0.408332 0.0447754i
\(508\) −235.837 880.155i −0.0205976 0.0768712i
\(509\) −7091.29 + 12282.5i −0.617517 + 1.06957i 0.372420 + 0.928064i \(0.378528\pi\)
−0.989937 + 0.141506i \(0.954805\pi\)
\(510\) 0 0
\(511\) −923.767 1600.01i −0.0799708 0.138513i
\(512\) −7018.72 + 7018.72i −0.605833 + 0.605833i
\(513\) −3897.22 + 1324.69i −0.335413 + 0.114009i
\(514\) 5293.18i 0.454226i
\(515\) 0 0
\(516\) −2138.44 5496.80i −0.182441 0.468959i
\(517\) −10248.6 + 2746.12i −0.871828 + 0.233606i
\(518\) 10832.1 2902.45i 0.918794 0.246190i
\(519\) −1175.54 + 1465.09i −0.0994226 + 0.123912i
\(520\) 0 0
\(521\) 5590.04i 0.470065i 0.971987 + 0.235033i \(0.0755197\pi\)
−0.971987 + 0.235033i \(0.924480\pi\)
\(522\) 2568.11 4033.52i 0.215331 0.338204i
\(523\) −7113.75 + 7113.75i −0.594766 + 0.594766i −0.938915 0.344149i \(-0.888167\pi\)
0.344149 + 0.938915i \(0.388167\pi\)
\(524\) −499.673 865.459i −0.0416571 0.0721522i
\(525\) 0 0
\(526\) 7461.77 12924.2i 0.618534 1.07133i
\(527\) 842.789 + 3145.33i 0.0696631 + 0.259986i
\(528\) −3796.34 5176.08i −0.312906 0.426629i
\(529\) 18418.6 10634.0i 1.51382 0.874004i
\(530\) 0 0
\(531\) 11268.0 2501.25i 0.920886 0.204416i
\(532\) 900.468 + 900.468i 0.0733839 + 0.0733839i
\(533\) −2584.77 + 9646.49i −0.210054 + 0.783932i
\(534\) −4081.20 3274.60i −0.330732 0.265367i
\(535\) 0 0
\(536\) 12711.9 + 7339.23i 1.02439 + 0.591430i
\(537\) −7243.86 3186.21i −0.582115 0.256043i
\(538\) 7238.77 + 1939.62i 0.580084 + 0.155433i
\(539\) −5613.13 −0.448562
\(540\) 0 0
\(541\) −1631.46 −0.129652 −0.0648261 0.997897i \(-0.520649\pi\)
−0.0648261 + 0.997897i \(0.520649\pi\)
\(542\) −14167.0 3796.04i −1.12274 0.300837i
\(543\) −9634.11 4237.56i −0.761398 0.334901i
\(544\) 2896.85 + 1672.50i 0.228311 + 0.131816i
\(545\) 0 0
\(546\) 7187.79 + 5767.22i 0.563387 + 0.452040i
\(547\) 4021.44 15008.2i 0.314341 1.17314i −0.610260 0.792201i \(-0.708935\pi\)
0.924601 0.380936i \(-0.124398\pi\)
\(548\) −2820.15 2820.15i −0.219838 0.219838i
\(549\) 6500.53 20636.5i 0.505348 1.60427i
\(550\) 0 0
\(551\) 2019.63 1166.03i 0.156151 0.0901538i
\(552\) −13816.8 18838.4i −1.06536 1.45256i
\(553\) −2262.27 8442.92i −0.173963 0.649239i
\(554\) 1280.04 2217.10i 0.0981658 0.170028i
\(555\) 0 0
\(556\) −3305.59 5725.45i −0.252137 0.436714i
\(557\) 1370.40 1370.40i 0.104247 0.104247i −0.653059 0.757307i \(-0.726515\pi\)
0.757307 + 0.653059i \(0.226515\pi\)
\(558\) −7533.08 326.864i −0.571507 0.0247979i
\(559\) 20816.6i 1.57504i
\(560\) 0 0
\(561\) −3421.97 + 4264.87i −0.257533 + 0.320968i
\(562\) 13861.4 3714.16i 1.04041 0.278776i
\(563\) −716.566 + 192.003i −0.0536406 + 0.0143730i −0.285540 0.958367i \(-0.592173\pi\)
0.231899 + 0.972740i \(0.425506\pi\)
\(564\) 1498.10 + 3850.82i 0.111847 + 0.287498i
\(565\) 0 0
\(566\) 12684.9i 0.942022i
\(567\) 9796.34 + 3559.59i 0.725586 + 0.263648i
\(568\) −11397.7 + 11397.7i −0.841965 + 0.841965i
\(569\) 1596.11 + 2764.54i 0.117596 + 0.203683i 0.918815 0.394689i \(-0.129148\pi\)
−0.801218 + 0.598372i \(0.795814\pi\)
\(570\) 0 0
\(571\) 5375.08 9309.91i 0.393941 0.682325i −0.599025 0.800730i \(-0.704445\pi\)
0.992965 + 0.118405i \(0.0377783\pi\)
\(572\) 1771.83 + 6612.57i 0.129517 + 0.483366i
\(573\) 6479.65 710.522i 0.472410 0.0518019i
\(574\) −4948.84 + 2857.21i −0.359861 + 0.207766i
\(575\) 0 0
\(576\) −10564.9 + 9686.21i −0.764244 + 0.700680i
\(577\) −6620.53 6620.53i −0.477671 0.477671i 0.426715 0.904386i \(-0.359671\pi\)
−0.904386 + 0.426715i \(0.859671\pi\)
\(578\) 2443.94 9120.90i 0.175873 0.656366i
\(579\) −2291.90 + 14904.1i −0.164504 + 1.06976i
\(580\) 0 0
\(581\) −2645.95 1527.64i −0.188937 0.109083i
\(582\) −11205.8 + 8218.74i −0.798100 + 0.585357i
\(583\) −3152.72 844.769i −0.223966 0.0600116i
\(584\) 3177.28 0.225132
\(585\) 0 0
\(586\) −2279.09 −0.160663
\(587\) 9951.28 + 2666.44i 0.699716 + 0.187488i 0.591103 0.806596i \(-0.298693\pi\)
0.108613 + 0.994084i \(0.465359\pi\)
\(588\) 238.270 + 2172.92i 0.0167111 + 0.152398i
\(589\) −3184.73 1838.71i −0.222792 0.128629i
\(590\) 0 0
\(591\) −10798.5 + 4200.97i −0.751590 + 0.292394i
\(592\) −2778.73 + 10370.4i −0.192914 + 0.719966i
\(593\) 670.349 + 670.349i 0.0464215 + 0.0464215i 0.729936 0.683515i \(-0.239550\pi\)
−0.683515 + 0.729936i \(0.739550\pi\)
\(594\) −7038.64 10524.8i −0.486194 0.727003i
\(595\) 0 0
\(596\) 1252.66 723.226i 0.0860925 0.0497055i
\(597\) −7604.89 + 17289.7i −0.521352 + 1.18530i
\(598\) −5870.41 21908.7i −0.401436 1.49818i
\(599\) 273.430 473.594i 0.0186511 0.0323047i −0.856549 0.516065i \(-0.827396\pi\)
0.875200 + 0.483761i \(0.160729\pi\)
\(600\) 0 0
\(601\) −536.667 929.535i −0.0364245 0.0630890i 0.847238 0.531213i \(-0.178264\pi\)
−0.883663 + 0.468124i \(0.844930\pi\)
\(602\) 8422.50 8422.50i 0.570225 0.570225i
\(603\) 13596.3 + 8656.61i 0.918213 + 0.584617i
\(604\) 6067.11i 0.408721i
\(605\) 0 0
\(606\) 12153.0 + 1868.85i 0.814658 + 0.125275i
\(607\) −9826.68 + 2633.05i −0.657089 + 0.176066i −0.571932 0.820301i \(-0.693806\pi\)
−0.0851568 + 0.996368i \(0.527139\pi\)
\(608\) −3648.87 + 977.713i −0.243390 + 0.0652163i
\(609\) −5836.63 897.536i −0.388361 0.0597209i
\(610\) 0 0
\(611\) 14583.2i 0.965586i
\(612\) 1796.25 + 1143.65i 0.118642 + 0.0755384i
\(613\) 10740.6 10740.6i 0.707681 0.707681i −0.258366 0.966047i \(-0.583184\pi\)
0.966047 + 0.258366i \(0.0831840\pi\)
\(614\) 531.028 + 919.767i 0.0349031 + 0.0604540i
\(615\) 0 0
\(616\) −7119.97 + 12332.2i −0.465701 + 0.806618i
\(617\) 5191.49 + 19374.9i 0.338738 + 1.26419i 0.899759 + 0.436387i \(0.143742\pi\)
−0.561021 + 0.827802i \(0.689591\pi\)
\(618\) −410.888 + 934.157i −0.0267449 + 0.0608047i
\(619\) −21899.4 + 12643.6i −1.42199 + 0.820987i −0.996469 0.0839615i \(-0.973243\pi\)
−0.425522 + 0.904948i \(0.639909\pi\)
\(620\) 0 0
\(621\) −14261.0 21324.3i −0.921533 1.37796i
\(622\) 7936.44 + 7936.44i 0.511611 + 0.511611i
\(623\) −1672.49 + 6241.82i −0.107555 + 0.401401i
\(624\) −8222.36 + 3198.78i −0.527497 + 0.205214i
\(625\) 0 0
\(626\) 9113.26 + 5261.54i 0.581852 + 0.335932i
\(627\) −673.099 6138.36i −0.0428724 0.390977i
\(628\) −4259.91 1141.44i −0.270683 0.0725293i
\(629\) 9145.54 0.579740
\(630\) 0 0
\(631\) −12431.8 −0.784313 −0.392156 0.919899i \(-0.628271\pi\)
−0.392156 + 0.919899i \(0.628271\pi\)
\(632\) 14519.7 + 3890.53i 0.913862 + 0.244869i
\(633\) 7296.65 5351.64i 0.458161 0.336033i
\(634\) 19115.2 + 11036.1i 1.19741 + 0.691327i
\(635\) 0 0
\(636\) −193.193 + 1256.32i −0.0120450 + 0.0783277i
\(637\) −1996.79 + 7452.11i −0.124200 + 0.463521i
\(638\) 5072.43 + 5072.43i 0.314764 + 0.314764i
\(639\) −13046.4 + 11961.3i −0.807679 + 0.740503i
\(640\) 0 0
\(641\) 19099.7 11027.2i 1.17690 0.679484i 0.221605 0.975136i \(-0.428870\pi\)
0.955296 + 0.295652i \(0.0955370\pi\)
\(642\) 6877.18 754.113i 0.422774 0.0463590i
\(643\) −1494.46 5577.39i −0.0916572 0.342069i 0.904834 0.425764i \(-0.139995\pi\)
−0.996491 + 0.0836947i \(0.973328\pi\)
\(644\) −3968.28 + 6873.27i −0.242814 + 0.420566i
\(645\) 0 0
\(646\) −849.141 1470.76i −0.0517167 0.0895760i
\(647\) −19898.4 + 19898.4i −1.20910 + 1.20910i −0.237779 + 0.971319i \(0.576419\pi\)
−0.971319 + 0.237779i \(0.923581\pi\)
\(648\) −13725.0 + 11529.3i −0.832053 + 0.698941i
\(649\) 17315.8i 1.04731i
\(650\) 0 0
\(651\) 3376.15 + 8678.30i 0.203259 + 0.522472i
\(652\) −6586.25 + 1764.78i −0.395610 + 0.106003i
\(653\) −5622.98 + 1506.67i −0.336974 + 0.0902920i −0.423338 0.905972i \(-0.639142\pi\)
0.0863641 + 0.996264i \(0.472475\pi\)
\(654\) 11083.4 13813.4i 0.662682 0.825914i
\(655\) 0 0
\(656\) 5470.84i 0.325610i
\(657\) 3485.64 + 151.244i 0.206983 + 0.00898109i
\(658\) −5900.45 + 5900.45i −0.349579 + 0.349579i
\(659\) 10262.3 + 17774.8i 0.606618 + 1.05069i 0.991794 + 0.127849i \(0.0408074\pi\)
−0.385176 + 0.922843i \(0.625859\pi\)
\(660\) 0 0
\(661\) −13997.3 + 24244.1i −0.823652 + 1.42661i 0.0792938 + 0.996851i \(0.474733\pi\)
−0.902945 + 0.429755i \(0.858600\pi\)
\(662\) 2669.18 + 9961.53i 0.156708 + 0.584843i
\(663\) 4444.81 + 6060.24i 0.260365 + 0.354993i
\(664\) 4550.35 2627.15i 0.265946 0.153544i
\(665\) 0 0
\(666\) −6362.64 + 20198.7i −0.370191 + 1.17520i
\(667\) 10277.2 + 10277.2i 0.596605 + 0.596605i
\(668\) −1520.37 + 5674.08i −0.0880610 + 0.328648i
\(669\) −21093.5 16924.6i −1.21902 0.978093i
\(670\) 0 0
\(671\) 28110.0 + 16229.3i 1.61725 + 0.933719i
\(672\) 8755.99 + 3851.32i 0.502633 + 0.221083i
\(673\) −20519.6 5498.22i −1.17530 0.314919i −0.382236 0.924065i \(-0.624846\pi\)
−0.793059 + 0.609145i \(0.791513\pi\)
\(674\) 2096.45 0.119810
\(675\) 0 0
\(676\) 2739.72 0.155878
\(677\) −4854.11 1300.65i −0.275567 0.0738379i 0.118389 0.992967i \(-0.462227\pi\)
−0.393956 + 0.919129i \(0.628894\pi\)
\(678\) 22402.4 + 9853.70i 1.26897 + 0.558155i
\(679\) 14862.7 + 8580.98i 0.840027 + 0.484990i
\(680\) 0 0
\(681\) 9464.37 + 7593.86i 0.532563 + 0.427309i
\(682\) 2927.71 10926.4i 0.164381 0.613478i
\(683\) −1391.88 1391.88i −0.0779778 0.0779778i 0.667042 0.745020i \(-0.267560\pi\)
−0.745020 + 0.667042i \(0.767560\pi\)
\(684\) −2347.67 + 521.132i −0.131236 + 0.0291315i
\(685\) 0 0
\(686\) −13285.8 + 7670.56i −0.739438 + 0.426915i
\(687\) 10148.9 + 13837.5i 0.563617 + 0.768460i
\(688\) 2951.44 + 11014.9i 0.163550 + 0.610378i
\(689\) −2243.06 + 3885.10i −0.124026 + 0.214819i
\(690\) 0 0
\(691\) 1846.79 + 3198.73i 0.101672 + 0.176100i 0.912373 0.409359i \(-0.134248\pi\)
−0.810702 + 0.585459i \(0.800914\pi\)
\(692\) −775.993 + 775.993i −0.0426284 + 0.0426284i
\(693\) −8398.00 + 13190.1i −0.460337 + 0.723015i
\(694\) 1338.22i 0.0731961i
\(695\) 0 0
\(696\) 6355.49 7920.96i 0.346127 0.431384i
\(697\) −4501.49 + 1206.17i −0.244629 + 0.0655480i
\(698\) −22325.0 + 5981.98i −1.21062 + 0.324386i
\(699\) −3678.62 9455.78i −0.199053 0.511660i
\(700\) 0 0
\(701\) 25198.2i 1.35766i 0.734294 + 0.678831i \(0.237513\pi\)
−0.734294 + 0.678831i \(0.762487\pi\)
\(702\) −16476.9 + 5600.59i −0.885869 + 0.301112i
\(703\) −7303.21 + 7303.21i −0.391815 + 0.391815i
\(704\) −10751.4 18621.9i −0.575578 0.996931i
\(705\) 0 0
\(706\) 10547.1 18268.0i 0.562243 0.973834i
\(707\) −3930.18 14667.6i −0.209066 0.780244i
\(708\) 6703.20 735.035i 0.355821 0.0390174i
\(709\) −215.222 + 124.258i −0.0114003 + 0.00658198i −0.505689 0.862716i \(-0.668762\pi\)
0.494289 + 0.869298i \(0.335428\pi\)
\(710\) 0 0
\(711\) 15743.6 + 4959.26i 0.830423 + 0.261585i
\(712\) −7858.07 7858.07i −0.413615 0.413615i
\(713\) 5931.82 22137.8i 0.311568 1.16279i
\(714\) −653.612 + 4250.40i −0.0342589 + 0.222783i
\(715\) 0 0
\(716\) −4003.97 2311.70i −0.208988 0.120659i
\(717\) −17121.3 + 12557.4i −0.891780 + 0.654066i
\(718\) −14445.3 3870.60i −0.750825 0.201183i
\(719\) −5173.80 −0.268359 −0.134180 0.990957i \(-0.542840\pi\)
−0.134180 + 0.990957i \(0.542840\pi\)
\(720\) 0 0
\(721\) 1260.32 0.0650997
\(722\) −12909.0 3458.94i −0.665404 0.178294i
\(723\) −2682.73 24465.3i −0.137997 1.25847i
\(724\) −5325.16 3074.48i −0.273354 0.157821i
\(725\) 0 0
\(726\) 3341.55 1299.98i 0.170822 0.0664554i
\(727\) 5344.55 19946.1i 0.272653 1.01755i −0.684745 0.728782i \(-0.740087\pi\)
0.957398 0.288771i \(-0.0932468\pi\)
\(728\) 13839.6 + 13839.6i 0.704573 + 0.704573i
\(729\) −15605.9 + 11994.9i −0.792860 + 0.609404i
\(730\) 0 0
\(731\) 8412.53 4856.98i 0.425648 0.245748i
\(732\) 5089.35 11570.7i 0.256978 0.584241i
\(733\) 5458.69 + 20372.1i 0.275063 + 1.02655i 0.955799 + 0.294021i \(0.0949934\pi\)
−0.680736 + 0.732529i \(0.738340\pi\)
\(734\) −3572.53 + 6187.80i −0.179652 + 0.311166i
\(735\) 0 0
\(736\) −11771.6 20389.0i −0.589546 1.02112i
\(737\) −17098.2 + 17098.2i −0.854575 + 0.854575i
\(738\) 467.797 10781.1i 0.0233331 0.537747i
\(739\) 3372.43i 0.167871i −0.996471 0.0839356i \(-0.973251\pi\)
0.996471 0.0839356i \(-0.0267490\pi\)
\(740\) 0 0
\(741\) −8388.86 1290.01i −0.415887 0.0639537i
\(742\) −2479.49 + 664.378i −0.122675 + 0.0328707i
\(743\) 19508.9 5227.39i 0.963273 0.258108i 0.257288 0.966335i \(-0.417171\pi\)
0.705985 + 0.708227i \(0.250504\pi\)
\(744\) −15828.0 2433.98i −0.779950 0.119938i
\(745\) 0 0
\(746\) 6829.76i 0.335195i
\(747\) 5117.02 2665.51i 0.250632 0.130557i
\(748\) −2258.91 + 2258.91i −0.110420 + 0.110420i
\(749\) −4272.01 7399.34i −0.208406 0.360970i
\(750\) 0 0
\(751\) −3536.97 + 6126.21i −0.171859 + 0.297668i −0.939070 0.343727i \(-0.888311\pi\)
0.767211 + 0.641395i \(0.221644\pi\)
\(752\) −2067.65 7716.59i −0.100265 0.374195i
\(753\) 7186.47 16338.5i 0.347795 0.790713i
\(754\) 8538.70 4929.82i 0.412415 0.238108i
\(755\) 0 0
\(756\) 5462.55 + 2691.08i 0.262792 + 0.129462i
\(757\) −6425.25 6425.25i −0.308494 0.308494i 0.535831 0.844325i \(-0.319998\pi\)
−0.844325 + 0.535831i \(0.819998\pi\)
\(758\) 4888.87 18245.5i 0.234263 0.874283i
\(759\) 35866.9 13953.5i 1.71527 0.667297i
\(760\) 0 0
\(761\) −11481.3 6628.75i −0.546909 0.315758i 0.200965 0.979598i \(-0.435592\pi\)
−0.747875 + 0.663840i \(0.768926\pi\)
\(762\) 378.781 + 3454.31i 0.0180076 + 0.164221i
\(763\) −21126.3 5660.79i −1.00239 0.268590i
\(764\) 3808.30 0.180340
\(765\) 0 0
\(766\) 14987.5 0.706947
\(767\) 22988.8 + 6159.84i 1.08224 + 0.289986i
\(768\) −16368.4 + 12005.2i −0.769067 + 0.564063i
\(769\) −19228.5 11101.6i −0.901686 0.520589i −0.0239392 0.999713i \(-0.507621\pi\)
−0.877747 + 0.479125i \(0.840954\pi\)
\(770\) 0 0
\(771\) 1876.23 12201.0i 0.0876406 0.569922i
\(772\) −2280.14 + 8509.60i −0.106301 + 0.396719i
\(773\) 13738.9 + 13738.9i 0.639265 + 0.639265i 0.950374 0.311109i \(-0.100700\pi\)
−0.311109 + 0.950374i \(0.600700\pi\)
\(774\) 4874.38 + 21958.9i 0.226364 + 1.01976i
\(775\) 0 0
\(776\) −25560.0 + 14757.1i −1.18241 + 0.682666i
\(777\) 25997.3 2850.72i 1.20032 0.131620i
\(778\) 2397.34 + 8947.01i 0.110474 + 0.412296i
\(779\) 2631.49 4557.88i 0.121031 0.209632i
\(780\) 0