Properties

Label 882.4.g.w.361.1
Level $882$
Weight $4$
Character 882.361
Analytic conductor $52.040$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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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: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Defining polynomial: \(x^{2} - x + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{25}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 42)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 361.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 882.361
Dual form 882.4.g.w.667.1

$q$-expansion

\(f(q)\) \(=\) \(q+(1.00000 + 1.73205i) q^{2} +(-2.00000 + 3.46410i) q^{4} +(9.00000 + 15.5885i) q^{5} -8.00000 q^{8} +O(q^{10})\) \(q+(1.00000 + 1.73205i) q^{2} +(-2.00000 + 3.46410i) q^{4} +(9.00000 + 15.5885i) q^{5} -8.00000 q^{8} +(-18.0000 + 31.1769i) q^{10} +(-36.0000 + 62.3538i) q^{11} -34.0000 q^{13} +(-8.00000 - 13.8564i) q^{16} +(3.00000 - 5.19615i) q^{17} +(-46.0000 - 79.6743i) q^{19} -72.0000 q^{20} -144.000 q^{22} +(-90.0000 - 155.885i) q^{23} +(-99.5000 + 172.339i) q^{25} +(-34.0000 - 58.8897i) q^{26} +114.000 q^{29} +(-28.0000 + 48.4974i) q^{31} +(16.0000 - 27.7128i) q^{32} +12.0000 q^{34} +(17.0000 + 29.4449i) q^{37} +(92.0000 - 159.349i) q^{38} +(-72.0000 - 124.708i) q^{40} -6.00000 q^{41} +164.000 q^{43} +(-144.000 - 249.415i) q^{44} +(180.000 - 311.769i) q^{46} +(84.0000 + 145.492i) q^{47} -398.000 q^{50} +(68.0000 - 117.779i) q^{52} +(327.000 - 566.381i) q^{53} -1296.00 q^{55} +(114.000 + 197.454i) q^{58} +(-246.000 + 426.084i) q^{59} +(125.000 + 216.506i) q^{61} -112.000 q^{62} +64.0000 q^{64} +(-306.000 - 530.008i) q^{65} +(62.0000 - 107.387i) q^{67} +(12.0000 + 20.7846i) q^{68} -36.0000 q^{71} +(-505.000 + 874.686i) q^{73} +(-34.0000 + 58.8897i) q^{74} +368.000 q^{76} +(-28.0000 - 48.4974i) q^{79} +(144.000 - 249.415i) q^{80} +(-6.00000 - 10.3923i) q^{82} -228.000 q^{83} +108.000 q^{85} +(164.000 + 284.056i) q^{86} +(288.000 - 498.831i) q^{88} +(195.000 + 337.750i) q^{89} +720.000 q^{92} +(-168.000 + 290.985i) q^{94} +(828.000 - 1434.14i) q^{95} -70.0000 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q + 2q^{2} - 4q^{4} + 18q^{5} - 16q^{8} + O(q^{10}) \) \( 2q + 2q^{2} - 4q^{4} + 18q^{5} - 16q^{8} - 36q^{10} - 72q^{11} - 68q^{13} - 16q^{16} + 6q^{17} - 92q^{19} - 144q^{20} - 288q^{22} - 180q^{23} - 199q^{25} - 68q^{26} + 228q^{29} - 56q^{31} + 32q^{32} + 24q^{34} + 34q^{37} + 184q^{38} - 144q^{40} - 12q^{41} + 328q^{43} - 288q^{44} + 360q^{46} + 168q^{47} - 796q^{50} + 136q^{52} + 654q^{53} - 2592q^{55} + 228q^{58} - 492q^{59} + 250q^{61} - 224q^{62} + 128q^{64} - 612q^{65} + 124q^{67} + 24q^{68} - 72q^{71} - 1010q^{73} - 68q^{74} + 736q^{76} - 56q^{79} + 288q^{80} - 12q^{82} - 456q^{83} + 216q^{85} + 328q^{86} + 576q^{88} + 390q^{89} + 1440q^{92} - 336q^{94} + 1656q^{95} - 140q^{97} + O(q^{100}) \)

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
\(5\) 9.00000 + 15.5885i 0.804984 + 1.39427i 0.916302 + 0.400489i \(0.131160\pi\)
−0.111317 + 0.993785i \(0.535507\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) −8.00000 −0.353553
\(9\) 0 0
\(10\) −18.0000 + 31.1769i −0.569210 + 0.985901i
\(11\) −36.0000 + 62.3538i −0.986764 + 1.70913i −0.352947 + 0.935643i \(0.614820\pi\)
−0.633817 + 0.773483i \(0.718513\pi\)
\(12\) 0 0
\(13\) −34.0000 −0.725377 −0.362689 0.931910i \(-0.618141\pi\)
−0.362689 + 0.931910i \(0.618141\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) −8.00000 13.8564i −0.125000 0.216506i
\(17\) 3.00000 5.19615i 0.0428004 0.0741325i −0.843832 0.536608i \(-0.819705\pi\)
0.886632 + 0.462476i \(0.153039\pi\)
\(18\) 0 0
\(19\) −46.0000 79.6743i −0.555428 0.962029i −0.997870 0.0652319i \(-0.979221\pi\)
0.442443 0.896797i \(-0.354112\pi\)
\(20\) −72.0000 −0.804984
\(21\) 0 0
\(22\) −144.000 −1.39550
\(23\) −90.0000 155.885i −0.815926 1.41323i −0.908661 0.417534i \(-0.862894\pi\)
0.0927351 0.995691i \(-0.470439\pi\)
\(24\) 0 0
\(25\) −99.5000 + 172.339i −0.796000 + 1.37871i
\(26\) −34.0000 58.8897i −0.256460 0.444201i
\(27\) 0 0
\(28\) 0 0
\(29\) 114.000 0.729975 0.364987 0.931012i \(-0.381073\pi\)
0.364987 + 0.931012i \(0.381073\pi\)
\(30\) 0 0
\(31\) −28.0000 + 48.4974i −0.162224 + 0.280980i −0.935666 0.352887i \(-0.885200\pi\)
0.773442 + 0.633867i \(0.218533\pi\)
\(32\) 16.0000 27.7128i 0.0883883 0.153093i
\(33\) 0 0
\(34\) 12.0000 0.0605289
\(35\) 0 0
\(36\) 0 0
\(37\) 17.0000 + 29.4449i 0.0755347 + 0.130830i 0.901319 0.433157i \(-0.142600\pi\)
−0.825784 + 0.563987i \(0.809267\pi\)
\(38\) 92.0000 159.349i 0.392747 0.680257i
\(39\) 0 0
\(40\) −72.0000 124.708i −0.284605 0.492950i
\(41\) −6.00000 −0.0228547 −0.0114273 0.999935i \(-0.503638\pi\)
−0.0114273 + 0.999935i \(0.503638\pi\)
\(42\) 0 0
\(43\) 164.000 0.581622 0.290811 0.956780i \(-0.406075\pi\)
0.290811 + 0.956780i \(0.406075\pi\)
\(44\) −144.000 249.415i −0.493382 0.854563i
\(45\) 0 0
\(46\) 180.000 311.769i 0.576947 0.999301i
\(47\) 84.0000 + 145.492i 0.260695 + 0.451537i 0.966427 0.256942i \(-0.0827150\pi\)
−0.705732 + 0.708479i \(0.749382\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) −398.000 −1.12571
\(51\) 0 0
\(52\) 68.0000 117.779i 0.181344 0.314098i
\(53\) 327.000 566.381i 0.847489 1.46789i −0.0359535 0.999353i \(-0.511447\pi\)
0.883442 0.468540i \(-0.155220\pi\)
\(54\) 0 0
\(55\) −1296.00 −3.17732
\(56\) 0 0
\(57\) 0 0
\(58\) 114.000 + 197.454i 0.258085 + 0.447016i
\(59\) −246.000 + 426.084i −0.542822 + 0.940195i 0.455919 + 0.890021i \(0.349311\pi\)
−0.998741 + 0.0501732i \(0.984023\pi\)
\(60\) 0 0
\(61\) 125.000 + 216.506i 0.262371 + 0.454439i 0.966871 0.255264i \(-0.0821624\pi\)
−0.704501 + 0.709703i \(0.748829\pi\)
\(62\) −112.000 −0.229420
\(63\) 0 0
\(64\) 64.0000 0.125000
\(65\) −306.000 530.008i −0.583917 1.01137i
\(66\) 0 0
\(67\) 62.0000 107.387i 0.113052 0.195812i −0.803947 0.594701i \(-0.797271\pi\)
0.917000 + 0.398888i \(0.130604\pi\)
\(68\) 12.0000 + 20.7846i 0.0214002 + 0.0370662i
\(69\) 0 0
\(70\) 0 0
\(71\) −36.0000 −0.0601748 −0.0300874 0.999547i \(-0.509579\pi\)
−0.0300874 + 0.999547i \(0.509579\pi\)
\(72\) 0 0
\(73\) −505.000 + 874.686i −0.809668 + 1.40239i 0.103426 + 0.994637i \(0.467020\pi\)
−0.913094 + 0.407749i \(0.866314\pi\)
\(74\) −34.0000 + 58.8897i −0.0534111 + 0.0925107i
\(75\) 0 0
\(76\) 368.000 0.555428
\(77\) 0 0
\(78\) 0 0
\(79\) −28.0000 48.4974i −0.0398765 0.0690682i 0.845398 0.534136i \(-0.179363\pi\)
−0.885275 + 0.465068i \(0.846030\pi\)
\(80\) 144.000 249.415i 0.201246 0.348569i
\(81\) 0 0
\(82\) −6.00000 10.3923i −0.00808036 0.0139956i
\(83\) −228.000 −0.301521 −0.150761 0.988570i \(-0.548172\pi\)
−0.150761 + 0.988570i \(0.548172\pi\)
\(84\) 0 0
\(85\) 108.000 0.137815
\(86\) 164.000 + 284.056i 0.205635 + 0.356170i
\(87\) 0 0
\(88\) 288.000 498.831i 0.348874 0.604267i
\(89\) 195.000 + 337.750i 0.232247 + 0.402263i 0.958469 0.285197i \(-0.0920590\pi\)
−0.726222 + 0.687460i \(0.758726\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 720.000 0.815926
\(93\) 0 0
\(94\) −168.000 + 290.985i −0.184339 + 0.319285i
\(95\) 828.000 1434.14i 0.894221 1.54884i
\(96\) 0 0
\(97\) −70.0000 −0.0732724 −0.0366362 0.999329i \(-0.511664\pi\)
−0.0366362 + 0.999329i \(0.511664\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) −398.000 689.356i −0.398000 0.689356i
\(101\) −675.000 + 1169.13i −0.665000 + 1.15181i 0.314285 + 0.949329i \(0.398235\pi\)
−0.979285 + 0.202485i \(0.935098\pi\)
\(102\) 0 0
\(103\) −1000.00 1732.05i −0.956630 1.65693i −0.730592 0.682814i \(-0.760756\pi\)
−0.226038 0.974118i \(-0.572577\pi\)
\(104\) 272.000 0.256460
\(105\) 0 0
\(106\) 1308.00 1.19853
\(107\) 348.000 + 602.754i 0.314415 + 0.544583i 0.979313 0.202351i \(-0.0648582\pi\)
−0.664898 + 0.746934i \(0.731525\pi\)
\(108\) 0 0
\(109\) 557.000 964.752i 0.489458 0.847766i −0.510468 0.859897i \(-0.670528\pi\)
0.999926 + 0.0121304i \(0.00386131\pi\)
\(110\) −1296.00 2244.74i −1.12335 1.94570i
\(111\) 0 0
\(112\) 0 0
\(113\) 462.000 0.384613 0.192307 0.981335i \(-0.438403\pi\)
0.192307 + 0.981335i \(0.438403\pi\)
\(114\) 0 0
\(115\) 1620.00 2805.92i 1.31362 2.27525i
\(116\) −228.000 + 394.908i −0.182494 + 0.316088i
\(117\) 0 0
\(118\) −984.000 −0.767666
\(119\) 0 0
\(120\) 0 0
\(121\) −1926.50 3336.80i −1.44741 2.50698i
\(122\) −250.000 + 433.013i −0.185524 + 0.321337i
\(123\) 0 0
\(124\) −112.000 193.990i −0.0811121 0.140490i
\(125\) −1332.00 −0.953102
\(126\) 0 0
\(127\) 1064.00 0.743423 0.371712 0.928348i \(-0.378771\pi\)
0.371712 + 0.928348i \(0.378771\pi\)
\(128\) 64.0000 + 110.851i 0.0441942 + 0.0765466i
\(129\) 0 0
\(130\) 612.000 1060.02i 0.412892 0.715150i
\(131\) 90.0000 + 155.885i 0.0600255 + 0.103967i 0.894477 0.447115i \(-0.147548\pi\)
−0.834451 + 0.551082i \(0.814215\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 248.000 0.159880
\(135\) 0 0
\(136\) −24.0000 + 41.5692i −0.0151322 + 0.0262098i
\(137\) −1359.00 + 2353.86i −0.847498 + 1.46791i 0.0359363 + 0.999354i \(0.488559\pi\)
−0.883434 + 0.468555i \(0.844775\pi\)
\(138\) 0 0
\(139\) −1348.00 −0.822560 −0.411280 0.911509i \(-0.634918\pi\)
−0.411280 + 0.911509i \(0.634918\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) −36.0000 62.3538i −0.0212750 0.0368494i
\(143\) 1224.00 2120.03i 0.715776 1.23976i
\(144\) 0 0
\(145\) 1026.00 + 1777.08i 0.587618 + 1.01778i
\(146\) −2020.00 −1.14504
\(147\) 0 0
\(148\) −136.000 −0.0755347
\(149\) 279.000 + 483.242i 0.153400 + 0.265696i 0.932475 0.361234i \(-0.117644\pi\)
−0.779075 + 0.626930i \(0.784311\pi\)
\(150\) 0 0
\(151\) −964.000 + 1669.70i −0.519531 + 0.899854i 0.480211 + 0.877153i \(0.340560\pi\)
−0.999742 + 0.0227014i \(0.992773\pi\)
\(152\) 368.000 + 637.395i 0.196373 + 0.340129i
\(153\) 0 0
\(154\) 0 0
\(155\) −1008.00 −0.522352
\(156\) 0 0
\(157\) 1205.00 2087.12i 0.612544 1.06096i −0.378266 0.925697i \(-0.623479\pi\)
0.990810 0.135261i \(-0.0431873\pi\)
\(158\) 56.0000 96.9948i 0.0281970 0.0488386i
\(159\) 0 0
\(160\) 576.000 0.284605
\(161\) 0 0
\(162\) 0 0
\(163\) −370.000 640.859i −0.177795 0.307951i 0.763330 0.646009i \(-0.223563\pi\)
−0.941125 + 0.338058i \(0.890230\pi\)
\(164\) 12.0000 20.7846i 0.00571367 0.00989637i
\(165\) 0 0
\(166\) −228.000 394.908i −0.106604 0.184643i
\(167\) −3984.00 −1.84605 −0.923027 0.384734i \(-0.874293\pi\)
−0.923027 + 0.384734i \(0.874293\pi\)
\(168\) 0 0
\(169\) −1041.00 −0.473828
\(170\) 108.000 + 187.061i 0.0487248 + 0.0843939i
\(171\) 0 0
\(172\) −328.000 + 568.113i −0.145406 + 0.251850i
\(173\) −519.000 898.934i −0.228086 0.395056i 0.729155 0.684349i \(-0.239913\pi\)
−0.957241 + 0.289292i \(0.906580\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 1152.00 0.493382
\(177\) 0 0
\(178\) −390.000 + 675.500i −0.164223 + 0.284443i
\(179\) −1284.00 + 2223.95i −0.536149 + 0.928637i 0.462958 + 0.886380i \(0.346788\pi\)
−0.999107 + 0.0422569i \(0.986545\pi\)
\(180\) 0 0
\(181\) −2698.00 −1.10796 −0.553980 0.832530i \(-0.686892\pi\)
−0.553980 + 0.832530i \(0.686892\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 720.000 + 1247.08i 0.288473 + 0.499651i
\(185\) −306.000 + 530.008i −0.121608 + 0.210632i
\(186\) 0 0
\(187\) 216.000 + 374.123i 0.0844678 + 0.146303i
\(188\) −672.000 −0.260695
\(189\) 0 0
\(190\) 3312.00 1.26462
\(191\) −2058.00 3564.56i −0.779642 1.35038i −0.932148 0.362077i \(-0.882068\pi\)
0.152506 0.988303i \(-0.451266\pi\)
\(192\) 0 0
\(193\) 1655.00 2866.54i 0.617251 1.06911i −0.372734 0.927938i \(-0.621580\pi\)
0.989985 0.141172i \(-0.0450872\pi\)
\(194\) −70.0000 121.244i −0.0259057 0.0448700i
\(195\) 0 0
\(196\) 0 0
\(197\) −1278.00 −0.462202 −0.231101 0.972930i \(-0.574233\pi\)
−0.231101 + 0.972930i \(0.574233\pi\)
\(198\) 0 0
\(199\) −1468.00 + 2542.65i −0.522933 + 0.905747i 0.476710 + 0.879060i \(0.341829\pi\)
−0.999644 + 0.0266869i \(0.991504\pi\)
\(200\) 796.000 1378.71i 0.281428 0.487448i
\(201\) 0 0
\(202\) −2700.00 −0.940452
\(203\) 0 0
\(204\) 0 0
\(205\) −54.0000 93.5307i −0.0183977 0.0318657i
\(206\) 2000.00 3464.10i 0.676440 1.17163i
\(207\) 0 0
\(208\) 272.000 + 471.118i 0.0906721 + 0.157049i
\(209\) 6624.00 2.19230
\(210\) 0 0
\(211\) −3508.00 −1.14455 −0.572276 0.820061i \(-0.693940\pi\)
−0.572276 + 0.820061i \(0.693940\pi\)
\(212\) 1308.00 + 2265.52i 0.423744 + 0.733947i
\(213\) 0 0
\(214\) −696.000 + 1205.51i −0.222325 + 0.385078i
\(215\) 1476.00 + 2556.51i 0.468197 + 0.810941i
\(216\) 0 0
\(217\) 0 0
\(218\) 2228.00 0.692198
\(219\) 0 0
\(220\) 2592.00 4489.48i 0.794330 1.37582i
\(221\) −102.000 + 176.669i −0.0310464 + 0.0537740i
\(222\) 0 0
\(223\) −1888.00 −0.566950 −0.283475 0.958980i \(-0.591487\pi\)
−0.283475 + 0.958980i \(0.591487\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 462.000 + 800.207i 0.135981 + 0.235527i
\(227\) 1782.00 3086.51i 0.521037 0.902463i −0.478663 0.877999i \(-0.658879\pi\)
0.999701 0.0244647i \(-0.00778814\pi\)
\(228\) 0 0
\(229\) −667.000 1155.28i −0.192474 0.333375i 0.753595 0.657339i \(-0.228318\pi\)
−0.946070 + 0.323963i \(0.894985\pi\)
\(230\) 6480.00 1.85773
\(231\) 0 0
\(232\) −912.000 −0.258085
\(233\) 1329.00 + 2301.90i 0.373672 + 0.647220i 0.990127 0.140171i \(-0.0447651\pi\)
−0.616455 + 0.787390i \(0.711432\pi\)
\(234\) 0 0
\(235\) −1512.00 + 2618.86i −0.419711 + 0.726960i
\(236\) −984.000 1704.34i −0.271411 0.470097i
\(237\) 0 0
\(238\) 0 0
\(239\) 588.000 0.159140 0.0795702 0.996829i \(-0.474645\pi\)
0.0795702 + 0.996829i \(0.474645\pi\)
\(240\) 0 0
\(241\) −2845.00 + 4927.68i −0.760426 + 1.31710i 0.182206 + 0.983260i \(0.441676\pi\)
−0.942631 + 0.333835i \(0.891657\pi\)
\(242\) 3853.00 6673.59i 1.02347 1.77271i
\(243\) 0 0
\(244\) −1000.00 −0.262371
\(245\) 0 0
\(246\) 0 0
\(247\) 1564.00 + 2708.93i 0.402894 + 0.697834i
\(248\) 224.000 387.979i 0.0573549 0.0993416i
\(249\) 0 0
\(250\) −1332.00 2307.09i −0.336972 0.583653i
\(251\) −180.000 −0.0452649 −0.0226325 0.999744i \(-0.507205\pi\)
−0.0226325 + 0.999744i \(0.507205\pi\)
\(252\) 0 0
\(253\) 12960.0 3.22051
\(254\) 1064.00 + 1842.90i 0.262840 + 0.455252i
\(255\) 0 0
\(256\) −128.000 + 221.703i −0.0312500 + 0.0541266i
\(257\) 2655.00 + 4598.59i 0.644414 + 1.11616i 0.984437 + 0.175740i \(0.0562319\pi\)
−0.340023 + 0.940417i \(0.610435\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 2448.00 0.583917
\(261\) 0 0
\(262\) −180.000 + 311.769i −0.0424444 + 0.0735159i
\(263\) 414.000 717.069i 0.0970659 0.168123i −0.813403 0.581701i \(-0.802388\pi\)
0.910469 + 0.413577i \(0.135721\pi\)
\(264\) 0 0
\(265\) 11772.0 2.72886
\(266\) 0 0
\(267\) 0 0
\(268\) 248.000 + 429.549i 0.0565262 + 0.0979062i
\(269\) −2067.00 + 3580.15i −0.468503 + 0.811470i −0.999352 0.0359958i \(-0.988540\pi\)
0.530849 + 0.847466i \(0.321873\pi\)
\(270\) 0 0
\(271\) 1484.00 + 2570.36i 0.332644 + 0.576157i 0.983029 0.183448i \(-0.0587259\pi\)
−0.650385 + 0.759605i \(0.725393\pi\)
\(272\) −96.0000 −0.0214002
\(273\) 0 0
\(274\) −5436.00 −1.19854
\(275\) −7164.00 12408.4i −1.57093 2.72093i
\(276\) 0 0
\(277\) 2393.00 4144.80i 0.519067 0.899050i −0.480688 0.876892i \(-0.659613\pi\)
0.999754 0.0221579i \(-0.00705366\pi\)
\(278\) −1348.00 2334.80i −0.290819 0.503713i
\(279\) 0 0
\(280\) 0 0
\(281\) 4398.00 0.933675 0.466838 0.884343i \(-0.345393\pi\)
0.466838 + 0.884343i \(0.345393\pi\)
\(282\) 0 0
\(283\) −2386.00 + 4132.67i −0.501177 + 0.868063i 0.498822 + 0.866704i \(0.333766\pi\)
−0.999999 + 0.00135915i \(0.999567\pi\)
\(284\) 72.0000 124.708i 0.0150437 0.0260565i
\(285\) 0 0
\(286\) 4896.00 1.01226
\(287\) 0 0
\(288\) 0 0
\(289\) 2438.50 + 4223.61i 0.496336 + 0.859680i
\(290\) −2052.00 + 3554.17i −0.415509 + 0.719683i
\(291\) 0 0
\(292\) −2020.00 3498.74i −0.404834 0.701193i
\(293\) −6522.00 −1.30041 −0.650204 0.759760i \(-0.725316\pi\)
−0.650204 + 0.759760i \(0.725316\pi\)
\(294\) 0 0
\(295\) −8856.00 −1.74785
\(296\) −136.000 235.559i −0.0267055 0.0462553i
\(297\) 0 0
\(298\) −558.000 + 966.484i −0.108470 + 0.187876i
\(299\) 3060.00 + 5300.08i 0.591854 + 1.02512i
\(300\) 0 0
\(301\) 0 0
\(302\) −3856.00 −0.734728
\(303\) 0 0
\(304\) −736.000 + 1274.79i −0.138857 + 0.240507i
\(305\) −2250.00 + 3897.11i −0.422409 + 0.731633i
\(306\) 0 0
\(307\) −6244.00 −1.16079 −0.580397 0.814333i \(-0.697103\pi\)
−0.580397 + 0.814333i \(0.697103\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) −1008.00 1745.91i −0.184679 0.319874i
\(311\) −264.000 + 457.261i −0.0481353 + 0.0833727i −0.889089 0.457734i \(-0.848661\pi\)
0.840954 + 0.541107i \(0.181995\pi\)
\(312\) 0 0
\(313\) 2915.00 + 5048.93i 0.526407 + 0.911765i 0.999527 + 0.0307660i \(0.00979468\pi\)
−0.473119 + 0.880998i \(0.656872\pi\)
\(314\) 4820.00 0.866269
\(315\) 0 0
\(316\) 224.000 0.0398765
\(317\) 2523.00 + 4369.96i 0.447021 + 0.774264i 0.998191 0.0601297i \(-0.0191514\pi\)
−0.551169 + 0.834394i \(0.685818\pi\)
\(318\) 0 0
\(319\) −4104.00 + 7108.34i −0.720313 + 1.24762i
\(320\) 576.000 + 997.661i 0.100623 + 0.174284i
\(321\) 0 0
\(322\) 0 0
\(323\) −552.000 −0.0950901
\(324\) 0 0
\(325\) 3383.00 5859.53i 0.577400 1.00009i
\(326\) 740.000 1281.72i 0.125720 0.217754i
\(327\) 0 0
\(328\) 48.0000 0.00808036
\(329\) 0 0
\(330\) 0 0
\(331\) 2510.00 + 4347.45i 0.416804 + 0.721925i 0.995616 0.0935355i \(-0.0298169\pi\)
−0.578812 + 0.815461i \(0.696484\pi\)
\(332\) 456.000 789.815i 0.0753803 0.130562i
\(333\) 0 0
\(334\) −3984.00 6900.49i −0.652679 1.13047i
\(335\) 2232.00 0.364021
\(336\) 0 0
\(337\) −7486.00 −1.21005 −0.605027 0.796205i \(-0.706838\pi\)
−0.605027 + 0.796205i \(0.706838\pi\)
\(338\) −1041.00 1803.06i −0.167523 0.290159i
\(339\) 0 0
\(340\) −216.000 + 374.123i −0.0344537 + 0.0596755i
\(341\) −2016.00 3491.81i −0.320154 0.554523i
\(342\) 0 0
\(343\) 0 0
\(344\) −1312.00 −0.205635
\(345\) 0 0
\(346\) 1038.00 1797.87i 0.161281 0.279347i
\(347\) −5016.00 + 8687.97i −0.776003 + 1.34408i 0.158226 + 0.987403i \(0.449422\pi\)
−0.934229 + 0.356673i \(0.883911\pi\)
\(348\) 0 0
\(349\) 5942.00 0.911370 0.455685 0.890141i \(-0.349394\pi\)
0.455685 + 0.890141i \(0.349394\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 1152.00 + 1995.32i 0.174437 + 0.302134i
\(353\) −45.0000 + 77.9423i −0.00678501 + 0.0117520i −0.869398 0.494113i \(-0.835493\pi\)
0.862613 + 0.505864i \(0.168826\pi\)
\(354\) 0 0
\(355\) −324.000 561.184i −0.0484398 0.0839002i
\(356\) −1560.00 −0.232247
\(357\) 0 0
\(358\) −5136.00 −0.758229
\(359\) 5298.00 + 9176.41i 0.778880 + 1.34906i 0.932588 + 0.360943i \(0.117545\pi\)
−0.153708 + 0.988116i \(0.549122\pi\)
\(360\) 0 0
\(361\) −802.500 + 1389.97i −0.117000 + 0.202649i
\(362\) −2698.00 4673.07i −0.391723 0.678484i
\(363\) 0 0
\(364\) 0 0
\(365\) −18180.0 −2.60708
\(366\) 0 0
\(367\) −2008.00 + 3477.96i −0.285604 + 0.494681i −0.972756 0.231833i \(-0.925528\pi\)
0.687151 + 0.726514i \(0.258861\pi\)
\(368\) −1440.00 + 2494.15i −0.203981 + 0.353306i
\(369\) 0 0
\(370\) −1224.00 −0.171980
\(371\) 0 0
\(372\) 0 0
\(373\) −1639.00 2838.83i −0.227518 0.394073i 0.729554 0.683923i \(-0.239728\pi\)
−0.957072 + 0.289851i \(0.906394\pi\)
\(374\) −432.000 + 748.246i −0.0597278 + 0.103452i
\(375\) 0 0
\(376\) −672.000 1163.94i −0.0921696 0.159642i
\(377\) −3876.00 −0.529507
\(378\) 0 0
\(379\) 4628.00 0.627241 0.313621 0.949548i \(-0.398458\pi\)
0.313621 + 0.949548i \(0.398458\pi\)
\(380\) 3312.00 + 5736.55i 0.447111 + 0.774418i
\(381\) 0 0
\(382\) 4116.00 7129.12i 0.551290 0.954863i
\(383\) −1440.00 2494.15i −0.192116 0.332755i 0.753835 0.657064i \(-0.228202\pi\)
−0.945951 + 0.324308i \(0.894868\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 6620.00 0.872925
\(387\) 0 0
\(388\) 140.000 242.487i 0.0183181 0.0317279i
\(389\) 3987.00 6905.69i 0.519663 0.900083i −0.480076 0.877227i \(-0.659391\pi\)
0.999739 0.0228557i \(-0.00727584\pi\)
\(390\) 0 0
\(391\) −1080.00 −0.139688
\(392\) 0 0
\(393\) 0 0
\(394\) −1278.00 2213.56i −0.163413 0.283040i
\(395\) 504.000 872.954i 0.0642000 0.111198i
\(396\) 0 0
\(397\) 6173.00 + 10691.9i 0.780388 + 1.35167i 0.931716 + 0.363188i \(0.118312\pi\)
−0.151328 + 0.988484i \(0.548355\pi\)
\(398\) −5872.00 −0.739540
\(399\) 0 0
\(400\) 3184.00 0.398000
\(401\) 4869.00 + 8433.36i 0.606350 + 1.05023i 0.991837 + 0.127515i \(0.0407002\pi\)
−0.385487 + 0.922713i \(0.625966\pi\)
\(402\) 0 0
\(403\) 952.000 1648.91i 0.117674 0.203817i
\(404\) −2700.00 4676.54i −0.332500 0.575907i
\(405\) 0 0
\(406\) 0 0
\(407\) −2448.00 −0.298140
\(408\) 0 0
\(409\) 215.000 372.391i 0.0259928 0.0450209i −0.852736 0.522342i \(-0.825059\pi\)
0.878729 + 0.477321i \(0.158392\pi\)
\(410\) 108.000 187.061i 0.0130091 0.0225325i
\(411\) 0 0
\(412\) 8000.00 0.956630
\(413\) 0 0
\(414\) 0 0
\(415\) −2052.00 3554.17i −0.242720 0.420403i
\(416\) −544.000 + 942.236i −0.0641149 + 0.111050i
\(417\) 0 0
\(418\) 6624.00 + 11473.1i 0.775097 + 1.34251i
\(419\) 1812.00 0.211270 0.105635 0.994405i \(-0.466313\pi\)
0.105635 + 0.994405i \(0.466313\pi\)
\(420\) 0 0
\(421\) −10690.0 −1.23753 −0.618763 0.785577i \(-0.712366\pi\)
−0.618763 + 0.785577i \(0.712366\pi\)
\(422\) −3508.00 6076.03i −0.404661 0.700893i
\(423\) 0 0
\(424\) −2616.00 + 4531.04i −0.299633 + 0.518979i
\(425\) 597.000 + 1034.03i 0.0681382 + 0.118019i
\(426\) 0 0
\(427\) 0 0
\(428\) −2784.00 −0.314415
\(429\) 0 0
\(430\) −2952.00 + 5113.01i −0.331065 + 0.573422i
\(431\) −2058.00 + 3564.56i −0.230001 + 0.398373i −0.957808 0.287409i \(-0.907206\pi\)
0.727807 + 0.685782i \(0.240540\pi\)
\(432\) 0 0
\(433\) 9938.00 1.10298 0.551489 0.834182i \(-0.314060\pi\)
0.551489 + 0.834182i \(0.314060\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 2228.00 + 3859.01i 0.244729 + 0.423883i
\(437\) −8280.00 + 14341.4i −0.906376 + 1.56989i
\(438\) 0 0
\(439\) −892.000 1544.99i −0.0969769 0.167969i 0.813455 0.581628i \(-0.197584\pi\)
−0.910432 + 0.413659i \(0.864251\pi\)
\(440\) 10368.0 1.12335
\(441\) 0 0
\(442\) −408.000 −0.0439063
\(443\) −5856.00 10142.9i −0.628052 1.08782i −0.987942 0.154823i \(-0.950519\pi\)
0.359890 0.932995i \(-0.382814\pi\)
\(444\) 0 0
\(445\) −3510.00 + 6079.50i −0.373910 + 0.647631i
\(446\) −1888.00 3270.11i −0.200447 0.347185i
\(447\) 0 0
\(448\) 0 0
\(449\) −7650.00 −0.804066 −0.402033 0.915625i \(-0.631696\pi\)
−0.402033 + 0.915625i \(0.631696\pi\)
\(450\) 0 0
\(451\) 216.000 374.123i 0.0225522 0.0390616i
\(452\) −924.000 + 1600.41i −0.0961533 + 0.166542i
\(453\) 0 0
\(454\) 7128.00 0.736858
\(455\) 0 0
\(456\) 0 0
\(457\) −1837.00 3181.78i −0.188033 0.325683i 0.756561 0.653923i \(-0.226878\pi\)
−0.944594 + 0.328240i \(0.893545\pi\)
\(458\) 1334.00 2310.56i 0.136100 0.235732i
\(459\) 0 0
\(460\) 6480.00 + 11223.7i 0.656808 + 1.13762i
\(461\) 3102.00 0.313394 0.156697 0.987647i \(-0.449915\pi\)
0.156697 + 0.987647i \(0.449915\pi\)
\(462\) 0 0
\(463\) 8984.00 0.901775 0.450888 0.892581i \(-0.351108\pi\)
0.450888 + 0.892581i \(0.351108\pi\)
\(464\) −912.000 1579.63i −0.0912468 0.158044i
\(465\) 0 0
\(466\) −2658.00 + 4603.79i −0.264226 + 0.457653i
\(467\) 1806.00 + 3128.08i 0.178954 + 0.309958i 0.941523 0.336950i \(-0.109395\pi\)
−0.762568 + 0.646908i \(0.776062\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) −6048.00 −0.593561
\(471\) 0 0
\(472\) 1968.00 3408.68i 0.191916 0.332409i
\(473\) −5904.00 + 10226.0i −0.573924 + 0.994066i
\(474\) 0 0
\(475\) 18308.0 1.76848
\(476\) 0 0
\(477\) 0 0
\(478\) 588.000 + 1018.45i 0.0562646 + 0.0974532i
\(479\) −4644.00 + 8043.64i −0.442985 + 0.767272i −0.997909 0.0646283i \(-0.979414\pi\)
0.554924 + 0.831901i \(0.312747\pi\)
\(480\) 0 0
\(481\) −578.000 1001.13i −0.0547911 0.0949010i
\(482\) −11380.0 −1.07540
\(483\) 0 0
\(484\) 15412.0 1.44741
\(485\) −630.000 1091.19i −0.0589831 0.102162i
\(486\) 0 0
\(487\) 2924.00 5064.52i 0.272072 0.471243i −0.697320 0.716760i \(-0.745624\pi\)
0.969392 + 0.245517i \(0.0789578\pi\)
\(488\) −1000.00 1732.05i −0.0927620 0.160669i
\(489\) 0 0
\(490\) 0 0
\(491\) 5952.00 0.547067 0.273534 0.961862i \(-0.411808\pi\)
0.273534 + 0.961862i \(0.411808\pi\)
\(492\) 0 0
\(493\) 342.000 592.361i 0.0312432 0.0541148i
\(494\) −3128.00 + 5417.85i −0.284889 + 0.493443i
\(495\) 0 0
\(496\) 896.000 0.0811121
\(497\) 0 0
\(498\) 0 0
\(499\) −5374.00 9308.04i −0.482111 0.835040i 0.517678 0.855575i \(-0.326796\pi\)
−0.999789 + 0.0205349i \(0.993463\pi\)
\(500\) 2664.00 4614.18i 0.238275 0.412705i
\(501\) 0 0
\(502\) −180.000 311.769i −0.0160036 0.0277190i
\(503\) 16488.0 1.46156 0.730779 0.682614i \(-0.239157\pi\)
0.730779 + 0.682614i \(0.239157\pi\)
\(504\) 0 0
\(505\) −24300.0 −2.14126
\(506\) 12960.0 + 22447.4i 1.13862 + 1.97215i
\(507\) 0 0
\(508\) −2128.00 + 3685.80i −0.185856 + 0.321912i
\(509\) 7029.00 + 12174.6i 0.612092 + 1.06017i 0.990887 + 0.134694i \(0.0430052\pi\)
−0.378795 + 0.925481i \(0.623661\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) −512.000 −0.0441942
\(513\) 0 0
\(514\) −5310.00 + 9197.19i −0.455669 + 0.789243i
\(515\) 18000.0 31176.9i 1.54015 2.66761i
\(516\) 0 0
\(517\) −12096.0 −1.02898
\(518\) 0 0
\(519\) 0 0
\(520\) 2448.00 + 4240.06i 0.206446 + 0.357575i
\(521\) −7233.00 + 12527.9i −0.608222 + 1.05347i 0.383312 + 0.923619i \(0.374783\pi\)
−0.991533 + 0.129852i \(0.958550\pi\)
\(522\) 0 0
\(523\) −9262.00 16042.3i −0.774377 1.34126i −0.935144 0.354267i \(-0.884730\pi\)
0.160768 0.986992i \(-0.448603\pi\)
\(524\) −720.000 −0.0600255
\(525\) 0 0
\(526\) 1656.00 0.137272
\(527\) 168.000 + 290.985i 0.0138865 + 0.0240522i
\(528\) 0 0
\(529\) −10116.5 + 17522.3i −0.831470 + 1.44015i
\(530\) 11772.0 + 20389.7i 0.964798 + 1.67108i
\(531\) 0 0
\(532\) 0 0
\(533\) 204.000 0.0165783
\(534\) 0 0
\(535\) −6264.00 + 10849.6i −0.506199 + 0.876762i
\(536\) −496.000 + 859.097i −0.0399700 + 0.0692301i
\(537\) 0 0
\(538\) −8268.00 −0.662563
\(539\) 0 0
\(540\) 0 0
\(541\) −2179.00 3774.14i −0.173165 0.299931i 0.766359 0.642412i \(-0.222066\pi\)
−0.939525 + 0.342481i \(0.888733\pi\)
\(542\) −2968.00 + 5140.73i −0.235215 + 0.407404i
\(543\) 0 0
\(544\) −96.0000 166.277i −0.00756611 0.0131049i
\(545\) 20052.0 1.57602
\(546\) 0 0
\(547\) −2140.00 −0.167276 −0.0836378 0.996496i \(-0.526654\pi\)
−0.0836378 + 0.996496i \(0.526654\pi\)
\(548\) −5436.00 9415.43i −0.423749 0.733955i
\(549\) 0 0
\(550\) 14328.0 24816.8i 1.11081 1.92399i
\(551\) −5244.00 9082.87i −0.405448 0.702257i
\(552\) 0 0
\(553\) 0 0
\(554\) 9572.00 0.734071
\(555\) 0 0
\(556\) 2696.00 4669.61i 0.205640 0.356179i
\(557\) 1011.00 1751.10i 0.0769074 0.133208i −0.825007 0.565123i \(-0.808829\pi\)
0.901914 + 0.431915i \(0.142162\pi\)
\(558\) 0 0
\(559\) −5576.00 −0.421896
\(560\) 0 0
\(561\) 0 0
\(562\) 4398.00 + 7617.56i 0.330104 + 0.571757i
\(563\) 3678.00 6370.48i 0.275327 0.476881i −0.694890 0.719116i \(-0.744547\pi\)
0.970218 + 0.242235i \(0.0778805\pi\)
\(564\) 0 0
\(565\) 4158.00 + 7201.87i 0.309608 + 0.536256i
\(566\) −9544.00 −0.708771
\(567\) 0 0
\(568\) 288.000 0.0212750
\(569\) 5601.00 + 9701.22i 0.412665 + 0.714756i 0.995180 0.0980635i \(-0.0312648\pi\)
−0.582516 + 0.812820i \(0.697932\pi\)
\(570\) 0 0
\(571\) 5282.00 9148.69i 0.387119 0.670509i −0.604942 0.796270i \(-0.706804\pi\)
0.992061 + 0.125760i \(0.0401370\pi\)
\(572\) 4896.00 + 8480.12i 0.357888 + 0.619881i
\(573\) 0 0
\(574\) 0 0
\(575\) 35820.0 2.59791
\(576\) 0 0
\(577\) 9287.00 16085.6i 0.670057 1.16057i −0.307831 0.951441i \(-0.599603\pi\)
0.977888 0.209132i \(-0.0670637\pi\)
\(578\) −4877.00 + 8447.21i −0.350963 + 0.607885i
\(579\) 0 0
\(580\) −8208.00 −0.587618
\(581\) 0 0
\(582\) 0 0
\(583\) 23544.0 + 40779.4i 1.67254 + 2.89693i
\(584\) 4040.00 6997.49i 0.286261 0.495818i
\(585\) 0 0
\(586\) −6522.00 11296.4i −0.459763 0.796334i
\(587\) −13188.0 −0.927303 −0.463652 0.886018i \(-0.653461\pi\)
−0.463652 + 0.886018i \(0.653461\pi\)
\(588\) 0 0
\(589\) 5152.00 0.360415
\(590\) −8856.00 15339.0i −0.617959 1.07034i
\(591\) 0 0
\(592\) 272.000 471.118i 0.0188837 0.0327075i
\(593\) −11253.0 19490.8i −0.779267 1.34973i −0.932365 0.361519i \(-0.882258\pi\)
0.153098 0.988211i \(-0.451075\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) −2232.00 −0.153400
\(597\) 0 0
\(598\) −6120.00 + 10600.2i −0.418504 + 0.724870i
\(599\) 5298.00 9176.41i 0.361386 0.625939i −0.626803 0.779178i \(-0.715637\pi\)
0.988189 + 0.153238i \(0.0489702\pi\)
\(600\) 0 0
\(601\) 14618.0 0.992148 0.496074 0.868280i \(-0.334775\pi\)
0.496074 + 0.868280i \(0.334775\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) −3856.00 6678.79i −0.259766 0.449927i
\(605\) 34677.0 60062.3i 2.33028 4.03617i
\(606\) 0 0
\(607\) −2584.00 4475.62i −0.172786 0.299275i 0.766607 0.642117i \(-0.221944\pi\)
−0.939393 + 0.342842i \(0.888610\pi\)
\(608\) −2944.00 −0.196373
\(609\) 0 0
\(610\) −9000.00 −0.597376
\(611\) −2856.00 4946.74i −0.189102 0.327534i
\(612\) 0 0
\(613\) −2863.00 + 4958.86i −0.188639 + 0.326732i −0.944797 0.327657i \(-0.893741\pi\)
0.756158 + 0.654389i \(0.227074\pi\)
\(614\) −6244.00 10814.9i −0.410403 0.710839i
\(615\) 0 0
\(616\) 0 0
\(617\) 7806.00 0.509332 0.254666 0.967029i \(-0.418035\pi\)
0.254666 + 0.967029i \(0.418035\pi\)
\(618\) 0 0
\(619\) 9026.00 15633.5i 0.586083 1.01513i −0.408656 0.912688i \(-0.634002\pi\)
0.994739 0.102438i \(-0.0326642\pi\)
\(620\) 2016.00 3491.81i 0.130588 0.226185i
\(621\) 0 0
\(622\) −1056.00 −0.0680735
\(623\) 0 0
\(624\) 0 0
\(625\) 449.500 + 778.557i 0.0287680 + 0.0498276i
\(626\) −5830.00 + 10097.9i −0.372226 + 0.644715i
\(627\) 0 0
\(628\) 4820.00 + 8348.48i 0.306272 + 0.530479i
\(629\) 204.000 0.0129317
\(630\) 0 0
\(631\) −6208.00 −0.391659 −0.195829 0.980638i \(-0.562740\pi\)
−0.195829 + 0.980638i \(0.562740\pi\)
\(632\) 224.000 + 387.979i 0.0140985 + 0.0244193i
\(633\) 0 0
\(634\) −5046.00 + 8739.93i −0.316092 + 0.547487i
\(635\) 9576.00 + 16586.1i 0.598444 + 1.03654i
\(636\) 0 0
\(637\) 0 0
\(638\) −16416.0 −1.01868
\(639\) 0 0
\(640\) −1152.00 + 1995.32i −0.0711512 + 0.123238i
\(641\) −10755.0 + 18628.2i −0.662710 + 1.14785i 0.317191 + 0.948362i \(0.397260\pi\)
−0.979901 + 0.199485i \(0.936073\pi\)
\(642\) 0 0
\(643\) −11140.0 −0.683233 −0.341616 0.939839i \(-0.610974\pi\)
−0.341616 + 0.939839i \(0.610974\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) −552.000 956.092i −0.0336194 0.0582306i
\(647\) 4656.00 8064.43i 0.282915 0.490024i −0.689186 0.724584i \(-0.742032\pi\)
0.972102 + 0.234561i \(0.0753651\pi\)
\(648\) 0 0
\(649\) −17712.0 30678.1i −1.07127 1.85550i
\(650\) 13532.0 0.816567
\(651\) 0 0
\(652\) 2960.00 0.177795
\(653\) 2439.00 + 4224.47i 0.146165 + 0.253164i 0.929807 0.368048i \(-0.119974\pi\)
−0.783642 + 0.621212i \(0.786640\pi\)
\(654\) 0 0
\(655\) −1620.00 + 2805.92i −0.0966391 + 0.167384i
\(656\) 48.0000 + 83.1384i 0.00285684 + 0.00494819i
\(657\) 0 0
\(658\) 0 0
\(659\) 9744.00 0.575982 0.287991 0.957633i \(-0.407013\pi\)
0.287991 + 0.957633i \(0.407013\pi\)
\(660\) 0 0
\(661\) −1495.00 + 2589.42i −0.0879709 + 0.152370i −0.906653 0.421876i \(-0.861372\pi\)
0.818682 + 0.574247i \(0.194705\pi\)
\(662\) −5020.00 + 8694.90i −0.294725 + 0.510478i
\(663\) 0 0
\(664\) 1824.00 0.106604
\(665\) 0 0
\(666\) 0 0
\(667\) −10260.0 17770.8i −0.595605 1.03162i
\(668\) 7968.00 13801.0i 0.461514 0.799365i
\(669\) 0 0
\(670\) 2232.00 + 3865.94i 0.128701 + 0.222917i
\(671\) −18000.0 −1.03559
\(672\) 0 0
\(673\) 33266.0 1.90536 0.952682 0.303969i \(-0.0983118\pi\)
0.952682 + 0.303969i \(0.0983118\pi\)
\(674\) −7486.00 12966.1i −0.427819 0.741004i
\(675\) 0 0
\(676\) 2082.00 3606.13i 0.118457 0.205174i
\(677\) 2685.00 + 4650.56i 0.152427 + 0.264011i 0.932119 0.362152i \(-0.117958\pi\)
−0.779692 + 0.626163i \(0.784625\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) −864.000 −0.0487248
\(681\) 0 0
\(682\) 4032.00 6983.63i 0.226383 0.392107i
\(683\) 192.000 332.554i 0.0107565 0.0186308i −0.860597 0.509286i \(-0.829909\pi\)
0.871354 + 0.490656i \(0.163243\pi\)
\(684\) 0 0
\(685\) −48924.0 −2.72889
\(686\) 0 0
\(687\) 0 0
\(688\) −1312.00 2272.45i −0.0727028 0.125925i
\(689\) −11118.0 + 19256.9i −0.614749 + 1.06478i
\(690\) 0 0
\(691\) 7262.00 + 12578.2i 0.399797 + 0.692468i 0.993701 0.112068i \(-0.0357474\pi\)
−0.593904 + 0.804536i \(0.702414\pi\)
\(692\) 4152.00 0.228086
\(693\) 0 0
\(694\) −20064.0 −1.09743
\(695\) −12132.0 21013.2i −0.662148 1.14687i
\(696\) 0 0
\(697\) −18.0000 + 31.1769i −0.000978190 + 0.00169428i
\(698\) 5942.00 + 10291.8i 0.322218 + 0.558098i
\(699\) 0 0
\(700\) 0 0
\(701\) −24750.0 −1.33352 −0.666758 0.745274i \(-0.732318\pi\)
−0.666758 + 0.745274i \(0.732318\pi\)
\(702\) 0 0
\(703\) 1564.00 2708.93i 0.0839081 0.145333i
\(704\) −2304.00 + 3990.65i −0.123346 + 0.213641i
\(705\) 0 0
\(706\) −180.000 −0.00959545
\(707\) 0 0
\(708\) 0 0
\(709\) 521.000 + 902.398i 0.0275974 + 0.0478001i 0.879494 0.475909i \(-0.157881\pi\)
−0.851897 + 0.523710i \(0.824548\pi\)
\(710\) 648.000 1122.37i 0.0342521 0.0593264i
\(711\) 0 0
\(712\) −1560.00 2702.00i −0.0821116 0.142221i
\(713\) 10080.0 0.529452
\(714\) 0 0
\(715\) 44064.0 2.30476
\(716\) −5136.00 8895.81i −0.268074 0.464319i
\(717\) 0 0
\(718\) −10596.0 + 18352.8i −0.550751 + 0.953929i
\(719\) −18480.0 32008.3i −0.958536 1.66023i −0.726059 0.687632i \(-0.758650\pi\)
−0.232477 0.972602i \(-0.574683\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) −3210.00 −0.165462
\(723\) 0 0
\(724\) 5396.00 9346.15i 0.276990 0.479761i
\(725\) −11343.0 + 19646.7i −0.581060 + 1.00643i
\(726\) 0 0
\(727\) −16288.0 −0.830933 −0.415467 0.909608i \(-0.636382\pi\)
−0.415467 + 0.909608i \(0.636382\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) −18180.0 31488.7i −0.921742 1.59650i
\(731\) 492.000 852.169i 0.0248937 0.0431171i
\(732\) 0 0
\(733\) 3905.00 + 6763.66i 0.196773 + 0.340820i 0.947480 0.319814i \(-0.103621\pi\)
−0.750707 + 0.660635i \(0.770287\pi\)
\(734\) −8032.00 −0.403905
\(735\) 0 0
\(736\) −5760.00 −0.288473
\(737\) 4464.00 + 7731.87i 0.223112 + 0.386441i
\(738\) 0 0
\(739\) 18350.0 31783.1i 0.913418 1.58209i 0.104216 0.994555i \(-0.466767\pi\)
0.809202 0.587531i \(-0.199900\pi\)
\(740\) −1224.00 2120.03i −0.0608042 0.105316i
\(741\) 0 0
\(742\) 0 0
\(743\) −29508.0 −1.45699 −0.728495 0.685051i \(-0.759780\pi\)
−0.728495 + 0.685051i \(0.759780\pi\)
\(744\) 0 0
\(745\) −5022.00 + 8698.36i −0.246969 + 0.427763i
\(746\) 3278.00 5677.66i 0.160880 0.278651i
\(747\) 0 0
\(748\) −1728.00 −0.0844678
\(749\) 0 0
\(750\) 0 0
\(751\) 7568.00 + 13108.2i 0.367723 + 0.636916i 0.989209 0.146510i \(-0.0468040\pi\)
−0.621486 + 0.783425i \(0.713471\pi\)
\(752\) 1344.00 2327.88i 0.0651737 0.112884i
\(753\) 0 0
\(754\) −3876.00 6713.43i −0.187209 0.324256i
\(755\) −34704.0 −1.67286
\(756\) 0 0
\(757\) 3422.00 0.164299 0.0821497 0.996620i \(-0.473821\pi\)
0.0821497 + 0.996620i \(0.473821\pi\)
\(758\) 4628.00 + 8015.93i 0.221763 + 0.384105i
\(759\) 0 0
\(760\) −6624.00 + 11473.1i −0.316155 + 0.547596i
\(761\) 15723.0 + 27233.0i 0.748960 + 1.29724i 0.948322 + 0.317310i \(0.102780\pi\)
−0.199362 + 0.979926i \(0.563887\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 16464.0 0.779642
\(765\) 0 0
\(766\) 2880.00 4988.31i 0.135847 0.235294i
\(767\) 8364.00 14486.9i 0.393750 0.681996i
\(768\) 0 0
\(769\) −18718.0 −0.877748 −0.438874 0.898549i \(-0.644623\pi\)
−0.438874 + 0.898549i \(0.644623\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 6620.00 + 11466.2i 0.308626 + 0.534555i
\(773\) −843.000 + 1460.12i −0.0392246 + 0.0679390i −0.884971 0.465646i \(-0.845822\pi\)
0.845747 + 0.533585i \(0.179155\pi\)
\(774\) 0 0
\(775\) −5572.00 9650.99i −0.258261 0.447321i
\(776\) 560.000 0.0259057
\(777\) 0 0
\(778\) 15948.0 0.734915
\(779\) 276.000 + 478.046i 0.0126941 + 0.0219869i
\(780\) 0 0
\(781\) 1296.00 2244.74i 0.0593784 0.102846i
\(782\) −1080.00 1870.61i −0.0493871 0.0855410i
\(783\) 0 0
\(784\) 0 0
\(785\) 43380.0 1.97235
\(786\) 0 0
\(787\) −2746.00 + 4756.21i −0.124377 + 0.215426i −0.921489 0.388404i \(-0.873026\pi\)
0.797113 + 0.603831i \(0.206360\pi\)
\(788\) 2556.00 4427.12i 0.115550 0.200139i
\(789\) 0 0
\(790\) 2016.00 0.0907925