Properties

Label 882.4.g.bh.361.1
Level $882$
Weight $4$
Character 882.361
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 361.1
Root \(-3.80789 - 6.59545i\) of defining polynomial
Character \(\chi\) \(=\) 882.361
Dual form 882.4.g.bh.667.1

$q$-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 \(\left(\mathbb{Z}/882\mathbb{Z}\right)^\times\).

\(n\) \(199\) \(785\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(1\)

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 −0.974622 0.223855i \(-0.928136\pi\)
0.293447 0.955975i \(-0.405198\pi\)
\(6\) 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 −0.851995 0.523550i \(-0.824607\pi\)
0.879405 + 0.476074i \(0.157941\pi\)
\(12\) 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 −0.655748 0.754980i \(-0.727646\pi\)
0.981706 + 0.190404i \(0.0609798\pi\)
\(18\) 0 0
\(19\) 76.1577 + 131.909i 0.919567 + 1.59274i 0.800073 + 0.599903i \(0.204794\pi\)
0.119494 + 0.992835i \(0.461873\pi\)
\(20\) 60.9262 0.681175
\(21\) 0 0
\(22\) 4.00000 0.0387638
\(23\) 15.0000 + 25.9808i 0.135988 + 0.235538i 0.925974 0.377586i \(-0.123246\pi\)
−0.789987 + 0.613124i \(0.789913\pi\)
\(24\) 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 −0.372168 0.928166i \(-0.621385\pi\)
0.989899 0.141776i \(-0.0452813\pi\)
\(32\) 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 −0.998510 0.0545719i \(-0.982621\pi\)
0.451994 0.892021i \(-0.350713\pi\)
\(38\) −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 0.814875 0.579637i \(-0.196805\pi\)
−0.909418 + 0.415884i \(0.863472\pi\)
\(48\) 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 −0.254680 0.967025i \(-0.581970\pi\)
0.964809 0.262953i \(-0.0846964\pi\)
\(54\) 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 −0.213343 0.976977i \(-0.568435\pi\)
0.952759 0.303728i \(-0.0982315\pi\)
\(60\) 0 0
\(61\) −258.936 448.491i −0.543498 0.941367i −0.998700 0.0509782i \(-0.983766\pi\)
0.455202 0.890388i \(-0.349567\pi\)
\(62\) 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 0.399190 + 0.916868i \(0.369291\pi\)
−0.993626 + 0.112726i \(0.964042\pi\)
\(68\) 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 0.149623 + 0.988743i \(0.452194\pi\)
−0.931088 + 0.364794i \(0.881139\pi\)
\(74\) 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 0.647594 0.761986i \(-0.275775\pi\)
−0.983696 + 0.179840i \(0.942442\pi\)
\(80\) −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 0.570231 0.821485i \(-0.306854\pi\)
−0.996542 + 0.0830918i \(0.973521\pi\)
\(90\) 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 0.497298 + 0.867580i \(0.334326\pi\)
−0.999995 + 0.00311763i \(0.999008\pi\)
\(102\) 0 0
\(103\) −289.399 501.254i −0.276848 0.479515i 0.693752 0.720214i \(-0.255957\pi\)
−0.970600 + 0.240699i \(0.922623\pi\)
\(104\) −243.705 −0.229781
\(105\) 0 0
\(106\) 1096.00 1.00427
\(107\) −823.000 1425.48i −0.743574 1.28791i −0.950858 0.309627i \(-0.899796\pi\)
0.207284 0.978281i \(-0.433538\pi\)
\(108\) 0 0
\(109\) −491.000 + 850.437i −0.431461 + 0.747313i −0.996999 0.0774094i \(-0.975335\pi\)
0.565538 + 0.824722i \(0.308668\pi\)
\(110\) −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 0.807951 + 0.589250i \(0.200577\pi\)
0.106330 + 0.994331i \(0.466090\pi\)
\(132\) 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 0.109264 0.994013i \(-0.465151\pi\)
0.806208 0.591632i \(-0.201516\pi\)
\(138\) 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 0.702554 0.711631i \(-0.252043\pi\)
−0.967567 + 0.252614i \(0.918710\pi\)
\(150\) 0 0
\(151\) 844.000 1461.85i 0.454859 0.787839i −0.543821 0.839201i \(-0.683023\pi\)
0.998680 + 0.0513620i \(0.0163562\pi\)
\(152\) −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 0.0180912 0.999836i \(-0.494241\pi\)
0.856838 0.515586i \(-0.172426\pi\)
\(158\) 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 0.920504 + 0.390734i \(0.127779\pi\)
−0.121866 + 0.992547i \(0.538888\pi\)
\(164\) 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 −0.961164 0.275979i \(-0.910998\pi\)
0.241577 0.970382i \(-0.422336\pi\)
\(174\) 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 −0.704912 0.709295i \(-0.749014\pi\)
0.966723 + 0.255825i \(0.0823469\pi\)
\(180\) 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 0.938984 0.343962i \(-0.111769\pi\)
−0.767371 + 0.641203i \(0.778436\pi\)
\(192\) 0 0
\(193\) −91.0000 + 157.617i −0.0339395 + 0.0587849i −0.882496 0.470319i \(-0.844139\pi\)
0.848557 + 0.529104i \(0.177472\pi\)
\(194\) −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 0.275844 + 0.961202i \(0.411043\pi\)
−0.970348 + 0.241713i \(0.922291\pi\)
\(200\) 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 −0.426507 0.904484i \(-0.640256\pi\)
0.996560 0.0828763i \(-0.0264106\pi\)
\(228\) 0 0
\(229\) −2756.91 4775.11i −0.795553 1.37794i −0.922487 0.386028i \(-0.873847\pi\)
0.126934 0.991911i \(-0.459486\pi\)
\(230\) 913.893 0.262001
\(231\) 0 0
\(232\) 1696.00 0.479948
\(233\) −356.000 616.610i −0.100096 0.173371i 0.811628 0.584174i \(-0.198582\pi\)
−0.911724 + 0.410803i \(0.865248\pi\)
\(234\) 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 −0.976423 0.215866i \(-0.930743\pi\)
0.675157 + 0.737674i \(0.264076\pi\)
\(242\) −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 −0.998079 0.0619561i \(-0.980266\pi\)
0.445384 0.895340i \(-0.353067\pi\)
\(258\) 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 −0.976638 0.214892i \(-0.931060\pi\)
0.674421 + 0.738347i \(0.264393\pi\)
\(264\) 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 −0.913859 0.406031i \(-0.866913\pi\)
0.808563 + 0.588410i \(0.200246\pi\)
\(270\) 0 0
\(271\) −563.567 976.127i −0.126326 0.218803i 0.795925 0.605396i \(-0.206985\pi\)
−0.922250 + 0.386593i \(0.873652\pi\)
\(272\) −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 −0.936217 0.351423i \(-0.885698\pi\)
0.772450 + 0.635076i \(0.219031\pi\)
\(278\) −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 −0.711532 0.702654i \(-0.751998\pi\)
0.964282 + 0.264878i \(0.0853316\pi\)
\(284\) 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 −0.305238 0.952276i \(-0.598736\pi\)
0.977314 0.211795i \(-0.0679308\pi\)
\(312\) 0 0
\(313\) 274.168 + 474.873i 0.0495108 + 0.0857552i 0.889719 0.456509i \(-0.150900\pi\)
−0.840208 + 0.542264i \(0.817567\pi\)
\(314\) 6884.66 1.23734
\(315\) 0 0
\(316\) 1888.00 0.336102
\(317\) 1890.00 + 3273.58i 0.334867 + 0.580007i 0.983459 0.181129i \(-0.0579751\pi\)
−0.648592 + 0.761136i \(0.724642\pi\)
\(318\) 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 −0.999736 0.0229685i \(-0.992688\pi\)
0.479977 0.877281i \(-0.340645\pi\)
\(332\) −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 −0.971350 0.237652i \(-0.923622\pi\)
0.691488 + 0.722388i \(0.256955\pi\)
\(348\) 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 −0.692110 0.721792i \(-0.743319\pi\)
0.971145 + 0.238489i \(0.0766522\pi\)
\(354\) 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 0.870764 0.491702i \(-0.163625\pi\)
−0.861208 + 0.508253i \(0.830292\pi\)
\(360\) 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 −0.443328 0.896360i \(-0.646202\pi\)
0.997934 0.0642468i \(-0.0204645\pi\)
\(368\) 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 0.867755 0.496992i \(-0.165562\pi\)
−0.864285 + 0.503002i \(0.832229\pi\)
\(374\) 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 0.547329 0.836917i \(-0.315645\pi\)
−0.998456 + 0.0555425i \(0.982311\pi\)
\(384\) 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 0.0190764 + 0.999818i \(0.493927\pi\)
−0.875406 + 0.483388i \(0.839406\pi\)
\(390\) 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 0.960913 0.276852i \(-0.0892911\pi\)
−0.720217 + 0.693749i \(0.755958\pi\)
\(398\) −7798.55 −0.982176
\(399\) 0 0
\(400\) 1712.00 0.214000
\(401\) 2412.00 + 4177.71i 0.300373 + 0.520261i 0.976220 0.216780i \(-0.0695555\pi\)
−0.675848 + 0.737041i \(0.736222\pi\)
\(402\) 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 −0.660161 0.751124i \(-0.729512\pi\)
0.980573 + 0.196155i \(0.0628454\pi\)
\(410\) −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 −0.0865097 + 0.996251i \(0.527571\pi\)
−0.819524 + 0.573045i \(0.805762\pi\)
\(432\) 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 0.532310 0.846549i \(-0.321324\pi\)
−0.999288 + 0.0377198i \(0.987991\pi\)
\(440\) 243.705 0.0264049
\(441\) 0 0
\(442\) 2784.00 0.299596
\(443\) 7503.00 + 12995.6i 0.804691 + 1.39377i 0.916499 + 0.400037i \(0.131003\pi\)
−0.111808 + 0.993730i \(0.535664\pi\)
\(444\) 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 0.880631 0.473802i \(-0.157119\pi\)
−0.850640 + 0.525748i \(0.823785\pi\)
\(458\) 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 0.999809 0.0195561i \(-0.00622529\pi\)
−0.516840 + 0.856082i \(0.672892\pi\)
\(468\) 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 −0.959381 0.282114i \(-0.908964\pi\)
0.724008 + 0.689791i \(0.242298\pi\)
\(480\) 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 −0.846221 0.532832i \(-0.821128\pi\)
0.884557 + 0.466433i \(0.154461\pi\)
\(488\) 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 0.704672 0.709533i \(-0.251094\pi\)
−0.966810 + 0.255497i \(0.917761\pi\)
\(500\) 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 0.999869 + 0.0162087i \(0.00515962\pi\)
−0.485897 + 0.874016i \(0.661507\pi\)
\(510\) 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 −0.831158 0.556036i \(-0.812322\pi\)
0.897120 + 0.441786i \(0.145655\pi\)
\(522\) 0 0
\(523\) −9565.41 16567.8i −0.799744 1.38520i −0.919783 0.392428i \(-0.871635\pi\)
0.120038 0.992769i \(-0.461698\pi\)
\(524\) −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 0.967113 0.254348i \(-0.0818608\pi\)
−0.703828 + 0.710370i \(0.748527\pi\)
\(542\) 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 −0.707794 0.706419i \(-0.750310\pi\)
0.965674 + 0.259758i \(0.0836429\pi\)
\(558\) 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 0.255947 + 0.966691i \(0.417613\pi\)
−0.965152 + 0.261688i \(0.915721\pi\)
\(564\) 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 0.862467 0.506113i \(-0.168918\pi\)
−0.869540 + 0.493862i \(0.835585\pi\)
\(570\) 0 0
\(571\) 11514.0 19942.8i 0.843863 1.46161i −0.0427415 0.999086i \(-0.513609\pi\)
0.886605 0.462528i \(-0.153057\pi\)
\(572\) 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 −0.605189 0.796082i \(-0.706902\pi\)
0.992022 + 0.126068i \(0.0402358\pi\)
\(578\) −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 0.999136 0.0415601i \(-0.0132328\pi\)
−0.535560 + 0.844497i \(0.679899\pi\)
\(594\) 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 −0.374023 0.927420i \(-0.622022\pi\)
0.990180 0.139797i \(-0.0446449\pi\)
\(600\) 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 0.940927 0.338610i \(-0.109957\pi\)
−0.763708 + 0.645562i \(0.776623\pi\)
\(608\) 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 0.474509 + 0.880251i \(0.342626\pi\)
−0.999574 + 0.0291886i \(0.990708\pi\)
\(614\) 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 −0.560319 0.828277i \(-0.689321\pi\)
0.997468 + 0.0711115i \(0.0226546\pi\)
\(620\) 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 −0.766611 0.642111i \(-0.778059\pi\)
0.939390 + 0.342849i \(0.111392\pi\)
\(642\) 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 −0.941093 0.338149i \(-0.890199\pi\)
0.763392 + 0.645936i \(0.223533\pi\)
\(648\) 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 −0.873786 0.486310i \(-0.838343\pi\)
0.0157364 0.999876i \(-0.494991\pi\)
\(654\) 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 −0.692330 0.721581i \(-0.743416\pi\)
0.971072 + 0.238786i \(0.0767493\pi\)
\(662\) 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 0.865376 0.501123i \(-0.167080\pi\)
−0.866673 + 0.498876i \(0.833746\pi\)
\(678\) 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 −0.0443782 0.999015i \(-0.514131\pi\)
0.887361 0.461075i \(-0.152536\pi\)
\(684\) 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 0.999256 0.0385629i \(-0.0122780\pi\)
−0.533025 + 0.846100i \(0.678945\pi\)
\(692\) 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 0.689748 0.724050i \(-0.257721\pi\)
−0.971919 + 0.235314i \(0.924388\pi\)
\(710\) −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 −0.716772 0.697308i \(-0.754381\pi\)
−0.245500 0.969396i \(-0.578952\pi\)
\(720\) 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 0.832414 0.554154i \(-0.186958\pi\)
−0.896118 + 0.443815i \(0.853625\pi\)
\(734\) 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 −0.746499 0.665387i \(-0.768267\pi\)
0.949491 + 0.313793i \(0.101600\pi\)
\(740\) −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 0.652497 0.757791i \(-0.273722\pi\)
−0.982515 + 0.186183i \(0.940388\pi\)
\(752\) −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 0.919511 0.393063i \(-0.128585\pi\)
−0.800159 + 0.599789i \(0.795251\pi\)
\(762\) 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 −0.446411 0.894828i \(-0.647298\pi\)
0.998149 0.0608111i \(-0.0193687\pi\)
\(774\) 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 0.0544230 + 0.998518i \(0.482668\pi\)
−0.891953 + 0.452127i \(0.850665\pi\)
\(788\) 6936.00 12013.5i 0.313559 0.543101i
\(789\) 0 0
\(790\) −14378.6 −0.647553
\(791\) 0 0