Properties

Label 225.4.e.f.76.9
Level $225$
Weight $4$
Character 225.76
Analytic conductor $13.275$
Analytic rank $0$
Dimension $24$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Newspace parameters

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

Newform invariants

Self dual: no
Analytic conductor: \(13.2754297513\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(12\) over \(\Q(\zeta_{3})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 76.9
Character \(\chi\) \(=\) 225.76
Dual form 225.4.e.f.151.9

$q$-expansion

\(f(q)\) \(=\) \(q+(1.48830 + 2.57780i) q^{2} +(-5.14295 + 0.741698i) q^{3} +(-0.430049 + 0.744867i) q^{4} +(-9.56618 - 12.1536i) q^{6} +(-12.4826 - 21.6204i) q^{7} +21.2526 q^{8} +(25.8998 - 7.62902i) q^{9} +O(q^{10})\) \(q+(1.48830 + 2.57780i) q^{2} +(-5.14295 + 0.741698i) q^{3} +(-0.430049 + 0.744867i) q^{4} +(-9.56618 - 12.1536i) q^{6} +(-12.4826 - 21.6204i) q^{7} +21.2526 q^{8} +(25.8998 - 7.62902i) q^{9} +(31.6260 + 54.7779i) q^{11} +(1.65925 - 4.14978i) q^{12} +(-45.2407 + 78.3591i) q^{13} +(37.1555 - 64.3552i) q^{14} +(35.0705 + 60.7439i) q^{16} +10.2256 q^{17} +(58.2126 + 55.4103i) q^{18} +24.7438 q^{19} +(80.2329 + 101.934i) q^{21} +(-94.1377 + 163.051i) q^{22} +(-1.34587 + 2.33111i) q^{23} +(-109.301 + 15.7630i) q^{24} -269.326 q^{26} +(-127.543 + 58.4454i) q^{27} +21.4725 q^{28} +(54.8481 + 94.9997i) q^{29} +(34.7253 - 60.1459i) q^{31} +(-19.3803 + 33.5677i) q^{32} +(-203.279 - 258.263i) q^{33} +(15.2187 + 26.3595i) q^{34} +(-5.45557 + 22.5727i) q^{36} +23.0916 q^{37} +(36.8262 + 63.7848i) q^{38} +(174.551 - 436.552i) q^{39} +(-133.285 + 230.856i) q^{41} +(-143.357 + 358.533i) q^{42} +(235.348 + 407.635i) q^{43} -54.4030 q^{44} -8.01221 q^{46} +(218.609 + 378.643i) q^{47} +(-225.419 - 286.391i) q^{48} +(-140.129 + 242.710i) q^{49} +(-52.5896 + 7.58429i) q^{51} +(-38.9114 - 67.3966i) q^{52} +114.841 q^{53} +(-340.482 - 241.796i) q^{54} +(-265.286 - 459.490i) q^{56} +(-127.256 + 18.3524i) q^{57} +(-163.260 + 282.775i) q^{58} +(237.113 - 410.692i) q^{59} +(166.782 + 288.875i) q^{61} +206.726 q^{62} +(-488.238 - 464.734i) q^{63} +445.754 q^{64} +(363.210 - 908.386i) q^{66} +(-38.0819 + 65.9599i) q^{67} +(-4.39750 + 7.61669i) q^{68} +(5.19275 - 12.9870i) q^{69} -658.251 q^{71} +(550.437 - 162.136i) q^{72} -549.827 q^{73} +(34.3671 + 59.5256i) q^{74} +(-10.6411 + 18.4309i) q^{76} +(789.547 - 1367.54i) q^{77} +(1385.13 - 199.758i) q^{78} +(85.7122 + 148.458i) q^{79} +(612.596 - 395.180i) q^{81} -793.470 q^{82} +(-166.418 - 288.244i) q^{83} +(-110.432 + 15.9261i) q^{84} +(-700.536 + 1213.36i) q^{86} +(-352.542 - 447.897i) q^{87} +(672.134 + 1164.17i) q^{88} -621.568 q^{89} +2258.88 q^{91} +(-1.15758 - 2.00499i) q^{92} +(-133.980 + 335.083i) q^{93} +(-650.711 + 1127.06i) q^{94} +(74.7748 - 187.011i) q^{96} +(-759.010 - 1314.64i) q^{97} -834.211 q^{98} +(1237.01 + 1177.46i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24 q + 4 q^{2} + q^{3} - 48 q^{4} - 13 q^{6} - 6 q^{7} - 90 q^{8} - 61 q^{9} + O(q^{10}) \) \( 24 q + 4 q^{2} + q^{3} - 48 q^{4} - 13 q^{6} - 6 q^{7} - 90 q^{8} - 61 q^{9} - 29 q^{11} + 77 q^{12} - 24 q^{13} + 69 q^{14} - 192 q^{16} - 158 q^{17} - 125 q^{18} - 150 q^{19} - 60 q^{21} + 18 q^{22} + 318 q^{23} + 342 q^{24} - 308 q^{26} + 394 q^{27} + 192 q^{28} - 106 q^{29} - 60 q^{31} + 914 q^{32} + 80 q^{33} + 108 q^{34} + 1303 q^{36} - 168 q^{37} + 640 q^{38} - 410 q^{39} + 353 q^{41} - 1521 q^{42} + 426 q^{43} + 1142 q^{44} + 540 q^{46} + 1210 q^{47} - 2680 q^{48} - 666 q^{49} - 1369 q^{51} + 75 q^{52} - 896 q^{53} - 2128 q^{54} + 570 q^{56} - 1544 q^{57} - 594 q^{58} - 482 q^{59} - 402 q^{61} - 5088 q^{62} + 1038 q^{63} + 1950 q^{64} + 2041 q^{66} + 201 q^{67} + 3437 q^{68} + 2856 q^{69} - 1888 q^{71} + 5493 q^{72} - 906 q^{73} - 10 q^{74} + 462 q^{76} + 2652 q^{77} + 4589 q^{78} - 258 q^{79} + 3071 q^{81} + 1746 q^{82} + 3012 q^{83} - 2703 q^{84} - 1952 q^{86} - 2708 q^{87} + 216 q^{88} - 1476 q^{89} - 1236 q^{91} + 5232 q^{92} - 3024 q^{93} - 63 q^{94} - 10424 q^{96} + 318 q^{97} - 15022 q^{98} - 1697 q^{99} + O(q^{100}) \)

Character values

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

\(n\) \(101\) \(127\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.48830 + 2.57780i 0.526192 + 0.911391i 0.999534 + 0.0305128i \(0.00971403\pi\)
−0.473342 + 0.880879i \(0.656953\pi\)
\(3\) −5.14295 + 0.741698i −0.989760 + 0.142740i
\(4\) −0.430049 + 0.744867i −0.0537561 + 0.0931084i
\(5\) 0 0
\(6\) −9.56618 12.1536i −0.650896 0.826950i
\(7\) −12.4826 21.6204i −0.673995 1.16739i −0.976762 0.214329i \(-0.931244\pi\)
0.302767 0.953065i \(-0.402090\pi\)
\(8\) 21.2526 0.939240
\(9\) 25.8998 7.62902i 0.959251 0.282556i
\(10\) 0 0
\(11\) 31.6260 + 54.7779i 0.866873 + 1.50147i 0.865175 + 0.501470i \(0.167207\pi\)
0.00169771 + 0.999999i \(0.499460\pi\)
\(12\) 1.65925 4.14978i 0.0399154 0.0998281i
\(13\) −45.2407 + 78.3591i −0.965193 + 1.67176i −0.256096 + 0.966651i \(0.582436\pi\)
−0.709097 + 0.705111i \(0.750897\pi\)
\(14\) 37.1555 64.3552i 0.709301 1.22855i
\(15\) 0 0
\(16\) 35.0705 + 60.7439i 0.547977 + 0.949123i
\(17\) 10.2256 0.145886 0.0729431 0.997336i \(-0.476761\pi\)
0.0729431 + 0.997336i \(0.476761\pi\)
\(18\) 58.2126 + 55.4103i 0.762270 + 0.725574i
\(19\) 24.7438 0.298770 0.149385 0.988779i \(-0.452271\pi\)
0.149385 + 0.988779i \(0.452271\pi\)
\(20\) 0 0
\(21\) 80.2329 + 101.934i 0.833727 + 1.05923i
\(22\) −94.1377 + 163.051i −0.912283 + 1.58012i
\(23\) −1.34587 + 2.33111i −0.0122014 + 0.0211335i −0.872062 0.489396i \(-0.837217\pi\)
0.859860 + 0.510530i \(0.170551\pi\)
\(24\) −109.301 + 15.7630i −0.929622 + 0.134067i
\(25\) 0 0
\(26\) −269.326 −2.03151
\(27\) −127.543 + 58.4454i −0.909096 + 0.416586i
\(28\) 21.4725 0.144925
\(29\) 54.8481 + 94.9997i 0.351208 + 0.608310i 0.986461 0.163994i \(-0.0524376\pi\)
−0.635253 + 0.772304i \(0.719104\pi\)
\(30\) 0 0
\(31\) 34.7253 60.1459i 0.201189 0.348469i −0.747723 0.664011i \(-0.768853\pi\)
0.948912 + 0.315542i \(0.102186\pi\)
\(32\) −19.3803 + 33.5677i −0.107062 + 0.185437i
\(33\) −203.279 258.263i −1.07232 1.36236i
\(34\) 15.2187 + 26.3595i 0.0767642 + 0.132959i
\(35\) 0 0
\(36\) −5.45557 + 22.5727i −0.0252573 + 0.104503i
\(37\) 23.0916 0.102601 0.0513005 0.998683i \(-0.483663\pi\)
0.0513005 + 0.998683i \(0.483663\pi\)
\(38\) 36.8262 + 63.7848i 0.157210 + 0.272296i
\(39\) 174.551 436.552i 0.716682 1.79242i
\(40\) 0 0
\(41\) −133.285 + 230.856i −0.507698 + 0.879359i 0.492262 + 0.870447i \(0.336170\pi\)
−0.999960 + 0.00891175i \(0.997163\pi\)
\(42\) −143.357 + 358.533i −0.526676 + 1.31721i
\(43\) 235.348 + 407.635i 0.834657 + 1.44567i 0.894309 + 0.447450i \(0.147668\pi\)
−0.0596515 + 0.998219i \(0.518999\pi\)
\(44\) −54.4030 −0.186399
\(45\) 0 0
\(46\) −8.01221 −0.0256812
\(47\) 218.609 + 378.643i 0.678456 + 1.17512i 0.975446 + 0.220240i \(0.0706841\pi\)
−0.296989 + 0.954881i \(0.595983\pi\)
\(48\) −225.419 286.391i −0.677843 0.861187i
\(49\) −140.129 + 242.710i −0.408538 + 0.707608i
\(50\) 0 0
\(51\) −52.5896 + 7.58429i −0.144392 + 0.0208238i
\(52\) −38.9114 67.3966i −0.103770 0.179735i
\(53\) 114.841 0.297634 0.148817 0.988865i \(-0.452453\pi\)
0.148817 + 0.988865i \(0.452453\pi\)
\(54\) −340.482 241.796i −0.858032 0.609338i
\(55\) 0 0
\(56\) −265.286 459.490i −0.633043 1.09646i
\(57\) −127.256 + 18.3524i −0.295710 + 0.0426463i
\(58\) −163.260 + 282.775i −0.369606 + 0.640176i
\(59\) 237.113 410.692i 0.523212 0.906229i −0.476423 0.879216i \(-0.658067\pi\)
0.999635 0.0270133i \(-0.00859965\pi\)
\(60\) 0 0
\(61\) 166.782 + 288.875i 0.350070 + 0.606338i 0.986261 0.165193i \(-0.0528246\pi\)
−0.636192 + 0.771531i \(0.719491\pi\)
\(62\) 206.726 0.423455
\(63\) −488.238 464.734i −0.976384 0.929381i
\(64\) 445.754 0.870613
\(65\) 0 0
\(66\) 363.210 908.386i 0.677396 1.69416i
\(67\) −38.0819 + 65.9599i −0.0694395 + 0.120273i −0.898655 0.438657i \(-0.855454\pi\)
0.829215 + 0.558929i \(0.188788\pi\)
\(68\) −4.39750 + 7.61669i −0.00784228 + 0.0135832i
\(69\) 5.19275 12.9870i 0.00905991 0.0226588i
\(70\) 0 0
\(71\) −658.251 −1.10028 −0.550141 0.835072i \(-0.685426\pi\)
−0.550141 + 0.835072i \(0.685426\pi\)
\(72\) 550.437 162.136i 0.900967 0.265388i
\(73\) −549.827 −0.881540 −0.440770 0.897620i \(-0.645294\pi\)
−0.440770 + 0.897620i \(0.645294\pi\)
\(74\) 34.3671 + 59.5256i 0.0539878 + 0.0935097i
\(75\) 0 0
\(76\) −10.6411 + 18.4309i −0.0160607 + 0.0278180i
\(77\) 789.547 1367.54i 1.16854 2.02396i
\(78\) 1385.13 199.758i 2.01070 0.289977i
\(79\) 85.7122 + 148.458i 0.122068 + 0.211428i 0.920583 0.390547i \(-0.127714\pi\)
−0.798515 + 0.601975i \(0.794381\pi\)
\(80\) 0 0
\(81\) 612.596 395.180i 0.840324 0.542085i
\(82\) −793.470 −1.06859
\(83\) −166.418 288.244i −0.220081 0.381191i 0.734752 0.678336i \(-0.237299\pi\)
−0.954832 + 0.297145i \(0.903965\pi\)
\(84\) −110.432 + 15.9261i −0.143441 + 0.0206866i
\(85\) 0 0
\(86\) −700.536 + 1213.36i −0.878380 + 1.52140i
\(87\) −352.542 447.897i −0.434442 0.551950i
\(88\) 672.134 + 1164.17i 0.814202 + 1.41024i
\(89\) −621.568 −0.740293 −0.370146 0.928973i \(-0.620692\pi\)
−0.370146 + 0.928973i \(0.620692\pi\)
\(90\) 0 0
\(91\) 2258.88 2.60214
\(92\) −1.15758 2.00499i −0.00131181 0.00227211i
\(93\) −133.980 + 335.083i −0.149388 + 0.373618i
\(94\) −650.711 + 1127.06i −0.713997 + 1.23668i
\(95\) 0 0
\(96\) 74.7748 187.011i 0.0794965 0.198820i
\(97\) −759.010 1314.64i −0.794492 1.37610i −0.923161 0.384413i \(-0.874404\pi\)
0.128669 0.991688i \(-0.458930\pi\)
\(98\) −834.211 −0.859878
\(99\) 1237.01 + 1177.46i 1.25580 + 1.19534i
\(100\) 0 0
\(101\) −42.5888 73.7660i −0.0419579 0.0726732i 0.844284 0.535896i \(-0.180026\pi\)
−0.886242 + 0.463223i \(0.846693\pi\)
\(102\) −97.8196 124.278i −0.0949567 0.120641i
\(103\) 692.546 1199.52i 0.662510 1.14750i −0.317444 0.948277i \(-0.602824\pi\)
0.979954 0.199224i \(-0.0638422\pi\)
\(104\) −961.481 + 1665.33i −0.906547 + 1.57019i
\(105\) 0 0
\(106\) 170.917 + 296.038i 0.156613 + 0.271262i
\(107\) 1051.56 0.950077 0.475039 0.879965i \(-0.342434\pi\)
0.475039 + 0.879965i \(0.342434\pi\)
\(108\) 11.3155 120.137i 0.0100818 0.107039i
\(109\) 89.9209 0.0790170 0.0395085 0.999219i \(-0.487421\pi\)
0.0395085 + 0.999219i \(0.487421\pi\)
\(110\) 0 0
\(111\) −118.759 + 17.1270i −0.101550 + 0.0146452i
\(112\) 875.539 1516.48i 0.738667 1.27941i
\(113\) 216.322 374.680i 0.180087 0.311920i −0.761823 0.647785i \(-0.775695\pi\)
0.941910 + 0.335865i \(0.109029\pi\)
\(114\) −236.704 300.728i −0.194468 0.247068i
\(115\) 0 0
\(116\) −94.3495 −0.0755184
\(117\) −573.919 + 2374.63i −0.453495 + 1.87636i
\(118\) 1411.58 1.10124
\(119\) −127.641 221.081i −0.0983266 0.170307i
\(120\) 0 0
\(121\) −1334.91 + 2312.13i −1.00294 + 1.73714i
\(122\) −496.442 + 859.863i −0.368408 + 0.638101i
\(123\) 514.252 1286.14i 0.376980 0.942823i
\(124\) 29.8672 + 51.7314i 0.0216302 + 0.0374647i
\(125\) 0 0
\(126\) 471.351 1950.24i 0.333264 1.37890i
\(127\) 2059.97 1.43931 0.719657 0.694330i \(-0.244299\pi\)
0.719657 + 0.694330i \(0.244299\pi\)
\(128\) 818.456 + 1417.61i 0.565171 + 0.978906i
\(129\) −1512.73 1921.89i −1.03247 1.31173i
\(130\) 0 0
\(131\) 936.224 1621.59i 0.624414 1.08152i −0.364240 0.931305i \(-0.618671\pi\)
0.988654 0.150212i \(-0.0479956\pi\)
\(132\) 279.792 40.3506i 0.184490 0.0266066i
\(133\) −308.866 534.972i −0.201369 0.348782i
\(134\) −226.709 −0.146154
\(135\) 0 0
\(136\) 217.320 0.137022
\(137\) −1120.99 1941.61i −0.699071 1.21083i −0.968789 0.247888i \(-0.920264\pi\)
0.269717 0.962940i \(-0.413070\pi\)
\(138\) 41.2064 5.94264i 0.0254182 0.00366573i
\(139\) 132.227 229.023i 0.0806857 0.139752i −0.822859 0.568246i \(-0.807622\pi\)
0.903545 + 0.428494i \(0.140956\pi\)
\(140\) 0 0
\(141\) −1405.13 1785.20i −0.839246 1.06625i
\(142\) −979.673 1696.84i −0.578960 1.00279i
\(143\) −5723.13 −3.34680
\(144\) 1371.73 + 1305.70i 0.793828 + 0.755613i
\(145\) 0 0
\(146\) −818.305 1417.35i −0.463859 0.803428i
\(147\) 540.656 1352.18i 0.303351 0.758677i
\(148\) −9.93053 + 17.2002i −0.00551543 + 0.00955301i
\(149\) −22.1989 + 38.4496i −0.0122054 + 0.0211404i −0.872064 0.489393i \(-0.837219\pi\)
0.859858 + 0.510533i \(0.170552\pi\)
\(150\) 0 0
\(151\) 609.223 + 1055.20i 0.328330 + 0.568685i 0.982181 0.187939i \(-0.0601808\pi\)
−0.653850 + 0.756624i \(0.726847\pi\)
\(152\) 525.870 0.280616
\(153\) 264.840 78.0111i 0.139941 0.0412211i
\(154\) 4700.32 2.45950
\(155\) 0 0
\(156\) 250.107 + 317.756i 0.128363 + 0.163082i
\(157\) −1793.39 + 3106.25i −0.911645 + 1.57902i −0.0999041 + 0.994997i \(0.531854\pi\)
−0.811741 + 0.584018i \(0.801480\pi\)
\(158\) −255.130 + 441.899i −0.128463 + 0.222504i
\(159\) −590.621 + 85.1773i −0.294587 + 0.0424843i
\(160\) 0 0
\(161\) 67.1996 0.0328948
\(162\) 1930.42 + 991.008i 0.936223 + 0.480623i
\(163\) 1138.29 0.546981 0.273490 0.961875i \(-0.411822\pi\)
0.273490 + 0.961875i \(0.411822\pi\)
\(164\) −114.638 198.559i −0.0545838 0.0945419i
\(165\) 0 0
\(166\) 495.357 857.984i 0.231609 0.401159i
\(167\) −112.979 + 195.685i −0.0523506 + 0.0906738i −0.891013 0.453977i \(-0.850005\pi\)
0.838663 + 0.544651i \(0.183338\pi\)
\(168\) 1705.16 + 2166.37i 0.783069 + 0.994874i
\(169\) −2994.94 5187.38i −1.36319 2.36112i
\(170\) 0 0
\(171\) 640.860 188.771i 0.286595 0.0844193i
\(172\) −404.845 −0.179472
\(173\) 318.937 + 552.415i 0.140164 + 0.242771i 0.927558 0.373679i \(-0.121904\pi\)
−0.787395 + 0.616449i \(0.788570\pi\)
\(174\) 629.905 1575.39i 0.274443 0.686378i
\(175\) 0 0
\(176\) −2218.28 + 3842.18i −0.950052 + 1.64554i
\(177\) −914.850 + 2288.03i −0.388499 + 0.971633i
\(178\) −925.077 1602.28i −0.389536 0.674697i
\(179\) −3726.05 −1.55586 −0.777928 0.628353i \(-0.783729\pi\)
−0.777928 + 0.628353i \(0.783729\pi\)
\(180\) 0 0
\(181\) −2524.11 −1.03655 −0.518275 0.855214i \(-0.673426\pi\)
−0.518275 + 0.855214i \(0.673426\pi\)
\(182\) 3361.88 + 5822.94i 1.36922 + 2.37157i
\(183\) −1072.01 1361.97i −0.433034 0.550161i
\(184\) −28.6032 + 49.5422i −0.0114601 + 0.0198494i
\(185\) 0 0
\(186\) −1063.18 + 153.328i −0.419119 + 0.0604439i
\(187\) 323.394 + 560.135i 0.126465 + 0.219044i
\(188\) −376.051 −0.145885
\(189\) 2855.67 + 2027.98i 1.09905 + 0.780496i
\(190\) 0 0
\(191\) 109.186 + 189.115i 0.0413634 + 0.0716435i 0.885966 0.463750i \(-0.153497\pi\)
−0.844603 + 0.535394i \(0.820163\pi\)
\(192\) −2292.49 + 330.614i −0.861698 + 0.124271i
\(193\) 942.571 1632.58i 0.351543 0.608890i −0.634977 0.772531i \(-0.718991\pi\)
0.986520 + 0.163641i \(0.0523239\pi\)
\(194\) 2259.26 3913.16i 0.836111 1.44819i
\(195\) 0 0
\(196\) −120.524 208.754i −0.0439229 0.0760766i
\(197\) −3145.83 −1.13772 −0.568861 0.822433i \(-0.692616\pi\)
−0.568861 + 0.822433i \(0.692616\pi\)
\(198\) −1194.22 + 4941.17i −0.428635 + 1.77350i
\(199\) −1725.22 −0.614562 −0.307281 0.951619i \(-0.599419\pi\)
−0.307281 + 0.951619i \(0.599419\pi\)
\(200\) 0 0
\(201\) 146.931 367.473i 0.0515608 0.128953i
\(202\) 126.769 219.571i 0.0441558 0.0764801i
\(203\) 1369.29 2371.68i 0.473425 0.819996i
\(204\) 16.9668 42.4339i 0.00582311 0.0145635i
\(205\) 0 0
\(206\) 4122.85 1.39443
\(207\) −17.0736 + 70.6430i −0.00573283 + 0.0237199i
\(208\) −6346.45 −2.11561
\(209\) 782.549 + 1355.41i 0.258995 + 0.448593i
\(210\) 0 0
\(211\) −291.383 + 504.690i −0.0950694 + 0.164665i −0.909638 0.415403i \(-0.863641\pi\)
0.814568 + 0.580068i \(0.196974\pi\)
\(212\) −49.3873 + 85.5413i −0.0159997 + 0.0277123i
\(213\) 3385.35 488.224i 1.08902 0.157054i
\(214\) 1565.03 + 2710.72i 0.499923 + 0.865892i
\(215\) 0 0
\(216\) −2710.61 + 1242.12i −0.853859 + 0.391274i
\(217\) −1733.84 −0.542400
\(218\) 133.829 + 231.798i 0.0415781 + 0.0720155i
\(219\) 2827.73 407.806i 0.872513 0.125831i
\(220\) 0 0
\(221\) −462.612 + 801.267i −0.140808 + 0.243887i
\(222\) −220.898 280.647i −0.0667826 0.0848459i
\(223\) 2832.72 + 4906.42i 0.850642 + 1.47336i 0.880630 + 0.473805i \(0.157120\pi\)
−0.0299878 + 0.999550i \(0.509547\pi\)
\(224\) 967.663 0.288637
\(225\) 0 0
\(226\) 1287.80 0.379041
\(227\) −1854.97 3212.91i −0.542374 0.939419i −0.998767 0.0496409i \(-0.984192\pi\)
0.456393 0.889778i \(-0.349141\pi\)
\(228\) 41.0563 102.681i 0.0119255 0.0298256i
\(229\) −1787.15 + 3095.43i −0.515712 + 0.893239i 0.484122 + 0.875001i \(0.339139\pi\)
−0.999834 + 0.0182383i \(0.994194\pi\)
\(230\) 0 0
\(231\) −3046.30 + 7618.77i −0.867670 + 2.17004i
\(232\) 1165.66 + 2018.99i 0.329869 + 0.571349i
\(233\) 4505.75 1.26687 0.633436 0.773795i \(-0.281644\pi\)
0.633436 + 0.773795i \(0.281644\pi\)
\(234\) −6975.48 + 2054.69i −1.94872 + 0.574015i
\(235\) 0 0
\(236\) 203.941 + 353.235i 0.0562517 + 0.0974308i
\(237\) −550.924 699.939i −0.150997 0.191839i
\(238\) 379.936 658.069i 0.103477 0.179228i
\(239\) 1145.81 1984.59i 0.310109 0.537124i −0.668277 0.743913i \(-0.732968\pi\)
0.978386 + 0.206789i \(0.0663012\pi\)
\(240\) 0 0
\(241\) 1128.08 + 1953.89i 0.301518 + 0.522245i 0.976480 0.215608i \(-0.0691733\pi\)
−0.674962 + 0.737853i \(0.735840\pi\)
\(242\) −7946.96 −2.11095
\(243\) −2857.44 + 2486.75i −0.754342 + 0.656482i
\(244\) −286.898 −0.0752736
\(245\) 0 0
\(246\) 4080.77 588.515i 1.05764 0.152530i
\(247\) −1119.43 + 1938.91i −0.288370 + 0.499472i
\(248\) 738.001 1278.26i 0.188964 0.327296i
\(249\) 1069.67 + 1358.99i 0.272238 + 0.345873i
\(250\) 0 0
\(251\) 3797.01 0.954841 0.477421 0.878675i \(-0.341572\pi\)
0.477421 + 0.878675i \(0.341572\pi\)
\(252\) 556.132 163.814i 0.139020 0.0409496i
\(253\) −170.258 −0.0423084
\(254\) 3065.85 + 5310.20i 0.757355 + 1.31178i
\(255\) 0 0
\(256\) −653.194 + 1131.37i −0.159471 + 0.276212i
\(257\) 2021.09 3500.63i 0.490553 0.849662i −0.509388 0.860537i \(-0.670128\pi\)
0.999941 + 0.0108747i \(0.00346159\pi\)
\(258\) 2702.87 6759.85i 0.652222 1.63120i
\(259\) −288.242 499.250i −0.0691525 0.119776i
\(260\) 0 0
\(261\) 2145.31 + 2042.03i 0.508779 + 0.484286i
\(262\) 5573.51 1.31425
\(263\) 3230.95 + 5596.18i 0.757525 + 1.31207i 0.944109 + 0.329633i \(0.106925\pi\)
−0.186584 + 0.982439i \(0.559742\pi\)
\(264\) −4320.21 5488.75i −1.00716 1.27958i
\(265\) 0 0
\(266\) 919.369 1592.39i 0.211918 0.367052i
\(267\) 3196.69 461.016i 0.732712 0.105669i
\(268\) −32.7542 56.7320i −0.00746560 0.0129308i
\(269\) 4397.95 0.996832 0.498416 0.866938i \(-0.333915\pi\)
0.498416 + 0.866938i \(0.333915\pi\)
\(270\) 0 0
\(271\) −2614.32 −0.586009 −0.293005 0.956111i \(-0.594655\pi\)
−0.293005 + 0.956111i \(0.594655\pi\)
\(272\) 358.616 + 621.141i 0.0799423 + 0.138464i
\(273\) −11617.3 + 1675.40i −2.57549 + 0.371429i
\(274\) 3336.73 5779.39i 0.735692 1.27426i
\(275\) 0 0
\(276\) 7.44047 + 9.45297i 0.00162269 + 0.00206160i
\(277\) 830.494 + 1438.46i 0.180143 + 0.312016i 0.941929 0.335812i \(-0.109011\pi\)
−0.761786 + 0.647828i \(0.775677\pi\)
\(278\) 787.170 0.169825
\(279\) 440.522 1822.69i 0.0945282 0.391116i
\(280\) 0 0
\(281\) −2504.38 4337.71i −0.531668 0.920876i −0.999317 0.0369615i \(-0.988232\pi\)
0.467649 0.883914i \(-0.345101\pi\)
\(282\) 2510.63 6279.06i 0.530162 1.32593i
\(283\) −136.204 + 235.913i −0.0286096 + 0.0495532i −0.879976 0.475019i \(-0.842441\pi\)
0.851366 + 0.524572i \(0.175775\pi\)
\(284\) 283.080 490.310i 0.0591469 0.102446i
\(285\) 0 0
\(286\) −8517.71 14753.1i −1.76106 3.05024i
\(287\) 6654.95 1.36874
\(288\) −245.857 + 1017.25i −0.0503030 + 0.208132i
\(289\) −4808.44 −0.978717
\(290\) 0 0
\(291\) 4878.61 + 6198.18i 0.982781 + 1.24860i
\(292\) 236.453 409.548i 0.0473882 0.0820787i
\(293\) 2448.54 4240.99i 0.488209 0.845602i −0.511699 0.859165i \(-0.670984\pi\)
0.999908 + 0.0135624i \(0.00431717\pi\)
\(294\) 4290.30 618.732i 0.851073 0.122739i
\(295\) 0 0
\(296\) 490.756 0.0963669
\(297\) −7235.18 5138.12i −1.41356 1.00385i
\(298\) −132.154 −0.0256896
\(299\) −121.776 210.922i −0.0235535 0.0407958i
\(300\) 0 0
\(301\) 5875.50 10176.7i 1.12511 1.94875i
\(302\) −1813.41 + 3140.91i −0.345529 + 0.598475i
\(303\) 273.744 + 347.786i 0.0519016 + 0.0659399i
\(304\) 867.779 + 1503.04i 0.163719 + 0.283569i
\(305\) 0 0
\(306\) 595.258 + 566.602i 0.111205 + 0.105851i
\(307\) 2095.63 0.389590 0.194795 0.980844i \(-0.437596\pi\)
0.194795 + 0.980844i \(0.437596\pi\)
\(308\) 679.088 + 1176.22i 0.125632 + 0.217601i
\(309\) −2672.04 + 6682.75i −0.491932 + 1.23032i
\(310\) 0 0
\(311\) 2525.57 4374.41i 0.460488 0.797589i −0.538497 0.842627i \(-0.681008\pi\)
0.998985 + 0.0450384i \(0.0143410\pi\)
\(312\) 3709.67 9277.85i 0.673136 1.68351i
\(313\) −2961.90 5130.16i −0.534876 0.926433i −0.999169 0.0407513i \(-0.987025\pi\)
0.464293 0.885682i \(-0.346308\pi\)
\(314\) −10676.4 −1.91880
\(315\) 0 0
\(316\) −147.442 −0.0262476
\(317\) 2355.68 + 4080.15i 0.417376 + 0.722916i 0.995675 0.0929092i \(-0.0296166\pi\)
−0.578299 + 0.815825i \(0.696283\pi\)
\(318\) −1098.59 1395.74i −0.193729 0.246129i
\(319\) −3469.25 + 6008.92i −0.608906 + 1.05466i
\(320\) 0 0
\(321\) −5408.12 + 779.941i −0.940349 + 0.135614i
\(322\) 100.013 + 173.227i 0.0173090 + 0.0299801i
\(323\) 253.020 0.0435864
\(324\) 30.9100 + 626.249i 0.00530006 + 0.107382i
\(325\) 0 0
\(326\) 1694.11 + 2934.29i 0.287817 + 0.498514i
\(327\) −462.458 + 66.6941i −0.0782079 + 0.0112789i
\(328\) −2832.65 + 4906.29i −0.476850 + 0.825929i
\(329\) 5457.61 9452.86i 0.914552 1.58405i
\(330\) 0 0
\(331\) −3180.59 5508.94i −0.528159 0.914799i −0.999461 0.0328269i \(-0.989549\pi\)
0.471302 0.881972i \(-0.343784\pi\)
\(332\) 286.271 0.0473228
\(333\) 598.067 176.166i 0.0984201 0.0289906i
\(334\) −672.582 −0.110186
\(335\) 0 0
\(336\) −3378.08 + 8448.55i −0.548481 + 1.37174i
\(337\) 1310.07 2269.11i 0.211763 0.366785i −0.740503 0.672053i \(-0.765413\pi\)
0.952266 + 0.305268i \(0.0987460\pi\)
\(338\) 8914.70 15440.7i 1.43460 2.48481i
\(339\) −834.631 + 2087.41i −0.133720 + 0.334432i
\(340\) 0 0
\(341\) 4392.89 0.697620
\(342\) 1440.40 + 1371.06i 0.227743 + 0.216780i
\(343\) −1566.39 −0.246580
\(344\) 5001.76 + 8663.29i 0.783944 + 1.35783i
\(345\) 0 0
\(346\) −949.344 + 1644.31i −0.147506 + 0.255488i
\(347\) 3841.31 6653.34i 0.594272 1.02931i −0.399378 0.916786i \(-0.630774\pi\)
0.993649 0.112522i \(-0.0358929\pi\)
\(348\) 485.234 69.9788i 0.0747451 0.0107795i
\(349\) 1840.37 + 3187.62i 0.282272 + 0.488910i 0.971944 0.235212i \(-0.0755785\pi\)
−0.689672 + 0.724122i \(0.742245\pi\)
\(350\) 0 0
\(351\) 1190.38 12638.2i 0.181019 1.92188i
\(352\) −2451.69 −0.371237
\(353\) 5064.30 + 8771.63i 0.763585 + 1.32257i 0.940991 + 0.338431i \(0.109896\pi\)
−0.177406 + 0.984138i \(0.556771\pi\)
\(354\) −7259.67 + 1046.96i −1.08996 + 0.157191i
\(355\) 0 0
\(356\) 267.305 462.985i 0.0397953 0.0689275i
\(357\) 820.428 + 1042.34i 0.121629 + 0.154528i
\(358\) −5545.47 9605.03i −0.818679 1.41799i
\(359\) 7181.79 1.05582 0.527911 0.849300i \(-0.322975\pi\)
0.527911 + 0.849300i \(0.322975\pi\)
\(360\) 0 0
\(361\) −6246.74 −0.910737
\(362\) −3756.62 6506.66i −0.545424 0.944702i
\(363\) 5150.47 12881.3i 0.744709 1.86251i
\(364\) −971.428 + 1682.56i −0.139881 + 0.242281i
\(365\) 0 0
\(366\) 1915.42 4790.44i 0.273553 0.684153i
\(367\) 4640.66 + 8037.87i 0.660056 + 1.14325i 0.980600 + 0.196018i \(0.0628010\pi\)
−0.320544 + 0.947234i \(0.603866\pi\)
\(368\) −188.801 −0.0267444
\(369\) −1690.84 + 6995.96i −0.238541 + 0.986979i
\(370\) 0 0
\(371\) −1433.51 2482.91i −0.200604 0.347456i
\(372\) −191.974 243.899i −0.0267564 0.0339935i
\(373\) −1833.25 + 3175.29i −0.254483 + 0.440778i −0.964755 0.263149i \(-0.915239\pi\)
0.710272 + 0.703928i \(0.248572\pi\)
\(374\) −962.613 + 1667.29i −0.133090 + 0.230518i
\(375\) 0 0
\(376\) 4646.01 + 8047.13i 0.637233 + 1.10372i
\(377\) −9925.46 −1.35593
\(378\) −977.642 + 10379.6i −0.133028 + 1.41235i
\(379\) −6530.29 −0.885062 −0.442531 0.896753i \(-0.645919\pi\)
−0.442531 + 0.896753i \(0.645919\pi\)
\(380\) 0 0
\(381\) −10594.3 + 1527.88i −1.42458 + 0.205447i
\(382\) −325.002 + 562.919i −0.0435302 + 0.0753965i
\(383\) 1657.53 2870.93i 0.221138 0.383022i −0.734016 0.679132i \(-0.762356\pi\)
0.955154 + 0.296110i \(0.0956896\pi\)
\(384\) −5260.71 6683.63i −0.699113 0.888210i
\(385\) 0 0
\(386\) 5611.30 0.739916
\(387\) 9205.32 + 8762.18i 1.20913 + 1.15092i
\(388\) 1305.65 0.170835
\(389\) −2338.24 4049.95i −0.304765 0.527868i 0.672444 0.740148i \(-0.265245\pi\)
−0.977209 + 0.212280i \(0.931911\pi\)
\(390\) 0 0
\(391\) −13.7623 + 23.8370i −0.00178002 + 0.00308309i
\(392\) −2978.09 + 5158.21i −0.383715 + 0.664614i
\(393\) −3612.22 + 9034.13i −0.463645 + 1.15957i
\(394\) −4681.93 8109.34i −0.598661 1.03691i
\(395\) 0 0
\(396\) −1409.02 + 415.041i −0.178803 + 0.0526682i
\(397\) −3995.97 −0.505169 −0.252584 0.967575i \(-0.581280\pi\)
−0.252584 + 0.967575i \(0.581280\pi\)
\(398\) −2567.64 4447.29i −0.323378 0.560107i
\(399\) 1985.27 + 2522.25i 0.249092 + 0.316467i
\(400\) 0 0
\(401\) −2543.18 + 4404.92i −0.316710 + 0.548557i −0.979799 0.199983i \(-0.935911\pi\)
0.663090 + 0.748540i \(0.269245\pi\)
\(402\) 1165.95 168.149i 0.144658 0.0208620i
\(403\) 3141.99 + 5442.09i 0.388371 + 0.672679i
\(404\) 73.2611 0.00902197
\(405\) 0 0
\(406\) 8151.63 0.996450
\(407\) 730.296 + 1264.91i 0.0889420 + 0.154052i
\(408\) −1117.66 + 161.186i −0.135619 + 0.0195585i
\(409\) 3737.95 6474.31i 0.451906 0.782724i −0.546599 0.837395i \(-0.684078\pi\)
0.998504 + 0.0546708i \(0.0174109\pi\)
\(410\) 0 0
\(411\) 7205.29 + 9154.18i 0.864746 + 1.09864i
\(412\) 595.657 + 1031.71i 0.0712280 + 0.123371i
\(413\) −11839.1 −1.41057
\(414\) −207.514 + 61.1253i −0.0246347 + 0.00725639i
\(415\) 0 0
\(416\) −1753.56 3037.25i −0.206671 0.357965i
\(417\) −510.168 + 1275.93i −0.0599114 + 0.149838i
\(418\) −2329.33 + 4034.52i −0.272563 + 0.472092i
\(419\) −4320.40 + 7483.15i −0.503736 + 0.872497i 0.496255 + 0.868177i \(0.334708\pi\)
−0.999991 + 0.00431947i \(0.998625\pi\)
\(420\) 0 0
\(421\) 1344.32 + 2328.42i 0.155625 + 0.269550i 0.933286 0.359133i \(-0.116928\pi\)
−0.777662 + 0.628683i \(0.783594\pi\)
\(422\) −1734.66 −0.200099
\(423\) 8550.60 + 8138.98i 0.982848 + 0.935534i
\(424\) 2440.67 0.279550
\(425\) 0 0
\(426\) 6296.95 + 8000.15i 0.716169 + 0.909879i
\(427\) 4163.73 7211.80i 0.471890 0.817338i
\(428\) −452.223 + 783.273i −0.0510725 + 0.0884602i
\(429\) 29433.7 4244.83i 3.31253 0.477721i
\(430\) 0 0
\(431\) 11019.7 1.23156 0.615779 0.787919i \(-0.288842\pi\)
0.615779 + 0.787919i \(0.288842\pi\)
\(432\) −8023.19 5697.73i −0.893555 0.634565i
\(433\) 13547.6 1.50360 0.751798 0.659394i \(-0.229187\pi\)
0.751798 + 0.659394i \(0.229187\pi\)
\(434\) −2580.47 4469.50i −0.285407 0.494339i
\(435\) 0 0
\(436\) −38.6704 + 66.9791i −0.00424765 + 0.00735715i
\(437\) −33.3020 + 57.6807i −0.00364542 + 0.00631406i
\(438\) 5259.74 + 6682.40i 0.573790 + 0.728990i
\(439\) 5105.54 + 8843.06i 0.555067 + 0.961404i 0.997898 + 0.0647988i \(0.0206406\pi\)
−0.442832 + 0.896605i \(0.646026\pi\)
\(440\) 0 0
\(441\) −1777.66 + 7355.17i −0.191951 + 0.794209i
\(442\) −2754.01 −0.296369
\(443\) 4916.42 + 8515.50i 0.527283 + 0.913281i 0.999494 + 0.0317956i \(0.0101226\pi\)
−0.472211 + 0.881485i \(0.656544\pi\)
\(444\) 38.3148 95.8250i 0.00409536 0.0102425i
\(445\) 0 0
\(446\) −8431.86 + 14604.4i −0.895202 + 1.55054i
\(447\) 85.6498 214.209i 0.00906285 0.0226661i
\(448\) −5564.15 9637.38i −0.586788 1.01635i
\(449\) 4038.48 0.424471 0.212235 0.977219i \(-0.431926\pi\)
0.212235 + 0.977219i \(0.431926\pi\)
\(450\) 0 0
\(451\) −16861.1 −1.76044
\(452\) 186.058 + 322.262i 0.0193616 + 0.0335352i
\(453\) −3915.84 4975.00i −0.406142 0.515996i
\(454\) 5521.50 9563.51i 0.570786 0.988630i
\(455\) 0 0
\(456\) −2704.52 + 390.037i −0.277743 + 0.0400551i
\(457\) −2944.34 5099.74i −0.301379 0.522004i 0.675069 0.737754i \(-0.264114\pi\)
−0.976449 + 0.215750i \(0.930780\pi\)
\(458\) −10639.2 −1.08545
\(459\) −1304.20 + 597.638i −0.132625 + 0.0607742i
\(460\) 0 0
\(461\) −1176.55 2037.84i −0.118866 0.205882i 0.800452 0.599396i \(-0.204593\pi\)
−0.919319 + 0.393514i \(0.871259\pi\)
\(462\) −24173.5 + 3486.22i −2.43431 + 0.351068i
\(463\) 6788.85 11758.6i 0.681435 1.18028i −0.293108 0.956079i \(-0.594690\pi\)
0.974543 0.224201i \(-0.0719771\pi\)
\(464\) −3847.10 + 6663.38i −0.384908 + 0.666680i
\(465\) 0 0
\(466\) 6705.88 + 11614.9i 0.666618 + 1.15462i
\(467\) 491.494 0.0487015 0.0243508 0.999703i \(-0.492248\pi\)
0.0243508 + 0.999703i \(0.492248\pi\)
\(468\) −1521.97 1448.70i −0.150327 0.143090i
\(469\) 1901.44 0.187208
\(470\) 0 0
\(471\) 6919.42 17305.4i 0.676921 1.69297i
\(472\) 5039.26 8728.26i 0.491421 0.851167i
\(473\) −14886.3 + 25783.8i −1.44708 + 2.50642i
\(474\) 984.366 2461.89i 0.0953870 0.238562i
\(475\) 0 0
\(476\) 219.568 0.0211426
\(477\) 2974.36 876.125i 0.285506 0.0840985i
\(478\) 6821.19 0.652707
\(479\) −6102.77 10570.3i −0.582135 1.00829i −0.995226 0.0975976i \(-0.968884\pi\)
0.413091 0.910690i \(-0.364449\pi\)
\(480\) 0 0
\(481\) −1044.68 + 1809.44i −0.0990297 + 0.171525i
\(482\) −3357.83 + 5815.93i −0.317313 + 0.549602i
\(483\) −345.604 + 49.8418i −0.0325580 + 0.00469540i
\(484\) −1148.15 1988.66i −0.107828 0.186764i
\(485\) 0 0
\(486\) −10663.1 3664.91i −0.995240 0.342065i
\(487\) −7900.12 −0.735089 −0.367545 0.930006i \(-0.619801\pi\)
−0.367545 + 0.930006i \(0.619801\pi\)
\(488\) 3544.55 + 6139.33i 0.328799 + 0.569497i
\(489\) −5854.17 + 844.268i −0.541380 + 0.0780759i
\(490\) 0 0
\(491\) 4723.85 8181.95i 0.434184 0.752029i −0.563044 0.826427i \(-0.690370\pi\)
0.997229 + 0.0743974i \(0.0237033\pi\)
\(492\) 736.849 + 936.152i 0.0675197 + 0.0857825i
\(493\) 560.853 + 971.426i 0.0512364 + 0.0887441i
\(494\) −6664.16 −0.606953
\(495\) 0 0
\(496\) 4871.33 0.440986
\(497\) 8216.66 + 14231.7i 0.741585 + 1.28446i
\(498\) −1911.23 + 4779.97i −0.171976 + 0.430111i
\(499\) 9371.20 16231.4i 0.840707 1.45615i −0.0485916 0.998819i \(-0.515473\pi\)
0.889298 0.457328i \(-0.151193\pi\)
\(500\) 0 0
\(501\) 435.904 1090.19i 0.0388717 0.0972179i
\(502\) 5651.07 + 9787.95i 0.502430 + 0.870234i
\(503\) −10305.9 −0.913553 −0.456777 0.889581i \(-0.650996\pi\)
−0.456777 + 0.889581i \(0.650996\pi\)
\(504\) −10376.3 9876.80i −0.917059 0.872912i
\(505\) 0 0
\(506\) −253.394 438.892i −0.0222624 0.0385595i
\(507\) 19250.3 + 24457.1i 1.68626 + 2.14236i
\(508\) −885.889 + 1534.40i −0.0773720 + 0.134012i
\(509\) 5844.86 10123.6i 0.508976 0.881572i −0.490970 0.871176i \(-0.663358\pi\)
0.999946 0.0103957i \(-0.00330910\pi\)
\(510\) 0 0
\(511\) 6863.25 + 11887.5i 0.594153 + 1.02910i
\(512\) 9206.71 0.794693
\(513\) −3155.89 + 1446.16i −0.271610 + 0.124463i
\(514\) 12031.9 1.03250
\(515\) 0 0
\(516\) 2082.10 300.273i 0.177634 0.0256178i
\(517\) −13827.5 + 23949.9i −1.17627 + 2.03736i
\(518\) 857.980 1486.06i 0.0727750 0.126050i
\(519\) −2050.00 2604.48i −0.173381 0.220278i
\(520\) 0 0
\(521\) −18320.4 −1.54056 −0.770278 0.637708i \(-0.779883\pi\)
−0.770278 + 0.637708i \(0.779883\pi\)
\(522\) −2071.11 + 8569.33i −0.173659 + 0.718524i
\(523\) −4497.23 −0.376004 −0.188002 0.982169i \(-0.560201\pi\)
−0.188002 + 0.982169i \(0.560201\pi\)
\(524\) 805.245 + 1394.72i 0.0671322 + 0.116276i
\(525\) 0 0
\(526\) −9617.23 + 16657.5i −0.797208 + 1.38080i
\(527\) 355.086 615.027i 0.0293506 0.0508368i
\(528\) 8558.76 21405.4i 0.705440 1.76430i
\(529\) 6079.88 + 10530.7i 0.499702 + 0.865510i
\(530\) 0 0
\(531\) 3008.00 12445.8i 0.245830 1.01714i
\(532\) 531.311 0.0432993
\(533\) −12059.8 20888.2i −0.980053 1.69750i
\(534\) 5946.03 + 7554.31i 0.481854 + 0.612185i
\(535\) 0 0
\(536\) −809.339 + 1401.82i −0.0652204 + 0.112965i
\(537\) 19162.9 2763.61i 1.53992 0.222083i
\(538\) 6545.45 + 11337.1i 0.524525 + 0.908504i
\(539\) −17726.8 −1.41660
\(540\) 0 0
\(541\) 85.5785 0.00680094 0.00340047 0.999994i \(-0.498918\pi\)
0.00340047 + 0.999994i \(0.498918\pi\)
\(542\) −3890.88 6739.20i −0.308353 0.534084i
\(543\) 12981.3 1872.13i 1.02594 0.147957i
\(544\) −198.175 + 343.249i −0.0156189 + 0.0270527i
\(545\) 0 0
\(546\) −21608.8 27453.6i −1.69372 2.15184i
\(547\) −9158.66 15863.3i −0.715897 1.23997i −0.962612 0.270883i \(-0.912684\pi\)
0.246715 0.969088i \(-0.420649\pi\)
\(548\) 1928.33 0.150318
\(549\) 6523.45 + 6209.41i 0.507129 + 0.482716i
\(550\) 0 0
\(551\) 1357.15 + 2350.66i 0.104930 + 0.181745i
\(552\) 110.359 276.008i 0.00850943 0.0212820i
\(553\) 2139.82 3706.27i 0.164547 0.285003i
\(554\) −2472.04 + 4281.70i −0.189579 + 0.328361i
\(555\) 0 0
\(556\) 113.728 + 196.983i 0.00867471 + 0.0150250i
\(557\) −21598.8 −1.64304 −0.821519 0.570181i \(-0.806873\pi\)
−0.821519 + 0.570181i \(0.806873\pi\)
\(558\) 5354.15 1577.12i 0.406200 0.119650i
\(559\) −42589.2 −3.22242
\(560\) 0 0
\(561\) −2078.65 2640.88i −0.156436 0.198749i
\(562\) 7454.51 12911.6i 0.559519 0.969115i
\(563\) 5576.22 9658.30i 0.417424 0.723000i −0.578255 0.815856i \(-0.696266\pi\)
0.995680 + 0.0928559i \(0.0295996\pi\)
\(564\) 1934.01 278.916i 0.144391 0.0208236i
\(565\) 0 0
\(566\) −810.849 −0.0602165
\(567\) −16190.7 8311.73i −1.19920 0.615626i
\(568\) −13989.5 −1.03343
\(569\) 10090.5 + 17477.2i 0.743436 + 1.28767i 0.950922 + 0.309430i \(0.100138\pi\)
−0.207487 + 0.978238i \(0.566528\pi\)
\(570\) 0 0
\(571\) −4075.42 + 7058.83i −0.298688 + 0.517343i −0.975836 0.218504i \(-0.929882\pi\)
0.677148 + 0.735847i \(0.263216\pi\)
\(572\) 2461.23 4262.97i 0.179911 0.311615i
\(573\) −701.803 891.627i −0.0511662 0.0650057i
\(574\) 9904.53 + 17155.2i 0.720222 + 1.24746i
\(575\) 0 0
\(576\) 11544.9 3400.66i 0.835136 0.245997i
\(577\) −11901.4 −0.858689 −0.429345 0.903141i \(-0.641255\pi\)
−0.429345 + 0.903141i \(0.641255\pi\)
\(578\) −7156.38 12395.2i −0.514993 0.891994i
\(579\) −3636.71 + 9095.37i −0.261030 + 0.652834i
\(580\) 0 0
\(581\) −4154.63 + 7196.04i −0.296666 + 0.513841i
\(582\) −8716.88 + 21800.8i −0.620836 + 1.55270i
\(583\) 3631.96 + 6290.75i 0.258011 + 0.446889i
\(584\) −11685.2 −0.827977
\(585\) 0 0
\(586\) 14576.6 1.02757
\(587\) 1613.51 + 2794.68i 0.113452 + 0.196505i 0.917160 0.398519i \(-0.130476\pi\)
−0.803708 + 0.595024i \(0.797142\pi\)
\(588\) 774.682 + 984.219i 0.0543323 + 0.0690281i
\(589\) 859.237 1488.24i 0.0601090 0.104112i
\(590\) 0 0
\(591\) 16178.8 2333.26i 1.12607 0.162398i
\(592\) 809.834 + 1402.67i 0.0562230 + 0.0973810i
\(593\) 7574.79 0.524552 0.262276 0.964993i \(-0.415527\pi\)
0.262276 + 0.964993i \(0.415527\pi\)
\(594\) 2476.97 26297.9i 0.171096 1.81653i
\(595\) 0 0
\(596\) −19.0932 33.0705i −0.00131223 0.00227285i
\(597\) 8872.73 1279.59i 0.608269 0.0877225i
\(598\) 362.478 627.830i 0.0247873 0.0429329i
\(599\) 4937.32 8551.69i 0.336784 0.583326i −0.647042 0.762454i \(-0.723994\pi\)
0.983826 + 0.179128i \(0.0573276\pi\)
\(600\) 0 0
\(601\) 175.136 + 303.345i 0.0118868 + 0.0205885i 0.871908 0.489670i \(-0.162883\pi\)
−0.860021 + 0.510259i \(0.829550\pi\)
\(602\) 34977.9 2.36809
\(603\) −483.104 + 1998.87i −0.0326261 + 0.134992i
\(604\) −1047.98 −0.0705991
\(605\) 0 0
\(606\) −489.113 + 1223.27i −0.0327869 + 0.0819997i
\(607\) 9468.84 16400.5i 0.633160 1.09667i −0.353741 0.935343i \(-0.615091\pi\)
0.986902 0.161323i \(-0.0515760\pi\)
\(608\) −479.543 + 830.593i −0.0319869 + 0.0554029i
\(609\) −5283.11 + 13213.0i −0.351531 + 0.879176i
\(610\) 0 0
\(611\) −39560.1 −2.61936
\(612\) −55.7863 + 230.819i −0.00368469 + 0.0152456i
\(613\) 4729.36 0.311610 0.155805 0.987788i \(-0.450203\pi\)
0.155805 + 0.987788i \(0.450203\pi\)
\(614\) 3118.92 + 5402.13i 0.204999 + 0.355069i
\(615\) 0 0
\(616\) 16779.9 29063.7i 1.09754 1.90099i
\(617\) 11066.2 19167.2i 0.722053 1.25063i −0.238122 0.971235i \(-0.576532\pi\)
0.960175 0.279398i \(-0.0901348\pi\)
\(618\) −21203.6 + 3057.91i −1.38015 + 0.199041i
\(619\) −2433.31 4214.61i −0.158001 0.273666i 0.776146 0.630553i \(-0.217172\pi\)
−0.934148 + 0.356886i \(0.883838\pi\)
\(620\) 0 0
\(621\) 35.4128 375.977i 0.00228835 0.0242954i
\(622\) 15035.2 0.969221
\(623\) 7758.76 + 13438.6i 0.498954 + 0.864213i
\(624\) 32639.5 4707.15i 2.09395 0.301982i
\(625\) 0 0
\(626\) 8816.36 15270.4i 0.562895 0.974963i
\(627\) −5029.91 6390.41i −0.320376 0.407031i
\(628\) −1542.49 2671.68i −0.0980130 0.169764i
\(629\) 236.125 0.0149681
\(630\) 0 0
\(631\) 24104.7 1.52075 0.760375 0.649484i \(-0.225015\pi\)
0.760375 + 0.649484i \(0.225015\pi\)
\(632\) 1821.61 + 3155.11i 0.114651 + 0.198582i
\(633\) 1124.24 2811.71i 0.0705916 0.176549i
\(634\) −7011.89 + 12145.0i −0.439239 + 0.760785i
\(635\) 0 0
\(636\) 190.550 476.565i 0.0118802 0.0297123i
\(637\) −12679.0 21960.7i −0.788636 1.36596i
\(638\) −20653.1 −1.28161
\(639\) −17048.6 + 5021.81i −1.05545 + 0.310892i
\(640\) 0 0
\(641\) 1638.33 + 2837.68i 0.100952 + 0.174854i 0.912077 0.410019i \(-0.134478\pi\)
−0.811125 + 0.584873i \(0.801144\pi\)
\(642\) −10059.4 12780.3i −0.618401 0.785667i
\(643\) −4751.07 + 8229.10i −0.291390 + 0.504703i −0.974139 0.225951i \(-0.927451\pi\)
0.682748 + 0.730654i \(0.260785\pi\)
\(644\) −28.8991 + 50.0548i −0.00176830 + 0.00306279i
\(645\) 0 0
\(646\) 376.569 + 652.236i 0.0229348 + 0.0397243i
\(647\) 15190.4 0.923024 0.461512 0.887134i \(-0.347307\pi\)
0.461512 + 0.887134i \(0.347307\pi\)
\(648\) 13019.2 8398.59i 0.789266 0.509148i
\(649\) 29995.8 1.81423
\(650\) 0 0
\(651\) 8917.05 1285.99i 0.536846 0.0774221i
\(652\) −489.521 + 847.876i −0.0294036 + 0.0509285i
\(653\) −3355.41 + 5811.73i −0.201083 + 0.348286i −0.948878 0.315644i \(-0.897779\pi\)
0.747795 + 0.663930i \(0.231113\pi\)
\(654\) −860.199 1092.87i −0.0514319 0.0653432i
\(655\) 0 0
\(656\) −18697.5 −1.11283
\(657\) −14240.4 + 4194.64i −0.845617 + 0.249085i
\(658\) 32490.1 1.92492
\(659\) −10490.6 18170.2i −0.620113 1.07407i −0.989464 0.144778i \(-0.953753\pi\)
0.369351 0.929290i \(-0.379580\pi\)
\(660\) 0 0
\(661\) 9666.37 16742.6i 0.568802 0.985194i −0.427883 0.903834i \(-0.640740\pi\)
0.996685 0.0813598i \(-0.0259263\pi\)
\(662\) 9467.30 16397.9i 0.555827 0.962720i
\(663\) 1784.89 4463.99i 0.104554 0.261489i
\(664\) −3536.80 6125.92i −0.206709 0.358030i
\(665\) 0 0
\(666\) 1344.22 + 1279.51i 0.0782096 + 0.0744446i
\(667\) −295.274 −0.0171410
\(668\) −97.1727 168.308i −0.00562833 0.00974855i
\(669\) −18207.6 23132.4i −1.05224 1.33685i
\(670\) 0 0
\(671\) −10549.3 + 18271.9i −0.606932 + 1.05124i
\(672\) −4976.64 + 717.713i −0.285681 + 0.0412000i
\(673\) 1657.53 + 2870.92i 0.0949374 + 0.164436i 0.909582 0.415523i \(-0.136402\pi\)
−0.814645 + 0.579960i \(0.803068\pi\)
\(674\) 7799.11 0.445713
\(675\) 0 0
\(676\) 5151.88 0.293120
\(677\) −9420.59 16316.9i −0.534804 0.926308i −0.999173 0.0406661i \(-0.987052\pi\)
0.464368 0.885642i \(-0.346281\pi\)
\(678\) −6623.10 + 955.160i −0.375160 + 0.0541043i
\(679\) −18948.8 + 32820.2i −1.07097 + 1.85497i
\(680\) 0 0
\(681\) 11923.0 + 15148.0i 0.670913 + 0.852381i
\(682\) 6537.92 + 11324.0i 0.367082 + 0.635804i
\(683\) 20540.7 1.15076 0.575379 0.817887i \(-0.304854\pi\)
0.575379 + 0.817887i \(0.304854\pi\)
\(684\) −134.992 + 558.536i −0.00754611 + 0.0312225i
\(685\) 0 0
\(686\) −2331.25 4037.84i −0.129748 0.224731i
\(687\) 6895.32 17245.1i 0.382930 0.957705i
\(688\) −16507.6 + 28591.9i −0.914746 + 1.58439i
\(689\) −5195.48 + 8998.84i −0.287275 + 0.497574i
\(690\) 0 0
\(691\) 12816.9 + 22199.5i 0.705611 + 1.22215i 0.966471 + 0.256777i \(0.0826607\pi\)
−0.260860 + 0.965377i \(0.584006\pi\)
\(692\) −548.634 −0.0301386
\(693\) 10016.1 41442.3i 0.549035 2.27167i
\(694\) 22868.0 1.25080
\(695\) 0 0
\(696\) −7492.42 9518.97i −0.408045 0.518413i
\(697\) −1362.92 + 2360.64i −0.0740661 + 0.128286i
\(698\) −5478.04 + 9488.25i −0.297059 + 0.514521i
\(699\) −23172.8 + 3341.90i −1.25390 + 0.180833i
\(700\) 0 0
\(701\) 35929.9 1.93588 0.967941 0.251178i \(-0.0808179\pi\)
0.967941 + 0.251178i \(0.0808179\pi\)
\(702\) 34350.6 15740.9i 1.84683 0.846298i
\(703\) 571.375 0.0306541
\(704\) 14097.4 + 24417.4i 0.754711 + 1.30720i
\(705\) 0 0
\(706\) −15074.4 + 26109.6i −0.803585 + 1.39185i
\(707\) −1063.23 + 1841.58i −0.0565588 + 0.0979626i
\(708\) −1310.85 1665.41i −0.0695829 0.0884038i
\(709\) 5590.21 + 9682.53i 0.296114 + 0.512884i 0.975243 0.221134i \(-0.0709759\pi\)
−0.679129 + 0.734019i \(0.737643\pi\)
\(710\) 0 0
\(711\) 3352.52 + 3191.13i 0.176834 + 0.168322i
\(712\) −13209.9 −0.695313
\(713\) 93.4714 + 161.897i 0.00490958 + 0.00850364i
\(714\) −1465.90 + 3666.21i −0.0768348 + 0.192163i
\(715\) 0 0
\(716\) 1602.39 2775.41i 0.0836368 0.144863i
\(717\) −4420.85 + 11056.5i −0.230264 + 0.575889i
\(718\) 10688.6 + 18513.2i 0.555565 + 0.962267i
\(719\) 33908.0 1.75877 0.879385 0.476111i \(-0.157954\pi\)
0.879385 + 0.476111i \(0.157954\pi\)
\(720\) 0 0
\(721\) −34579.0 −1.78611
\(722\) −9297.00 16102.9i −0.479222 0.830037i
\(723\) −7250.84 9212.05i −0.372976 0.473858i
\(724\) 1085.49 1880.12i 0.0557209 0.0965115i
\(725\) 0 0
\(726\) 40870.8 5894.25i 2.08934 0.301317i
\(727\) −1790.58 3101.37i −0.0913465 0.158217i 0.816731 0.577018i \(-0.195784\pi\)
−0.908078 + 0.418801i \(0.862450\pi\)
\(728\) 48006.9 2.44403
\(729\) 12851.3 14908.6i 0.652912 0.757434i
\(730\) 0 0
\(731\) 2406.57 + 4168.30i 0.121765 + 0.210903i
\(732\) 1475.50 212.792i 0.0745028 0.0107445i
\(733\) −5008.11 + 8674.31i −0.252359 + 0.437098i −0.964175 0.265268i \(-0.914540\pi\)
0.711816 + 0.702366i \(0.247873\pi\)
\(734\) −13813.4 + 23925.4i −0.694633 + 1.20314i
\(735\) 0 0
\(736\) −52.1667 90.3554i −0.00261262 0.00452520i
\(737\) −4817.52 −0.240781
\(738\) −20550.7 + 6053.40i −1.02504 + 0.301936i
\(739\) 7686.38 0.382609 0.191304 0.981531i \(-0.438728\pi\)
0.191304 + 0.981531i \(0.438728\pi\)
\(740\) 0 0
\(741\) 4319.07 10802.0i 0.214123 0.535520i
\(742\) 4266.97 7390.61i 0.211113 0.365658i
\(743\) −5342.39 + 9253.29i −0.263786 + 0.456891i −0.967245 0.253845i \(-0.918305\pi\)
0.703459 + 0.710736i \(0.251638\pi\)
\(744\) −2847.42 + 7121.37i −0.140311 + 0.350917i
\(745\) 0 0
\(746\) −10913.7 −0.535629
\(747\) −6509.19 6195.84i −0.318820 0.303472i
\(748\) −556.302 −0.0271931
\(749\) −13126.2 22735.2i −0.640347 1.10911i
\(750\) 0 0
\(751\) −949.678 + 1644.89i −0.0461441 + 0.0799240i −0.888175 0.459505i \(-0.848027\pi\)
0.842031 + 0.539429i \(0.181360\pi\)
\(752\) −15333.5 + 26558.4i −0.743557 + 1.28788i
\(753\) −19527.8 + 2816.23i −0.945064 + 0.136294i
\(754\) −14772.0 25585.9i −0.713482 1.23579i
\(755\) 0 0
\(756\) −2738.65 + 1254.97i −0.131751 + 0.0603740i
\(757\) −3716.63 −0.178445 −0.0892227 0.996012i \(-0.528438\pi\)
−0.0892227 + 0.996012i \(0.528438\pi\)
\(758\) −9719.01 16833.8i −0.465713 0.806638i
\(759\) 875.628 126.280i 0.0418752 0.00603909i
\(760\) 0 0
\(761\) 6324.33 10954.1i 0.301257 0.521793i −0.675164 0.737668i \(-0.735927\pi\)
0.976421 + 0.215875i \(0.0692604\pi\)
\(762\) −19706.0 25036.1i −0.936843 1.19024i
\(763\) −1122.44 1944.13i −0.0532571 0.0922440i
\(764\) −187.821 −0.00889415
\(765\) 0 0
\(766\) 9867.58 0.465444
\(767\) 21454.3 + 37160.0i 1.01000 + 1.74937i
\(768\) 2520.21 6303.02i 0.118412 0.296147i
\(769\) −7749.61 + 13422.7i −0.363404 + 0.629435i −0.988519 0.151098i \(-0.951719\pi\)
0.625114 + 0.780533i \(0.285052\pi\)
\(770\) 0 0
\(771\) −7797.94 + 19502.6i −0.364249 + 0.910983i
\(772\) 810.704 + 1404.18i 0.0377952 + 0.0654631i
\(773\) 14179.9 0.659789 0.329895 0.944018i \(-0.392987\pi\)
0.329895 + 0.944018i \(0.392987\pi\)
\(774\) −8886.94 + 36770.2i −0.412706 + 1.70760i
\(775\) 0 0
\(776\) −16130.9 27939.5i −0.746219 1.29249i
\(777\) 1852.71 + 2353.83i 0.0855412 + 0.108678i
\(778\) 6959.99 12055.1i 0.320730 0.555520i
\(779\) −3297.98 + 5712.27i −0.151685 + 0.262726i
\(780\) 0 0
\(781\) −20817.9 36057.6i −0.953805 1.65204i