Properties

Label 882.4.g.bh.667.1
Level $882$
Weight $4$
Character 882.667
Analytic conductor $52.040$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 882 = 2 \cdot 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 882.g (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(52.0396846251\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\sqrt{-3}, \sqrt{58})\)
Defining polynomial: \(x^{4} + 58 x^{2} + 3364\)
Coefficient ring: \(\Z[a_1, \ldots, a_{25}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 667.1
Root \(-3.80789 + 6.59545i\) of defining polynomial
Character \(\chi\) \(=\) 882.667
Dual form 882.4.g.bh.361.1

$q$-expansion

\(f(q)\) \(=\) \(q+(1.00000 - 1.73205i) q^{2} +(-2.00000 - 3.46410i) q^{4} +(-7.61577 + 13.1909i) q^{5} -8.00000 q^{8} +O(q^{10})\) \(q+(1.00000 - 1.73205i) q^{2} +(-2.00000 - 3.46410i) q^{4} +(-7.61577 + 13.1909i) q^{5} -8.00000 q^{8} +(15.2315 + 26.3818i) q^{10} +(1.00000 + 1.73205i) q^{11} +30.4631 q^{13} +(-8.00000 + 13.8564i) q^{16} +(22.8473 + 39.5727i) q^{17} +(76.1577 - 131.909i) q^{19} +60.9262 q^{20} +4.00000 q^{22} +(15.0000 - 25.9808i) q^{23} +(-53.5000 - 92.6647i) q^{25} +(30.4631 - 52.7636i) q^{26} -212.000 q^{29} +(106.621 + 184.673i) q^{31} +(16.0000 + 27.7128i) q^{32} +91.3893 q^{34} +(-123.000 + 213.042i) q^{37} +(-152.315 - 263.818i) q^{38} +(60.9262 - 105.527i) q^{40} -319.862 q^{41} -284.000 q^{43} +(4.00000 - 6.92820i) q^{44} +(-30.0000 - 51.9615i) q^{46} +(-30.4631 + 52.7636i) q^{47} -214.000 q^{50} +(-60.9262 - 105.527i) q^{52} +(274.000 + 474.582i) q^{53} -30.4631 q^{55} +(-212.000 + 367.195i) q^{58} +(335.094 + 580.400i) q^{59} +(-258.936 + 448.491i) q^{61} +426.483 q^{62} +64.0000 q^{64} +(-232.000 + 401.836i) q^{65} +(-326.000 - 564.649i) q^{67} +(91.3893 - 158.291i) q^{68} -770.000 q^{71} +(-487.409 - 844.218i) q^{73} +(246.000 + 426.084i) q^{74} -609.262 q^{76} +(-236.000 + 408.764i) q^{79} +(-121.852 - 211.054i) q^{80} +(-319.862 + 554.018i) q^{82} +182.779 q^{83} -696.000 q^{85} +(-284.000 + 491.902i) q^{86} +(-8.00000 - 13.8564i) q^{88} +(-357.941 + 619.973i) q^{89} -120.000 q^{92} +(60.9262 + 105.527i) q^{94} +(1160.00 + 2009.18i) q^{95} -304.631 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q + 4q^{2} - 8q^{4} - 32q^{8} + O(q^{10}) \) \( 4q + 4q^{2} - 8q^{4} - 32q^{8} + 4q^{11} - 32q^{16} + 16q^{22} + 60q^{23} - 214q^{25} - 848q^{29} + 64q^{32} - 492q^{37} - 1136q^{43} + 16q^{44} - 120q^{46} - 856q^{50} + 1096q^{53} - 848q^{58} + 256q^{64} - 928q^{65} - 1304q^{67} - 3080q^{71} + 984q^{74} - 944q^{79} - 2784q^{85} - 1136q^{86} - 32q^{88} - 480q^{92} + 4640q^{95} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/882\mathbb{Z}\right)^\times\).

\(n\) \(199\) \(785\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 1.73205i 0.353553 0.612372i
\(3\) 0 0
\(4\) −2.00000 3.46410i −0.250000 0.433013i
\(5\) −7.61577 + 13.1909i −0.681175 + 1.17983i 0.293447 + 0.955975i \(0.405198\pi\)
−0.974622 + 0.223855i \(0.928136\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) −8.00000 −0.353553
\(9\) 0 0
\(10\) 15.2315 + 26.3818i 0.481664 + 0.834266i
\(11\) 1.00000 + 1.73205i 0.0274101 + 0.0474757i 0.879405 0.476074i \(-0.157941\pi\)
−0.851995 + 0.523550i \(0.824607\pi\)
\(12\) 0 0
\(13\) 30.4631 0.649919 0.324959 0.945728i \(-0.394649\pi\)
0.324959 + 0.945728i \(0.394649\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) −8.00000 + 13.8564i −0.125000 + 0.216506i
\(17\) 22.8473 + 39.5727i 0.325958 + 0.564576i 0.981706 0.190404i \(-0.0609798\pi\)
−0.655748 + 0.754980i \(0.727646\pi\)
\(18\) 0 0
\(19\) 76.1577 131.909i 0.919567 1.59274i 0.119494 0.992835i \(-0.461873\pi\)
0.800073 0.599903i \(-0.204794\pi\)
\(20\) 60.9262 0.681175
\(21\) 0 0
\(22\) 4.00000 0.0387638
\(23\) 15.0000 25.9808i 0.135988 0.235538i −0.789987 0.613124i \(-0.789913\pi\)
0.925974 + 0.377586i \(0.123246\pi\)
\(24\) 0 0
\(25\) −53.5000 92.6647i −0.428000 0.741318i
\(26\) 30.4631 52.7636i 0.229781 0.397992i
\(27\) 0 0
\(28\) 0 0
\(29\) −212.000 −1.35750 −0.678748 0.734371i \(-0.737477\pi\)
−0.678748 + 0.734371i \(0.737477\pi\)
\(30\) 0 0
\(31\) 106.621 + 184.673i 0.617731 + 1.06994i 0.989899 + 0.141776i \(0.0452813\pi\)
−0.372168 + 0.928166i \(0.621385\pi\)
\(32\) 16.0000 + 27.7128i 0.0883883 + 0.153093i
\(33\) 0 0
\(34\) 91.3893 0.460974
\(35\) 0 0
\(36\) 0 0
\(37\) −123.000 + 213.042i −0.546516 + 0.946593i 0.451994 + 0.892021i \(0.350713\pi\)
−0.998510 + 0.0545719i \(0.982621\pi\)
\(38\) −152.315 263.818i −0.650232 1.12624i
\(39\) 0 0
\(40\) 60.9262 105.527i 0.240832 0.417133i
\(41\) −319.862 −1.21839 −0.609197 0.793019i \(-0.708508\pi\)
−0.609197 + 0.793019i \(0.708508\pi\)
\(42\) 0 0
\(43\) −284.000 −1.00720 −0.503600 0.863937i \(-0.667991\pi\)
−0.503600 + 0.863937i \(0.667991\pi\)
\(44\) 4.00000 6.92820i 0.0137051 0.0237379i
\(45\) 0 0
\(46\) −30.0000 51.9615i −0.0961578 0.166550i
\(47\) −30.4631 + 52.7636i −0.0945425 + 0.163752i −0.909418 0.415884i \(-0.863472\pi\)
0.814875 + 0.579637i \(0.196805\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) −214.000 −0.605283
\(51\) 0 0
\(52\) −60.9262 105.527i −0.162480 0.281423i
\(53\) 274.000 + 474.582i 0.710128 + 1.22998i 0.964809 + 0.262953i \(0.0846964\pi\)
−0.254680 + 0.967025i \(0.581970\pi\)
\(54\) 0 0
\(55\) −30.4631 −0.0746844
\(56\) 0 0
\(57\) 0 0
\(58\) −212.000 + 367.195i −0.479948 + 0.831294i
\(59\) 335.094 + 580.400i 0.739416 + 1.28071i 0.952759 + 0.303728i \(0.0982315\pi\)
−0.213343 + 0.976977i \(0.568435\pi\)
\(60\) 0 0
\(61\) −258.936 + 448.491i −0.543498 + 0.941367i 0.455202 + 0.890388i \(0.349567\pi\)
−0.998700 + 0.0509782i \(0.983766\pi\)
\(62\) 426.483 0.873604
\(63\) 0 0
\(64\) 64.0000 0.125000
\(65\) −232.000 + 401.836i −0.442709 + 0.766794i
\(66\) 0 0
\(67\) −326.000 564.649i −0.594436 1.02959i −0.993626 0.112726i \(-0.964042\pi\)
0.399190 0.916868i \(-0.369291\pi\)
\(68\) 91.3893 158.291i 0.162979 0.282288i
\(69\) 0 0
\(70\) 0 0
\(71\) −770.000 −1.28707 −0.643537 0.765415i \(-0.722534\pi\)
−0.643537 + 0.765415i \(0.722534\pi\)
\(72\) 0 0
\(73\) −487.409 844.218i −0.781465 1.35354i −0.931088 0.364794i \(-0.881139\pi\)
0.149623 0.988743i \(-0.452194\pi\)
\(74\) 246.000 + 426.084i 0.386445 + 0.669342i
\(75\) 0 0
\(76\) −609.262 −0.919567
\(77\) 0 0
\(78\) 0 0
\(79\) −236.000 + 408.764i −0.336102 + 0.582146i −0.983696 0.179840i \(-0.942442\pi\)
0.647594 + 0.761986i \(0.275775\pi\)
\(80\) −121.852 211.054i −0.170294 0.294958i
\(81\) 0 0
\(82\) −319.862 + 554.018i −0.430767 + 0.746110i
\(83\) 182.779 0.241718 0.120859 0.992670i \(-0.461435\pi\)
0.120859 + 0.992670i \(0.461435\pi\)
\(84\) 0 0
\(85\) −696.000 −0.888139
\(86\) −284.000 + 491.902i −0.356099 + 0.616781i
\(87\) 0 0
\(88\) −8.00000 13.8564i −0.00969094 0.0167852i
\(89\) −357.941 + 619.973i −0.426311 + 0.738393i −0.996542 0.0830918i \(-0.973521\pi\)
0.570231 + 0.821485i \(0.306854\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) −120.000 −0.135988
\(93\) 0 0
\(94\) 60.9262 + 105.527i 0.0668517 + 0.115790i
\(95\) 1160.00 + 2009.18i 1.25277 + 2.16987i
\(96\) 0 0
\(97\) −304.631 −0.318872 −0.159436 0.987208i \(-0.550968\pi\)
−0.159436 + 0.987208i \(0.550968\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) −214.000 + 370.659i −0.214000 + 0.370659i
\(101\) −510.257 883.791i −0.502698 0.870698i −0.999995 0.00311763i \(-0.999008\pi\)
0.497298 0.867580i \(-0.334326\pi\)
\(102\) 0 0
\(103\) −289.399 + 501.254i −0.276848 + 0.479515i −0.970600 0.240699i \(-0.922623\pi\)
0.693752 + 0.720214i \(0.255957\pi\)
\(104\) −243.705 −0.229781
\(105\) 0 0
\(106\) 1096.00 1.00427
\(107\) −823.000 + 1425.48i −0.743574 + 1.28791i 0.207284 + 0.978281i \(0.433538\pi\)
−0.950858 + 0.309627i \(0.899796\pi\)
\(108\) 0 0
\(109\) −491.000 850.437i −0.431461 0.747313i 0.565538 0.824722i \(-0.308668\pi\)
−0.996999 + 0.0774094i \(0.975335\pi\)
\(110\) −30.4631 + 52.7636i −0.0264049 + 0.0457347i
\(111\) 0 0
\(112\) 0 0
\(113\) −1288.00 −1.07226 −0.536128 0.844137i \(-0.680113\pi\)
−0.536128 + 0.844137i \(0.680113\pi\)
\(114\) 0 0
\(115\) 228.473 + 395.727i 0.185263 + 0.320885i
\(116\) 424.000 + 734.390i 0.339374 + 0.587813i
\(117\) 0 0
\(118\) 1340.38 1.04569
\(119\) 0 0
\(120\) 0 0
\(121\) 663.500 1149.22i 0.498497 0.863423i
\(122\) 517.873 + 896.982i 0.384311 + 0.665647i
\(123\) 0 0
\(124\) 426.483 738.691i 0.308866 0.534971i
\(125\) −274.168 −0.196179
\(126\) 0 0
\(127\) −1072.00 −0.749013 −0.374506 0.927224i \(-0.622188\pi\)
−0.374506 + 0.927224i \(0.622188\pi\)
\(128\) 64.0000 110.851i 0.0441942 0.0765466i
\(129\) 0 0
\(130\) 464.000 + 803.672i 0.313042 + 0.542205i
\(131\) 1370.84 2374.36i 0.914281 1.58358i 0.106330 0.994331i \(-0.466090\pi\)
0.807951 0.589250i \(-0.200577\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) −1304.00 −0.840660
\(135\) 0 0
\(136\) −182.779 316.582i −0.115244 0.199608i
\(137\) 1468.00 + 2542.65i 0.915472 + 1.58564i 0.806208 + 0.591632i \(0.201516\pi\)
0.109264 + 0.994013i \(0.465151\pi\)
\(138\) 0 0
\(139\) −182.779 −0.111533 −0.0557665 0.998444i \(-0.517760\pi\)
−0.0557665 + 0.998444i \(0.517760\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) −770.000 + 1333.68i −0.455049 + 0.788168i
\(143\) 30.4631 + 52.7636i 0.0178143 + 0.0308554i
\(144\) 0 0
\(145\) 1614.54 2796.47i 0.924694 1.60162i
\(146\) −1949.64 −1.10516
\(147\) 0 0
\(148\) 984.000 0.546516
\(149\) −482.000 + 834.848i −0.265013 + 0.459016i −0.967567 0.252614i \(-0.918710\pi\)
0.702554 + 0.711631i \(0.252043\pi\)
\(150\) 0 0
\(151\) 844.000 + 1461.85i 0.454859 + 0.787839i 0.998680 0.0513620i \(-0.0163562\pi\)
−0.543821 + 0.839201i \(0.683023\pi\)
\(152\) −609.262 + 1055.27i −0.325116 + 0.563118i
\(153\) 0 0
\(154\) 0 0
\(155\) −3248.00 −1.68313
\(156\) 0 0
\(157\) 1721.16 + 2981.14i 0.874929 + 1.51542i 0.856838 + 0.515586i \(0.172426\pi\)
0.0180912 + 0.999836i \(0.494241\pi\)
\(158\) 472.000 + 817.528i 0.237660 + 0.411639i
\(159\) 0 0
\(160\) −487.409 −0.240832
\(161\) 0 0
\(162\) 0 0
\(163\) 1662.00 2878.67i 0.798637 1.38328i −0.121866 0.992547i \(-0.538888\pi\)
0.920504 0.390734i \(-0.127779\pi\)
\(164\) 639.725 + 1108.04i 0.304598 + 0.527580i
\(165\) 0 0
\(166\) 182.779 316.582i 0.0854600 0.148021i
\(167\) 3046.31 1.41156 0.705780 0.708431i \(-0.250597\pi\)
0.705780 + 0.708431i \(0.250597\pi\)
\(168\) 0 0
\(169\) −1269.00 −0.577606
\(170\) −696.000 + 1205.51i −0.314004 + 0.543872i
\(171\) 0 0
\(172\) 568.000 + 983.805i 0.251800 + 0.436130i
\(173\) −1637.39 + 2836.04i −0.719587 + 1.24636i 0.241577 + 0.970382i \(0.422336\pi\)
−0.961164 + 0.275979i \(0.910998\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) −32.0000 −0.0137051
\(177\) 0 0
\(178\) 715.883 + 1239.95i 0.301448 + 0.522123i
\(179\) 627.000 + 1086.00i 0.261811 + 0.453470i 0.966723 0.255825i \(-0.0823469\pi\)
−0.704912 + 0.709295i \(0.749014\pi\)
\(180\) 0 0
\(181\) 3076.77 1.26351 0.631753 0.775170i \(-0.282336\pi\)
0.631753 + 0.775170i \(0.282336\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) −120.000 + 207.846i −0.0480789 + 0.0832751i
\(185\) −1873.48 3244.96i −0.744546 1.28959i
\(186\) 0 0
\(187\) −45.6946 + 79.1454i −0.0178691 + 0.0309502i
\(188\) 243.705 0.0945425
\(189\) 0 0
\(190\) 4640.00 1.77169
\(191\) 453.000 784.619i 0.171612 0.297241i −0.767371 0.641203i \(-0.778436\pi\)
0.938984 + 0.343962i \(0.111769\pi\)
\(192\) 0 0
\(193\) −91.0000 157.617i −0.0339395 0.0587849i 0.848557 0.529104i \(-0.177472\pi\)
−0.882496 + 0.470319i \(0.844139\pi\)
\(194\) −304.631 + 527.636i −0.112738 + 0.195268i
\(195\) 0 0
\(196\) 0 0
\(197\) −3468.00 −1.25424 −0.627119 0.778924i \(-0.715766\pi\)
−0.627119 + 0.778924i \(0.715766\pi\)
\(198\) 0 0
\(199\) −1949.64 3376.87i −0.694503 1.20292i −0.970348 0.241713i \(-0.922291\pi\)
0.275844 0.961202i \(-0.411043\pi\)
\(200\) 428.000 + 741.318i 0.151321 + 0.262095i
\(201\) 0 0
\(202\) −2041.03 −0.710922
\(203\) 0 0
\(204\) 0 0
\(205\) 2436.00 4219.28i 0.829940 1.43750i
\(206\) 578.799 + 1002.51i 0.195761 + 0.339068i
\(207\) 0 0
\(208\) −243.705 + 422.109i −0.0812398 + 0.140712i
\(209\) 304.631 0.100822
\(210\) 0 0
\(211\) −2620.00 −0.854826 −0.427413 0.904057i \(-0.640575\pi\)
−0.427413 + 0.904057i \(0.640575\pi\)
\(212\) 1096.00 1898.33i 0.355064 0.614989i
\(213\) 0 0
\(214\) 1646.00 + 2850.96i 0.525786 + 0.910688i
\(215\) 2162.88 3746.22i 0.686080 1.18833i
\(216\) 0 0
\(217\) 0 0
\(218\) −1964.00 −0.610178
\(219\) 0 0
\(220\) 60.9262 + 105.527i 0.0186711 + 0.0323393i
\(221\) 696.000 + 1205.51i 0.211846 + 0.366929i
\(222\) 0 0
\(223\) −1401.30 −0.420799 −0.210399 0.977616i \(-0.567476\pi\)
−0.210399 + 0.977616i \(0.567476\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) −1288.00 + 2230.88i −0.379099 + 0.656620i
\(227\) 1949.64 + 3376.87i 0.570053 + 0.987361i 0.996560 + 0.0828763i \(0.0264106\pi\)
−0.426507 + 0.904484i \(0.640256\pi\)
\(228\) 0 0
\(229\) −2756.91 + 4775.11i −0.795553 + 1.37794i 0.126934 + 0.991911i \(0.459486\pi\)
−0.922487 + 0.386028i \(0.873847\pi\)
\(230\) 913.893 0.262001
\(231\) 0 0
\(232\) 1696.00 0.479948
\(233\) −356.000 + 616.610i −0.100096 + 0.173371i −0.911724 0.410803i \(-0.865248\pi\)
0.811628 + 0.584174i \(0.198582\pi\)
\(234\) 0 0
\(235\) −464.000 803.672i −0.128800 0.223088i
\(236\) 1340.38 2321.60i 0.369708 0.640353i
\(237\) 0 0
\(238\) 0 0
\(239\) 2586.00 0.699893 0.349947 0.936770i \(-0.386200\pi\)
0.349947 + 0.936770i \(0.386200\pi\)
\(240\) 0 0
\(241\) −1127.13 1952.25i −0.301266 0.521808i 0.675157 0.737674i \(-0.264076\pi\)
−0.976423 + 0.215866i \(0.930743\pi\)
\(242\) −1327.00 2298.43i −0.352491 0.610532i
\(243\) 0 0
\(244\) 2071.49 0.543498
\(245\) 0 0
\(246\) 0 0
\(247\) 2320.00 4018.36i 0.597644 1.03515i
\(248\) −852.967 1477.38i −0.218401 0.378282i
\(249\) 0 0
\(250\) −274.168 + 474.873i −0.0693596 + 0.120134i
\(251\) −4508.54 −1.13377 −0.566885 0.823797i \(-0.691852\pi\)
−0.566885 + 0.823797i \(0.691852\pi\)
\(252\) 0 0
\(253\) 60.0000 0.0149098
\(254\) −1072.00 + 1856.76i −0.264816 + 0.458675i
\(255\) 0 0
\(256\) −128.000 221.703i −0.0312500 0.0541266i
\(257\) −2277.12 + 3944.08i −0.552695 + 0.957296i 0.445384 + 0.895340i \(0.353067\pi\)
−0.998079 + 0.0619561i \(0.980266\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 1856.00 0.442709
\(261\) 0 0
\(262\) −2741.68 4748.73i −0.646494 1.11976i
\(263\) −1289.00 2232.61i −0.302217 0.523456i 0.674421 0.738347i \(-0.264393\pi\)
−0.976638 + 0.214892i \(0.931060\pi\)
\(264\) 0 0
\(265\) −8346.89 −1.93489
\(266\) 0 0
\(267\) 0 0
\(268\) −1304.00 + 2258.59i −0.297218 + 0.514797i
\(269\) −464.562 804.645i −0.105297 0.182380i 0.808563 0.588410i \(-0.200246\pi\)
−0.913859 + 0.406031i \(0.866913\pi\)
\(270\) 0 0
\(271\) −563.567 + 976.127i −0.126326 + 0.218803i −0.922250 0.386593i \(-0.873652\pi\)
0.795925 + 0.605396i \(0.206985\pi\)
\(272\) −731.114 −0.162979
\(273\) 0 0
\(274\) 5872.00 1.29467
\(275\) 107.000 185.329i 0.0234631 0.0406392i
\(276\) 0 0
\(277\) −755.000 1307.70i −0.163767 0.283653i 0.772450 0.635076i \(-0.219031\pi\)
−0.936217 + 0.351423i \(0.885698\pi\)
\(278\) −182.779 + 316.582i −0.0394328 + 0.0682997i
\(279\) 0 0
\(280\) 0 0
\(281\) 4008.00 0.850880 0.425440 0.904987i \(-0.360119\pi\)
0.425440 + 0.904987i \(0.360119\pi\)
\(282\) 0 0
\(283\) 1203.29 + 2084.16i 0.252750 + 0.437776i 0.964282 0.264878i \(-0.0853316\pi\)
−0.711532 + 0.702654i \(0.751998\pi\)
\(284\) 1540.00 + 2667.36i 0.321768 + 0.557319i
\(285\) 0 0
\(286\) 121.852 0.0251933
\(287\) 0 0
\(288\) 0 0
\(289\) 1412.50 2446.52i 0.287503 0.497969i
\(290\) −3229.09 5592.94i −0.653857 1.13251i
\(291\) 0 0
\(292\) −1949.64 + 3376.87i −0.390733 + 0.676769i
\(293\) −5254.88 −1.04776 −0.523880 0.851792i \(-0.675516\pi\)
−0.523880 + 0.851792i \(0.675516\pi\)
\(294\) 0 0
\(295\) −10208.0 −2.01469
\(296\) 984.000 1704.34i 0.193222 0.334671i
\(297\) 0 0
\(298\) 964.000 + 1669.70i 0.187393 + 0.324574i
\(299\) 456.946 791.454i 0.0883809 0.153080i
\(300\) 0 0
\(301\) 0 0
\(302\) 3376.00 0.643268
\(303\) 0 0
\(304\) 1218.52 + 2110.54i 0.229892 + 0.398184i
\(305\) −3944.00 6831.21i −0.740435 1.28247i
\(306\) 0 0
\(307\) 6366.79 1.18362 0.591811 0.806077i \(-0.298413\pi\)
0.591811 + 0.806077i \(0.298413\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) −3248.00 + 5625.70i −0.595077 + 1.03070i
\(311\) 3686.03 + 6384.40i 0.672077 + 1.16407i 0.977314 + 0.211795i \(0.0679308\pi\)
−0.305238 + 0.952276i \(0.598736\pi\)
\(312\) 0 0
\(313\) 274.168 474.873i 0.0495108 0.0857552i −0.840208 0.542264i \(-0.817567\pi\)
0.889719 + 0.456509i \(0.150900\pi\)
\(314\) 6884.66 1.23734
\(315\) 0 0
\(316\) 1888.00 0.336102
\(317\) 1890.00 3273.58i 0.334867 0.580007i −0.648592 0.761136i \(-0.724642\pi\)
0.983459 + 0.181129i \(0.0579751\pi\)
\(318\) 0 0
\(319\) −212.000 367.195i −0.0372092 0.0644482i
\(320\) −487.409 + 844.218i −0.0851469 + 0.147479i
\(321\) 0 0
\(322\) 0 0
\(323\) 6960.00 1.19896
\(324\) 0 0
\(325\) −1629.78 2822.85i −0.278165 0.481796i
\(326\) −3324.00 5757.34i −0.564722 0.978127i
\(327\) 0 0
\(328\) 2558.90 0.430767
\(329\) 0 0
\(330\) 0 0
\(331\) −3130.00 + 5421.32i −0.519759 + 0.900250i 0.479977 + 0.877281i \(0.340645\pi\)
−0.999736 + 0.0229685i \(0.992688\pi\)
\(332\) −365.557 633.163i −0.0604294 0.104667i
\(333\) 0 0
\(334\) 3046.31 5276.36i 0.499062 0.864400i
\(335\) 9930.97 1.61966
\(336\) 0 0
\(337\) −3166.00 −0.511760 −0.255880 0.966709i \(-0.582365\pi\)
−0.255880 + 0.966709i \(0.582365\pi\)
\(338\) −1269.00 + 2197.97i −0.204214 + 0.353710i
\(339\) 0 0
\(340\) 1392.00 + 2411.01i 0.222035 + 0.384575i
\(341\) −213.242 + 369.345i −0.0338642 + 0.0586545i
\(342\) 0 0
\(343\) 0 0
\(344\) 2272.00 0.356099
\(345\) 0 0
\(346\) 3274.78 + 5672.09i 0.508825 + 0.881310i
\(347\) −1809.00 3133.28i −0.279862 0.484736i 0.691488 0.722388i \(-0.256955\pi\)
−0.971350 + 0.237652i \(0.923622\pi\)
\(348\) 0 0
\(349\) 4478.07 0.686836 0.343418 0.939183i \(-0.388415\pi\)
0.343418 + 0.939183i \(0.388415\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) −32.0000 + 55.4256i −0.00484547 + 0.00839260i
\(353\) 1850.63 + 3205.39i 0.279035 + 0.483302i 0.971145 0.238489i \(-0.0766522\pi\)
−0.692110 + 0.721792i \(0.743319\pi\)
\(354\) 0 0
\(355\) 5864.15 10157.0i 0.876723 1.51853i
\(356\) 2863.53 0.426311
\(357\) 0 0
\(358\) 2508.00 0.370257
\(359\) 65.0000 112.583i 0.00955590 0.0165513i −0.861208 0.508253i \(-0.830292\pi\)
0.870764 + 0.491702i \(0.163625\pi\)
\(360\) 0 0
\(361\) −8170.50 14151.7i −1.19121 2.06323i
\(362\) 3076.77 5329.13i 0.446717 0.773737i
\(363\) 0 0
\(364\) 0 0
\(365\) 14848.0 2.12926
\(366\) 0 0
\(367\) 3899.28 + 6753.74i 0.554606 + 0.960606i 0.997934 + 0.0642468i \(0.0204645\pi\)
−0.443328 + 0.896360i \(0.646202\pi\)
\(368\) 240.000 + 415.692i 0.0339969 + 0.0588844i
\(369\) 0 0
\(370\) −7493.92 −1.05295
\(371\) 0 0
\(372\) 0 0
\(373\) 25.0000 43.3013i 0.00347038 0.00601087i −0.864285 0.503002i \(-0.832229\pi\)
0.867755 + 0.496992i \(0.165562\pi\)
\(374\) 91.3893 + 158.291i 0.0126354 + 0.0218851i
\(375\) 0 0
\(376\) 243.705 422.109i 0.0334258 0.0578952i
\(377\) −6458.18 −0.882263
\(378\) 0 0
\(379\) −4956.00 −0.671696 −0.335848 0.941916i \(-0.609023\pi\)
−0.335848 + 0.941916i \(0.609023\pi\)
\(380\) 4640.00 8036.72i 0.626387 1.08493i
\(381\) 0 0
\(382\) −906.000 1569.24i −0.121348 0.210181i
\(383\) −3381.40 + 5856.76i −0.451127 + 0.781375i −0.998456 0.0555425i \(-0.982311\pi\)
0.547329 + 0.836917i \(0.315645\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) −364.000 −0.0479977
\(387\) 0 0
\(388\) 609.262 + 1055.27i 0.0797180 + 0.138076i
\(389\) −6570.00 11379.6i −0.856330 1.48321i −0.875406 0.483388i \(-0.839406\pi\)
0.0190764 0.999818i \(-0.493927\pi\)
\(390\) 0 0
\(391\) 1370.84 0.177305
\(392\) 0 0
\(393\) 0 0
\(394\) −3468.00 + 6006.75i −0.443440 + 0.768060i
\(395\) −3594.64 6226.11i −0.457889 0.793087i
\(396\) 0 0
\(397\) 1903.94 3297.73i 0.240696 0.416897i −0.720217 0.693749i \(-0.755958\pi\)
0.960913 + 0.276852i \(0.0892911\pi\)
\(398\) −7798.55 −0.982176
\(399\) 0 0
\(400\) 1712.00 0.214000
\(401\) 2412.00 4177.71i 0.300373 0.520261i −0.675848 0.737041i \(-0.736222\pi\)
0.976220 + 0.216780i \(0.0695555\pi\)
\(402\) 0 0
\(403\) 3248.00 + 5625.70i 0.401475 + 0.695375i
\(404\) −2041.03 + 3535.16i −0.251349 + 0.435349i
\(405\) 0 0
\(406\) 0 0
\(407\) −492.000 −0.0599202
\(408\) 0 0
\(409\) 2650.29 + 4590.44i 0.320412 + 0.554969i 0.980573 0.196155i \(-0.0628454\pi\)
−0.660161 + 0.751124i \(0.729512\pi\)
\(410\) −4872.00 8438.55i −0.586856 1.01646i
\(411\) 0 0
\(412\) 2315.20 0.276848
\(413\) 0 0
\(414\) 0 0
\(415\) −1392.00 + 2411.01i −0.164652 + 0.285186i
\(416\) 487.409 + 844.218i 0.0574452 + 0.0994981i
\(417\) 0 0
\(418\) 304.631 527.636i 0.0356459 0.0617405i
\(419\) −10540.2 −1.22894 −0.614468 0.788942i \(-0.710629\pi\)
−0.614468 + 0.788942i \(0.710629\pi\)
\(420\) 0 0
\(421\) −4458.00 −0.516080 −0.258040 0.966134i \(-0.583077\pi\)
−0.258040 + 0.966134i \(0.583077\pi\)
\(422\) −2620.00 + 4537.97i −0.302227 + 0.523472i
\(423\) 0 0
\(424\) −2192.00 3796.66i −0.251068 0.434863i
\(425\) 2444.66 4234.28i 0.279020 0.483277i
\(426\) 0 0
\(427\) 0 0
\(428\) 6584.00 0.743574
\(429\) 0 0
\(430\) −4325.76 7492.43i −0.485132 0.840273i
\(431\) −8107.00 14041.7i −0.906034 1.56930i −0.819524 0.573045i \(-0.805762\pi\)
−0.0865097 0.996251i \(-0.527571\pi\)
\(432\) 0 0
\(433\) 3594.64 0.398955 0.199478 0.979902i \(-0.436075\pi\)
0.199478 + 0.979902i \(0.436075\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) −1964.00 + 3401.75i −0.215731 + 0.373656i
\(437\) −2284.73 3957.27i −0.250100 0.433185i
\(438\) 0 0
\(439\) −4295.30 + 7439.67i −0.466978 + 0.808829i −0.999288 0.0377198i \(-0.987991\pi\)
0.532310 + 0.846549i \(0.321324\pi\)
\(440\) 243.705 0.0264049
\(441\) 0 0
\(442\) 2784.00 0.299596
\(443\) 7503.00 12995.6i 0.804691 1.39377i −0.111808 0.993730i \(-0.535664\pi\)
0.916499 0.400037i \(-0.131003\pi\)
\(444\) 0 0
\(445\) −5452.00 9443.14i −0.580786 1.00595i
\(446\) −1401.30 + 2427.13i −0.148775 + 0.257686i
\(447\) 0 0
\(448\) 0 0
\(449\) −1824.00 −0.191715 −0.0958573 0.995395i \(-0.530559\pi\)
−0.0958573 + 0.995395i \(0.530559\pi\)
\(450\) 0 0
\(451\) −319.862 554.018i −0.0333963 0.0578441i
\(452\) 2576.00 + 4461.76i 0.268064 + 0.464300i
\(453\) 0 0
\(454\) 7798.55 0.806177
\(455\) 0 0
\(456\) 0 0
\(457\) 293.000 507.491i 0.0299912 0.0519462i −0.850640 0.525748i \(-0.823785\pi\)
0.880631 + 0.473802i \(0.157119\pi\)
\(458\) 5513.82 + 9550.22i 0.562541 + 0.974350i
\(459\) 0 0
\(460\) 913.893 1582.91i 0.0926315 0.160442i
\(461\) 15399.1 1.55576 0.777882 0.628410i \(-0.216294\pi\)
0.777882 + 0.628410i \(0.216294\pi\)
\(462\) 0 0
\(463\) −88.0000 −0.00883306 −0.00441653 0.999990i \(-0.501406\pi\)
−0.00441653 + 0.999990i \(0.501406\pi\)
\(464\) 1696.00 2937.56i 0.169687 0.293907i
\(465\) 0 0
\(466\) 712.000 + 1233.22i 0.0707785 + 0.122592i
\(467\) 4874.09 8442.18i 0.482968 0.836526i −0.516840 0.856082i \(-0.672892\pi\)
0.999809 + 0.0195561i \(0.00622529\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) −1856.00 −0.182151
\(471\) 0 0
\(472\) −2680.75 4643.20i −0.261423 0.452798i
\(473\) −284.000 491.902i −0.0276075 0.0478175i
\(474\) 0 0
\(475\) −16297.8 −1.57430
\(476\) 0 0
\(477\) 0 0
\(478\) 2586.00 4479.08i 0.247450 0.428595i
\(479\) −2467.51 4273.85i −0.235373 0.407677i 0.724008 0.689791i \(-0.242298\pi\)
−0.959381 + 0.282114i \(0.908964\pi\)
\(480\) 0 0
\(481\) −3746.96 + 6489.93i −0.355191 + 0.615208i
\(482\) −4508.54 −0.426054
\(483\) 0 0
\(484\) −5308.00 −0.498497
\(485\) 2320.00 4018.36i 0.217208 0.376215i
\(486\) 0 0
\(487\) 412.000 + 713.605i 0.0383357 + 0.0663994i 0.884557 0.466433i \(-0.154461\pi\)
−0.846221 + 0.532832i \(0.821128\pi\)
\(488\) 2071.49 3587.93i 0.192156 0.332823i
\(489\) 0 0
\(490\) 0 0
\(491\) 15426.0 1.41785 0.708926 0.705283i \(-0.249180\pi\)
0.708926 + 0.705283i \(0.249180\pi\)
\(492\) 0 0
\(493\) −4843.63 8389.42i −0.442487 0.766410i
\(494\) −4640.00 8036.72i −0.422598 0.731961i
\(495\) 0 0
\(496\) −3411.87 −0.308866
\(497\) 0 0
\(498\) 0 0
\(499\) −2922.00 + 5061.05i −0.262138 + 0.454036i −0.966810 0.255497i \(-0.917761\pi\)
0.704672 + 0.709533i \(0.251094\pi\)
\(500\) 548.336 + 949.745i 0.0490446 + 0.0849478i
\(501\) 0 0
\(502\) −4508.54 + 7809.02i −0.400848 + 0.694290i
\(503\) 10174.7 0.901921 0.450960 0.892544i \(-0.351082\pi\)
0.450960 + 0.892544i \(0.351082\pi\)
\(504\) 0 0
\(505\) 15544.0 1.36970
\(506\) 60.0000 103.923i 0.00527139 0.00913032i
\(507\) 0 0
\(508\) 2144.00 + 3713.52i 0.187253 + 0.324332i
\(509\) 5902.22 10223.0i 0.513971 0.890225i −0.485897 0.874016i \(-0.661507\pi\)
0.999869 0.0162087i \(-0.00515962\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) −512.000 −0.0441942
\(513\) 0 0
\(514\) 4554.23 + 7888.16i 0.390814 + 0.676910i
\(515\) −4408.00 7634.88i −0.377164 0.653268i
\(516\) 0 0
\(517\) −121.852 −0.0103657
\(518\) 0 0
\(519\) 0 0
\(520\) 1856.00 3214.69i 0.156521 0.271103i
\(521\) 784.425 + 1358.66i 0.0659621 + 0.114250i 0.897120 0.441786i \(-0.145655\pi\)
−0.831158 + 0.556036i \(0.812322\pi\)
\(522\) 0 0
\(523\) −9565.41 + 16567.8i −0.799744 + 1.38520i 0.120038 + 0.992769i \(0.461698\pi\)
−0.919783 + 0.392428i \(0.871635\pi\)
\(524\) −10966.7 −0.914281
\(525\) 0 0
\(526\) −5156.00 −0.427400
\(527\) −4872.00 + 8438.55i −0.402709 + 0.697512i
\(528\) 0 0
\(529\) 5633.50 + 9757.51i 0.463015 + 0.801965i
\(530\) −8346.89 + 14457.2i −0.684086 + 1.18487i
\(531\) 0 0
\(532\) 0 0
\(533\) −9744.00 −0.791856
\(534\) 0 0
\(535\) −12535.6 21712.2i −1.01301 1.75458i
\(536\) 2608.00 + 4517.19i 0.210165 + 0.364016i
\(537\) 0 0
\(538\) −1858.25 −0.148912
\(539\) 0 0
\(540\) 0 0
\(541\) 3313.00 5738.28i 0.263285 0.456022i −0.703828 0.710370i \(-0.748527\pi\)
0.967113 + 0.254348i \(0.0818608\pi\)
\(542\) 1127.13 + 1952.25i 0.0893258 + 0.154717i
\(543\) 0 0
\(544\) −731.114 + 1266.33i −0.0576218 + 0.0998039i
\(545\) 14957.4 1.17560
\(546\) 0 0
\(547\) −19964.0 −1.56051 −0.780255 0.625462i \(-0.784911\pi\)
−0.780255 + 0.625462i \(0.784911\pi\)
\(548\) 5872.00 10170.6i 0.457736 0.792822i
\(549\) 0 0
\(550\) −214.000 370.659i −0.0165909 0.0287363i
\(551\) −16145.4 + 27964.7i −1.24831 + 2.16214i
\(552\) 0 0
\(553\) 0 0
\(554\) −3020.00 −0.231602
\(555\) 0 0
\(556\) 365.557 + 633.163i 0.0278832 + 0.0482952i
\(557\) 3390.00 + 5871.65i 0.257880 + 0.446660i 0.965674 0.259758i \(-0.0836429\pi\)
−0.707794 + 0.706419i \(0.750310\pi\)
\(558\) 0 0
\(559\) −8651.52 −0.654598
\(560\) 0 0
\(561\) 0 0
\(562\) 4008.00 6942.06i 0.300831 0.521055i
\(563\) −9474.02 16409.5i −0.709205 1.22838i −0.965152 0.261688i \(-0.915721\pi\)
0.255947 0.966691i \(-0.417613\pi\)
\(564\) 0 0
\(565\) 9809.12 16989.9i 0.730394 1.26508i
\(566\) 4813.17 0.357443
\(567\) 0 0
\(568\) 6160.00 0.455049
\(569\) −96.0000 + 166.277i −0.00707299 + 0.0122508i −0.869540 0.493862i \(-0.835585\pi\)
0.862467 + 0.506113i \(0.168918\pi\)
\(570\) 0 0
\(571\) 11514.0 + 19942.8i 0.843863 + 1.46161i 0.886605 + 0.462528i \(0.153057\pi\)
−0.0427415 + 0.999086i \(0.513609\pi\)
\(572\) 121.852 211.054i 0.00890717 0.0154277i
\(573\) 0 0
\(574\) 0 0
\(575\) −3210.00 −0.232811
\(576\) 0 0
\(577\) 5361.50 + 9286.40i 0.386832 + 0.670014i 0.992022 0.126068i \(-0.0402358\pi\)
−0.605189 + 0.796082i \(0.706902\pi\)
\(578\) −2825.00 4893.04i −0.203295 0.352117i
\(579\) 0 0
\(580\) −12916.4 −0.924694
\(581\) 0 0
\(582\) 0 0
\(583\) −548.000 + 949.164i −0.0389294 + 0.0674277i
\(584\) 3899.28 + 6753.74i 0.276290 + 0.478548i
\(585\) 0 0
\(586\) −5254.88 + 9101.73i −0.370439 + 0.641619i
\(587\) −19496.4 −1.37087 −0.685436 0.728133i \(-0.740388\pi\)
−0.685436 + 0.728133i \(0.740388\pi\)
\(588\) 0 0
\(589\) 32480.0 2.27218
\(590\) −10208.0 + 17680.8i −0.712300 + 1.23374i
\(591\) 0 0
\(592\) −1968.00 3408.68i −0.136629 0.236648i
\(593\) 6694.26 11594.8i 0.463576 0.802937i −0.535560 0.844497i \(-0.679899\pi\)
0.999136 + 0.0415601i \(0.0132328\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 3856.00 0.265013
\(597\) 0 0
\(598\) −913.893 1582.91i −0.0624947 0.108244i
\(599\) 9033.00 + 15645.6i 0.616158 + 1.06722i 0.990180 + 0.139797i \(0.0446449\pi\)
−0.374023 + 0.927420i \(0.622022\pi\)
\(600\) 0 0
\(601\) 19861.9 1.34806 0.674031 0.738703i \(-0.264561\pi\)
0.674031 + 0.738703i \(0.264561\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 3376.00 5847.40i 0.227430 0.393920i
\(605\) 10106.1 + 17504.3i 0.679128 + 1.17628i
\(606\) 0 0
\(607\) 2650.29 4590.44i 0.177219 0.306952i −0.763708 0.645562i \(-0.776623\pi\)
0.940927 + 0.338610i \(0.109957\pi\)
\(608\) 4874.09 0.325116
\(609\) 0 0
\(610\) −15776.0 −1.04713
\(611\) −928.000 + 1607.34i −0.0614449 + 0.106426i
\(612\) 0 0
\(613\) −7969.00 13802.7i −0.525065 0.909439i −0.999574 0.0291886i \(-0.990708\pi\)
0.474509 0.880251i \(-0.342626\pi\)
\(614\) 6366.79 11027.6i 0.418473 0.724817i
\(615\) 0 0
\(616\) 0 0
\(617\) 11696.0 0.763149 0.381575 0.924338i \(-0.375382\pi\)
0.381575 + 0.924338i \(0.375382\pi\)
\(618\) 0 0
\(619\) 6732.34 + 11660.8i 0.437150 + 0.757166i 0.997468 0.0711115i \(-0.0226546\pi\)
−0.560319 + 0.828277i \(0.689321\pi\)
\(620\) 6496.00 + 11251.4i 0.420783 + 0.728818i
\(621\) 0 0
\(622\) 14744.1 0.950460
\(623\) 0 0
\(624\) 0 0
\(625\) 8775.50 15199.6i 0.561632 0.972775i
\(626\) −548.336 949.745i −0.0350094 0.0606381i
\(627\) 0 0
\(628\) 6884.66 11924.6i 0.437465 0.757711i
\(629\) −11240.9 −0.712565
\(630\) 0 0
\(631\) 11856.0 0.747987 0.373994 0.927431i \(-0.377988\pi\)
0.373994 + 0.927431i \(0.377988\pi\)
\(632\) 1888.00 3270.11i 0.118830 0.205820i
\(633\) 0 0
\(634\) −3780.00 6547.15i −0.236787 0.410127i
\(635\) 8164.11 14140.7i 0.510209 0.883708i
\(636\) 0 0
\(637\) 0 0
\(638\) −848.000 −0.0526217
\(639\) 0 0
\(640\) 974.819 + 1688.44i 0.0602080 + 0.104283i
\(641\) 2804.00 + 4856.67i 0.172779 + 0.299262i 0.939390 0.342849i \(-0.111392\pi\)
−0.766611 + 0.642111i \(0.778059\pi\)
\(642\) 0 0
\(643\) 25314.8 1.55260 0.776298 0.630366i \(-0.217095\pi\)
0.776298 + 0.630366i \(0.217095\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 6960.00 12055.1i 0.423897 0.734211i
\(647\) −2924.46 5065.31i −0.177701 0.307786i 0.763392 0.645936i \(-0.223533\pi\)
−0.941093 + 0.338149i \(0.890199\pi\)
\(648\) 0 0
\(649\) −670.188 + 1160.80i −0.0405349 + 0.0702086i
\(650\) −6519.10 −0.393385
\(651\) 0 0
\(652\) −13296.0 −0.798637
\(653\) −14318.0 + 24799.5i −0.858050 + 1.48619i 0.0157364 + 0.999876i \(0.494991\pi\)
−0.873786 + 0.486310i \(0.838343\pi\)
\(654\) 0 0
\(655\) 20880.0 + 36165.2i 1.24557 + 2.15739i
\(656\) 2558.90 4432.14i 0.152299 0.263790i
\(657\) 0 0
\(658\) 0 0
\(659\) −31786.0 −1.87892 −0.939459 0.342662i \(-0.888672\pi\)
−0.939459 + 0.342662i \(0.888672\pi\)
\(660\) 0 0
\(661\) 4737.01 + 8204.74i 0.278742 + 0.482795i 0.971072 0.238786i \(-0.0767493\pi\)
−0.692330 + 0.721581i \(0.743416\pi\)
\(662\) 6260.00 + 10842.6i 0.367525 + 0.636573i
\(663\) 0 0
\(664\) −1462.23 −0.0854600
\(665\) 0 0
\(666\) 0 0
\(667\) −3180.00 + 5507.92i −0.184603 + 0.319741i
\(668\) −6092.62 10552.7i −0.352890 0.611223i
\(669\) 0 0
\(670\) 9930.97 17200.9i 0.572637 0.991836i
\(671\) −1035.75 −0.0595894
\(672\) 0 0
\(673\) 24986.0 1.43111 0.715557 0.698555i \(-0.246173\pi\)
0.715557 + 0.698555i \(0.246173\pi\)
\(674\) −3166.00 + 5483.67i −0.180934 + 0.313388i
\(675\) 0 0
\(676\) 2538.00 + 4395.94i 0.144401 + 0.250111i
\(677\) −22.8473 + 39.5727i −0.00129704 + 0.00224653i −0.866673 0.498876i \(-0.833746\pi\)
0.865376 + 0.501123i \(0.167080\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 5568.00 0.314004
\(681\) 0 0
\(682\) 426.483 + 738.691i 0.0239456 + 0.0414750i
\(683\) 15047.0 + 26062.2i 0.842983 + 1.46009i 0.887361 + 0.461075i \(0.152536\pi\)
−0.0443782 + 0.999015i \(0.514131\pi\)
\(684\) 0 0
\(685\) −44719.8 −2.49439
\(686\) 0 0
\(687\) 0 0
\(688\) 2272.00 3935.22i 0.125900 0.218065i
\(689\) 8346.89 + 14457.2i 0.461526 + 0.799386i
\(690\) 0 0
\(691\) 8468.74 14668.3i 0.466232 0.807537i −0.533025 0.846100i \(-0.678945\pi\)
0.999256 + 0.0385629i \(0.0122780\pi\)
\(692\) 13099.1 0.719587
\(693\) 0 0
\(694\) −7236.00 −0.395785
\(695\) 1392.00 2411.01i 0.0759735 0.131590i
\(696\) 0 0
\(697\) −7308.00 12657.8i −0.397145 0.687876i
\(698\) 4478.07 7756.25i 0.242833 0.420600i
\(699\) 0 0
\(700\) 0 0
\(701\) −7660.00 −0.412716 −0.206358 0.978477i \(-0.566161\pi\)
−0.206358 + 0.978477i \(0.566161\pi\)
\(702\) 0 0
\(703\) 18734.8 + 32449.6i 1.00512 + 1.74091i
\(704\) 64.0000 + 110.851i 0.00342627 + 0.00593447i
\(705\) 0 0
\(706\) 7402.53 0.394615
\(707\) 0 0
\(708\) 0 0
\(709\) −5327.00 + 9226.63i −0.282172 + 0.488736i −0.971919 0.235314i \(-0.924388\pi\)
0.689748 + 0.724050i \(0.257721\pi\)
\(710\) −11728.3 20314.0i −0.619936 1.07376i
\(711\) 0 0
\(712\) 2863.53 4959.78i 0.150724 0.261061i
\(713\) 6397.25 0.336015
\(714\) 0 0
\(715\) −928.000 −0.0485388
\(716\) 2508.00 4343.98i 0.130906 0.226735i
\(717\) 0 0
\(718\) −130.000 225.167i −0.00675704 0.0117035i
\(719\) −18552.0 + 32133.0i −0.962272 + 1.66670i −0.245500 + 0.969396i \(0.578952\pi\)
−0.716772 + 0.697308i \(0.754381\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) −32682.0 −1.68462
\(723\) 0 0
\(724\) −6153.54 10658.3i −0.315877 0.547114i
\(725\) 11342.0 + 19644.9i 0.581009 + 1.00634i
\(726\) 0 0
\(727\) 17760.0 0.906027 0.453013 0.891504i \(-0.350349\pi\)
0.453013 + 0.891504i \(0.350349\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 14848.0 25717.5i 0.752807 1.30390i
\(731\) −6488.64 11238.7i −0.328305 0.568641i
\(732\) 0 0
\(733\) −1264.22 + 2189.69i −0.0637039 + 0.110338i −0.896118 0.443815i \(-0.853625\pi\)
0.832414 + 0.554154i \(0.186958\pi\)
\(734\) 15597.1 0.784332
\(735\) 0 0
\(736\) 960.000 0.0480789
\(737\) 652.000 1129.30i 0.0325871 0.0564426i
\(738\) 0 0
\(739\) 4078.00 + 7063.30i 0.202993 + 0.351594i 0.949491 0.313793i \(-0.101600\pi\)
−0.746499 + 0.665387i \(0.768267\pi\)
\(740\) −7493.92 + 12979.9i −0.372273 + 0.644796i
\(741\) 0 0
\(742\) 0 0
\(743\) 2910.00 0.143684 0.0718422 0.997416i \(-0.477112\pi\)
0.0718422 + 0.997416i \(0.477112\pi\)
\(744\) 0 0
\(745\) −7341.61 12716.0i −0.361041 0.625341i
\(746\) −50.0000 86.6025i −0.00245393 0.00425033i
\(747\) 0 0
\(748\) 365.557 0.0178691
\(749\) 0 0
\(750\) 0 0
\(751\) −6792.00 + 11764.1i −0.330018 + 0.571608i −0.982515 0.186183i \(-0.940388\pi\)
0.652497 + 0.757791i \(0.273722\pi\)
\(752\) −487.409 844.218i −0.0236356 0.0409381i
\(753\) 0 0
\(754\) −6458.18 + 11185.9i −0.311927 + 0.540273i
\(755\) −25710.9 −1.23936
\(756\) 0 0
\(757\) 19054.0 0.914834 0.457417 0.889252i \(-0.348775\pi\)
0.457417 + 0.889252i \(0.348775\pi\)
\(758\) −4956.00 + 8584.04i −0.237480 + 0.411328i
\(759\) 0 0
\(760\) −9280.00 16073.4i −0.442922 0.767164i
\(761\) 2505.59 4339.81i 0.119353 0.206725i −0.800159 0.599789i \(-0.795251\pi\)
0.919511 + 0.393063i \(0.128585\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) −3624.00 −0.171612
\(765\) 0 0
\(766\) 6762.81 + 11713.5i 0.318995 + 0.552515i
\(767\) 10208.0 + 17680.8i 0.480560 + 0.832354i
\(768\) 0 0
\(769\) 21506.9 1.00853 0.504265 0.863549i \(-0.331763\pi\)
0.504265 + 0.863549i \(0.331763\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −364.000 + 630.466i −0.0169697 + 0.0293925i
\(773\) 11857.8 + 20538.2i 0.551739 + 0.955639i 0.998149 + 0.0608111i \(0.0193687\pi\)
−0.446411 + 0.894828i \(0.647298\pi\)
\(774\) 0 0
\(775\) 11408.4 19760.0i 0.528778 0.915870i
\(776\) 2437.05 0.112738
\(777\) 0 0
\(778\) −26280.0 −1.21103
\(779\) −24360.0 + 42192.8i −1.12039 + 1.94058i
\(780\) 0 0
\(781\) −770.000 1333.68i −0.0352788 0.0611047i
\(782\) 1370.84 2374.36i 0.0626868 0.108577i
\(783\) 0 0
\(784\) 0 0
\(785\) −52432.0 −2.38392
\(786\) 0 0
\(787\) −18491.1 32027.5i −0.837530 1.45065i −0.891953 0.452127i \(-0.850665\pi\)
0.0544230 0.998518i \(-0.482668\pi\)
\(788\) 6936.00 + 12013.5i 0.313559 + 0.543101i
\(789\) 0 0
\(790\) −14378.6 −0.647553
\(791\) 0 0
\(792\) 0