Properties

Label 882.4.g.bb.667.2
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 667.2
Root \(3.80789 - 6.59545i\) of defining polynomial
Character \(\chi\) \(=\) 882.667
Dual form 882.4.g.bb.361.2

$q$-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 \(-0.594802\pi\)
0.974622 0.223855i \(-0.0718643\pi\)
\(6\) 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 \(-0.175393\pi\)
−0.879405 + 0.476074i \(0.842059\pi\)
\(12\) 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 \(-0.272354\pi\)
−0.981706 + 0.190404i \(0.939020\pi\)
\(18\) 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 −0.925974 0.377586i \(-0.876754\pi\)
0.789987 + 0.613124i \(0.210087\pi\)
\(24\) 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 \(-0.262523\pi\)
0.678748 + 0.734371i \(0.262523\pi\)
\(30\) 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 \(-0.291492\pi\)
0.609197 + 0.793019i \(0.291492\pi\)
\(42\) 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 \(-0.803195\pi\)
0.909418 + 0.415884i \(0.136528\pi\)
\(48\) 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 \(-0.915304\pi\)
0.254680 0.967025i \(-0.418030\pi\)
\(54\) 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 \(-0.901769\pi\)
0.213343 0.976977i \(-0.431565\pi\)
\(60\) 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 \(-0.277466\pi\)
0.643537 + 0.765415i \(0.277466\pi\)
\(72\) 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 \(-0.538565\pi\)
−0.120859 + 0.992670i \(0.538565\pi\)
\(84\) 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 \(-0.693146\pi\)
0.996542 + 0.0830918i \(0.0264795\pi\)
\(90\) 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 \(0.000992374\pi\)
−0.497298 + 0.867580i \(0.665674\pi\)
\(102\) 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 \(-0.566462\pi\)
0.950858 0.309627i \(-0.100204\pi\)
\(108\) 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 \(-0.319887\pi\)
0.536128 + 0.844137i \(0.319887\pi\)
\(114\) 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 \(0.533910\pi\)
−0.807951 + 0.589250i \(0.799423\pi\)
\(132\) 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 \(-0.798484\pi\)
−0.109264 0.994013i \(-0.534849\pi\)
\(138\) 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 \(-0.747957\pi\)
0.967567 + 0.252614i \(0.0812903\pi\)
\(150\) 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 \(-0.749403\pi\)
−0.705780 + 0.708431i \(0.749403\pi\)
\(168\) 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 \(-0.577664\pi\)
0.961164 0.275979i \(-0.0890022\pi\)
\(174\) 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 \(-0.250986\pi\)
−0.966723 + 0.255825i \(0.917653\pi\)
\(180\) 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 \(-0.888231\pi\)
0.767371 + 0.641203i \(0.221564\pi\)
\(192\) 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 \(-0.284234\pi\)
0.627119 + 0.778924i \(0.284234\pi\)
\(198\) 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 \(-0.973589\pi\)
0.426507 0.904484i \(-0.359744\pi\)
\(228\) 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 −0.811628 0.584174i \(-0.801418\pi\)
0.911724 + 0.410803i \(0.134752\pi\)
\(234\) 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 \(-0.613800\pi\)
−0.349947 + 0.936770i \(0.613800\pi\)
\(240\) 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 \(-0.308148\pi\)
0.566885 + 0.823797i \(0.308148\pi\)
\(252\) 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 \(-0.646933\pi\)
0.998079 0.0619561i \(-0.0197339\pi\)
\(258\) 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 \(-0.0689399\pi\)
−0.674421 + 0.738347i \(0.735607\pi\)
\(264\) 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 \(-0.133087\pi\)
−0.808563 + 0.588410i \(0.799754\pi\)
\(270\) 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 \(-0.639881\pi\)
−0.425440 + 0.904987i \(0.639881\pi\)
\(282\) 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 \(-0.324484\pi\)
0.523880 + 0.851792i \(0.324484\pi\)
\(294\) 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 \(-0.932069\pi\)
0.305238 0.952276i \(-0.401264\pi\)
\(312\) 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 −0.983459 0.181129i \(-0.942025\pi\)
0.648592 + 0.761136i \(0.275358\pi\)
\(318\) 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 0.971350 0.237652i \(-0.0763779\pi\)
−0.691488 + 0.722388i \(0.743045\pi\)
\(348\) 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 \(-0.256681\pi\)
−0.971145 + 0.238489i \(0.923348\pi\)
\(354\) 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 \(-0.836375\pi\)
0.861208 + 0.508253i \(0.169708\pi\)
\(360\) 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 −0.547329 0.836917i \(-0.684355\pi\)
0.998456 + 0.0555425i \(0.0176888\pi\)
\(384\) 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 \(0.160594\pi\)
−0.0190764 + 0.999818i \(0.506073\pi\)
\(390\) 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 −0.976220 0.216780i \(-0.930444\pi\)
0.675848 + 0.737041i \(0.263778\pi\)
\(402\) 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 \(-0.289371\pi\)
0.614468 + 0.788942i \(0.289371\pi\)
\(420\) 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 \(0.194238\pi\)
0.0865097 + 0.996251i \(0.472429\pi\)
\(432\) 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 \(0.464336\pi\)
−0.916499 + 0.400037i \(0.868997\pi\)
\(444\) 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 \(-0.469441\pi\)
0.0958573 + 0.995395i \(0.469441\pi\)
\(450\) 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 \(-0.783706\pi\)
−0.777882 + 0.628410i \(0.783706\pi\)
\(462\) 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 \(-0.993775\pi\)
0.516840 + 0.856082i \(0.327108\pi\)
\(468\) 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 \(-0.0910357\pi\)
−0.724008 + 0.689791i \(0.757702\pi\)
\(480\) 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 \(-0.750820\pi\)
−0.708926 + 0.705283i \(0.750820\pi\)
\(492\) 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 \(-0.648918\pi\)
−0.450960 + 0.892544i \(0.648918\pi\)
\(504\) 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 \(0.338493\pi\)
−0.999869 + 0.0162087i \(0.994840\pi\)
\(510\) 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 \(-0.187678\pi\)
−0.897120 + 0.441786i \(0.854345\pi\)
\(522\) 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 0.707794 0.706419i \(-0.249690\pi\)
−0.965674 + 0.259758i \(0.916357\pi\)
\(558\) 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 \(0.0842793\pi\)
−0.255947 + 0.966691i \(0.582387\pi\)
\(564\) 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 \(-0.831082\pi\)
0.869540 + 0.493862i \(0.164415\pi\)
\(570\) 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 \(-0.259612\pi\)
0.685436 + 0.728133i \(0.259612\pi\)
\(588\) 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 \(-0.986767\pi\)
0.535560 + 0.844497i \(0.320101\pi\)
\(594\) 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 \(-0.955355\pi\)
0.374023 0.927420i \(-0.377978\pi\)
\(600\) 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 \(-0.624618\pi\)
−0.381575 + 0.924338i \(0.624618\pi\)
\(618\) 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 0.766611 0.642111i \(-0.221941\pi\)
−0.939390 + 0.342849i \(0.888608\pi\)
\(642\) 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 \(-0.109801\pi\)
−0.763392 + 0.645936i \(0.776467\pi\)
\(648\) 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 \(-0.505009\pi\)
0.873786 0.486310i \(-0.161657\pi\)
\(654\) 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 \(-0.111328\pi\)
0.939459 + 0.342662i \(0.111328\pi\)
\(660\) 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 −0.865376 0.501123i \(-0.832920\pi\)
0.866673 + 0.498876i \(0.166254\pi\)
\(678\) 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 \(-0.847464\pi\)
0.0443782 0.999015i \(-0.485869\pi\)
\(684\) 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 \(-0.433839\pi\)
0.206358 + 0.978477i \(0.433839\pi\)
\(702\) 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 \(-0.421048\pi\)
0.716772 0.697308i \(-0.245619\pi\)
\(720\) 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 \(-0.522888\pi\)
−0.0718422 + 0.997416i \(0.522888\pi\)
\(744\) 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 −0.919511 0.393063i \(-0.871415\pi\)
0.800159 + 0.599789i \(0.204749\pi\)
\(762\) 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 \(-0.980631\pi\)
0.446411 0.894828i \(-0.352702\pi\)
\(774\) 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