Properties

Label 405.4.e.w.271.3
Level $405$
Weight $4$
Character 405.271
Analytic conductor $23.896$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 405 = 3^{4} \cdot 5 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 405.e (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(23.8957735523\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
Defining polynomial: \(x^{12} - 2 x^{11} + 2 x^{10} + 32 x^{9} + 583 x^{8} - 624 x^{7} + 594 x^{6} + 9450 x^{5} + 90513 x^{4} - 20304 x^{3} + 10368 x^{2} + 124416 x + 746496\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{2}\cdot 3^{9} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 271.3
Root \(-2.82176 + 2.82176i\) of defining polynomial
Character \(\chi\) \(=\) 405.271
Dual form 405.4.e.w.136.3

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.03663 - 1.79550i) q^{2} +(1.85079 - 3.20567i) q^{4} +(-2.50000 + 4.33013i) q^{5} +(2.33056 + 4.03665i) q^{7} -24.2604 q^{8} +O(q^{10})\) \(q+(-1.03663 - 1.79550i) q^{2} +(1.85079 - 3.20567i) q^{4} +(-2.50000 + 4.33013i) q^{5} +(2.33056 + 4.03665i) q^{7} -24.2604 q^{8} +10.3663 q^{10} +(-4.44705 - 7.70252i) q^{11} +(-17.3086 + 29.9793i) q^{13} +(4.83186 - 8.36903i) q^{14} +(10.3428 + 17.9142i) q^{16} +2.66659 q^{17} +125.599 q^{19} +(9.25397 + 16.0283i) q^{20} +(-9.21990 + 15.9693i) q^{22} +(-65.9874 + 114.294i) q^{23} +(-12.5000 - 21.6506i) q^{25} +71.7704 q^{26} +17.2535 q^{28} +(35.6053 + 61.6702i) q^{29} +(-6.71252 + 11.6264i) q^{31} +(-75.5985 + 130.940i) q^{32} +(-2.76427 - 4.78785i) q^{34} -23.3056 q^{35} +283.849 q^{37} +(-130.200 - 225.513i) q^{38} +(60.6511 - 105.051i) q^{40} +(-191.726 + 332.079i) q^{41} +(169.588 + 293.734i) q^{43} -32.9223 q^{44} +273.618 q^{46} +(-39.1434 - 67.7983i) q^{47} +(160.637 - 278.231i) q^{49} +(-25.9158 + 44.8874i) q^{50} +(64.0692 + 110.971i) q^{52} +254.626 q^{53} +44.4705 q^{55} +(-56.5404 - 97.9309i) q^{56} +(73.8191 - 127.858i) q^{58} +(16.4098 - 28.4226i) q^{59} +(-93.4914 - 161.932i) q^{61} +27.8336 q^{62} +478.955 q^{64} +(-86.5429 - 149.897i) q^{65} +(-203.307 + 352.138i) q^{67} +(4.93530 - 8.54819i) q^{68} +(24.1593 + 41.8451i) q^{70} +966.124 q^{71} +276.177 q^{73} +(-294.246 - 509.649i) q^{74} +(232.458 - 402.629i) q^{76} +(20.7282 - 35.9024i) q^{77} +(573.426 + 993.204i) q^{79} -103.428 q^{80} +794.996 q^{82} +(-89.0225 - 154.191i) q^{83} +(-6.66647 + 11.5467i) q^{85} +(351.599 - 608.988i) q^{86} +(107.887 + 186.867i) q^{88} +806.486 q^{89} -161.355 q^{91} +(244.258 + 423.068i) q^{92} +(-81.1544 + 140.564i) q^{94} +(-313.998 + 543.860i) q^{95} +(619.023 + 1072.18i) q^{97} -666.085 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q - 4 q^{2} - 34 q^{4} - 30 q^{5} - 40 q^{7} + 132 q^{8} + O(q^{10}) \) \( 12 q - 4 q^{2} - 34 q^{4} - 30 q^{5} - 40 q^{7} + 132 q^{8} + 40 q^{10} - 88 q^{11} - 20 q^{13} - 180 q^{14} - 58 q^{16} + 248 q^{17} - 92 q^{19} - 170 q^{20} + 74 q^{22} - 210 q^{23} - 150 q^{25} + 8 q^{26} + 704 q^{28} - 296 q^{29} + 104 q^{31} - 722 q^{32} + 428 q^{34} + 400 q^{35} - 408 q^{37} + 20 q^{38} - 330 q^{40} - 344 q^{41} - 512 q^{43} + 1432 q^{44} - 372 q^{46} - 238 q^{47} - 68 q^{49} - 100 q^{50} + 468 q^{52} + 1700 q^{53} + 880 q^{55} - 2316 q^{56} - 890 q^{58} - 1840 q^{59} + 364 q^{61} + 2076 q^{62} - 1980 q^{64} - 100 q^{65} - 88 q^{67} - 236 q^{68} - 900 q^{70} + 2728 q^{71} + 1672 q^{73} - 1316 q^{74} + 2106 q^{76} - 840 q^{77} + 680 q^{79} + 580 q^{80} + 3484 q^{82} - 2148 q^{83} - 620 q^{85} - 2872 q^{86} - 1296 q^{88} + 6000 q^{89} - 6116 q^{91} - 1002 q^{92} + 3662 q^{94} + 230 q^{95} + 612 q^{97} + 3964 q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/405\mathbb{Z}\right)^\times\).

\(n\) \(82\) \(326\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.03663 1.79550i −0.366504 0.634804i 0.622512 0.782610i \(-0.286112\pi\)
−0.989016 + 0.147806i \(0.952779\pi\)
\(3\) 0 0
\(4\) 1.85079 3.20567i 0.231349 0.400709i
\(5\) −2.50000 + 4.33013i −0.223607 + 0.387298i
\(6\) 0 0
\(7\) 2.33056 + 4.03665i 0.125838 + 0.217959i 0.922060 0.387046i \(-0.126505\pi\)
−0.796222 + 0.605005i \(0.793171\pi\)
\(8\) −24.2604 −1.07217
\(9\) 0 0
\(10\) 10.3663 0.327811
\(11\) −4.44705 7.70252i −0.121894 0.211127i 0.798620 0.601835i \(-0.205564\pi\)
−0.920515 + 0.390708i \(0.872230\pi\)
\(12\) 0 0
\(13\) −17.3086 + 29.9793i −0.369272 + 0.639598i −0.989452 0.144862i \(-0.953726\pi\)
0.620180 + 0.784460i \(0.287060\pi\)
\(14\) 4.83186 8.36903i 0.0922407 0.159766i
\(15\) 0 0
\(16\) 10.3428 + 17.9142i 0.161606 + 0.279910i
\(17\) 2.66659 0.0380437 0.0190218 0.999819i \(-0.493945\pi\)
0.0190218 + 0.999819i \(0.493945\pi\)
\(18\) 0 0
\(19\) 125.599 1.51655 0.758273 0.651937i \(-0.226043\pi\)
0.758273 + 0.651937i \(0.226043\pi\)
\(20\) 9.25397 + 16.0283i 0.103463 + 0.179202i
\(21\) 0 0
\(22\) −9.21990 + 15.9693i −0.0893495 + 0.154758i
\(23\) −65.9874 + 114.294i −0.598231 + 1.03617i 0.394851 + 0.918745i \(0.370796\pi\)
−0.993082 + 0.117422i \(0.962537\pi\)
\(24\) 0 0
\(25\) −12.5000 21.6506i −0.100000 0.173205i
\(26\) 71.7704 0.541359
\(27\) 0 0
\(28\) 17.2535 0.116451
\(29\) 35.6053 + 61.6702i 0.227991 + 0.394892i 0.957213 0.289386i \(-0.0934510\pi\)
−0.729222 + 0.684278i \(0.760118\pi\)
\(30\) 0 0
\(31\) −6.71252 + 11.6264i −0.0388905 + 0.0673603i −0.884815 0.465942i \(-0.845716\pi\)
0.845925 + 0.533302i \(0.179049\pi\)
\(32\) −75.5985 + 130.940i −0.417627 + 0.723351i
\(33\) 0 0
\(34\) −2.76427 4.78785i −0.0139432 0.0241503i
\(35\) −23.3056 −0.112553
\(36\) 0 0
\(37\) 283.849 1.26120 0.630600 0.776108i \(-0.282809\pi\)
0.630600 + 0.776108i \(0.282809\pi\)
\(38\) −130.200 225.513i −0.555821 0.962710i
\(39\) 0 0
\(40\) 60.6511 105.051i 0.239745 0.415250i
\(41\) −191.726 + 332.079i −0.730307 + 1.26493i 0.226445 + 0.974024i \(0.427289\pi\)
−0.956752 + 0.290904i \(0.906044\pi\)
\(42\) 0 0
\(43\) 169.588 + 293.734i 0.601438 + 1.04172i 0.992604 + 0.121401i \(0.0387388\pi\)
−0.391165 + 0.920321i \(0.627928\pi\)
\(44\) −32.9223 −0.112801
\(45\) 0 0
\(46\) 273.618 0.877018
\(47\) −39.1434 67.7983i −0.121482 0.210413i 0.798870 0.601503i \(-0.205431\pi\)
−0.920352 + 0.391090i \(0.872098\pi\)
\(48\) 0 0
\(49\) 160.637 278.231i 0.468329 0.811170i
\(50\) −25.9158 + 44.8874i −0.0733009 + 0.126961i
\(51\) 0 0
\(52\) 64.0692 + 110.971i 0.170862 + 0.295941i
\(53\) 254.626 0.659915 0.329958 0.943996i \(-0.392966\pi\)
0.329958 + 0.943996i \(0.392966\pi\)
\(54\) 0 0
\(55\) 44.4705 0.109026
\(56\) −56.5404 97.9309i −0.134920 0.233689i
\(57\) 0 0
\(58\) 73.8191 127.858i 0.167119 0.289459i
\(59\) 16.4098 28.4226i 0.0362097 0.0627171i −0.847353 0.531031i \(-0.821805\pi\)
0.883562 + 0.468314i \(0.155138\pi\)
\(60\) 0 0
\(61\) −93.4914 161.932i −0.196235 0.339889i 0.751070 0.660223i \(-0.229538\pi\)
−0.947305 + 0.320334i \(0.896205\pi\)
\(62\) 27.8336 0.0570141
\(63\) 0 0
\(64\) 478.955 0.935460
\(65\) −86.5429 149.897i −0.165143 0.286037i
\(66\) 0 0
\(67\) −203.307 + 352.138i −0.370715 + 0.642097i −0.989676 0.143325i \(-0.954221\pi\)
0.618961 + 0.785422i \(0.287554\pi\)
\(68\) 4.93530 8.54819i 0.00880137 0.0152444i
\(69\) 0 0
\(70\) 24.1593 + 41.8451i 0.0412513 + 0.0714493i
\(71\) 966.124 1.61490 0.807450 0.589936i \(-0.200847\pi\)
0.807450 + 0.589936i \(0.200847\pi\)
\(72\) 0 0
\(73\) 276.177 0.442796 0.221398 0.975184i \(-0.428938\pi\)
0.221398 + 0.975184i \(0.428938\pi\)
\(74\) −294.246 509.649i −0.462235 0.800615i
\(75\) 0 0
\(76\) 232.458 402.629i 0.350852 0.607693i
\(77\) 20.7282 35.9024i 0.0306780 0.0531358i
\(78\) 0 0
\(79\) 573.426 + 993.204i 0.816652 + 1.41448i 0.908136 + 0.418676i \(0.137506\pi\)
−0.0914836 + 0.995807i \(0.529161\pi\)
\(80\) −103.428 −0.144545
\(81\) 0 0
\(82\) 794.996 1.07064
\(83\) −89.0225 154.191i −0.117729 0.203912i 0.801139 0.598479i \(-0.204228\pi\)
−0.918867 + 0.394567i \(0.870895\pi\)
\(84\) 0 0
\(85\) −6.66647 + 11.5467i −0.00850682 + 0.0147342i
\(86\) 351.599 608.988i 0.440860 0.763591i
\(87\) 0 0
\(88\) 107.887 + 186.867i 0.130691 + 0.226364i
\(89\) 806.486 0.960532 0.480266 0.877123i \(-0.340540\pi\)
0.480266 + 0.877123i \(0.340540\pi\)
\(90\) 0 0
\(91\) −161.355 −0.185874
\(92\) 244.258 + 423.068i 0.276801 + 0.479433i
\(93\) 0 0
\(94\) −81.1544 + 140.564i −0.0890472 + 0.154234i
\(95\) −313.998 + 543.860i −0.339110 + 0.587356i
\(96\) 0 0
\(97\) 619.023 + 1072.18i 0.647961 + 1.12230i 0.983609 + 0.180314i \(0.0577115\pi\)
−0.335648 + 0.941988i \(0.608955\pi\)
\(98\) −666.085 −0.686579
\(99\) 0 0
\(100\) −92.5397 −0.0925397
\(101\) −283.428 490.912i −0.279229 0.483639i 0.691964 0.721932i \(-0.256746\pi\)
−0.971193 + 0.238293i \(0.923412\pi\)
\(102\) 0 0
\(103\) 409.509 709.290i 0.391748 0.678528i −0.600932 0.799300i \(-0.705204\pi\)
0.992680 + 0.120772i \(0.0385371\pi\)
\(104\) 419.914 727.312i 0.395923 0.685758i
\(105\) 0 0
\(106\) −263.953 457.179i −0.241862 0.418917i
\(107\) −543.772 −0.491293 −0.245647 0.969359i \(-0.579000\pi\)
−0.245647 + 0.969359i \(0.579000\pi\)
\(108\) 0 0
\(109\) −1636.54 −1.43809 −0.719046 0.694963i \(-0.755421\pi\)
−0.719046 + 0.694963i \(0.755421\pi\)
\(110\) −46.0995 79.8467i −0.0399583 0.0692098i
\(111\) 0 0
\(112\) −48.2089 + 83.5003i −0.0406725 + 0.0704468i
\(113\) 272.899 472.675i 0.227188 0.393500i −0.729786 0.683676i \(-0.760380\pi\)
0.956974 + 0.290175i \(0.0937136\pi\)
\(114\) 0 0
\(115\) −329.937 571.468i −0.267537 0.463388i
\(116\) 263.592 0.210982
\(117\) 0 0
\(118\) −68.0436 −0.0530841
\(119\) 6.21464 + 10.7641i 0.00478736 + 0.00829194i
\(120\) 0 0
\(121\) 625.947 1084.17i 0.470284 0.814555i
\(122\) −193.832 + 335.727i −0.143842 + 0.249142i
\(123\) 0 0
\(124\) 24.8470 + 43.0363i 0.0179946 + 0.0311675i
\(125\) 125.000 0.0894427
\(126\) 0 0
\(127\) 36.0480 0.0251869 0.0125935 0.999921i \(-0.495991\pi\)
0.0125935 + 0.999921i \(0.495991\pi\)
\(128\) 108.288 + 187.561i 0.0747768 + 0.129517i
\(129\) 0 0
\(130\) −179.426 + 310.775i −0.121052 + 0.209667i
\(131\) −655.075 + 1134.62i −0.436902 + 0.756737i −0.997449 0.0713860i \(-0.977258\pi\)
0.560547 + 0.828123i \(0.310591\pi\)
\(132\) 0 0
\(133\) 292.716 + 506.999i 0.190840 + 0.330544i
\(134\) 843.016 0.543474
\(135\) 0 0
\(136\) −64.6926 −0.0407893
\(137\) 1098.60 + 1902.83i 0.685109 + 1.18664i 0.973403 + 0.229101i \(0.0735786\pi\)
−0.288294 + 0.957542i \(0.593088\pi\)
\(138\) 0 0
\(139\) −863.005 + 1494.77i −0.526612 + 0.912119i 0.472907 + 0.881112i \(0.343205\pi\)
−0.999519 + 0.0310067i \(0.990129\pi\)
\(140\) −43.1339 + 74.7101i −0.0260391 + 0.0451011i
\(141\) 0 0
\(142\) −1001.51 1734.67i −0.591868 1.02514i
\(143\) 307.889 0.180049
\(144\) 0 0
\(145\) −356.053 −0.203921
\(146\) −286.294 495.875i −0.162286 0.281088i
\(147\) 0 0
\(148\) 525.345 909.925i 0.291778 0.505374i
\(149\) 900.699 1560.06i 0.495222 0.857750i −0.504763 0.863258i \(-0.668420\pi\)
0.999985 + 0.00550809i \(0.00175329\pi\)
\(150\) 0 0
\(151\) −1664.09 2882.30i −0.896835 1.55336i −0.831517 0.555500i \(-0.812527\pi\)
−0.0653185 0.997864i \(-0.520806\pi\)
\(152\) −3047.09 −1.62600
\(153\) 0 0
\(154\) −85.9501 −0.0449744
\(155\) −33.5626 58.1322i −0.0173924 0.0301244i
\(156\) 0 0
\(157\) −1915.09 + 3317.04i −0.973510 + 1.68617i −0.288745 + 0.957406i \(0.593238\pi\)
−0.684766 + 0.728763i \(0.740096\pi\)
\(158\) 1188.86 2059.17i 0.598613 1.03683i
\(159\) 0 0
\(160\) −377.993 654.702i −0.186768 0.323492i
\(161\) −615.151 −0.301122
\(162\) 0 0
\(163\) −2404.51 −1.15543 −0.577717 0.816237i \(-0.696056\pi\)
−0.577717 + 0.816237i \(0.696056\pi\)
\(164\) 709.691 + 1229.22i 0.337912 + 0.585280i
\(165\) 0 0
\(166\) −184.567 + 319.679i −0.0862962 + 0.149469i
\(167\) −1785.48 + 3092.53i −0.827331 + 1.43298i 0.0727941 + 0.997347i \(0.476808\pi\)
−0.900125 + 0.435632i \(0.856525\pi\)
\(168\) 0 0
\(169\) 499.326 + 864.859i 0.227276 + 0.393654i
\(170\) 27.6427 0.0124711
\(171\) 0 0
\(172\) 1255.49 0.556569
\(173\) 79.9681 + 138.509i 0.0351437 + 0.0608707i 0.883062 0.469256i \(-0.155478\pi\)
−0.847919 + 0.530126i \(0.822144\pi\)
\(174\) 0 0
\(175\) 58.2640 100.916i 0.0251677 0.0435917i
\(176\) 91.9897 159.331i 0.0393976 0.0682387i
\(177\) 0 0
\(178\) −836.028 1448.04i −0.352039 0.609750i
\(179\) −1120.87 −0.468030 −0.234015 0.972233i \(-0.575187\pi\)
−0.234015 + 0.972233i \(0.575187\pi\)
\(180\) 0 0
\(181\) −3856.65 −1.58377 −0.791886 0.610669i \(-0.790901\pi\)
−0.791886 + 0.610669i \(0.790901\pi\)
\(182\) 167.265 + 289.712i 0.0681238 + 0.117994i
\(183\) 0 0
\(184\) 1600.88 2772.81i 0.641406 1.11095i
\(185\) −709.621 + 1229.10i −0.282013 + 0.488461i
\(186\) 0 0
\(187\) −11.8584 20.5394i −0.00463730 0.00803204i
\(188\) −289.785 −0.112419
\(189\) 0 0
\(190\) 1302.00 0.497141
\(191\) 39.5050 + 68.4246i 0.0149659 + 0.0259216i 0.873411 0.486983i \(-0.161903\pi\)
−0.858445 + 0.512905i \(0.828569\pi\)
\(192\) 0 0
\(193\) −2285.75 + 3959.03i −0.852496 + 1.47657i 0.0264535 + 0.999650i \(0.491579\pi\)
−0.878949 + 0.476916i \(0.841755\pi\)
\(194\) 1283.40 2222.91i 0.474961 0.822657i
\(195\) 0 0
\(196\) −594.612 1029.90i −0.216695 0.375327i
\(197\) −4081.61 −1.47615 −0.738077 0.674717i \(-0.764266\pi\)
−0.738077 + 0.674717i \(0.764266\pi\)
\(198\) 0 0
\(199\) −2518.98 −0.897316 −0.448658 0.893703i \(-0.648098\pi\)
−0.448658 + 0.893703i \(0.648098\pi\)
\(200\) 303.256 + 525.254i 0.107217 + 0.185705i
\(201\) 0 0
\(202\) −587.620 + 1017.79i −0.204677 + 0.354512i
\(203\) −165.961 + 287.452i −0.0573801 + 0.0993852i
\(204\) 0 0
\(205\) −958.630 1660.40i −0.326603 0.565693i
\(206\) −1698.04 −0.574310
\(207\) 0 0
\(208\) −716.075 −0.238706
\(209\) −558.545 967.429i −0.184858 0.320184i
\(210\) 0 0
\(211\) −113.622 + 196.799i −0.0370714 + 0.0642095i −0.883966 0.467552i \(-0.845136\pi\)
0.846894 + 0.531761i \(0.178470\pi\)
\(212\) 471.259 816.245i 0.152671 0.264434i
\(213\) 0 0
\(214\) 563.690 + 976.340i 0.180061 + 0.311875i
\(215\) −1695.88 −0.537943
\(216\) 0 0
\(217\) −62.5758 −0.0195757
\(218\) 1696.49 + 2938.40i 0.527067 + 0.912906i
\(219\) 0 0
\(220\) 82.3058 142.558i 0.0252230 0.0436875i
\(221\) −46.1548 + 79.9425i −0.0140485 + 0.0243326i
\(222\) 0 0
\(223\) 257.612 + 446.196i 0.0773585 + 0.133989i 0.902109 0.431507i \(-0.142018\pi\)
−0.824751 + 0.565496i \(0.808685\pi\)
\(224\) −704.748 −0.210214
\(225\) 0 0
\(226\) −1131.58 −0.333061
\(227\) 1978.02 + 3426.03i 0.578352 + 1.00173i 0.995669 + 0.0929736i \(0.0296372\pi\)
−0.417317 + 0.908761i \(0.637029\pi\)
\(228\) 0 0
\(229\) 838.285 1451.95i 0.241901 0.418985i −0.719355 0.694643i \(-0.755562\pi\)
0.961256 + 0.275658i \(0.0888956\pi\)
\(230\) −684.046 + 1184.80i −0.196107 + 0.339667i
\(231\) 0 0
\(232\) −863.801 1496.15i −0.244445 0.423392i
\(233\) 4610.01 1.29619 0.648095 0.761560i \(-0.275566\pi\)
0.648095 + 0.761560i \(0.275566\pi\)
\(234\) 0 0
\(235\) 391.434 0.108657
\(236\) −60.7423 105.209i −0.0167542 0.0290191i
\(237\) 0 0
\(238\) 12.8846 22.3167i 0.00350917 0.00607806i
\(239\) 3454.12 5982.71i 0.934846 1.61920i 0.159939 0.987127i \(-0.448870\pi\)
0.774907 0.632075i \(-0.217796\pi\)
\(240\) 0 0
\(241\) 1490.48 + 2581.59i 0.398383 + 0.690019i 0.993527 0.113600i \(-0.0362383\pi\)
−0.595144 + 0.803619i \(0.702905\pi\)
\(242\) −2595.51 −0.689444
\(243\) 0 0
\(244\) −692.133 −0.181595
\(245\) 803.185 + 1391.16i 0.209443 + 0.362766i
\(246\) 0 0
\(247\) −2173.94 + 3765.37i −0.560018 + 0.969980i
\(248\) 162.849 282.062i 0.0416972 0.0722217i
\(249\) 0 0
\(250\) −129.579 224.437i −0.0327811 0.0567786i
\(251\) 7132.90 1.79372 0.896862 0.442310i \(-0.145841\pi\)
0.896862 + 0.442310i \(0.145841\pi\)
\(252\) 0 0
\(253\) 1173.80 0.291684
\(254\) −37.3684 64.7240i −0.00923112 0.0159888i
\(255\) 0 0
\(256\) 2140.33 3707.16i 0.522542 0.905069i
\(257\) −3281.28 + 5683.35i −0.796423 + 1.37945i 0.125509 + 0.992093i \(0.459944\pi\)
−0.921932 + 0.387353i \(0.873390\pi\)
\(258\) 0 0
\(259\) 661.526 + 1145.80i 0.158708 + 0.274889i
\(260\) −640.692 −0.152823
\(261\) 0 0
\(262\) 2716.28 0.640506
\(263\) −2831.75 4904.73i −0.663928 1.14996i −0.979575 0.201080i \(-0.935555\pi\)
0.315647 0.948877i \(-0.397779\pi\)
\(264\) 0 0
\(265\) −636.564 + 1102.56i −0.147562 + 0.255584i
\(266\) 606.877 1051.14i 0.139887 0.242292i
\(267\) 0 0
\(268\) 752.558 + 1303.47i 0.171529 + 0.297097i
\(269\) 4018.43 0.910811 0.455406 0.890284i \(-0.349494\pi\)
0.455406 + 0.890284i \(0.349494\pi\)
\(270\) 0 0
\(271\) −1518.33 −0.340340 −0.170170 0.985415i \(-0.554432\pi\)
−0.170170 + 0.985415i \(0.554432\pi\)
\(272\) 27.5799 + 47.7698i 0.00614808 + 0.0106488i
\(273\) 0 0
\(274\) 2277.69 3945.07i 0.502190 0.869819i
\(275\) −111.176 + 192.563i −0.0243788 + 0.0422254i
\(276\) 0 0
\(277\) −1091.22 1890.05i −0.236697 0.409971i 0.723068 0.690777i \(-0.242731\pi\)
−0.959764 + 0.280806i \(0.909398\pi\)
\(278\) 3578.47 0.772022
\(279\) 0 0
\(280\) 565.404 0.120676
\(281\) −2551.28 4418.95i −0.541626 0.938123i −0.998811 0.0487518i \(-0.984476\pi\)
0.457185 0.889372i \(-0.348858\pi\)
\(282\) 0 0
\(283\) 1288.97 2232.56i 0.270747 0.468947i −0.698307 0.715799i \(-0.746063\pi\)
0.969053 + 0.246852i \(0.0793961\pi\)
\(284\) 1788.10 3097.08i 0.373606 0.647104i
\(285\) 0 0
\(286\) −319.167 552.813i −0.0659885 0.114296i
\(287\) −1787.32 −0.367603
\(288\) 0 0
\(289\) −4905.89 −0.998553
\(290\) 369.095 + 639.292i 0.0747380 + 0.129450i
\(291\) 0 0
\(292\) 511.147 885.332i 0.102440 0.177432i
\(293\) 4169.93 7222.52i 0.831432 1.44008i −0.0654699 0.997855i \(-0.520855\pi\)
0.896902 0.442229i \(-0.145812\pi\)
\(294\) 0 0
\(295\) 82.0490 + 142.113i 0.0161935 + 0.0280479i
\(296\) −6886.29 −1.35222
\(297\) 0 0
\(298\) −3734.77 −0.726004
\(299\) −2284.30 3956.52i −0.441820 0.765255i
\(300\) 0 0
\(301\) −790.468 + 1369.13i −0.151368 + 0.262177i
\(302\) −3450.10 + 5975.75i −0.657388 + 1.13863i
\(303\) 0 0
\(304\) 1299.04 + 2250.01i 0.245083 + 0.424496i
\(305\) 934.914 0.175518
\(306\) 0 0
\(307\) 7042.31 1.30921 0.654603 0.755973i \(-0.272836\pi\)
0.654603 + 0.755973i \(0.272836\pi\)
\(308\) −76.7274 132.896i −0.0141946 0.0245858i
\(309\) 0 0
\(310\) −69.5841 + 120.523i −0.0127487 + 0.0220815i
\(311\) −1171.46 + 2029.03i −0.213593 + 0.369954i −0.952836 0.303485i \(-0.901850\pi\)
0.739243 + 0.673438i \(0.235183\pi\)
\(312\) 0 0
\(313\) 1916.73 + 3319.88i 0.346135 + 0.599523i 0.985559 0.169331i \(-0.0541607\pi\)
−0.639425 + 0.768854i \(0.720827\pi\)
\(314\) 7940.98 1.42718
\(315\) 0 0
\(316\) 4245.18 0.755727
\(317\) −2944.99 5100.87i −0.521789 0.903765i −0.999679 0.0253451i \(-0.991932\pi\)
0.477890 0.878420i \(-0.341402\pi\)
\(318\) 0 0
\(319\) 316.677 548.501i 0.0555816 0.0962701i
\(320\) −1197.39 + 2073.94i −0.209175 + 0.362302i
\(321\) 0 0
\(322\) 637.684 + 1104.50i 0.110363 + 0.191154i
\(323\) 334.921 0.0576950
\(324\) 0 0
\(325\) 865.429 0.147709
\(326\) 2492.59 + 4317.29i 0.423472 + 0.733474i
\(327\) 0 0
\(328\) 4651.36 8056.39i 0.783013 1.35622i
\(329\) 182.452 316.016i 0.0305742 0.0529560i
\(330\) 0 0
\(331\) 3169.48 + 5489.69i 0.526315 + 0.911604i 0.999530 + 0.0306570i \(0.00975997\pi\)
−0.473215 + 0.880947i \(0.656907\pi\)
\(332\) −659.049 −0.108946
\(333\) 0 0
\(334\) 7403.51 1.21288
\(335\) −1016.53 1760.69i −0.165789 0.287154i
\(336\) 0 0
\(337\) −484.171 + 838.609i −0.0782625 + 0.135555i −0.902500 0.430689i \(-0.858271\pi\)
0.824238 + 0.566244i \(0.191604\pi\)
\(338\) 1035.23 1793.08i 0.166596 0.288552i
\(339\) 0 0
\(340\) 24.6765 + 42.7410i 0.00393609 + 0.00681751i
\(341\) 119.404 0.0189621
\(342\) 0 0
\(343\) 3096.26 0.487412
\(344\) −4114.27 7126.12i −0.644845 1.11690i
\(345\) 0 0
\(346\) 165.795 287.165i 0.0257606 0.0446188i
\(347\) −3228.85 + 5592.54i −0.499521 + 0.865196i −1.00000 0.000552683i \(-0.999824\pi\)
0.500479 + 0.865749i \(0.333157\pi\)
\(348\) 0 0
\(349\) 3077.59 + 5330.54i 0.472033 + 0.817586i 0.999488 0.0319976i \(-0.0101869\pi\)
−0.527455 + 0.849583i \(0.676854\pi\)
\(350\) −241.593 −0.0368963
\(351\) 0 0
\(352\) 1344.76 0.203625
\(353\) −1831.77 3172.71i −0.276190 0.478375i 0.694245 0.719739i \(-0.255739\pi\)
−0.970435 + 0.241364i \(0.922405\pi\)
\(354\) 0 0
\(355\) −2415.31 + 4183.44i −0.361103 + 0.625448i
\(356\) 1492.64 2585.33i 0.222218 0.384894i
\(357\) 0 0
\(358\) 1161.92 + 2012.51i 0.171535 + 0.297107i
\(359\) 12112.6 1.78073 0.890364 0.455250i \(-0.150450\pi\)
0.890364 + 0.455250i \(0.150450\pi\)
\(360\) 0 0
\(361\) 8916.11 1.29991
\(362\) 3997.92 + 6924.61i 0.580459 + 1.00538i
\(363\) 0 0
\(364\) −298.634 + 517.250i −0.0430019 + 0.0744815i
\(365\) −690.443 + 1195.88i −0.0990121 + 0.171494i
\(366\) 0 0
\(367\) −5808.08 10059.9i −0.826101 1.43085i −0.901075 0.433664i \(-0.857221\pi\)
0.0749736 0.997186i \(-0.476113\pi\)
\(368\) −2729.97 −0.386711
\(369\) 0 0
\(370\) 2942.46 0.413436
\(371\) 593.420 + 1027.83i 0.0830427 + 0.143834i
\(372\) 0 0
\(373\) 1107.86 1918.87i 0.153788 0.266369i −0.778829 0.627236i \(-0.784186\pi\)
0.932617 + 0.360868i \(0.117519\pi\)
\(374\) −24.5857 + 42.5836i −0.00339918 + 0.00588756i
\(375\) 0 0
\(376\) 949.636 + 1644.82i 0.130249 + 0.225598i
\(377\) −2465.11 −0.336763
\(378\) 0 0
\(379\) −6539.83 −0.886354 −0.443177 0.896434i \(-0.646149\pi\)
−0.443177 + 0.896434i \(0.646149\pi\)
\(380\) 1162.29 + 2013.14i 0.156906 + 0.271769i
\(381\) 0 0
\(382\) 81.9041 141.862i 0.0109701 0.0190008i
\(383\) −4247.63 + 7357.12i −0.566694 + 0.981543i 0.430196 + 0.902736i \(0.358445\pi\)
−0.996890 + 0.0788075i \(0.974889\pi\)
\(384\) 0 0
\(385\) 103.641 + 179.512i 0.0137196 + 0.0237630i
\(386\) 9477.90 1.24977
\(387\) 0 0
\(388\) 4582.74 0.599621
\(389\) 1768.42 + 3062.99i 0.230494 + 0.399228i 0.957954 0.286923i \(-0.0926323\pi\)
−0.727459 + 0.686151i \(0.759299\pi\)
\(390\) 0 0
\(391\) −175.961 + 304.774i −0.0227589 + 0.0394196i
\(392\) −3897.13 + 6750.02i −0.502129 + 0.869713i
\(393\) 0 0
\(394\) 4231.12 + 7328.51i 0.541017 + 0.937068i
\(395\) −5734.26 −0.730436
\(396\) 0 0
\(397\) 8586.22 1.08547 0.542733 0.839905i \(-0.317390\pi\)
0.542733 + 0.839905i \(0.317390\pi\)
\(398\) 2611.25 + 4522.82i 0.328870 + 0.569620i
\(399\) 0 0
\(400\) 258.569 447.855i 0.0323212 0.0559819i
\(401\) 3616.39 6263.78i 0.450359 0.780045i −0.548049 0.836446i \(-0.684629\pi\)
0.998408 + 0.0564010i \(0.0179625\pi\)
\(402\) 0 0
\(403\) −232.369 402.474i −0.0287223 0.0497485i
\(404\) −2098.27 −0.258398
\(405\) 0 0
\(406\) 688.160 0.0841202
\(407\) −1262.29 2186.35i −0.153733 0.266274i
\(408\) 0 0
\(409\) −615.480 + 1066.04i −0.0744096 + 0.128881i −0.900829 0.434173i \(-0.857041\pi\)
0.826420 + 0.563054i \(0.190374\pi\)
\(410\) −1987.49 + 3442.43i −0.239403 + 0.414658i
\(411\) 0 0
\(412\) −1515.83 2625.50i −0.181261 0.313954i
\(413\) 152.976 0.0182263
\(414\) 0 0
\(415\) 890.225 0.105300
\(416\) −2617.01 4532.79i −0.308436 0.534226i
\(417\) 0 0
\(418\) −1158.01 + 2005.73i −0.135503 + 0.234698i
\(419\) 291.219 504.407i 0.0339547 0.0588112i −0.848549 0.529117i \(-0.822523\pi\)
0.882503 + 0.470306i \(0.155856\pi\)
\(420\) 0 0
\(421\) 6281.14 + 10879.3i 0.727135 + 1.25944i 0.958089 + 0.286471i \(0.0924821\pi\)
−0.230954 + 0.972965i \(0.574185\pi\)
\(422\) 471.136 0.0543473
\(423\) 0 0
\(424\) −6177.33 −0.707542
\(425\) −33.3323 57.7333i −0.00380437 0.00658936i
\(426\) 0 0
\(427\) 435.775 754.784i 0.0493878 0.0855422i
\(428\) −1006.41 + 1743.15i −0.113660 + 0.196865i
\(429\) 0 0
\(430\) 1758.00 + 3044.94i 0.197158 + 0.341488i
\(431\) −9612.85 −1.07433 −0.537163 0.843478i \(-0.680504\pi\)
−0.537163 + 0.843478i \(0.680504\pi\)
\(432\) 0 0
\(433\) 8285.20 0.919541 0.459771 0.888038i \(-0.347932\pi\)
0.459771 + 0.888038i \(0.347932\pi\)
\(434\) 64.8680 + 112.355i 0.00717457 + 0.0124267i
\(435\) 0 0
\(436\) −3028.90 + 5246.20i −0.332701 + 0.576256i
\(437\) −8287.95 + 14355.2i −0.907246 + 1.57140i
\(438\) 0 0
\(439\) −5384.48 9326.20i −0.585393 1.01393i −0.994826 0.101590i \(-0.967607\pi\)
0.409434 0.912340i \(-0.365726\pi\)
\(440\) −1078.87 −0.116894
\(441\) 0 0
\(442\) 191.382 0.0205953
\(443\) −4404.96 7629.62i −0.472429 0.818271i 0.527073 0.849820i \(-0.323289\pi\)
−0.999502 + 0.0315487i \(0.989956\pi\)
\(444\) 0 0
\(445\) −2016.22 + 3492.19i −0.214782 + 0.372013i
\(446\) 534.096 925.082i 0.0567045 0.0982150i
\(447\) 0 0
\(448\) 1116.23 + 1933.37i 0.117717 + 0.203891i
\(449\) −9060.10 −0.952277 −0.476139 0.879370i \(-0.657964\pi\)
−0.476139 + 0.879370i \(0.657964\pi\)
\(450\) 0 0
\(451\) 3410.46 0.356081
\(452\) −1010.16 1749.65i −0.105119 0.182072i
\(453\) 0 0
\(454\) 4100.95 7103.06i 0.423937 0.734280i
\(455\) 403.387 698.687i 0.0415628 0.0719889i
\(456\) 0 0
\(457\) −1238.78 2145.62i −0.126800 0.219624i 0.795635 0.605776i \(-0.207137\pi\)
−0.922435 + 0.386152i \(0.873804\pi\)
\(458\) −3475.97 −0.354631
\(459\) 0 0
\(460\) −2442.58 −0.247578
\(461\) 7650.77 + 13251.5i 0.772954 + 1.33880i 0.935937 + 0.352167i \(0.114555\pi\)
−0.162983 + 0.986629i \(0.552112\pi\)
\(462\) 0 0
\(463\) 341.506 591.506i 0.0342789 0.0593728i −0.848377 0.529393i \(-0.822420\pi\)
0.882656 + 0.470020i \(0.155753\pi\)
\(464\) −736.515 + 1275.68i −0.0736894 + 0.127634i
\(465\) 0 0
\(466\) −4778.88 8277.27i −0.475059 0.822826i
\(467\) 6569.32 0.650946 0.325473 0.945551i \(-0.394477\pi\)
0.325473 + 0.945551i \(0.394477\pi\)
\(468\) 0 0
\(469\) −1895.28 −0.186601
\(470\) −405.772 702.818i −0.0398231 0.0689757i
\(471\) 0 0
\(472\) −398.109 + 689.545i −0.0388230 + 0.0672434i
\(473\) 1508.33 2612.50i 0.146624 0.253960i
\(474\) 0 0
\(475\) −1569.99 2719.30i −0.151655 0.262674i
\(476\) 46.0081 0.00443020
\(477\) 0 0
\(478\) −14322.6 −1.37050
\(479\) −5644.33 9776.26i −0.538405 0.932544i −0.998990 0.0449289i \(-0.985694\pi\)
0.460585 0.887615i \(-0.347639\pi\)
\(480\) 0 0
\(481\) −4913.02 + 8509.59i −0.465726 + 0.806661i
\(482\) 3090.15 5352.30i 0.292018 0.505790i
\(483\) 0 0
\(484\) −2317.00 4013.16i −0.217599 0.376893i
\(485\) −6190.23 −0.579554
\(486\) 0 0
\(487\) −8937.53 −0.831618 −0.415809 0.909452i \(-0.636502\pi\)
−0.415809 + 0.909452i \(0.636502\pi\)
\(488\) 2268.14 + 3928.54i 0.210397 + 0.364419i
\(489\) 0 0
\(490\) 1665.21 2884.23i 0.153524 0.265911i
\(491\) −1846.57 + 3198.35i −0.169724 + 0.293971i −0.938323 0.345760i \(-0.887621\pi\)
0.768599 + 0.639731i \(0.220954\pi\)
\(492\) 0 0
\(493\) 94.9446 + 164.449i 0.00867361 + 0.0150231i
\(494\) 9014.29 0.820996
\(495\) 0 0
\(496\) −277.705 −0.0251397
\(497\) 2251.61 + 3899.91i 0.203216 + 0.351981i
\(498\) 0 0
\(499\) 5593.22 9687.74i 0.501777 0.869104i −0.498220 0.867050i \(-0.666013\pi\)
0.999998 0.00205364i \(-0.000653694\pi\)
\(500\) 231.349 400.709i 0.0206925 0.0358405i
\(501\) 0 0
\(502\) −7394.19 12807.1i −0.657408 1.13866i
\(503\) 6553.81 0.580954 0.290477 0.956882i \(-0.406186\pi\)
0.290477 + 0.956882i \(0.406186\pi\)
\(504\) 0 0
\(505\) 2834.28 0.249750
\(506\) −1216.79 2107.55i −0.106903 0.185162i
\(507\) 0 0
\(508\) 66.7174 115.558i 0.00582698 0.0100926i
\(509\) 7513.86 13014.4i 0.654314 1.13331i −0.327751 0.944764i \(-0.606291\pi\)
0.982065 0.188542i \(-0.0603760\pi\)
\(510\) 0 0
\(511\) 643.647 + 1114.83i 0.0557207 + 0.0965111i
\(512\) −7142.32 −0.616502
\(513\) 0 0
\(514\) 13605.9 1.16757
\(515\) 2047.54 + 3546.45i 0.175195 + 0.303447i
\(516\) 0 0
\(517\) −348.145 + 603.005i −0.0296159 + 0.0512962i
\(518\) 1371.52 2375.54i 0.116334 0.201496i
\(519\) 0 0
\(520\) 2099.57 + 3636.56i 0.177062 + 0.306680i
\(521\) −835.969 −0.0702965 −0.0351483 0.999382i \(-0.511190\pi\)
−0.0351483 + 0.999382i \(0.511190\pi\)
\(522\) 0 0
\(523\) −13032.4 −1.08961 −0.544805 0.838563i \(-0.683396\pi\)
−0.544805 + 0.838563i \(0.683396\pi\)
\(524\) 2424.82 + 4199.91i 0.202154 + 0.350141i
\(525\) 0 0
\(526\) −5870.95 + 10168.8i −0.486665 + 0.842928i
\(527\) −17.8995 + 31.0029i −0.00147954 + 0.00256263i
\(528\) 0 0
\(529\) −2625.17 4546.93i −0.215762 0.373710i
\(530\) 2639.53 0.216328
\(531\) 0 0
\(532\) 2167.03 0.176603
\(533\) −6637.01 11495.6i −0.539364 0.934205i
\(534\) 0 0
\(535\) 1359.43 2354.60i 0.109857 0.190277i
\(536\) 4932.32 8543.02i 0.397469 0.688437i
\(537\) 0 0
\(538\) −4165.63 7215.09i −0.333816 0.578187i
\(539\) −2857.44 −0.228347
\(540\) 0 0
\(541\) −4182.33 −0.332370 −0.166185 0.986095i \(-0.553145\pi\)
−0.166185 + 0.986095i \(0.553145\pi\)
\(542\) 1573.95 + 2726.16i 0.124736 + 0.216049i
\(543\) 0 0
\(544\) −201.590 + 349.164i −0.0158881 + 0.0275189i
\(545\) 4091.35 7086.42i 0.321567 0.556970i
\(546\) 0 0
\(547\) −2506.95 4342.17i −0.195959 0.339411i 0.751256 0.660011i \(-0.229449\pi\)
−0.947214 + 0.320601i \(0.896115\pi\)
\(548\) 8133.14 0.633997
\(549\) 0 0
\(550\) 460.995 0.0357398
\(551\) 4471.99 + 7745.72i 0.345759 + 0.598872i
\(552\) 0 0
\(553\) −2672.81 + 4629.44i −0.205532 + 0.355993i
\(554\) −2262.38 + 3918.56i −0.173501 + 0.300512i
\(555\) 0 0
\(556\) 3194.49 + 5533.01i 0.243663 + 0.422036i
\(557\) −2611.86 −0.198686 −0.0993430 0.995053i \(-0.531674\pi\)
−0.0993430 + 0.995053i \(0.531674\pi\)
\(558\) 0 0
\(559\) −11741.3 −0.888377
\(560\) −241.045 417.502i −0.0181893 0.0315048i
\(561\) 0 0
\(562\) −5289.48 + 9161.64i −0.397016 + 0.687652i
\(563\) 9337.00 16172.2i 0.698948 1.21061i −0.269884 0.962893i \(-0.586985\pi\)
0.968832 0.247720i \(-0.0796813\pi\)
\(564\) 0 0
\(565\) 1364.50 + 2363.38i 0.101601 + 0.175979i
\(566\) −5344.74 −0.396919
\(567\) 0 0
\(568\) −23438.6 −1.73145
\(569\) 11835.5 + 20499.7i 0.872004 + 1.51036i 0.859920 + 0.510429i \(0.170513\pi\)
0.0120843 + 0.999927i \(0.496153\pi\)
\(570\) 0 0
\(571\) 4677.77 8102.14i 0.342835 0.593807i −0.642123 0.766601i \(-0.721946\pi\)
0.984958 + 0.172794i \(0.0552796\pi\)
\(572\) 569.838 986.989i 0.0416541 0.0721470i
\(573\) 0 0
\(574\) 1852.79 + 3209.12i 0.134728 + 0.233356i
\(575\) 3299.37 0.239293
\(576\) 0 0
\(577\) −21695.2 −1.56531 −0.782653 0.622459i \(-0.786134\pi\)
−0.782653 + 0.622459i \(0.786134\pi\)
\(578\) 5085.60 + 8808.51i 0.365974 + 0.633885i
\(579\) 0 0
\(580\) −658.981 + 1141.39i −0.0471770 + 0.0817130i
\(581\) 414.944 718.705i 0.0296296 0.0513200i
\(582\) 0 0
\(583\) −1132.33 1961.26i −0.0804399 0.139326i
\(584\) −6700.18 −0.474752
\(585\) 0 0
\(586\) −17290.7 −1.21889
\(587\) −368.574 638.389i −0.0259160 0.0448878i 0.852777 0.522276i \(-0.174917\pi\)
−0.878693 + 0.477388i \(0.841584\pi\)
\(588\) 0 0
\(589\) −843.086 + 1460.27i −0.0589792 + 0.102155i
\(590\) 170.109 294.637i 0.0118700 0.0205594i
\(591\) 0 0
\(592\) 2935.78 + 5084.92i 0.203817 + 0.353022i
\(593\) −21908.1 −1.51713 −0.758565 0.651597i \(-0.774099\pi\)
−0.758565 + 0.651597i \(0.774099\pi\)
\(594\) 0 0
\(595\) −62.1464 −0.00428194
\(596\) −3334.02 5774.68i −0.229139 0.396880i
\(597\) 0 0
\(598\) −4735.94 + 8202.89i −0.323858 + 0.560939i
\(599\) 3797.92 6578.19i 0.259063 0.448710i −0.706928 0.707285i \(-0.749920\pi\)
0.965991 + 0.258575i \(0.0832529\pi\)
\(600\) 0 0
\(601\) 3251.26 + 5631.35i 0.220668 + 0.382209i 0.955011 0.296570i \(-0.0958428\pi\)
−0.734343 + 0.678779i \(0.762509\pi\)
\(602\) 3277.69 0.221908
\(603\) 0 0
\(604\) −12319.6 −0.829929
\(605\) 3129.74 + 5420.86i 0.210317 + 0.364280i
\(606\) 0 0
\(607\) 13078.4 22652.5i 0.874524 1.51472i 0.0172560 0.999851i \(-0.494507\pi\)
0.857268 0.514870i \(-0.172160\pi\)
\(608\) −9495.10 + 16446.0i −0.633351 + 1.09700i
\(609\) 0 0
\(610\) −969.160 1678.63i −0.0643281 0.111420i
\(611\) 2710.06 0.179439
\(612\) 0 0
\(613\) 18172.8 1.19738 0.598690 0.800981i \(-0.295688\pi\)
0.598690 + 0.800981i \(0.295688\pi\)
\(614\) −7300.28 12644.4i −0.479829 0.831089i
\(615\) 0 0
\(616\) −502.877 + 871.008i −0.0328920 + 0.0569706i
\(617\) 13292.4 23023.1i 0.867312 1.50223i 0.00257822 0.999997i \(-0.499179\pi\)
0.864733 0.502231i \(-0.167487\pi\)
\(618\) 0 0
\(619\) −10843.9 18782.2i −0.704124 1.21958i −0.967007 0.254751i \(-0.918006\pi\)
0.262882 0.964828i \(-0.415327\pi\)
\(620\) −248.470 −0.0160948
\(621\) 0 0
\(622\) 4857.48 0.313131
\(623\) 1879.57 + 3255.50i 0.120872 + 0.209356i
\(624\) 0 0
\(625\) −312.500 + 541.266i −0.0200000 + 0.0346410i
\(626\) 3973.89 6882.98i 0.253720 0.439455i
\(627\) 0 0
\(628\) 7088.89 + 12278.3i 0.450442 + 0.780188i
\(629\) 756.907 0.0479807
\(630\) 0 0
\(631\) −7685.15 −0.484851 −0.242426 0.970170i \(-0.577943\pi\)
−0.242426 + 0.970170i \(0.577943\pi\)
\(632\) −13911.6 24095.6i −0.875590 1.51657i
\(633\) 0 0
\(634\) −6105.73 + 10575.4i −0.382476 + 0.662467i
\(635\) −90.1199 + 156.092i −0.00563197 + 0.00975486i
\(636\) 0 0
\(637\) 5560.79 + 9631.58i 0.345882 + 0.599085i
\(638\) −1313.11 −0.0814835
\(639\) 0 0
\(640\) −1082.88 −0.0668824
\(641\) 4027.84 + 6976.43i 0.248191 + 0.429879i 0.963024 0.269416i \(-0.0868307\pi\)
−0.714833 + 0.699295i \(0.753497\pi\)
\(642\) 0 0
\(643\) 3561.01 6167.85i 0.218402 0.378283i −0.735918 0.677071i \(-0.763249\pi\)
0.954320 + 0.298788i \(0.0965823\pi\)
\(644\) −1138.52 + 1971.97i −0.0696644 + 0.120662i
\(645\) 0 0
\(646\) −347.189 601.349i −0.0211455 0.0366250i
\(647\) 10280.7 0.624692 0.312346 0.949968i \(-0.398885\pi\)
0.312346 + 0.949968i \(0.398885\pi\)
\(648\) 0 0
\(649\) −291.901 −0.0176550
\(650\) −897.130 1553.87i −0.0541359 0.0937661i
\(651\) 0 0
\(652\) −4450.25 + 7708.06i −0.267309 + 0.462992i
\(653\) −4492.52 + 7781.27i −0.269228 + 0.466316i −0.968663 0.248380i \(-0.920102\pi\)
0.699435 + 0.714696i \(0.253435\pi\)
\(654\) 0 0
\(655\) −3275.38 5673.12i −0.195389 0.338423i
\(656\) −7931.92 −0.472087
\(657\) 0 0
\(658\) −756.541 −0.0448223
\(659\) 6269.36 + 10858.9i 0.370591 + 0.641883i 0.989657 0.143457i \(-0.0458217\pi\)
−0.619065 + 0.785340i \(0.712488\pi\)
\(660\) 0 0
\(661\) 6239.95 10807.9i 0.367180 0.635974i −0.621944 0.783062i \(-0.713657\pi\)
0.989123 + 0.147088i \(0.0469900\pi\)
\(662\) 6571.15 11381.6i 0.385793 0.668213i
\(663\) 0 0
\(664\) 2159.72 + 3740.75i 0.126225 + 0.218629i
\(665\) −2927.16 −0.170692
\(666\) 0 0
\(667\) −9398.01 −0.545566
\(668\) 6609.09 + 11447.3i 0.382805 + 0.663037i
\(669\) 0 0
\(670\) −2107.54 + 3650.37i −0.121524 + 0.210487i
\(671\) −831.522 + 1440.24i −0.0478399 + 0.0828611i
\(672\) 0 0
\(673\) −6592.82 11419.1i −0.377614 0.654047i 0.613100 0.790005i \(-0.289922\pi\)
−0.990715 + 0.135958i \(0.956589\pi\)
\(674\) 2007.63 0.114734
\(675\) 0 0
\(676\) 3696.60 0.210321
\(677\) 13284.1 + 23008.8i 0.754136 + 1.30620i 0.945802 + 0.324742i \(0.105278\pi\)
−0.191666 + 0.981460i \(0.561389\pi\)
\(678\) 0 0
\(679\) −2885.34 + 4997.56i −0.163077 + 0.282457i
\(680\) 161.731 280.127i 0.00912076 0.0157976i
\(681\) 0 0
\(682\) −123.778 214.389i −0.00694969 0.0120372i
\(683\) 7602.40 0.425912 0.212956 0.977062i \(-0.431691\pi\)
0.212956 + 0.977062i \(0.431691\pi\)
\(684\) 0 0
\(685\) −10986.0 −0.612780
\(686\) −3209.68 5559.33i −0.178639 0.309411i
\(687\) 0 0
\(688\) −3508.01 + 6076.05i −0.194392 + 0.336697i
\(689\) −4407.21 + 7633.51i −0.243688 + 0.422080i
\(690\) 0 0
\(691\) −3128.66 5418.99i −0.172243 0.298333i 0.766961 0.641694i \(-0.221768\pi\)
−0.939204 + 0.343361i \(0.888435\pi\)
\(692\) 592.018 0.0325219
\(693\) 0 0
\(694\) 13388.5 0.732307
\(695\) −4315.02 7473.84i −0.235508 0.407912i
\(696\) 0 0
\(697\) −511.254 + 885.518i −0.0277835 + 0.0481225i
\(698\) 6380.65 11051.6i 0.346004 0.599297i
\(699\) 0 0
\(700\) −215.669 373.550i −0.0116451 0.0201698i
\(701\) −769.271 −0.0414479 −0.0207239 0.999785i \(-0.506597\pi\)
−0.0207239 + 0.999785i \(0.506597\pi\)
\(702\) 0 0
\(703\) 35651.1 1.91267
\(704\) −2129.94 3689.16i −0.114027 0.197501i
\(705\) 0 0
\(706\) −3797.73 + 6577.87i −0.202450 + 0.350653i
\(707\) 1321.09 2288.20i 0.0702755 0.121721i
\(708\) 0 0
\(709\) 4225.16 + 7318.19i 0.223807 + 0.387645i 0.955961 0.293494i \(-0.0948181\pi\)
−0.732154 + 0.681139i \(0.761485\pi\)
\(710\) 10015.1 0.529383
\(711\) 0 0
\(712\) −19565.7 −1.02985
\(713\) −885.884 1534.40i −0.0465310 0.0805941i
\(714\) 0 0
\(715\) −769.721 + 1333.20i −0.0402601 + 0.0697325i
\(716\) −2074.49 + 3593.12i −0.108278 + 0.187544i
\(717\) 0 0
\(718\) −12556.3 21748.2i −0.652644 1.13041i
\(719\) −25350.0 −1.31488 −0.657438 0.753508i \(-0.728360\pi\)
−0.657438 + 0.753508i \(0.728360\pi\)
\(720\) 0 0
\(721\) 3817.54 0.197188
\(722\) −9242.71 16008.9i −0.476424 0.825191i
\(723\) 0 0
\(724\) −7137.87 + 12363.2i −0.366404 + 0.634631i
\(725\) 890.133 1541.75i 0.0455982 0.0789784i
\(726\) 0 0
\(727\) 1912.57 + 3312.68i 0.0975701 + 0.168996i 0.910678 0.413116i \(-0.135560\pi\)
−0.813108 + 0.582113i \(0.802226\pi\)
\(728\) 3914.54 0.199289
\(729\) 0 0
\(730\) 2862.94 0.145153
\(731\) 452.220 + 783.268i 0.0228809 + 0.0396309i
\(732\) 0 0
\(733\) 1846.41 3198.08i 0.0930407 0.161151i −0.815749 0.578407i \(-0.803675\pi\)
0.908789 + 0.417256i \(0.137008\pi\)
\(734\) −12041.7 + 20856.8i −0.605539 + 1.04882i
\(735\) 0 0
\(736\) −9977.10 17280.8i −0.499675 0.865462i
\(737\) 3616.46 0.180752
\(738\) 0 0
\(739\) 4181.32 0.208136 0.104068 0.994570i \(-0.466814\pi\)
0.104068 + 0.994570i \(0.466814\pi\)
\(740\) 2626.73 + 4549.62i 0.130487 + 0.226010i
\(741\) 0 0
\(742\) 1230.32 2130.97i 0.0608710 0.105432i
\(743\) 463.991 803.656i 0.0229101 0.0396814i −0.854343 0.519709i \(-0.826040\pi\)
0.877253 + 0.480028i \(0.159374\pi\)
\(744\) 0 0
\(745\) 4503.49 + 7800.28i 0.221470 + 0.383598i
\(746\) −4593.78 −0.225456
\(747\) 0 0
\(748\) −87.7902 −0.00429135
\(749\) −1267.29 2195.02i −0.0618236 0.107082i
\(750\) 0 0
\(751\) 11184.7 19372.5i 0.543458 0.941297i −0.455244 0.890367i \(-0.650448\pi\)
0.998702 0.0509306i \(-0.0162187\pi\)
\(752\) 809.702 1402.45i 0.0392644 0.0680079i
\(753\) 0 0
\(754\) 2555.41 + 4426.09i 0.123425 + 0.213778i
\(755\) 16640.9 0.802154
\(756\) 0 0
\(757\) 35390.0 1.69917 0.849586 0.527451i \(-0.176852\pi\)
0.849586 + 0.527451i \(0.176852\pi\)
\(758\) 6779.38 + 11742.2i 0.324853 + 0.562661i
\(759\) 0 0
\(760\) 7617.72 13194.3i 0.363584 0.629746i
\(761\) −16717.3 + 28955.2i −0.796323 + 1.37927i 0.125673 + 0.992072i \(0.459891\pi\)
−0.921996 + 0.387200i \(0.873442\pi\)
\(762\) 0 0
\(763\) −3814.05 6606.13i −0.180967 0.313444i
\(764\) 292.462 0.0138494
\(765\) 0 0
\(766\) 17612.9 0.830783
\(767\) 568.060 + 983.909i 0.0267425 + 0.0463193i
\(768\) 0 0
\(769\) −12510.7 + 21669.2i −0.586668 + 1.01614i 0.407998 + 0.912983i \(0.366227\pi\)
−0.994665 + 0.103155i \(0.967106\pi\)
\(770\) 214.875 372.175i 0.0100566 0.0174185i
\(771\) 0 0
\(772\) 8460.89 + 14654.7i 0.394448 + 0.683205i
\(773\) −3065.27 −0.142626 −0.0713132 0.997454i \(-0.522719\pi\)
−0.0713132 + 0.997454i \(0.522719\pi\)
\(774\) 0 0
\(775\) 335.626 0.0155562
\(776\) −15017.8 26011.5i −0.694725 1.20330i
\(777\) 0 0
\(778\) 3666.39 6350.38i 0.168954 0.292638i
\(779\) −24080.6 + 41708.8i −1.10754 + 1.91832i
\(780\) 0 0
\(781\) −4296.41 7441.59i −0.196847 0.340949i
\(782\) 729.627 0.0333650
\(783\) 0 0
\(784\) 6645.73 0.302739
\(785\) −9575.47 16585.2i −0.435367 0.754078i
\(786\) 0 0
\(787\) 17841.6 30902.5i 0.808111 1.39969i