Properties

Label 882.4.g.o.667.1
Level $882$
Weight $4$
Character 882.667
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 667.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 882.667
Dual form 882.4.g.o.361.1

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

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

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
\(5\) −9.00000 + 15.5885i −0.804984 + 1.39427i 0.111317 + 0.993785i \(0.464493\pi\)
−0.916302 + 0.400489i \(0.868840\pi\)
\(6\) 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 −0.633817 0.773483i \(-0.718513\pi\)
−0.352947 0.935643i \(-0.614820\pi\)
\(12\) 0 0
\(13\) 34.0000 0.725377 0.362689 0.931910i \(-0.381859\pi\)
0.362689 + 0.931910i \(0.381859\pi\)
\(14\) 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 \(-0.180295\pi\)
−0.886632 + 0.462476i \(0.846961\pi\)
\(18\) 0 0
\(19\) 46.0000 79.6743i 0.555428 0.962029i −0.442443 0.896797i \(-0.645888\pi\)
0.997870 0.0652319i \(-0.0207787\pi\)
\(20\) 72.0000 0.804984
\(21\) 0 0
\(22\) −144.000 −1.39550
\(23\) −90.0000 + 155.885i −0.815926 + 1.41323i 0.0927351 + 0.995691i \(0.470439\pi\)
−0.908661 + 0.417534i \(0.862894\pi\)
\(24\) 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 \(-0.114800\pi\)
−0.773442 + 0.633867i \(0.781467\pi\)
\(32\) 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 −0.825784 0.563987i \(-0.809267\pi\)
0.901319 + 0.433157i \(0.142600\pi\)
\(38\) −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 \(-0.496362\pi\)
0.0114273 + 0.999935i \(0.496362\pi\)
\(42\) 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 \(-0.917285\pi\)
0.705732 + 0.708479i \(0.250618\pi\)
\(48\) 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 0.883442 + 0.468540i \(0.155220\pi\)
−0.0359535 + 0.999353i \(0.511447\pi\)
\(54\) 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 0.998741 + 0.0501732i \(0.0159773\pi\)
−0.455919 + 0.890021i \(0.650689\pi\)
\(60\) 0 0
\(61\) −125.000 + 216.506i −0.262371 + 0.454439i −0.966871 0.255264i \(-0.917838\pi\)
0.704501 + 0.709703i \(0.251171\pi\)
\(62\) 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 0.917000 0.398888i \(-0.130604\pi\)
−0.803947 + 0.594701i \(0.797271\pi\)
\(68\) −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 0.913094 + 0.407749i \(0.133686\pi\)
−0.103426 + 0.994637i \(0.532980\pi\)
\(74\) −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 −0.885275 0.465068i \(-0.846030\pi\)
0.845398 + 0.534136i \(0.179363\pi\)
\(80\) −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 \(-0.451828\pi\)
0.150761 + 0.988570i \(0.451828\pi\)
\(84\) 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 \(-0.907941\pi\)
0.726222 + 0.687460i \(0.241274\pi\)
\(90\) 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 \(-0.488336\pi\)
0.0366362 + 0.999329i \(0.488336\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) −398.000 + 689.356i −0.398000 + 0.689356i
\(101\) 675.000 + 1169.13i 0.665000 + 1.15181i 0.979285 + 0.202485i \(0.0649019\pi\)
−0.314285 + 0.949329i \(0.601765\pi\)
\(102\) 0 0
\(103\) 1000.00 1732.05i 0.956630 1.65693i 0.226038 0.974118i \(-0.427423\pi\)
0.730592 0.682814i \(-0.239244\pi\)
\(104\) −272.000 −0.256460
\(105\) 0 0
\(106\) 1308.00 1.19853
\(107\) 348.000 602.754i 0.314415 0.544583i −0.664898 0.746934i \(-0.731525\pi\)
0.979313 + 0.202351i \(0.0648582\pi\)
\(108\) 0 0
\(109\) 557.000 + 964.752i 0.489458 + 0.847766i 0.999926 0.0121304i \(-0.00386131\pi\)
−0.510468 + 0.859897i \(0.670528\pi\)
\(110\) 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 \(-0.852452\pi\)
0.834451 + 0.551082i \(0.185785\pi\)
\(132\) 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 −0.883434 0.468555i \(-0.844775\pi\)
0.0359363 0.999354i \(-0.488559\pi\)
\(138\) 0 0
\(139\) 1348.00 0.822560 0.411280 0.911509i \(-0.365082\pi\)
0.411280 + 0.911509i \(0.365082\pi\)
\(140\) 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 −0.779075 0.626930i \(-0.784311\pi\)
0.932475 + 0.361234i \(0.117644\pi\)
\(150\) 0 0
\(151\) −964.000 1669.70i −0.519531 0.899854i −0.999742 0.0227014i \(-0.992773\pi\)
0.480211 0.877153i \(-0.340560\pi\)
\(152\) −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 −0.990810 0.135261i \(-0.956813\pi\)
0.378266 0.925697i \(-0.376521\pi\)
\(158\) 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 −0.941125 0.338058i \(-0.890230\pi\)
0.763330 + 0.646009i \(0.223563\pi\)
\(164\) −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 \(-0.125707\pi\)
0.923027 + 0.384734i \(0.125707\pi\)
\(168\) 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 \(-0.760087\pi\)
0.957241 + 0.289292i \(0.0934200\pi\)
\(174\) 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 −0.999107 0.0422569i \(-0.986545\pi\)
0.462958 0.886380i \(-0.346788\pi\)
\(180\) 0 0
\(181\) 2698.00 1.10796 0.553980 0.832530i \(-0.313108\pi\)
0.553980 + 0.832530i \(0.313108\pi\)
\(182\) 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 0.152506 + 0.988303i \(0.451266\pi\)
−0.932148 + 0.362077i \(0.882068\pi\)
\(192\) 0 0
\(193\) 1655.00 + 2866.54i 0.617251 + 1.06911i 0.989985 + 0.141172i \(0.0450872\pi\)
−0.372734 + 0.927938i \(0.621580\pi\)
\(194\) 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 0.999644 + 0.0266869i \(0.00849572\pi\)
−0.476710 + 0.879060i \(0.658171\pi\)
\(200\) 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 \(-0.408513\pi\)
0.283475 + 0.958980i \(0.408513\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 462.000 800.207i 0.135981 0.235527i
\(227\) −1782.00 3086.51i −0.521037 0.902463i −0.999701 0.0244647i \(-0.992212\pi\)
0.478663 0.877999i \(-0.341121\pi\)
\(228\) 0 0
\(229\) 667.000 1155.28i 0.192474 0.333375i −0.753595 0.657339i \(-0.771682\pi\)
0.946070 + 0.323963i \(0.105015\pi\)
\(230\) −6480.00 −1.85773
\(231\) 0 0
\(232\) −912.000 −0.258085
\(233\) 1329.00 2301.90i 0.373672 0.647220i −0.616455 0.787390i \(-0.711432\pi\)
0.990127 + 0.140171i \(0.0447651\pi\)
\(234\) 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 0.942631 + 0.333835i \(0.108343\pi\)
−0.182206 + 0.983260i \(0.558324\pi\)
\(242\) 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 \(-0.492795\pi\)
0.0226325 + 0.999744i \(0.492795\pi\)
\(252\) 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 0.340023 + 0.940417i \(0.389565\pi\)
−0.984437 + 0.175740i \(0.943768\pi\)
\(258\) 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 0.910469 0.413577i \(-0.135721\pi\)
−0.813403 + 0.581701i \(0.802388\pi\)
\(264\) 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 \(-0.0114603\pi\)
−0.530849 + 0.847466i \(0.678127\pi\)
\(270\) 0 0
\(271\) −1484.00 + 2570.36i −0.332644 + 0.576157i −0.983029 0.183448i \(-0.941274\pi\)
0.650385 + 0.759605i \(0.274607\pi\)
\(272\) 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 0.999754 + 0.0221579i \(0.00705366\pi\)
−0.480688 + 0.876892i \(0.659613\pi\)
\(278\) 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 0.999999 + 0.00135915i \(0.000432632\pi\)
−0.498822 + 0.866704i \(0.666234\pi\)
\(284\) 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 \(-0.274684\pi\)
0.650204 + 0.759760i \(0.274684\pi\)
\(294\) 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 \(-0.302897\pi\)
0.580397 + 0.814333i \(0.302897\pi\)
\(308\) 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 \(-0.151339\pi\)
−0.840954 + 0.541107i \(0.818005\pi\)
\(312\) 0 0
\(313\) −2915.00 + 5048.93i −0.526407 + 0.911765i 0.473119 + 0.880998i \(0.343128\pi\)
−0.999527 + 0.0307660i \(0.990205\pi\)
\(314\) −4820.00 −0.866269
\(315\) 0 0
\(316\) 224.000 0.0398765
\(317\) 2523.00 4369.96i 0.447021 0.774264i −0.551169 0.834394i \(-0.685818\pi\)
0.998191 + 0.0601297i \(0.0191514\pi\)
\(318\) 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 −0.578812 0.815461i \(-0.696484\pi\)
0.995616 + 0.0935355i \(0.0298169\pi\)
\(332\) −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 −0.934229 0.356673i \(-0.883911\pi\)
0.158226 0.987403i \(-0.449422\pi\)
\(348\) 0 0
\(349\) −5942.00 −0.911370 −0.455685 0.890141i \(-0.650606\pi\)
−0.455685 + 0.890141i \(0.650606\pi\)
\(350\) 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 \(-0.164507\pi\)
−0.862613 + 0.505864i \(0.831174\pi\)
\(354\) 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 −0.153708 0.988116i \(-0.549122\pi\)
0.932588 0.360943i \(-0.117545\pi\)
\(360\) 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 \(-0.0744724\pi\)
−0.687151 + 0.726514i \(0.741139\pi\)
\(368\) −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 −0.957072 0.289851i \(-0.906394\pi\)
0.729554 + 0.683923i \(0.239728\pi\)
\(374\) 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 \(-0.771798\pi\)
0.945951 + 0.324308i \(0.105132\pi\)
\(384\) 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 0.999739 + 0.0228557i \(0.00727584\pi\)
−0.480076 + 0.877227i \(0.659391\pi\)
\(390\) 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 0.151328 + 0.988484i \(0.451645\pi\)
−0.931716 + 0.363188i \(0.881688\pi\)
\(398\) 5872.00 0.739540
\(399\) 0 0
\(400\) 3184.00 0.398000
\(401\) 4869.00 8433.36i 0.606350 1.05023i −0.385487 0.922713i \(-0.625966\pi\)
0.991837 0.127515i \(-0.0407002\pi\)
\(402\) 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 \(-0.174941\pi\)
−0.878729 + 0.477321i \(0.841608\pi\)
\(410\) 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 \(-0.533687\pi\)
−0.105635 + 0.994405i \(0.533687\pi\)
\(420\) 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 0.727807 0.685782i \(-0.240540\pi\)
−0.957808 + 0.287409i \(0.907206\pi\)
\(432\) 0 0
\(433\) −9938.00 −1.10298 −0.551489 0.834182i \(-0.685940\pi\)
−0.551489 + 0.834182i \(0.685940\pi\)
\(434\) 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 \(-0.802416\pi\)
0.910432 + 0.413659i \(0.135749\pi\)
\(440\) −10368.0 −1.12335
\(441\) 0 0
\(442\) −408.000 −0.0439063
\(443\) −5856.00 + 10142.9i −0.628052 + 1.08782i 0.359890 + 0.932995i \(0.382814\pi\)
−0.987942 + 0.154823i \(0.950519\pi\)
\(444\) 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 −0.944594 0.328240i \(-0.893545\pi\)
0.756561 + 0.653923i \(0.226878\pi\)
\(458\) −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 \(-0.550085\pi\)
−0.156697 + 0.987647i \(0.550085\pi\)
\(462\) 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 \(-0.890605\pi\)
0.762568 + 0.646908i \(0.223938\pi\)
\(468\) 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 \(-0.0205862\pi\)
−0.554924 + 0.831901i \(0.687253\pi\)
\(480\) 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 0.969392 0.245517i \(-0.0789578\pi\)
−0.697320 + 0.716760i \(0.745624\pi\)
\(488\) 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 −0.999789 0.0205349i \(-0.993463\pi\)
0.517678 + 0.855575i \(0.326796\pi\)
\(500\) −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 \(-0.760843\pi\)
−0.730779 + 0.682614i \(0.760843\pi\)
\(504\) 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 0.378795 + 0.925481i \(0.376339\pi\)
−0.990887 + 0.134694i \(0.956995\pi\)
\(510\) 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 0.991533 + 0.129852i \(0.0414502\pi\)
−0.383312 + 0.923619i \(0.625217\pi\)
\(522\) 0 0
\(523\) 9262.00 16042.3i 0.774377 1.34126i −0.160768 0.986992i \(-0.551397\pi\)
0.935144 0.354267i \(-0.115270\pi\)
\(524\) 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 −0.939525 0.342481i \(-0.888733\pi\)
0.766359 + 0.642412i \(0.222066\pi\)
\(542\) 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 0.901914 0.431915i \(-0.142162\pi\)
−0.825007 + 0.565123i \(0.808829\pi\)
\(558\) 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 \(-0.255453\pi\)
−0.970218 + 0.242235i \(0.922120\pi\)
\(564\) 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 −0.582516 0.812820i \(-0.697932\pi\)
0.995180 + 0.0980635i \(0.0312648\pi\)
\(570\) 0 0
\(571\) 5282.00 + 9148.69i 0.387119 + 0.670509i 0.992061 0.125760i \(-0.0401370\pi\)
−0.604942 + 0.796270i \(0.706804\pi\)
\(572\) −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 −0.977888 0.209132i \(-0.932936\pi\)
0.307831 0.951441i \(-0.400397\pi\)
\(578\) −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 \(-0.346539\pi\)
0.463652 + 0.886018i \(0.346539\pi\)
\(588\) 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 −0.153098 0.988211i \(-0.548925\pi\)
0.932365 0.361519i \(-0.117742\pi\)
\(594\) 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 0.988189 0.153238i \(-0.0489702\pi\)
−0.626803 + 0.779178i \(0.715637\pi\)
\(600\) 0 0
\(601\) −14618.0 −0.992148 −0.496074 0.868280i \(-0.665225\pi\)
−0.496074 + 0.868280i \(0.665225\pi\)
\(602\) 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 \(-0.778056\pi\)
0.939393 + 0.342842i \(0.111390\pi\)
\(608\) 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 0.756158 0.654389i \(-0.227074\pi\)
−0.944797 + 0.327657i \(0.893741\pi\)
\(614\) 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 −0.994739 0.102438i \(-0.967336\pi\)
0.408656 0.912688i \(-0.365998\pi\)
\(620\) 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 −0.979901 0.199485i \(-0.936073\pi\)
0.317191 0.948362i \(-0.397260\pi\)
\(642\) 0 0
\(643\) 11140.0 0.683233 0.341616 0.939839i \(-0.389026\pi\)
0.341616 + 0.939839i \(0.389026\pi\)
\(644\) 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 \(-0.257968\pi\)
−0.972102 + 0.234561i \(0.924635\pi\)
\(648\) 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 −0.783642 0.621212i \(-0.786640\pi\)
0.929807 + 0.368048i \(0.119974\pi\)
\(654\) 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 \(-0.138628\pi\)
−0.818682 + 0.574247i \(0.805295\pi\)
\(662\) −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 \(-0.882042\pi\)
0.779692 + 0.626163i \(0.215375\pi\)
\(678\) 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 0.871354 0.490656i \(-0.163243\pi\)
−0.860597 + 0.509286i \(0.829909\pi\)
\(684\) 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 \(-0.964253\pi\)
0.593904 + 0.804536i \(0.297586\pi\)
\(692\) −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 −0.851897 0.523710i \(-0.824548\pi\)
0.879494 + 0.475909i \(0.157881\pi\)
\(710\) −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 0.232477 0.972602i \(-0.425317\pi\)
0.726059 0.687632i \(-0.241350\pi\)
\(720\) 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 \(-0.363618\pi\)
0.415467 + 0.909608i \(0.363618\pi\)
\(728\) 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 \(-0.896379\pi\)
0.750707 + 0.660635i \(0.229713\pi\)
\(734\) 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 0.809202 + 0.587531i \(0.199900\pi\)
0.104216 + 0.994555i \(0.466767\pi\)
\(740\) 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 −0.621486 0.783425i \(-0.713471\pi\)
0.989209 + 0.146510i \(0.0468040\pi\)
\(752\) −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 0.199362 + 0.979926i \(0.436113\pi\)
−0.948322 + 0.317310i \(0.897220\pi\)
\(762\) 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 \(-0.355377\pi\)
0.438874 + 0.898549i \(0.355377\pi\)
\(770\) 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 \(-0.154178\pi\)
−0.845747 + 0.533585i \(0.820845\pi\)
\(774\) 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 \(-0.126974\pi\)
−0.797113 + 0.603831i \(0.793640\pi\)
\(788\) 2556.00 + 4427.12i 0.115550 + 0.200139i
\(789\) 0 0
\(790\) −2016.00