Properties

Label 63.4.p.a.17.3
Level $63$
Weight $4$
Character 63.17
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 17.3
Root \(-1.57646 + 0.910170i\) of defining polynomial
Character \(\chi\) \(=\) 63.17
Dual form 63.4.p.a.26.3

$q$-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 \(\left(\mathbb{Z}/63\mathbb{Z}\right)^\times\).

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

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 \(-0.770952\pi\)
0.194723 + 0.980858i \(0.437619\pi\)
\(3\) 0 0
\(4\) −2.34318 + 4.05851i −0.292898 + 0.507314i
\(5\) −7.54372 13.0661i −0.674731 1.16867i −0.976547 0.215302i \(-0.930926\pi\)
0.301817 0.953366i \(-0.402407\pi\)
\(6\) 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 \(-0.376613\pi\)
−0.612773 + 0.790259i \(0.709946\pi\)
\(12\) 0 0
\(13\) 67.8891i 1.44839i −0.689596 0.724194i \(-0.742212\pi\)
0.689596 0.724194i \(-0.257788\pi\)
\(14\) −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 −0.499682 0.866209i \(-0.666550\pi\)
1.00000 0.000366661i \(-0.000116712\pi\)
\(18\) 0 0
\(19\) −53.2242 + 30.7290i −0.642656 + 0.371038i −0.785637 0.618688i \(-0.787665\pi\)
0.142981 + 0.989725i \(0.454331\pi\)
\(20\) 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 \(-0.869969\pi\)
−0.114841 + 0.993384i \(0.536636\pi\)
\(24\) 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 0.295701 0.955281i \(-0.404447\pi\)
−0.679447 + 0.733725i \(0.737780\pi\)
\(32\) 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 −0.935000 0.354648i \(-0.884601\pi\)
0.160366 0.987058i \(-0.448733\pi\)
\(38\) 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 \(-0.414773\pi\)
0.264560 + 0.964369i \(0.414773\pi\)
\(42\) 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 \(-0.0538538\pi\)
−0.638683 + 0.769470i \(0.720520\pi\)
\(48\) 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 \(-0.574326\pi\)
−0.958216 + 0.286045i \(0.907659\pi\)
\(54\) 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 −0.394023 0.919101i \(-0.628917\pi\)
0.992976 0.118317i \(-0.0377498\pi\)
\(60\) 0 0
\(61\) −116.218 + 67.0983i −0.243937 + 0.140837i −0.616985 0.786975i \(-0.711646\pi\)
0.373048 + 0.927812i \(0.378313\pi\)
\(62\) 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 −0.974348 0.225048i \(-0.927746\pi\)
0.682071 + 0.731286i \(0.261079\pi\)
\(68\) 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 0.828425 0.560100i \(-0.189237\pi\)
−0.0708484 + 0.997487i \(0.522571\pi\)
\(74\) 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 0.957753 0.287591i \(-0.0928545\pi\)
−0.727938 + 0.685643i \(0.759521\pi\)
\(80\) 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 \(-0.300976\pi\)
0.585301 + 0.810816i \(0.300976\pi\)
\(84\) 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 0.702826 + 0.711362i \(0.251921\pi\)
0.264645 + 0.964346i \(0.414745\pi\)
\(90\) 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 \(0.126439\pi\)
−0.922141 + 0.386855i \(0.873561\pi\)
\(98\) −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 \(-0.795690\pi\)
0.918969 + 0.394331i \(0.129024\pi\)
\(102\) 0 0
\(103\) −44.2852 + 25.5681i −0.0423645 + 0.0244592i −0.521033 0.853537i \(-0.674453\pi\)
0.478668 + 0.877996i \(0.341120\pi\)
\(104\) −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 \(-0.485837\pi\)
0.887408 + 0.460986i \(0.152504\pi\)
\(108\) 0 0
\(109\) −194.585 + 337.031i −0.170989 + 0.296162i −0.938766 0.344555i \(-0.888030\pi\)
0.767777 + 0.640718i \(0.221363\pi\)
\(110\) −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 −0.908630 0.417601i \(-0.862871\pi\)
0.0926619 0.995698i \(-0.470462\pi\)
\(132\) 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 \(-0.384324\pi\)
−0.631736 + 0.775183i \(0.717658\pi\)
\(138\) 0 0
\(139\) 599.427i 0.365775i 0.983134 + 0.182888i \(0.0585444\pi\)
−0.983134 + 0.182888i \(0.941456\pi\)
\(140\) 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 \(-0.460632\pi\)
0.921092 + 0.389346i \(0.127299\pi\)
\(150\) 0 0
\(151\) 358.683 621.257i 0.193306 0.334816i −0.753038 0.657977i \(-0.771412\pi\)
0.946344 + 0.323161i \(0.104746\pi\)
\(152\) 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 0.0475556 0.998869i \(-0.484857\pi\)
−0.841268 + 0.540619i \(0.818190\pi\)
\(158\) −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 0.968938 + 0.247305i \(0.0795451\pi\)
−0.270296 + 0.962777i \(0.587122\pi\)
\(164\) −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 \(-0.200067\pi\)
0.808893 + 0.587956i \(0.200067\pi\)
\(168\) 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 \(-0.292666\pi\)
−0.991850 + 0.127412i \(0.959333\pi\)
\(174\) 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 \(-0.386190\pi\)
−0.636270 + 0.771466i \(0.719524\pi\)
\(180\) 0 0
\(181\) 2522.19i 1.03576i −0.855452 0.517882i \(-0.826721\pi\)
0.855452 0.517882i \(-0.173279\pi\)
\(182\) 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 \(-0.721398\pi\)
0.344452 + 0.938804i \(0.388065\pi\)
\(192\) 0 0
\(193\) 99.4374 172.231i 0.0370863 0.0642354i −0.846886 0.531774i \(-0.821526\pi\)
0.883973 + 0.467538i \(0.154859\pi\)
\(194\) −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 0.870392 0.492360i \(-0.163866\pi\)
0.00879944 + 0.999961i \(0.497199\pi\)
\(200\) 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 \(-0.830699\pi\)
0.861857 0.507151i \(-0.169301\pi\)
\(224\) 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 −0.318875 0.947797i \(-0.603305\pi\)
0.980254 0.197744i \(-0.0633615\pi\)
\(228\) 0 0
\(229\) 3389.61 1956.99i 0.978131 0.564724i 0.0764258 0.997075i \(-0.475649\pi\)
0.901705 + 0.432351i \(0.142316\pi\)
\(230\) −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 \(-0.456132\pi\)
0.926504 + 0.376284i \(0.122798\pi\)
\(234\) 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 −0.0469158 0.998899i \(-0.514939\pi\)
−0.888530 + 0.458819i \(0.848273\pi\)
\(242\) 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 \(-0.687363\pi\)
−0.555212 + 0.831709i \(0.687363\pi\)
\(252\) 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 \(-0.193647\pi\)
−0.905246 + 0.424888i \(0.860314\pi\)
\(258\) 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 \(-0.303531\pi\)
−0.416844 + 0.908978i \(0.636864\pi\)
\(264\) 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 \(-0.818512\pi\)
0.888359 + 0.459149i \(0.151846\pi\)
\(270\) 0 0
\(271\) 3283.42 1895.69i 0.735992 0.424925i −0.0846182 0.996413i \(-0.526967\pi\)
0.820610 + 0.571488i \(0.193634\pi\)
\(272\) 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 −0.986619 0.163040i \(-0.947870\pi\)
0.634507 + 0.772917i \(0.281203\pi\)
\(278\) −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 0.0589678 0.998260i \(-0.481219\pi\)
−0.835034 + 0.550198i \(0.814552\pi\)
\(284\) 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 \(-0.405752\pi\)
0.291781 + 0.956485i \(0.405752\pi\)
\(294\) 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 \(0.107712\pi\)
−0.943291 + 0.331968i \(0.892288\pi\)
\(308\) 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 \(-0.757953\pi\)
0.959158 + 0.282871i \(0.0912867\pi\)
\(312\) 0 0
\(313\) −1278.56 + 738.176i −0.230889 + 0.133304i −0.610982 0.791644i \(-0.709225\pi\)
0.380093 + 0.924948i \(0.375892\pi\)
\(314\) 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 \(-0.738531\pi\)
0.293446 + 0.955976i \(0.405198\pi\)
\(318\) 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 0.798245 0.602333i \(-0.205762\pi\)
−0.920758 + 0.390134i \(0.872429\pi\)
\(332\) −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 \(-0.320079\pi\)
−0.463516 + 0.886089i \(0.653412\pi\)
\(348\) 0 0
\(349\) 6975.93i 1.06995i 0.844867 + 0.534976i \(0.179679\pi\)
−0.844867 + 0.534976i \(0.820321\pi\)
\(350\) −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 −0.308912 0.951091i \(-0.599965\pi\)
0.978125 0.208020i \(-0.0667019\pi\)
\(354\) 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 \(-0.968257\pi\)
−0.411297 + 0.911502i \(0.634924\pi\)
\(360\) 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 0.915717 0.401824i \(-0.131624\pi\)
0.109868 + 0.993946i \(0.464957\pi\)
\(368\) −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 0.979539 0.201253i \(-0.0645014\pi\)
−0.664060 + 0.747679i \(0.731168\pi\)
\(374\) 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 \(-0.250891\pi\)
−0.966647 + 0.256114i \(0.917558\pi\)
\(384\) 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 \(-0.349862\pi\)
−0.544276 + 0.838906i \(0.683195\pi\)
\(390\) 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 −0.273896 0.961759i \(-0.588313\pi\)
0.695960 + 0.718081i \(0.254979\pi\)
\(398\) −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 \(-0.760279\pi\)
0.227496 + 0.973779i \(0.426946\pi\)
\(402\) 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 −0.109497 0.993987i \(-0.534924\pi\)
−0.915566 + 0.402167i \(0.868257\pi\)
\(410\) 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 \(-0.556098\pi\)
−0.175327 + 0.984510i \(0.556098\pi\)
\(420\) 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 \(-0.0172175\pi\)
0.452448 + 0.891791i \(0.350551\pi\)
\(432\) 0 0
\(433\) 5666.63i 0.628916i −0.949271 0.314458i \(-0.898177\pi\)
0.949271 0.314458i \(-0.101823\pi\)
\(434\) 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 −0.737249 0.675621i \(-0.763876\pi\)
0.216480 + 0.976287i \(0.430542\pi\)
\(440\) 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 \(-0.659783\pi\)
0.518609 + 0.855012i \(0.326450\pi\)
\(444\) 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 0.847946 0.530082i \(-0.177839\pi\)
−0.883038 + 0.469302i \(0.844506\pi\)
\(458\) −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 \(-0.420973\pi\)
0.245728 + 0.969339i \(0.420973\pi\)
\(462\) 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 \(-0.150843\pi\)
−0.840111 + 0.542415i \(0.817510\pi\)
\(468\) 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 \(-0.926550\pi\)
0.684813 + 0.728719i \(0.259884\pi\)
\(480\) 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 0.251753 + 0.967791i \(0.418993\pi\)
−0.964009 + 0.265871i \(0.914340\pi\)
\(488\) 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 0.669046 0.743221i \(-0.266703\pi\)
−0.978171 + 0.207800i \(0.933370\pi\)
\(500\) 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 \(-0.704784\pi\)
−0.599877 + 0.800092i \(0.704784\pi\)
\(504\) 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 −0.999530 0.0306510i \(-0.990242\pi\)
0.473221 0.880944i \(-0.343091\pi\)
\(510\) 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 \(-0.937228\pi\)
0.659989 + 0.751275i \(0.270561\pi\)
\(522\) 0 0
\(523\) 13328.7 7695.34i 1.11439 0.643392i 0.174425 0.984670i \(-0.444193\pi\)
0.939962 + 0.341279i \(0.110860\pi\)
\(524\) 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 0.998644 + 0.0520584i \(0.0165782\pi\)
−0.454238 + 0.890880i \(0.650088\pi\)
\(542\) −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 \(-0.665791\pi\)
−0.999996 + 0.00275234i \(0.999124\pi\)
\(558\) 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 \(-0.954389\pi\)
0.618546 + 0.785749i \(0.287722\pi\)
\(564\) 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 \(-0.606064\pi\)
0.654852 + 0.755757i \(0.272731\pi\)
\(570\) 0 0
\(571\) 9093.02 15749.6i 0.666429 1.15429i −0.312467 0.949929i \(-0.601155\pi\)
0.978896 0.204360i \(-0.0655114\pi\)
\(572\) −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 0.834553 0.550927i \(-0.185726\pi\)
−0.0598401 + 0.998208i \(0.519059\pi\)
\(578\) 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 \(-0.732505\pi\)
−0.667195 + 0.744883i \(0.732505\pi\)
\(588\) 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 \(-0.0455151\pi\)
−0.618308 + 0.785936i \(0.712182\pi\)
\(594\) 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 \(-0.353119\pi\)
−0.552832 + 0.833293i \(0.686453\pi\)
\(600\) 0 0
\(601\) 18933.3i 1.28503i 0.766273 + 0.642516i \(0.222109\pi\)
−0.766273 + 0.642516i \(0.777891\pi\)
\(602\) −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 0.0166621 0.999861i \(-0.494696\pi\)
0.874236 + 0.485501i \(0.161363\pi\)
\(608\) −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 −0.760937 0.648825i \(-0.775261\pi\)
0.942368 + 0.334578i \(0.108594\pi\)
\(614\) −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 0.598732 0.800949i \(-0.295671\pi\)
−0.394276 + 0.918992i \(0.629005\pi\)
\(620\) −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 \(-0.0122018\pi\)
0.466443 + 0.884551i \(0.345535\pi\)
\(642\) 0 0
\(643\) 28474.0i 1.74635i 0.487403 + 0.873177i \(0.337944\pi\)
−0.487403 + 0.873177i \(0.662056\pi\)
\(644\) −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 \(-0.820532\pi\)
0.885428 + 0.464776i \(0.153865\pi\)
\(648\) 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 \(-0.703438\pi\)
0.396846 + 0.917885i \(0.370105\pi\)
\(654\) 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 −0.994413 0.105559i \(-0.966337\pi\)
−0.588623 0.808408i \(-0.700330\pi\)
\(662\) 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 −0.861273 0.508142i \(-0.830332\pi\)
−0.00942744 0.999956i \(-0.503001\pi\)
\(678\) 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 \(-0.168630\pi\)
−0.00616869 + 0.999981i \(0.501964\pi\)
\(684\) 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 −0.152141 0.988359i \(-0.548617\pi\)
0.779874 + 0.625937i \(0.215283\pi\)
\(692\) 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 0.772021 0.635597i \(-0.219246\pi\)
−0.936454 + 0.350792i \(0.885913\pi\)
\(710\) 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 0.949800 + 0.312858i \(0.101287\pi\)
−0.203957 + 0.978980i \(0.565380\pi\)
\(720\) 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 \(-0.643716\pi\)
0.436312 0.899795i \(-0.356284\pi\)
\(728\) −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 −0.663338 0.748320i \(-0.730861\pi\)
0.316395 + 0.948627i \(0.397527\pi\)
\(734\) −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 0.0678046 + 0.997699i \(0.478401\pi\)
−0.897935 + 0.440129i \(0.854933\pi\)
\(740\) −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 0.715010 + 0.699114i \(0.246422\pi\)
0.247945 + 0.968774i \(0.420245\pi\)
\(752\) −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 0.988567 + 0.150781i \(0.0481787\pi\)
−0.363704 + 0.931515i \(0.618488\pi\)
\(762\) 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 \(-0.673685\pi\)
0.518971 0.854792i \(-0.326315\pi\)
\(770\) −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 \(-0.904009\pi\)
0.734660 + 0.678436i \(0.237342\pi\)
\(774\) 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