Properties

Label 63.4.p.a.26.6
Level $63$
Weight $4$
Character 63.26
Analytic conductor $3.717$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 63 = 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 63.p (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.71712033036\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
Defining polynomial: \(x^{16} - 48 x^{14} + 1647 x^{12} - 27620 x^{10} + 336765 x^{8} - 1200006 x^{6} + 3242464 x^{4} - 1762200 x^{2} + 810000\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{4}\cdot 3^{8} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 26.6
Root \(1.57646 + 0.910170i\) of defining polynomial
Character \(\chi\) \(=\) 63.26
Dual form 63.4.p.a.17.6

$q$-expansion

\(f(q)\) \(=\) \(q+(1.57646 + 0.910170i) q^{2} +(-2.34318 - 4.05851i) q^{4} +(7.54372 - 13.0661i) q^{5} +(16.2919 + 8.80760i) q^{7} -23.0935i q^{8} +O(q^{10})\) \(q+(1.57646 + 0.910170i) q^{2} +(-2.34318 - 4.05851i) q^{4} +(7.54372 - 13.0661i) q^{5} +(16.2919 + 8.80760i) q^{7} -23.0935i q^{8} +(23.7848 - 13.7321i) q^{10} +(8.56529 - 4.94517i) q^{11} +67.8891i q^{13} +(17.6671 + 28.7132i) q^{14} +(2.27356 - 3.93792i) q^{16} +(-35.0687 - 60.7407i) q^{17} +(-53.2242 - 30.7290i) q^{19} -70.7052 q^{20} +18.0038 q^{22} +(113.895 + 65.7575i) q^{23} +(-51.3154 - 88.8809i) q^{25} +(-61.7906 + 107.025i) q^{26} +(-2.42915 - 86.7586i) q^{28} +158.738i q^{29} +(-66.2349 + 38.2407i) q^{31} +(-152.828 + 88.2353i) q^{32} -127.674i q^{34} +(237.983 - 146.430i) q^{35} +(-174.341 + 301.967i) q^{37} +(-55.9372 - 96.8861i) q^{38} +(-301.742 - 174.211i) q^{40} -138.909 q^{41} +539.651 q^{43} +(-40.1400 - 23.1749i) q^{44} +(119.701 + 207.328i) q^{46} +(-111.821 + 193.680i) q^{47} +(187.852 + 286.985i) q^{49} -186.823i q^{50} +(275.529 - 159.076i) q^{52} +(459.003 - 265.005i) q^{53} -149.220i q^{55} +(203.398 - 376.237i) q^{56} +(-144.479 + 250.245i) q^{58} +(-271.438 - 470.145i) q^{59} +(-116.218 - 67.0983i) q^{61} -139.222 q^{62} -357.614 q^{64} +(887.046 + 512.136i) q^{65} +(-160.290 - 277.630i) q^{67} +(-164.344 + 284.653i) q^{68} +(508.446 - 14.2359i) q^{70} -416.958i q^{71} +(472.510 - 272.804i) q^{73} +(-549.683 + 317.360i) q^{74} +288.014i q^{76} +(183.100 - 5.12660i) q^{77} +(161.369 - 279.499i) q^{79} +(-34.3022 - 59.4132i) q^{80} +(-218.984 - 126.431i) q^{82} -885.170 q^{83} -1058.19 q^{85} +(850.739 + 491.174i) q^{86} +(-114.201 - 197.802i) q^{88} +(-812.312 + 1406.97i) q^{89} +(-597.940 + 1106.04i) q^{91} -616.327i q^{92} +(-352.564 + 203.553i) q^{94} +(-803.017 + 463.622i) q^{95} -739.155i q^{97} +(34.9363 + 623.398i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q + 32q^{4} + 56q^{7} + O(q^{10}) \) \( 16q + 32q^{4} + 56q^{7} - 72q^{10} - 188q^{16} - 612q^{19} + 528q^{22} - 20q^{25} + 1036q^{28} + 1128q^{31} - 1196q^{37} - 3204q^{40} + 328q^{43} - 1392q^{46} + 784q^{49} + 4452q^{52} - 3372q^{58} - 1632q^{61} + 5432q^{64} + 308q^{67} + 3612q^{70} + 4068q^{73} - 2176q^{79} - 10188q^{82} - 4608q^{85} + 708q^{88} + 924q^{91} - 2916q^{94} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/63\mathbb{Z}\right)^\times\).

\(n\) \(10\) \(29\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(-1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.57646 + 0.910170i 0.557363 + 0.321794i 0.752086 0.659064i \(-0.229048\pi\)
−0.194723 + 0.980858i \(0.562381\pi\)
\(3\) 0 0
\(4\) −2.34318 4.05851i −0.292898 0.507314i
\(5\) 7.54372 13.0661i 0.674731 1.16867i −0.301817 0.953366i \(-0.597593\pi\)
0.976547 0.215302i \(-0.0690736\pi\)
\(6\) 0 0
\(7\) 16.2919 + 8.80760i 0.879680 + 0.475566i
\(8\) 23.0935i 1.02060i
\(9\) 0 0
\(10\) 23.7848 13.7321i 0.752140 0.434248i
\(11\) 8.56529 4.94517i 0.234776 0.135548i −0.377998 0.925807i \(-0.623387\pi\)
0.612773 + 0.790259i \(0.290054\pi\)
\(12\) 0 0
\(13\) 67.8891i 1.44839i 0.689596 + 0.724194i \(0.257788\pi\)
−0.689596 + 0.724194i \(0.742212\pi\)
\(14\) 17.6671 + 28.7132i 0.337267 + 0.548138i
\(15\) 0 0
\(16\) 2.27356 3.93792i 0.0355244 0.0615300i
\(17\) −35.0687 60.7407i −0.500318 0.866575i −1.00000 0.000366661i \(-0.999883\pi\)
0.499682 0.866209i \(-0.333450\pi\)
\(18\) 0 0
\(19\) −53.2242 30.7290i −0.642656 0.371038i 0.142981 0.989725i \(-0.454331\pi\)
−0.785637 + 0.618688i \(0.787665\pi\)
\(20\) −70.7052 −0.790508
\(21\) 0 0
\(22\) 18.0038 0.174474
\(23\) 113.895 + 65.7575i 1.03256 + 0.596147i 0.917716 0.397236i \(-0.130031\pi\)
0.114841 + 0.993384i \(0.463364\pi\)
\(24\) 0 0
\(25\) −51.3154 88.8809i −0.410523 0.711047i
\(26\) −61.7906 + 107.025i −0.466082 + 0.807278i
\(27\) 0 0
\(28\) −2.42915 86.7586i −0.0163952 0.585566i
\(29\) 158.738i 1.01645i 0.861225 + 0.508223i \(0.169698\pi\)
−0.861225 + 0.508223i \(0.830302\pi\)
\(30\) 0 0
\(31\) −66.2349 + 38.2407i −0.383746 + 0.221556i −0.679447 0.733725i \(-0.737780\pi\)
0.295701 + 0.955281i \(0.404447\pi\)
\(32\) −152.828 + 88.2353i −0.844264 + 0.487436i
\(33\) 0 0
\(34\) 127.674i 0.643996i
\(35\) 237.983 146.430i 1.14933 0.707175i
\(36\) 0 0
\(37\) −174.341 + 301.967i −0.774634 + 1.34171i 0.160366 + 0.987058i \(0.448733\pi\)
−0.935000 + 0.354648i \(0.884601\pi\)
\(38\) −55.9372 96.8861i −0.238795 0.413605i
\(39\) 0 0
\(40\) −301.742 174.211i −1.19274 0.688629i
\(41\) −138.909 −0.529120 −0.264560 0.964369i \(-0.585227\pi\)
−0.264560 + 0.964369i \(0.585227\pi\)
\(42\) 0 0
\(43\) 539.651 1.91386 0.956931 0.290316i \(-0.0937604\pi\)
0.956931 + 0.290316i \(0.0937604\pi\)
\(44\) −40.1400 23.1749i −0.137530 0.0794032i
\(45\) 0 0
\(46\) 119.701 + 207.328i 0.383673 + 0.664541i
\(47\) −111.821 + 193.680i −0.347039 + 0.601089i −0.985722 0.168381i \(-0.946146\pi\)
0.638683 + 0.769470i \(0.279480\pi\)
\(48\) 0 0
\(49\) 187.852 + 286.985i 0.547674 + 0.836692i
\(50\) 186.823i 0.528415i
\(51\) 0 0
\(52\) 275.529 159.076i 0.734787 0.424230i
\(53\) 459.003 265.005i 1.18960 0.686817i 0.231386 0.972862i \(-0.425674\pi\)
0.958216 + 0.286045i \(0.0923407\pi\)
\(54\) 0 0
\(55\) 149.220i 0.365833i
\(56\) 203.398 376.237i 0.485362 0.897800i
\(57\) 0 0
\(58\) −144.479 + 250.245i −0.327086 + 0.566530i
\(59\) −271.438 470.145i −0.598953 1.03742i −0.992976 0.118317i \(-0.962250\pi\)
0.394023 0.919101i \(-0.371083\pi\)
\(60\) 0 0
\(61\) −116.218 67.0983i −0.243937 0.140837i 0.373048 0.927812i \(-0.378313\pi\)
−0.616985 + 0.786975i \(0.711646\pi\)
\(62\) −139.222 −0.285181
\(63\) 0 0
\(64\) −357.614 −0.698464
\(65\) 887.046 + 512.136i 1.69269 + 0.977272i
\(66\) 0 0
\(67\) −160.290 277.630i −0.292276 0.506238i 0.682071 0.731286i \(-0.261079\pi\)
−0.974348 + 0.225048i \(0.927746\pi\)
\(68\) −164.344 + 284.653i −0.293084 + 0.507636i
\(69\) 0 0
\(70\) 508.446 14.2359i 0.868156 0.0243074i
\(71\) 416.958i 0.696955i −0.937317 0.348478i \(-0.886699\pi\)
0.937317 0.348478i \(-0.113301\pi\)
\(72\) 0 0
\(73\) 472.510 272.804i 0.757577 0.437387i −0.0708484 0.997487i \(-0.522571\pi\)
0.828425 + 0.560100i \(0.189237\pi\)
\(74\) −549.683 + 317.360i −0.863505 + 0.498545i
\(75\) 0 0
\(76\) 288.014i 0.434704i
\(77\) 183.100 5.12660i 0.270989 0.00758740i
\(78\) 0 0
\(79\) 161.369 279.499i 0.229815 0.398052i −0.727938 0.685643i \(-0.759521\pi\)
0.957753 + 0.287591i \(0.0928545\pi\)
\(80\) −34.3022 59.4132i −0.0479388 0.0830324i
\(81\) 0 0
\(82\) −218.984 126.431i −0.294912 0.170267i
\(83\) −885.170 −1.17060 −0.585301 0.810816i \(-0.699024\pi\)
−0.585301 + 0.810816i \(0.699024\pi\)
\(84\) 0 0
\(85\) −1058.19 −1.35032
\(86\) 850.739 + 491.174i 1.06672 + 0.615869i
\(87\) 0 0
\(88\) −114.201 197.802i −0.138340 0.239612i
\(89\) −812.312 + 1406.97i −0.967471 + 1.67571i −0.264645 + 0.964346i \(0.585255\pi\)
−0.702826 + 0.711362i \(0.748079\pi\)
\(90\) 0 0
\(91\) −597.940 + 1106.04i −0.688804 + 1.27412i
\(92\) 616.327i 0.698441i
\(93\) 0 0
\(94\) −352.564 + 203.553i −0.386853 + 0.223350i
\(95\) −803.017 + 463.622i −0.867240 + 0.500701i
\(96\) 0 0
\(97\) 739.155i 0.773710i −0.922141 0.386855i \(-0.873561\pi\)
0.922141 0.386855i \(-0.126439\pi\)
\(98\) 34.9363 + 623.398i 0.0360112 + 0.642579i
\(99\) 0 0
\(100\) −240.483 + 416.528i −0.240483 + 0.416528i
\(101\) −119.758 207.427i −0.117984 0.204354i 0.800985 0.598685i \(-0.204310\pi\)
−0.918969 + 0.394331i \(0.870976\pi\)
\(102\) 0 0
\(103\) −44.2852 25.5681i −0.0423645 0.0244592i 0.478668 0.877996i \(-0.341120\pi\)
−0.521033 + 0.853537i \(0.674453\pi\)
\(104\) 1567.80 1.47822
\(105\) 0 0
\(106\) 964.800 0.884054
\(107\) −1031.43 595.495i −0.931886 0.538025i −0.0444785 0.999010i \(-0.514163\pi\)
−0.887408 + 0.460986i \(0.847496\pi\)
\(108\) 0 0
\(109\) −194.585 337.031i −0.170989 0.296162i 0.767777 0.640718i \(-0.221363\pi\)
−0.938766 + 0.344555i \(0.888030\pi\)
\(110\) 135.816 235.239i 0.117723 0.203902i
\(111\) 0 0
\(112\) 71.7243 44.1316i 0.0605117 0.0372326i
\(113\) 718.545i 0.598186i 0.954224 + 0.299093i \(0.0966841\pi\)
−0.954224 + 0.299093i \(0.903316\pi\)
\(114\) 0 0
\(115\) 1718.39 992.113i 1.39340 0.804478i
\(116\) 644.240 371.952i 0.515657 0.297715i
\(117\) 0 0
\(118\) 988.220i 0.770958i
\(119\) −36.3552 1298.45i −0.0280057 1.00024i
\(120\) 0 0
\(121\) −616.591 + 1067.97i −0.463254 + 0.802379i
\(122\) −122.142 211.556i −0.0906409 0.156995i
\(123\) 0 0
\(124\) 310.401 + 179.210i 0.224797 + 0.129786i
\(125\) 337.493 0.241490
\(126\) 0 0
\(127\) −179.456 −0.125387 −0.0626934 0.998033i \(-0.519969\pi\)
−0.0626934 + 0.998033i \(0.519969\pi\)
\(128\) 658.861 + 380.393i 0.454966 + 0.262675i
\(129\) 0 0
\(130\) 932.263 + 1614.73i 0.628960 + 1.08939i
\(131\) 1223.43 2119.05i 0.815968 1.41330i −0.0926619 0.995698i \(-0.529538\pi\)
0.908630 0.417601i \(-0.137129\pi\)
\(132\) 0 0
\(133\) −596.474 969.411i −0.388879 0.632020i
\(134\) 583.564i 0.376211i
\(135\) 0 0
\(136\) −1402.71 + 809.858i −0.884425 + 0.510623i
\(137\) 443.021 255.778i 0.276276 0.159508i −0.355460 0.934691i \(-0.615676\pi\)
0.631736 + 0.775183i \(0.282342\pi\)
\(138\) 0 0
\(139\) 599.427i 0.365775i −0.983134 0.182888i \(-0.941456\pi\)
0.983134 0.182888i \(-0.0585444\pi\)
\(140\) −1151.92 622.743i −0.695394 0.375939i
\(141\) 0 0
\(142\) 379.503 657.318i 0.224276 0.388457i
\(143\) 335.723 + 581.490i 0.196326 + 0.340046i
\(144\) 0 0
\(145\) 2074.09 + 1197.48i 1.18789 + 0.685828i
\(146\) 993.191 0.562994
\(147\) 0 0
\(148\) 1634.05 0.907554
\(149\) −1899.63 1096.75i −1.04445 0.603016i −0.123362 0.992362i \(-0.539368\pi\)
−0.921092 + 0.389346i \(0.872701\pi\)
\(150\) 0 0
\(151\) 358.683 + 621.257i 0.193306 + 0.334816i 0.946344 0.323161i \(-0.104746\pi\)
−0.753038 + 0.657977i \(0.771412\pi\)
\(152\) −709.640 + 1229.13i −0.378680 + 0.655893i
\(153\) 0 0
\(154\) 293.316 + 158.570i 0.153481 + 0.0829737i
\(155\) 1153.91i 0.597963i
\(156\) 0 0
\(157\) −1561.39 + 901.471i −0.793712 + 0.458250i −0.841268 0.540619i \(-0.818190\pi\)
0.0475556 + 0.998869i \(0.484857\pi\)
\(158\) 508.783 293.746i 0.256181 0.147906i
\(159\) 0 0
\(160\) 2662.49i 1.31555i
\(161\) 1276.41 + 2074.46i 0.624813 + 1.01547i
\(162\) 0 0
\(163\) 1453.90 2518.24i 0.698642 1.21008i −0.270296 0.962777i \(-0.587122\pi\)
0.968938 0.247305i \(-0.0795451\pi\)
\(164\) 325.489 + 563.763i 0.154978 + 0.268430i
\(165\) 0 0
\(166\) −1395.44 805.655i −0.652451 0.376693i
\(167\) −3491.37 −1.61779 −0.808893 0.587956i \(-0.799933\pi\)
−0.808893 + 0.587956i \(0.799933\pi\)
\(168\) 0 0
\(169\) −2411.93 −1.09783
\(170\) −1668.20 963.135i −0.752618 0.434524i
\(171\) 0 0
\(172\) −1264.50 2190.18i −0.560566 0.970928i
\(173\) 877.377 1519.66i 0.385583 0.667848i −0.606267 0.795261i \(-0.707334\pi\)
0.991850 + 0.127412i \(0.0406672\pi\)
\(174\) 0 0
\(175\) −53.1981 1900.01i −0.0229794 0.820725i
\(176\) 44.9726i 0.0192610i
\(177\) 0 0
\(178\) −2561.16 + 1478.68i −1.07846 + 0.622652i
\(179\) 685.639 395.854i 0.286296 0.165293i −0.349974 0.936759i \(-0.613810\pi\)
0.636270 + 0.771466i \(0.280476\pi\)
\(180\) 0 0
\(181\) 2522.19i 1.03576i 0.855452 + 0.517882i \(0.173279\pi\)
−0.855452 + 0.517882i \(0.826721\pi\)
\(182\) −1949.32 + 1199.41i −0.793917 + 0.488494i
\(183\) 0 0
\(184\) 1518.57 2630.24i 0.608427 1.05383i
\(185\) 2630.36 + 4555.91i 1.04534 + 1.81058i
\(186\) 0 0
\(187\) −600.746 346.841i −0.234925 0.135634i
\(188\) 1048.07 0.406588
\(189\) 0 0
\(190\) −1687.90 −0.644490
\(191\) 782.266 + 451.642i 0.296350 + 0.171098i 0.640802 0.767706i \(-0.278602\pi\)
−0.344452 + 0.938804i \(0.611935\pi\)
\(192\) 0 0
\(193\) 99.4374 + 172.231i 0.0370863 + 0.0642354i 0.883973 0.467538i \(-0.154859\pi\)
−0.846886 + 0.531774i \(0.821526\pi\)
\(194\) 672.757 1165.25i 0.248975 0.431237i
\(195\) 0 0
\(196\) 724.560 1434.86i 0.264053 0.522908i
\(197\) 3220.69i 1.16480i 0.812904 + 0.582398i \(0.197886\pi\)
−0.812904 + 0.582398i \(0.802114\pi\)
\(198\) 0 0
\(199\) 2468.10 1424.96i 0.879191 0.507601i 0.00879944 0.999961i \(-0.497199\pi\)
0.870392 + 0.492360i \(0.163866\pi\)
\(200\) −2052.57 + 1185.05i −0.725694 + 0.418979i
\(201\) 0 0
\(202\) 436.000i 0.151866i
\(203\) −1398.10 + 2586.15i −0.483387 + 0.894148i
\(204\) 0 0
\(205\) −1047.89 + 1815.00i −0.357014 + 0.618366i
\(206\) −46.5426 80.6141i −0.0157416 0.0272653i
\(207\) 0 0
\(208\) 267.342 + 154.350i 0.0891194 + 0.0514531i
\(209\) −607.841 −0.201173
\(210\) 0 0
\(211\) 1204.50 0.392993 0.196496 0.980505i \(-0.437044\pi\)
0.196496 + 0.980505i \(0.437044\pi\)
\(212\) −2151.05 1241.91i −0.696863 0.402334i
\(213\) 0 0
\(214\) −1084.00 1877.55i −0.346266 0.599750i
\(215\) 4070.98 7051.14i 1.29134 2.23667i
\(216\) 0 0
\(217\) −1415.90 + 39.6437i −0.442938 + 0.0124018i
\(218\) 708.421i 0.220093i
\(219\) 0 0
\(220\) −605.611 + 349.649i −0.185592 + 0.107152i
\(221\) 4123.63 2380.78i 1.25514 0.724654i
\(222\) 0 0
\(223\) 3377.73i 1.01430i 0.861857 + 0.507151i \(0.169301\pi\)
−0.861857 + 0.507151i \(0.830699\pi\)
\(224\) −3267.00 + 91.4725i −0.974490 + 0.0272846i
\(225\) 0 0
\(226\) −653.998 + 1132.76i −0.192493 + 0.333407i
\(227\) −2261.98 3917.86i −0.661378 1.14554i −0.980254 0.197744i \(-0.936638\pi\)
0.318875 0.947797i \(-0.396695\pi\)
\(228\) 0 0
\(229\) 3389.61 + 1956.99i 0.978131 + 0.564724i 0.901705 0.432351i \(-0.142316\pi\)
0.0764258 + 0.997075i \(0.475649\pi\)
\(230\) 3611.96 1.03550
\(231\) 0 0
\(232\) 3665.82 1.03738
\(233\) −3783.80 2184.58i −1.06388 0.614234i −0.137381 0.990518i \(-0.543868\pi\)
−0.926504 + 0.376284i \(0.877202\pi\)
\(234\) 0 0
\(235\) 1687.10 + 2922.14i 0.468316 + 0.811147i
\(236\) −1272.06 + 2203.27i −0.350864 + 0.607714i
\(237\) 0 0
\(238\) 1124.50 2080.05i 0.306263 0.566511i
\(239\) 1945.23i 0.526471i 0.964732 + 0.263235i \(0.0847896\pi\)
−0.964732 + 0.263235i \(0.915210\pi\)
\(240\) 0 0
\(241\) −3499.81 + 2020.61i −0.935446 + 0.540080i −0.888530 0.458819i \(-0.848273\pi\)
−0.0469158 + 0.998899i \(0.514939\pi\)
\(242\) −1944.06 + 1122.40i −0.516401 + 0.298144i
\(243\) 0 0
\(244\) 628.894i 0.165003i
\(245\) 5166.88 289.561i 1.34735 0.0755077i
\(246\) 0 0
\(247\) 2086.16 3613.34i 0.537407 0.930816i
\(248\) 883.112 + 1529.59i 0.226120 + 0.391651i
\(249\) 0 0
\(250\) 532.045 + 307.176i 0.134598 + 0.0777101i
\(251\) 4415.70 1.11042 0.555212 0.831709i \(-0.312637\pi\)
0.555212 + 0.831709i \(0.312637\pi\)
\(252\) 0 0
\(253\) 1300.73 0.323226
\(254\) −282.905 163.335i −0.0698860 0.0403487i
\(255\) 0 0
\(256\) 2122.90 + 3676.97i 0.518286 + 0.897698i
\(257\) 348.800 604.139i 0.0846597 0.146635i −0.820586 0.571522i \(-0.806353\pi\)
0.905246 + 0.424888i \(0.139686\pi\)
\(258\) 0 0
\(259\) −5499.95 + 3384.10i −1.31950 + 0.811882i
\(260\) 4800.11i 1.14496i
\(261\) 0 0
\(262\) 3857.39 2227.06i 0.909581 0.525147i
\(263\) −690.664 + 398.755i −0.161932 + 0.0934915i −0.578776 0.815487i \(-0.696469\pi\)
0.416844 + 0.908978i \(0.363136\pi\)
\(264\) 0 0
\(265\) 7996.51i 1.85367i
\(266\) −57.9894 2071.13i −0.0133668 0.477403i
\(267\) 0 0
\(268\) −751.176 + 1301.08i −0.171214 + 0.296552i
\(269\) −205.351 355.679i −0.0465446 0.0806176i 0.841815 0.539767i \(-0.181488\pi\)
−0.888359 + 0.459149i \(0.848154\pi\)
\(270\) 0 0
\(271\) 3283.42 + 1895.69i 0.735992 + 0.424925i 0.820610 0.571488i \(-0.193634\pi\)
−0.0846182 + 0.996413i \(0.526967\pi\)
\(272\) −318.923 −0.0710939
\(273\) 0 0
\(274\) 931.207 0.205315
\(275\) −879.063 507.527i −0.192762 0.111291i
\(276\) 0 0
\(277\) −1623.31 2811.66i −0.352113 0.609877i 0.634507 0.772917i \(-0.281203\pi\)
−0.986619 + 0.163040i \(0.947870\pi\)
\(278\) 545.581 944.973i 0.117704 0.203870i
\(279\) 0 0
\(280\) −3381.57 5495.85i −0.721741 1.17300i
\(281\) 1599.58i 0.339583i 0.985480 + 0.169791i \(0.0543094\pi\)
−0.985480 + 0.169791i \(0.945691\pi\)
\(282\) 0 0
\(283\) −3694.70 + 2133.13i −0.776067 + 0.448062i −0.835034 0.550198i \(-0.814552\pi\)
0.0589678 + 0.998260i \(0.481219\pi\)
\(284\) −1692.23 + 977.008i −0.353575 + 0.204137i
\(285\) 0 0
\(286\) 1222.26i 0.252706i
\(287\) −2263.09 1223.45i −0.465456 0.251631i
\(288\) 0 0
\(289\) −3.12079 + 5.40536i −0.000635210 + 0.00110022i
\(290\) 2179.82 + 3775.55i 0.441390 + 0.764510i
\(291\) 0 0
\(292\) −2214.35 1278.46i −0.443785 0.256219i
\(293\) −2926.77 −0.583562 −0.291781 0.956485i \(-0.594248\pi\)
−0.291781 + 0.956485i \(0.594248\pi\)
\(294\) 0 0
\(295\) −8190.62 −1.61653
\(296\) 6973.48 + 4026.14i 1.36934 + 0.790590i
\(297\) 0 0
\(298\) −1996.46 3457.97i −0.388093 0.672198i
\(299\) −4464.22 + 7732.25i −0.863453 + 1.49554i
\(300\) 0 0
\(301\) 8791.95 + 4753.03i 1.68359 + 0.910167i
\(302\) 1305.85i 0.248819i
\(303\) 0 0
\(304\) −242.017 + 139.728i −0.0456599 + 0.0263618i
\(305\) −1753.43 + 1012.34i −0.329183 + 0.190054i
\(306\) 0 0
\(307\) 3571.36i 0.663935i −0.943291 0.331968i \(-0.892288\pi\)
0.943291 0.331968i \(-0.107712\pi\)
\(308\) −449.843 731.100i −0.0832213 0.135254i
\(309\) 0 0
\(310\) −1050.25 + 1819.09i −0.192421 + 0.333282i
\(311\) −1286.71 2228.64i −0.234606 0.406349i 0.724552 0.689220i \(-0.242047\pi\)
−0.959158 + 0.282871i \(0.908713\pi\)
\(312\) 0 0
\(313\) −1278.56 738.176i −0.230889 0.133304i 0.380093 0.924948i \(-0.375892\pi\)
−0.610982 + 0.791644i \(0.709225\pi\)
\(314\) −3281.97 −0.589848
\(315\) 0 0
\(316\) −1512.46 −0.269249
\(317\) 2188.36 + 1263.45i 0.387730 + 0.223856i 0.681176 0.732120i \(-0.261469\pi\)
−0.293446 + 0.955976i \(0.594802\pi\)
\(318\) 0 0
\(319\) 784.988 + 1359.64i 0.137777 + 0.238637i
\(320\) −2697.74 + 4672.62i −0.471275 + 0.816273i
\(321\) 0 0
\(322\) 124.093 + 4432.05i 0.0214764 + 0.767045i
\(323\) 4310.50i 0.742546i
\(324\) 0 0
\(325\) 6034.05 3483.76i 1.02987 0.594597i
\(326\) 4584.05 2646.60i 0.778794 0.449637i
\(327\) 0 0
\(328\) 3207.89i 0.540019i
\(329\) −3527.64 + 2170.54i −0.591141 + 0.363726i
\(330\) 0 0
\(331\) −737.778 + 1277.87i −0.122513 + 0.212200i −0.920758 0.390134i \(-0.872429\pi\)
0.798245 + 0.602333i \(0.205762\pi\)
\(332\) 2074.11 + 3592.47i 0.342867 + 0.593863i
\(333\) 0 0
\(334\) −5504.01 3177.74i −0.901694 0.520593i
\(335\) −4836.73 −0.788832
\(336\) 0 0
\(337\) −6727.28 −1.08741 −0.543706 0.839275i \(-0.682979\pi\)
−0.543706 + 0.839275i \(0.682979\pi\)
\(338\) −3802.32 2195.27i −0.611890 0.353275i
\(339\) 0 0
\(340\) 2479.54 + 4294.68i 0.395505 + 0.685035i
\(341\) −378.214 + 655.086i −0.0600629 + 0.104032i
\(342\) 0 0
\(343\) 532.819 + 6330.06i 0.0838761 + 0.996476i
\(344\) 12462.4i 1.95328i
\(345\) 0 0
\(346\) 2766.30 1597.13i 0.429819 0.248156i
\(347\) −466.060 + 269.080i −0.0721021 + 0.0416281i −0.535618 0.844461i \(-0.679921\pi\)
0.463516 + 0.886089i \(0.346588\pi\)
\(348\) 0 0
\(349\) 6975.93i 1.06995i −0.844867 0.534976i \(-0.820321\pi\)
0.844867 0.534976i \(-0.179679\pi\)
\(350\) 1645.46 3043.70i 0.251296 0.464837i
\(351\) 0 0
\(352\) −872.678 + 1511.52i −0.132142 + 0.228876i
\(353\) −4438.40 7687.53i −0.669213 1.15911i −0.978125 0.208020i \(-0.933298\pi\)
0.308912 0.951091i \(-0.400035\pi\)
\(354\) 0 0
\(355\) −5448.02 3145.42i −0.814509 0.470257i
\(356\) 7613.57 1.13348
\(357\) 0 0
\(358\) 1441.18 0.212761
\(359\) 9565.96 + 5522.91i 1.40633 + 0.811944i 0.995032 0.0995575i \(-0.0317427\pi\)
0.411297 + 0.911502i \(0.365076\pi\)
\(360\) 0 0
\(361\) −1540.96 2669.02i −0.224662 0.389126i
\(362\) −2295.62 + 3976.14i −0.333302 + 0.577296i
\(363\) 0 0
\(364\) 5889.97 164.913i 0.848127 0.0237466i
\(365\) 8231.82i 1.18047i
\(366\) 0 0
\(367\) 7210.59 4163.04i 1.02559 0.592122i 0.109868 0.993946i \(-0.464957\pi\)
0.915717 + 0.401824i \(0.131624\pi\)
\(368\) 517.896 299.007i 0.0733619 0.0423555i
\(369\) 0 0
\(370\) 9576.29i 1.34553i
\(371\) 9812.09 274.728i 1.37310 0.0384452i
\(372\) 0 0
\(373\) 2272.66 3936.36i 0.315479 0.546426i −0.664060 0.747679i \(-0.731168\pi\)
0.979539 + 0.201253i \(0.0645014\pi\)
\(374\) −631.369 1093.56i −0.0872922 0.151195i
\(375\) 0 0
\(376\) 4472.76 + 2582.35i 0.613470 + 0.354187i
\(377\) −10776.6 −1.47221
\(378\) 0 0
\(379\) 11527.2 1.56230 0.781151 0.624343i \(-0.214633\pi\)
0.781151 + 0.624343i \(0.214633\pi\)
\(380\) 3763.23 + 2172.70i 0.508025 + 0.293308i
\(381\) 0 0
\(382\) 822.141 + 1423.99i 0.110116 + 0.190727i
\(383\) 1960.23 3395.22i 0.261522 0.452970i −0.705124 0.709084i \(-0.749109\pi\)
0.966647 + 0.256114i \(0.0824422\pi\)
\(384\) 0 0
\(385\) 1314.27 2431.08i 0.173978 0.321816i
\(386\) 362.020i 0.0477366i
\(387\) 0 0
\(388\) −2999.87 + 1731.97i −0.392513 + 0.226618i
\(389\) 689.734 398.218i 0.0898995 0.0519035i −0.454376 0.890810i \(-0.650138\pi\)
0.544276 + 0.838906i \(0.316805\pi\)
\(390\) 0 0
\(391\) 9224.11i 1.19305i
\(392\) 6627.49 4338.16i 0.853926 0.558955i
\(393\) 0 0
\(394\) −2931.38 + 5077.30i −0.374824 + 0.649214i
\(395\) −2434.64 4216.92i −0.310127 0.537155i
\(396\) 0 0
\(397\) 3338.59 + 1927.54i 0.422063 + 0.243678i 0.695960 0.718081i \(-0.254979\pi\)
−0.273896 + 0.961759i \(0.588313\pi\)
\(398\) 5187.82 0.653371
\(399\) 0 0
\(400\) −466.675 −0.0583344
\(401\) 4031.65 + 2327.68i 0.502073 + 0.289872i 0.729569 0.683907i \(-0.239721\pi\)
−0.227496 + 0.973779i \(0.573054\pi\)
\(402\) 0 0
\(403\) −2596.13 4496.63i −0.320899 0.555814i
\(404\) −561.229 + 972.077i −0.0691143 + 0.119709i
\(405\) 0 0
\(406\) −4557.89 + 2804.45i −0.557153 + 0.342814i
\(407\) 3448.58i 0.420000i
\(408\) 0 0
\(409\) −8478.82 + 4895.25i −1.02506 + 0.591821i −0.915566 0.402167i \(-0.868257\pi\)
−0.109497 + 0.993987i \(0.534924\pi\)
\(410\) −3303.91 + 1907.52i −0.397972 + 0.229769i
\(411\) 0 0
\(412\) 239.642i 0.0286561i
\(413\) −281.397 10050.3i −0.0335269 1.19744i
\(414\) 0 0
\(415\) −6677.47 + 11565.7i −0.789842 + 1.36805i
\(416\) −5990.22 10375.4i −0.705997 1.22282i
\(417\) 0 0
\(418\) −958.237 553.238i −0.112127 0.0647363i
\(419\) 3007.46 0.350654 0.175327 0.984510i \(-0.443902\pi\)
0.175327 + 0.984510i \(0.443902\pi\)
\(420\) 0 0
\(421\) 7646.06 0.885145 0.442573 0.896733i \(-0.354066\pi\)
0.442573 + 0.896733i \(0.354066\pi\)
\(422\) 1898.85 + 1096.30i 0.219040 + 0.126463i
\(423\) 0 0
\(424\) −6119.90 10600.0i −0.700964 1.21411i
\(425\) −3599.13 + 6233.87i −0.410784 + 0.711499i
\(426\) 0 0
\(427\) −1302.43 2116.76i −0.147609 0.239899i
\(428\) 5581.41i 0.630345i
\(429\) 0 0
\(430\) 12835.5 7410.57i 1.43949 0.831091i
\(431\) −12983.1 + 7495.81i −1.45099 + 0.837727i −0.998537 0.0540641i \(-0.982782\pi\)
−0.452448 + 0.891791i \(0.649449\pi\)
\(432\) 0 0
\(433\) 5666.63i 0.628916i 0.949271 + 0.314458i \(0.101823\pi\)
−0.949271 + 0.314458i \(0.898177\pi\)
\(434\) −2268.20 1226.21i −0.250868 0.135623i
\(435\) 0 0
\(436\) −911.895 + 1579.45i −0.100165 + 0.173491i
\(437\) −4041.32 6999.78i −0.442386 0.766235i
\(438\) 0 0
\(439\) −4790.07 2765.55i −0.520769 0.300666i 0.216480 0.976287i \(-0.430542\pi\)
−0.737249 + 0.675621i \(0.763876\pi\)
\(440\) −3446.01 −0.373368
\(441\) 0 0
\(442\) 8667.66 0.932757
\(443\) −349.200 201.611i −0.0374515 0.0216226i 0.481157 0.876634i \(-0.340217\pi\)
−0.518609 + 0.855012i \(0.673550\pi\)
\(444\) 0 0
\(445\) 12255.7 + 21227.5i 1.30556 + 2.26130i
\(446\) −3074.31 + 5324.85i −0.326396 + 0.565334i
\(447\) 0 0
\(448\) −5826.21 3149.72i −0.614425 0.332166i
\(449\) 8429.03i 0.885948i 0.896534 + 0.442974i \(0.146077\pi\)
−0.896534 + 0.442974i \(0.853923\pi\)
\(450\) 0 0
\(451\) −1189.79 + 686.928i −0.124224 + 0.0717210i
\(452\) 2916.22 1683.68i 0.303468 0.175207i
\(453\) 0 0
\(454\) 8235.15i 0.851310i
\(455\) 9940.98 + 16156.4i 1.02426 + 1.66467i
\(456\) 0 0
\(457\) −342.830 + 593.799i −0.0350917 + 0.0607807i −0.883038 0.469302i \(-0.844506\pi\)
0.847946 + 0.530082i \(0.177839\pi\)
\(458\) 3562.40 + 6170.25i 0.363449 + 0.629513i
\(459\) 0 0
\(460\) −8052.99 4649.40i −0.816245 0.471259i
\(461\) −4864.48 −0.491456 −0.245728 0.969339i \(-0.579027\pi\)
−0.245728 + 0.969339i \(0.579027\pi\)
\(462\) 0 0
\(463\) −8354.23 −0.838562 −0.419281 0.907857i \(-0.637718\pi\)
−0.419281 + 0.907857i \(0.637718\pi\)
\(464\) 625.099 + 360.901i 0.0625420 + 0.0361086i
\(465\) 0 0
\(466\) −3976.68 6887.81i −0.395313 0.684703i
\(467\) −501.469 + 868.570i −0.0496900 + 0.0860656i −0.889801 0.456350i \(-0.849157\pi\)
0.840111 + 0.542415i \(0.182490\pi\)
\(468\) 0 0
\(469\) −166.170 5934.89i −0.0163604 0.584324i
\(470\) 6142.19i 0.602804i
\(471\) 0 0
\(472\) −10857.3 + 6268.46i −1.05879 + 0.611290i
\(473\) 4622.27 2668.67i 0.449328 0.259420i
\(474\) 0 0
\(475\) 6307.49i 0.609279i
\(476\) −5184.59 + 3190.06i −0.499234 + 0.307176i
\(477\) 0 0
\(478\) −1770.49 + 3066.58i −0.169415 + 0.293435i
\(479\) 3026.38 + 5241.84i 0.288682 + 0.500012i 0.973495 0.228706i \(-0.0734496\pi\)
−0.684813 + 0.728719i \(0.740116\pi\)
\(480\) 0 0
\(481\) −20500.3 11835.8i −1.94331 1.12197i
\(482\) −7356.41 −0.695177
\(483\) 0 0
\(484\) 5779.13 0.542743
\(485\) −9657.88 5575.98i −0.904210 0.522046i
\(486\) 0 0
\(487\) −7654.72 13258.4i −0.712255 1.23366i −0.964009 0.265871i \(-0.914340\pi\)
0.251753 0.967791i \(-0.418993\pi\)
\(488\) −1549.53 + 2683.87i −0.143738 + 0.248961i
\(489\) 0 0
\(490\) 8408.94 + 4246.26i 0.775260 + 0.391483i
\(491\) 4291.01i 0.394400i −0.980363 0.197200i \(-0.936815\pi\)
0.980363 0.197200i \(-0.0631848\pi\)
\(492\) 0 0
\(493\) 9641.87 5566.74i 0.880828 0.508546i
\(494\) 6577.51 3797.53i 0.599061 0.345868i
\(495\) 0 0
\(496\) 347.770i 0.0314826i
\(497\) 3672.40 6793.04i 0.331448 0.613098i
\(498\) 0 0
\(499\) −3445.77 + 5968.24i −0.309126 + 0.535421i −0.978171 0.207800i \(-0.933370\pi\)
0.669046 + 0.743221i \(0.266703\pi\)
\(500\) −790.807 1369.72i −0.0707319 0.122511i
\(501\) 0 0
\(502\) 6961.17 + 4019.03i 0.618909 + 0.357327i
\(503\) 13534.6 1.19975 0.599877 0.800092i \(-0.295216\pi\)
0.599877 + 0.800092i \(0.295216\pi\)
\(504\) 0 0
\(505\) −3613.68 −0.318429
\(506\) 2050.55 + 1183.88i 0.180154 + 0.104012i
\(507\) 0 0
\(508\) 420.498 + 728.323i 0.0367255 + 0.0636105i
\(509\) 6043.91 10468.4i 0.526310 0.911595i −0.473221 0.880944i \(-0.656909\pi\)
0.999530 0.0306510i \(-0.00975805\pi\)
\(510\) 0 0
\(511\) 10100.8 282.812i 0.874431 0.0244831i
\(512\) 1642.50i 0.141776i
\(513\) 0 0
\(514\) 1099.74 634.934i 0.0943724 0.0544859i
\(515\) −668.150 + 385.757i −0.0571693 + 0.0330067i
\(516\) 0 0
\(517\) 2211.91i 0.188161i
\(518\) −11750.6 + 329.003i −0.996699 + 0.0279065i
\(519\) 0 0
\(520\) 11827.0 20485.0i 0.997402 1.72755i
\(521\) 3812.94 + 6604.20i 0.320629 + 0.555346i 0.980618 0.195930i \(-0.0627724\pi\)
−0.659989 + 0.751275i \(0.729439\pi\)
\(522\) 0 0
\(523\) 13328.7 + 7695.34i 1.11439 + 0.643392i 0.939962 0.341279i \(-0.110860\pi\)
0.174425 + 0.984670i \(0.444193\pi\)
\(524\) −11466.9 −0.955981
\(525\) 0 0
\(526\) −1451.74 −0.120340
\(527\) 4645.54 + 2682.10i 0.383990 + 0.221697i
\(528\) 0 0
\(529\) 2564.60 + 4442.02i 0.210783 + 0.365088i
\(530\) 7278.18 12606.2i 0.596498 1.03317i
\(531\) 0 0
\(532\) −2536.72 + 4692.30i −0.206730 + 0.382401i
\(533\) 9430.40i 0.766371i
\(534\) 0 0
\(535\) −15561.6 + 8984.49i −1.25754 + 0.726044i
\(536\) −6411.45 + 3701.65i −0.516665 + 0.298297i
\(537\) 0 0
\(538\) 747.619i 0.0599110i
\(539\) 3028.20 + 1529.15i 0.241992 + 0.122199i
\(540\) 0 0
\(541\) 6850.44 11865.3i 0.544406 0.942939i −0.454238 0.890880i \(-0.650088\pi\)
0.998644 0.0520584i \(-0.0165782\pi\)
\(542\) 3450.79 + 5976.95i 0.273477 + 0.473675i
\(543\) 0 0
\(544\) 10718.9 + 6188.59i 0.844800 + 0.487745i
\(545\) −5871.58 −0.461487
\(546\) 0 0
\(547\) −6139.00 −0.479863 −0.239931 0.970790i \(-0.577125\pi\)
−0.239931 + 0.970790i \(0.577125\pi\)
\(548\) −2076.16 1198.67i −0.161841 0.0934391i
\(549\) 0 0
\(550\) −923.872 1600.19i −0.0716255 0.124059i
\(551\) 4877.87 8448.71i 0.377140 0.653226i
\(552\) 0 0
\(553\) 5090.72 3132.30i 0.391464 0.240866i
\(554\) 5909.95i 0.453231i
\(555\) 0 0
\(556\) −2432.78 + 1404.57i −0.185563 + 0.107135i
\(557\) 19687.1 11366.4i 1.49761 0.864646i 0.497615 0.867398i \(-0.334209\pi\)
0.999996 + 0.00275234i \(0.000876098\pi\)
\(558\) 0 0
\(559\) 36636.4i 2.77202i
\(560\) −35.5607 1270.07i −0.00268341 0.0958400i
\(561\) 0 0
\(562\) −1455.89 + 2521.67i −0.109276 + 0.189271i
\(563\) 4958.81 + 8588.90i 0.371206 + 0.642947i 0.989751 0.142802i \(-0.0456112\pi\)
−0.618546 + 0.785749i \(0.712278\pi\)
\(564\) 0 0
\(565\) 9388.59 + 5420.51i 0.699081 + 0.403615i
\(566\) −7766.06 −0.576735
\(567\) 0 0
\(568\) −9629.02 −0.711311
\(569\) −4448.79 2568.51i −0.327773 0.189240i 0.327079 0.944997i \(-0.393936\pi\)
−0.654852 + 0.755757i \(0.727269\pi\)
\(570\) 0 0
\(571\) 9093.02 + 15749.6i 0.666429 + 1.15429i 0.978896 + 0.204360i \(0.0655114\pi\)
−0.312467 + 0.949929i \(0.601155\pi\)
\(572\) 1573.32 2725.07i 0.115007 0.199198i
\(573\) 0 0
\(574\) −2454.12 3988.52i −0.178455 0.290031i
\(575\) 13497.5i 0.978930i
\(576\) 0 0
\(577\) 10737.5 6199.32i 0.774713 0.447281i −0.0598401 0.998208i \(-0.519059\pi\)
0.834553 + 0.550927i \(0.185726\pi\)
\(578\) −9.83959 + 5.68089i −0.000708085 + 0.000408813i
\(579\) 0 0
\(580\) 11223.6i 0.803509i
\(581\) −14421.1 7796.23i −1.02976 0.556699i
\(582\) 0 0
\(583\) 2621.00 4539.70i 0.186193 0.322496i
\(584\) −6299.99 10911.9i −0.446396 0.773181i
\(585\) 0 0
\(586\) −4613.94 2663.86i −0.325256 0.187787i
\(587\) 18977.6 1.33439 0.667195 0.744883i \(-0.267495\pi\)
0.667195 + 0.744883i \(0.267495\pi\)
\(588\) 0 0
\(589\) 4700.40 0.328822
\(590\) −12912.2 7454.85i −0.900994 0.520189i
\(591\) 0 0
\(592\) 792.749 + 1373.08i 0.0550368 + 0.0953265i
\(593\) −5364.44 + 9291.48i −0.371486 + 0.643432i −0.989794 0.142503i \(-0.954485\pi\)
0.618308 + 0.785936i \(0.287818\pi\)
\(594\) 0 0
\(595\) −17240.0 9320.14i −1.18785 0.642165i
\(596\) 10279.5i 0.706488i
\(597\) 0 0
\(598\) −14075.3 + 8126.40i −0.962514 + 0.555708i
\(599\) 1577.36 910.687i 0.107594 0.0621196i −0.445237 0.895413i \(-0.646881\pi\)
0.552832 + 0.833293i \(0.313547\pi\)
\(600\) 0 0
\(601\) 18933.3i 1.28503i −0.766273 0.642516i \(-0.777891\pi\)
0.766273 0.642516i \(-0.222109\pi\)
\(602\) 9534.09 + 15495.1i 0.645483 + 1.04906i
\(603\) 0 0
\(604\) 1680.92 2911.43i 0.113238 0.196133i
\(605\) 9302.77 + 16112.9i 0.625143 + 1.08278i
\(606\) 0 0
\(607\) 13323.3 + 7692.20i 0.890898 + 0.514360i 0.874236 0.485501i \(-0.161363\pi\)
0.0166621 + 0.999861i \(0.494696\pi\)
\(608\) 10845.5 0.723428
\(609\) 0 0
\(610\) −3685.61 −0.244633
\(611\) −13148.8 7591.46i −0.870611 0.502647i
\(612\) 0 0
\(613\) 2753.60 + 4769.38i 0.181431 + 0.314247i 0.942368 0.334578i \(-0.108594\pi\)
−0.760937 + 0.648825i \(0.775261\pi\)
\(614\) 3250.54 5630.10i 0.213650 0.370053i
\(615\) 0 0
\(616\) −118.391 4228.42i −0.00774369 0.276571i
\(617\) 18134.0i 1.18322i 0.806224 + 0.591610i \(0.201507\pi\)
−0.806224 + 0.591610i \(0.798493\pi\)
\(618\) 0 0
\(619\) 3148.73 1817.92i 0.204456 0.118043i −0.394276 0.918992i \(-0.629005\pi\)
0.598732 + 0.800949i \(0.295671\pi\)
\(620\) 4683.15 2703.82i 0.303355 0.175142i
\(621\) 0 0
\(622\) 4684.49i 0.301979i
\(623\) −25626.1 + 15767.6i −1.64797 + 1.01399i
\(624\) 0 0
\(625\) 8960.38 15519.8i 0.573464 0.993270i
\(626\) −1343.73 2327.41i −0.0857928 0.148597i
\(627\) 0 0
\(628\) 7317.26 + 4224.62i 0.464953 + 0.268441i
\(629\) 24455.6 1.55025
\(630\) 0 0
\(631\) −5912.59 −0.373021 −0.186511 0.982453i \(-0.559718\pi\)
−0.186511 + 0.982453i \(0.559718\pi\)
\(632\) −6454.60 3726.57i −0.406251 0.234549i
\(633\) 0 0
\(634\) 2299.90 + 3983.55i 0.144071 + 0.249538i
\(635\) −1353.76 + 2344.79i −0.0846024 + 0.146536i
\(636\) 0 0
\(637\) −19483.2 + 12753.1i −1.21185 + 0.793245i
\(638\) 2857.89i 0.177343i
\(639\) 0 0
\(640\) 9940.52 5739.16i 0.613959 0.354469i
\(641\) −23786.7 + 13733.3i −1.46571 + 0.846227i −0.999265 0.0383236i \(-0.987798\pi\)
−0.466443 + 0.884551i \(0.654465\pi\)
\(642\) 0 0
\(643\) 28474.0i 1.74635i −0.487403 0.873177i \(-0.662056\pi\)
0.487403 0.873177i \(-0.337944\pi\)
\(644\) 5428.36 10041.1i 0.332154 0.614404i
\(645\) 0 0
\(646\) −3923.29 + 6795.33i −0.238947 + 0.413868i
\(647\) −661.681 1146.06i −0.0402061 0.0696390i 0.845222 0.534415i \(-0.179468\pi\)
−0.885428 + 0.464776i \(0.846135\pi\)
\(648\) 0 0
\(649\) −4649.89 2684.62i −0.281239 0.162374i
\(650\) 12683.3 0.765351
\(651\) 0 0
\(652\) −13627.0 −0.818522
\(653\) 3331.38 + 1923.37i 0.199643 + 0.115264i 0.596489 0.802621i \(-0.296562\pi\)
−0.396846 + 0.917885i \(0.629895\pi\)
\(654\) 0 0
\(655\) −18458.5 31971.0i −1.10112 1.90719i
\(656\) −315.818 + 547.012i −0.0187967 + 0.0325568i
\(657\) 0 0
\(658\) −7536.76 + 211.021i −0.446525 + 0.0125022i
\(659\) 6796.84i 0.401771i 0.979615 + 0.200886i \(0.0643819\pi\)
−0.979615 + 0.200886i \(0.935618\pi\)
\(660\) 0 0
\(661\) −26902.5 + 15532.2i −1.58304 + 0.913966i −0.588623 + 0.808408i \(0.700330\pi\)
−0.994413 + 0.105559i \(0.966337\pi\)
\(662\) −2326.16 + 1343.01i −0.136569 + 0.0788481i
\(663\) 0 0
\(664\) 20441.7i 1.19471i
\(665\) −17166.1 + 480.631i −1.00101 + 0.0280272i
\(666\) 0 0
\(667\) −10438.2 + 18079.5i −0.605952 + 1.04954i
\(668\) 8180.91 + 14169.7i 0.473846 + 0.820725i
\(669\) 0 0
\(670\) −7624.91 4402.24i −0.439666 0.253841i
\(671\) −1327.25 −0.0763605
\(672\) 0 0
\(673\) 15508.2 0.888259 0.444129 0.895963i \(-0.353513\pi\)
0.444129 + 0.895963i \(0.353513\pi\)
\(674\) −10605.3 6122.97i −0.606084 0.349923i
\(675\) 0 0
\(676\) 5651.59 + 9788.84i 0.321552 + 0.556944i
\(677\) 15337.4 26565.2i 0.870701 1.50810i 0.00942744 0.999956i \(-0.496999\pi\)
0.861273 0.508142i \(-0.169668\pi\)
\(678\) 0 0
\(679\) 6510.19 12042.2i 0.367950 0.680617i
\(680\) 24437.4i 1.37813i
\(681\) 0 0
\(682\) −1192.48 + 688.478i −0.0669536 + 0.0386557i
\(683\) −15292.8 + 8829.33i −0.856756 + 0.494648i −0.862925 0.505333i \(-0.831370\pi\)
0.00616869 + 0.999981i \(0.498036\pi\)
\(684\) 0 0
\(685\) 7718.08i 0.430500i
\(686\) −4921.47 + 10464.1i −0.273910 + 0.582390i
\(687\) 0 0
\(688\) 1226.93 2125.10i 0.0679887 0.117760i
\(689\) 17991.0 + 31161.3i 0.994778 + 1.72301i
\(690\) 0 0
\(691\) 11402.3 + 6583.11i 0.627733 + 0.362422i 0.779874 0.625937i \(-0.215283\pi\)
−0.152141 + 0.988359i \(0.548617\pi\)
\(692\) −8223.42 −0.451745
\(693\) 0 0
\(694\) −979.634 −0.0535827
\(695\) −7832.18 4521.91i −0.427470 0.246800i
\(696\) 0 0
\(697\) 4871.35 + 8437.42i 0.264728 + 0.458522i
\(698\) 6349.29 10997.3i 0.344304 0.596352i
\(699\) 0 0
\(700\) −7586.54 + 4667.96i −0.409634 + 0.252046i
\(701\) 25910.0i 1.39602i −0.716090 0.698008i \(-0.754070\pi\)
0.716090 0.698008i \(-0.245930\pi\)
\(702\) 0 0
\(703\) 18558.3 10714.6i 0.995646 0.574837i
\(704\) −3063.06 + 1768.46i −0.163982 + 0.0946752i
\(705\) 0 0
\(706\) 16158.8i 0.861394i
\(707\) −124.152 4434.16i −0.00660424 0.235875i
\(708\) 0 0
\(709\) −3104.25 + 5376.71i −0.164432 + 0.284805i −0.936454 0.350792i \(-0.885913\pi\)
0.772021 + 0.635597i \(0.219246\pi\)
\(710\) −5725.73 9917.25i −0.302652 0.524208i
\(711\) 0 0
\(712\) 32491.7 + 18759.1i 1.71022 + 0.987398i
\(713\) −10058.5 −0.528320
\(714\) 0 0
\(715\) 10130.4 0.529868
\(716\) −3213.15 1855.11i −0.167711 0.0968280i
\(717\) 0 0
\(718\) 10053.6 + 17413.3i 0.522557 + 0.905095i
\(719\) −14379.4 + 24905.9i −0.745843 + 1.29184i 0.203957 + 0.978980i \(0.434620\pi\)
−0.949800 + 0.312858i \(0.898713\pi\)
\(720\) 0 0
\(721\) −496.296 806.599i −0.0256353 0.0416634i
\(722\) 5610.13i 0.289180i
\(723\) 0 0
\(724\) 10236.3 5909.95i 0.525457 0.303373i
\(725\) 14108.8 8145.72i 0.722742 0.417275i
\(726\) 0 0
\(727\) 35275.7i 1.79959i 0.436312 + 0.899795i \(0.356284\pi\)
−0.436312 + 0.899795i \(0.643716\pi\)
\(728\) 25542.4 + 13808.5i 1.30036 + 0.702992i
\(729\) 0 0
\(730\) 7492.35 12977.1i 0.379869 0.657953i
\(731\) −18924.8 32778.8i −0.957539 1.65851i
\(732\) 0 0
\(733\) −6885.15 3975.14i −0.346942 0.200307i 0.316395 0.948627i \(-0.397527\pi\)
−0.663338 + 0.748320i \(0.730861\pi\)
\(734\) 15156.3 0.762164
\(735\) 0 0
\(736\) −23208.5 −1.16233
\(737\) −2745.86 1585.32i −0.137239 0.0792348i
\(738\) 0 0
\(739\) −16676.8 28885.1i −0.830130 1.43783i −0.897935 0.440129i \(-0.854933\pi\)
0.0678046 0.997699i \(-0.478401\pi\)
\(740\) 12326.8 21350.6i 0.612354 1.06063i
\(741\) 0 0
\(742\) 15718.4 + 8497.58i 0.777684 + 0.420426i
\(743\) 32933.6i 1.62613i −0.582171 0.813066i \(-0.697797\pi\)
0.582171 0.813066i \(-0.302203\pi\)
\(744\) 0 0
\(745\) −28660.5 + 16547.2i −1.40945 + 0.813747i
\(746\) 7165.51 4137.01i 0.351673 0.203039i
\(747\) 0 0
\(748\) 3250.85i 0.158907i
\(749\) −11559.0 18786.1i −0.563895 0.916463i
\(750\) 0 0
\(751\) 19818.3 34326.3i 0.962956 1.66789i 0.247945 0.968774i \(-0.420245\pi\)
0.715010 0.699114i \(-0.246422\pi\)
\(752\) 508.466 + 880.688i 0.0246567 + 0.0427066i
\(753\) 0 0
\(754\) −16988.9 9808.54i −0.820555 0.473748i
\(755\) 10823.2 0.521718
\(756\) 0 0
\(757\) −3996.51 −0.191883 −0.0959417 0.995387i \(-0.530586\pi\)
−0.0959417 + 0.995387i \(0.530586\pi\)
\(758\) 18172.2 + 10491.7i 0.870769 + 0.502739i
\(759\) 0 0
\(760\) 10706.6 + 18544.5i 0.511014 + 0.885103i
\(761\) −13117.8 + 22720.8i −0.624863 + 1.08230i 0.363704 + 0.931515i \(0.381512\pi\)
−0.988567 + 0.150781i \(0.951821\pi\)
\(762\) 0 0
\(763\) −201.724 7204.70i −0.00957128 0.341845i
\(764\) 4233.11i 0.200456i
\(765\) 0 0
\(766\) 6180.45 3568.28i 0.291526 0.168312i
\(767\) 31917.7 18427.7i 1.50258 0.867517i
\(768\) 0 0
\(769\) 36456.9i 1.70958i 0.518971 + 0.854792i \(0.326315\pi\)
−0.518971 + 0.854792i \(0.673685\pi\)
\(770\) 4284.59 2636.29i 0.200527 0.123383i
\(771\) 0 0
\(772\) 466.000 807.135i 0.0217250 0.0376288i
\(773\) 4732.74 + 8197.34i 0.220213 + 0.381420i 0.954873 0.297016i \(-0.0959914\pi\)
−0.734660 + 0.678436i \(0.762658\pi\)
\(774\) 0 0
\(775\) 6797.74 + 3924.68i 0.315074 + 0.181908i
\(776\) −17069.7 −0.789646
\(777\) 0 0
\(778\) 1449.79 0.0668089
\(779\) 7393.31 + 4268.53i 0.340042 + 0.196323i
\(780\) 0 0
\(781\) −2061.93 3571.37i −0.0944707 0.163628i
\(782\) 8395.51 14541.4i 0.383917 0.664963i
\(783\) 0 0
\(784\) 1557.22 87.2692i 0.0709374 0.00397546i
\(785\) 27201.8i 1.23678i
\(786\) 0 0