Properties

Label 882.4.g.v.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 14)
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.v.667.1

$q$-expansion

\(f(q)\) \(=\) \(q+(1.00000 + 1.73205i) q^{2} +(-2.00000 + 3.46410i) q^{4} +(6.00000 + 10.3923i) q^{5} -8.00000 q^{8} +O(q^{10})\) \(q+(1.00000 + 1.73205i) q^{2} +(-2.00000 + 3.46410i) q^{4} +(6.00000 + 10.3923i) q^{5} -8.00000 q^{8} +(-12.0000 + 20.7846i) q^{10} +(24.0000 - 41.5692i) q^{11} -56.0000 q^{13} +(-8.00000 - 13.8564i) q^{16} +(57.0000 - 98.7269i) q^{17} +(1.00000 + 1.73205i) q^{19} -48.0000 q^{20} +96.0000 q^{22} +(-60.0000 - 103.923i) q^{23} +(-9.50000 + 16.4545i) q^{25} +(-56.0000 - 96.9948i) q^{26} +54.0000 q^{29} +(118.000 - 204.382i) q^{31} +(16.0000 - 27.7128i) q^{32} +228.000 q^{34} +(-73.0000 - 126.440i) q^{37} +(-2.00000 + 3.46410i) q^{38} +(-48.0000 - 83.1384i) q^{40} +126.000 q^{41} -376.000 q^{43} +(96.0000 + 166.277i) q^{44} +(120.000 - 207.846i) q^{46} +(6.00000 + 10.3923i) q^{47} -38.0000 q^{50} +(112.000 - 193.990i) q^{52} +(87.0000 - 150.688i) q^{53} +576.000 q^{55} +(54.0000 + 93.5307i) q^{58} +(-69.0000 + 119.512i) q^{59} +(190.000 + 329.090i) q^{61} +472.000 q^{62} +64.0000 q^{64} +(-336.000 - 581.969i) q^{65} +(242.000 - 419.156i) q^{67} +(228.000 + 394.908i) q^{68} -576.000 q^{71} +(-575.000 + 995.929i) q^{73} +(146.000 - 252.879i) q^{74} -8.00000 q^{76} +(-388.000 - 672.036i) q^{79} +(96.0000 - 166.277i) q^{80} +(126.000 + 218.238i) q^{82} +378.000 q^{83} +1368.00 q^{85} +(-376.000 - 651.251i) q^{86} +(-192.000 + 332.554i) q^{88} +(195.000 + 337.750i) q^{89} +480.000 q^{92} +(-12.0000 + 20.7846i) q^{94} +(-12.0000 + 20.7846i) q^{95} +1330.00 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q + 2q^{2} - 4q^{4} + 12q^{5} - 16q^{8} + O(q^{10}) \) \( 2q + 2q^{2} - 4q^{4} + 12q^{5} - 16q^{8} - 24q^{10} + 48q^{11} - 112q^{13} - 16q^{16} + 114q^{17} + 2q^{19} - 96q^{20} + 192q^{22} - 120q^{23} - 19q^{25} - 112q^{26} + 108q^{29} + 236q^{31} + 32q^{32} + 456q^{34} - 146q^{37} - 4q^{38} - 96q^{40} + 252q^{41} - 752q^{43} + 192q^{44} + 240q^{46} + 12q^{47} - 76q^{50} + 224q^{52} + 174q^{53} + 1152q^{55} + 108q^{58} - 138q^{59} + 380q^{61} + 944q^{62} + 128q^{64} - 672q^{65} + 484q^{67} + 456q^{68} - 1152q^{71} - 1150q^{73} + 292q^{74} - 16q^{76} - 776q^{79} + 192q^{80} + 252q^{82} + 756q^{83} + 2736q^{85} - 752q^{86} - 384q^{88} + 390q^{89} + 960q^{92} - 24q^{94} - 24q^{95} + 2660q^{97} + O(q^{100}) \)

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
\(5\) 6.00000 + 10.3923i 0.536656 + 0.929516i 0.999081 + 0.0428575i \(0.0136462\pi\)
−0.462425 + 0.886658i \(0.653021\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) −8.00000 −0.353553
\(9\) 0 0
\(10\) −12.0000 + 20.7846i −0.379473 + 0.657267i
\(11\) 24.0000 41.5692i 0.657843 1.13942i −0.323330 0.946286i \(-0.604802\pi\)
0.981173 0.193131i \(-0.0618643\pi\)
\(12\) 0 0
\(13\) −56.0000 −1.19474 −0.597369 0.801966i \(-0.703787\pi\)
−0.597369 + 0.801966i \(0.703787\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) −8.00000 13.8564i −0.125000 0.216506i
\(17\) 57.0000 98.7269i 0.813208 1.40852i −0.0974001 0.995245i \(-0.531053\pi\)
0.910608 0.413272i \(-0.135614\pi\)
\(18\) 0 0
\(19\) 1.00000 + 1.73205i 0.0120745 + 0.0209137i 0.872000 0.489507i \(-0.162823\pi\)
−0.859925 + 0.510420i \(0.829490\pi\)
\(20\) −48.0000 −0.536656
\(21\) 0 0
\(22\) 96.0000 0.930330
\(23\) −60.0000 103.923i −0.543951 0.942150i −0.998672 0.0515165i \(-0.983595\pi\)
0.454721 0.890634i \(-0.349739\pi\)
\(24\) 0 0
\(25\) −9.50000 + 16.4545i −0.0760000 + 0.131636i
\(26\) −56.0000 96.9948i −0.422404 0.731625i
\(27\) 0 0
\(28\) 0 0
\(29\) 54.0000 0.345778 0.172889 0.984941i \(-0.444690\pi\)
0.172889 + 0.984941i \(0.444690\pi\)
\(30\) 0 0
\(31\) 118.000 204.382i 0.683659 1.18413i −0.290197 0.956967i \(-0.593721\pi\)
0.973856 0.227165i \(-0.0729457\pi\)
\(32\) 16.0000 27.7128i 0.0883883 0.153093i
\(33\) 0 0
\(34\) 228.000 1.15005
\(35\) 0 0
\(36\) 0 0
\(37\) −73.0000 126.440i −0.324355 0.561799i 0.657027 0.753867i \(-0.271814\pi\)
−0.981382 + 0.192068i \(0.938480\pi\)
\(38\) −2.00000 + 3.46410i −0.00853797 + 0.0147882i
\(39\) 0 0
\(40\) −48.0000 83.1384i −0.189737 0.328634i
\(41\) 126.000 0.479949 0.239974 0.970779i \(-0.422861\pi\)
0.239974 + 0.970779i \(0.422861\pi\)
\(42\) 0 0
\(43\) −376.000 −1.33348 −0.666738 0.745292i \(-0.732310\pi\)
−0.666738 + 0.745292i \(0.732310\pi\)
\(44\) 96.0000 + 166.277i 0.328921 + 0.569709i
\(45\) 0 0
\(46\) 120.000 207.846i 0.384631 0.666201i
\(47\) 6.00000 + 10.3923i 0.0186211 + 0.0322526i 0.875186 0.483787i \(-0.160739\pi\)
−0.856565 + 0.516040i \(0.827406\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) −38.0000 −0.107480
\(51\) 0 0
\(52\) 112.000 193.990i 0.298685 0.517337i
\(53\) 87.0000 150.688i 0.225479 0.390540i −0.730984 0.682394i \(-0.760939\pi\)
0.956463 + 0.291854i \(0.0942721\pi\)
\(54\) 0 0
\(55\) 576.000 1.41214
\(56\) 0 0
\(57\) 0 0
\(58\) 54.0000 + 93.5307i 0.122251 + 0.211745i
\(59\) −69.0000 + 119.512i −0.152255 + 0.263713i −0.932056 0.362314i \(-0.881987\pi\)
0.779801 + 0.626027i \(0.215320\pi\)
\(60\) 0 0
\(61\) 190.000 + 329.090i 0.398803 + 0.690748i 0.993579 0.113144i \(-0.0360923\pi\)
−0.594775 + 0.803892i \(0.702759\pi\)
\(62\) 472.000 0.966840
\(63\) 0 0
\(64\) 64.0000 0.125000
\(65\) −336.000 581.969i −0.641164 1.11053i
\(66\) 0 0
\(67\) 242.000 419.156i 0.441269 0.764300i −0.556515 0.830837i \(-0.687862\pi\)
0.997784 + 0.0665376i \(0.0211952\pi\)
\(68\) 228.000 + 394.908i 0.406604 + 0.704259i
\(69\) 0 0
\(70\) 0 0
\(71\) −576.000 −0.962798 −0.481399 0.876502i \(-0.659871\pi\)
−0.481399 + 0.876502i \(0.659871\pi\)
\(72\) 0 0
\(73\) −575.000 + 995.929i −0.921899 + 1.59678i −0.125426 + 0.992103i \(0.540030\pi\)
−0.796473 + 0.604674i \(0.793304\pi\)
\(74\) 146.000 252.879i 0.229353 0.397252i
\(75\) 0 0
\(76\) −8.00000 −0.0120745
\(77\) 0 0
\(78\) 0 0
\(79\) −388.000 672.036i −0.552575 0.957088i −0.998088 0.0618122i \(-0.980312\pi\)
0.445513 0.895275i \(-0.353021\pi\)
\(80\) 96.0000 166.277i 0.134164 0.232379i
\(81\) 0 0
\(82\) 126.000 + 218.238i 0.169687 + 0.293907i
\(83\) 378.000 0.499890 0.249945 0.968260i \(-0.419587\pi\)
0.249945 + 0.968260i \(0.419587\pi\)
\(84\) 0 0
\(85\) 1368.00 1.74565
\(86\) −376.000 651.251i −0.471455 0.816584i
\(87\) 0 0
\(88\) −192.000 + 332.554i −0.232583 + 0.402845i
\(89\) 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
\(92\) 480.000 0.543951
\(93\) 0 0
\(94\) −12.0000 + 20.7846i −0.0131671 + 0.0228061i
\(95\) −12.0000 + 20.7846i −0.0129597 + 0.0224469i
\(96\) 0 0
\(97\) 1330.00 1.39218 0.696088 0.717957i \(-0.254922\pi\)
0.696088 + 0.717957i \(0.254922\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) −38.0000 65.8179i −0.0380000 0.0658179i
\(101\) 750.000 1299.04i 0.738889 1.27979i −0.214107 0.976810i \(-0.568684\pi\)
0.952996 0.302983i \(-0.0979826\pi\)
\(102\) 0 0
\(103\) 190.000 + 329.090i 0.181760 + 0.314817i 0.942480 0.334263i \(-0.108487\pi\)
−0.760720 + 0.649080i \(0.775154\pi\)
\(104\) 448.000 0.422404
\(105\) 0 0
\(106\) 348.000 0.318875
\(107\) 318.000 + 550.792i 0.287310 + 0.497636i 0.973167 0.230101i \(-0.0739055\pi\)
−0.685856 + 0.727737i \(0.740572\pi\)
\(108\) 0 0
\(109\) −73.0000 + 126.440i −0.0641480 + 0.111108i −0.896316 0.443416i \(-0.853766\pi\)
0.832168 + 0.554524i \(0.187100\pi\)
\(110\) 576.000 + 997.661i 0.499268 + 0.864757i
\(111\) 0 0
\(112\) 0 0
\(113\) −198.000 −0.164834 −0.0824171 0.996598i \(-0.526264\pi\)
−0.0824171 + 0.996598i \(0.526264\pi\)
\(114\) 0 0
\(115\) 720.000 1247.08i 0.583829 1.01122i
\(116\) −108.000 + 187.061i −0.0864444 + 0.149726i
\(117\) 0 0
\(118\) −276.000 −0.215321
\(119\) 0 0
\(120\) 0 0
\(121\) −486.500 842.643i −0.365515 0.633090i
\(122\) −380.000 + 658.179i −0.281997 + 0.488432i
\(123\) 0 0
\(124\) 472.000 + 817.528i 0.341829 + 0.592066i
\(125\) 1272.00 0.910169
\(126\) 0 0
\(127\) −376.000 −0.262713 −0.131357 0.991335i \(-0.541933\pi\)
−0.131357 + 0.991335i \(0.541933\pi\)
\(128\) 64.0000 + 110.851i 0.0441942 + 0.0765466i
\(129\) 0 0
\(130\) 672.000 1163.94i 0.453372 0.785263i
\(131\) −1065.00 1844.63i −0.710301 1.23028i −0.964744 0.263190i \(-0.915225\pi\)
0.254443 0.967088i \(-0.418108\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 968.000 0.624048
\(135\) 0 0
\(136\) −456.000 + 789.815i −0.287512 + 0.497986i
\(137\) −39.0000 + 67.5500i −0.0243211 + 0.0421254i −0.877930 0.478789i \(-0.841076\pi\)
0.853609 + 0.520915i \(0.174409\pi\)
\(138\) 0 0
\(139\) 2338.00 1.42667 0.713333 0.700825i \(-0.247185\pi\)
0.713333 + 0.700825i \(0.247185\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) −576.000 997.661i −0.340400 0.589591i
\(143\) −1344.00 + 2327.88i −0.785951 + 1.36131i
\(144\) 0 0
\(145\) 324.000 + 561.184i 0.185564 + 0.321406i
\(146\) −2300.00 −1.30376
\(147\) 0 0
\(148\) 584.000 0.324355
\(149\) −501.000 867.757i −0.275460 0.477110i 0.694791 0.719212i \(-0.255497\pi\)
−0.970251 + 0.242101i \(0.922163\pi\)
\(150\) 0 0
\(151\) 1376.00 2383.30i 0.741571 1.28444i −0.210208 0.977657i \(-0.567414\pi\)
0.951780 0.306783i \(-0.0992525\pi\)
\(152\) −8.00000 13.8564i −0.00426898 0.00739410i
\(153\) 0 0
\(154\) 0 0
\(155\) 2832.00 1.46756
\(156\) 0 0
\(157\) −260.000 + 450.333i −0.132167 + 0.228920i −0.924512 0.381154i \(-0.875527\pi\)
0.792345 + 0.610074i \(0.208860\pi\)
\(158\) 776.000 1344.07i 0.390729 0.676763i
\(159\) 0 0
\(160\) 384.000 0.189737
\(161\) 0 0
\(162\) 0 0
\(163\) −640.000 1108.51i −0.307538 0.532671i 0.670285 0.742104i \(-0.266172\pi\)
−0.977823 + 0.209432i \(0.932838\pi\)
\(164\) −252.000 + 436.477i −0.119987 + 0.207824i
\(165\) 0 0
\(166\) 378.000 + 654.715i 0.176738 + 0.306119i
\(167\) 1764.00 0.817380 0.408690 0.912673i \(-0.365986\pi\)
0.408690 + 0.912673i \(0.365986\pi\)
\(168\) 0 0
\(169\) 939.000 0.427401
\(170\) 1368.00 + 2369.45i 0.617181 + 1.06899i
\(171\) 0 0
\(172\) 752.000 1302.50i 0.333369 0.577412i
\(173\) 384.000 + 665.108i 0.168757 + 0.292296i 0.937983 0.346681i \(-0.112691\pi\)
−0.769226 + 0.638977i \(0.779358\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) −768.000 −0.328921
\(177\) 0 0
\(178\) −390.000 + 675.500i −0.164223 + 0.284443i
\(179\) 906.000 1569.24i 0.378311 0.655253i −0.612506 0.790466i \(-0.709838\pi\)
0.990817 + 0.135213i \(0.0431718\pi\)
\(180\) 0 0
\(181\) 448.000 0.183976 0.0919878 0.995760i \(-0.470678\pi\)
0.0919878 + 0.995760i \(0.470678\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 480.000 + 831.384i 0.192316 + 0.333100i
\(185\) 876.000 1517.28i 0.348134 0.602986i
\(186\) 0 0
\(187\) −2736.00 4738.89i −1.06993 1.85317i
\(188\) −48.0000 −0.0186211
\(189\) 0 0
\(190\) −48.0000 −0.0183278
\(191\) −1068.00 1849.83i −0.404596 0.700780i 0.589679 0.807638i \(-0.299254\pi\)
−0.994274 + 0.106858i \(0.965921\pi\)
\(192\) 0 0
\(193\) −2215.00 + 3836.49i −0.826110 + 1.43086i 0.0749584 + 0.997187i \(0.476118\pi\)
−0.901068 + 0.433677i \(0.857216\pi\)
\(194\) 1330.00 + 2303.63i 0.492208 + 0.852530i
\(195\) 0 0
\(196\) 0 0
\(197\) −198.000 −0.0716087 −0.0358044 0.999359i \(-0.511399\pi\)
−0.0358044 + 0.999359i \(0.511399\pi\)
\(198\) 0 0
\(199\) −1142.00 + 1978.00i −0.406805 + 0.704607i −0.994530 0.104454i \(-0.966691\pi\)
0.587725 + 0.809061i \(0.300024\pi\)
\(200\) 76.0000 131.636i 0.0268701 0.0465403i
\(201\) 0 0
\(202\) 3000.00 1.04495
\(203\) 0 0
\(204\) 0 0
\(205\) 756.000 + 1309.43i 0.257567 + 0.446120i
\(206\) −380.000 + 658.179i −0.128524 + 0.222609i
\(207\) 0 0
\(208\) 448.000 + 775.959i 0.149342 + 0.258669i
\(209\) 96.0000 0.0317725
\(210\) 0 0
\(211\) 4412.00 1.43950 0.719750 0.694233i \(-0.244256\pi\)
0.719750 + 0.694233i \(0.244256\pi\)
\(212\) 348.000 + 602.754i 0.112739 + 0.195270i
\(213\) 0 0
\(214\) −636.000 + 1101.58i −0.203159 + 0.351882i
\(215\) −2256.00 3907.51i −0.715618 1.23949i
\(216\) 0 0
\(217\) 0 0
\(218\) −292.000 −0.0907190
\(219\) 0 0
\(220\) −1152.00 + 1995.32i −0.353036 + 0.611476i
\(221\) −3192.00 + 5528.71i −0.971571 + 1.68281i
\(222\) 0 0
\(223\) −2072.00 −0.622204 −0.311102 0.950377i \(-0.600698\pi\)
−0.311102 + 0.950377i \(0.600698\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) −198.000 342.946i −0.0582777 0.100940i
\(227\) 183.000 316.965i 0.0535072 0.0926772i −0.838031 0.545622i \(-0.816293\pi\)
0.891538 + 0.452945i \(0.149627\pi\)
\(228\) 0 0
\(229\) −188.000 325.626i −0.0542506 0.0939648i 0.837625 0.546246i \(-0.183944\pi\)
−0.891875 + 0.452281i \(0.850610\pi\)
\(230\) 2880.00 0.825659
\(231\) 0 0
\(232\) −432.000 −0.122251
\(233\) −1131.00 1958.95i −0.318001 0.550794i 0.662070 0.749442i \(-0.269678\pi\)
−0.980071 + 0.198648i \(0.936345\pi\)
\(234\) 0 0
\(235\) −72.0000 + 124.708i −0.0199862 + 0.0346172i
\(236\) −276.000 478.046i −0.0761274 0.131857i
\(237\) 0 0
\(238\) 0 0
\(239\) −2592.00 −0.701517 −0.350758 0.936466i \(-0.614076\pi\)
−0.350758 + 0.936466i \(0.614076\pi\)
\(240\) 0 0
\(241\) 55.0000 95.2628i 0.0147007 0.0254623i −0.858581 0.512677i \(-0.828654\pi\)
0.873282 + 0.487215i \(0.161987\pi\)
\(242\) 973.000 1685.29i 0.258458 0.447662i
\(243\) 0 0
\(244\) −1520.00 −0.398803
\(245\) 0 0
\(246\) 0 0
\(247\) −56.0000 96.9948i −0.0144259 0.0249864i
\(248\) −944.000 + 1635.06i −0.241710 + 0.418654i
\(249\) 0 0
\(250\) 1272.00 + 2203.17i 0.321793 + 0.557362i
\(251\) −1890.00 −0.475282 −0.237641 0.971353i \(-0.576374\pi\)
−0.237641 + 0.971353i \(0.576374\pi\)
\(252\) 0 0
\(253\) −5760.00 −1.43134
\(254\) −376.000 651.251i −0.0928832 0.160878i
\(255\) 0 0
\(256\) −128.000 + 221.703i −0.0312500 + 0.0541266i
\(257\) −1065.00 1844.63i −0.258494 0.447724i 0.707345 0.706869i \(-0.249893\pi\)
−0.965839 + 0.259144i \(0.916559\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 2688.00 0.641164
\(261\) 0 0
\(262\) 2130.00 3689.27i 0.502259 0.869938i
\(263\) −2496.00 + 4323.20i −0.585209 + 1.01361i 0.409640 + 0.912247i \(0.365654\pi\)
−0.994849 + 0.101365i \(0.967679\pi\)
\(264\) 0 0
\(265\) 2088.00 0.484018
\(266\) 0 0
\(267\) 0 0
\(268\) 968.000 + 1676.63i 0.220634 + 0.382150i
\(269\) −3408.00 + 5902.83i −0.772451 + 1.33793i 0.163764 + 0.986499i \(0.447636\pi\)
−0.936216 + 0.351426i \(0.885697\pi\)
\(270\) 0 0
\(271\) 4096.00 + 7094.48i 0.918134 + 1.59025i 0.802247 + 0.596992i \(0.203638\pi\)
0.115887 + 0.993262i \(0.463029\pi\)
\(272\) −1824.00 −0.406604
\(273\) 0 0
\(274\) −156.000 −0.0343953
\(275\) 456.000 + 789.815i 0.0999921 + 0.173191i
\(276\) 0 0
\(277\) −1207.00 + 2090.59i −0.261811 + 0.453470i −0.966723 0.255825i \(-0.917653\pi\)
0.704912 + 0.709294i \(0.250986\pi\)
\(278\) 2338.00 + 4049.53i 0.504403 + 0.873651i
\(279\) 0 0
\(280\) 0 0
\(281\) −1962.00 −0.416524 −0.208262 0.978073i \(-0.566781\pi\)
−0.208262 + 0.978073i \(0.566781\pi\)
\(282\) 0 0
\(283\) 2701.00 4678.27i 0.567342 0.982665i −0.429486 0.903074i \(-0.641305\pi\)
0.996828 0.0795914i \(-0.0253616\pi\)
\(284\) 1152.00 1995.32i 0.240699 0.416904i
\(285\) 0 0
\(286\) −5376.00 −1.11150
\(287\) 0 0
\(288\) 0 0
\(289\) −4041.50 7000.08i −0.822613 1.42481i
\(290\) −648.000 + 1122.37i −0.131213 + 0.227268i
\(291\) 0 0
\(292\) −2300.00 3983.72i −0.460950 0.798388i
\(293\) −4788.00 −0.954669 −0.477334 0.878722i \(-0.658397\pi\)
−0.477334 + 0.878722i \(0.658397\pi\)
\(294\) 0 0
\(295\) −1656.00 −0.326834
\(296\) 584.000 + 1011.52i 0.114677 + 0.198626i
\(297\) 0 0
\(298\) 1002.00 1735.51i 0.194780 0.337368i
\(299\) 3360.00 + 5819.69i 0.649879 + 1.12562i
\(300\) 0 0
\(301\) 0 0
\(302\) 5504.00 1.04874
\(303\) 0 0
\(304\) 16.0000 27.7128i 0.00301863 0.00522842i
\(305\) −2280.00 + 3949.08i −0.428041 + 0.741388i
\(306\) 0 0
\(307\) 574.000 0.106710 0.0533549 0.998576i \(-0.483009\pi\)
0.0533549 + 0.998576i \(0.483009\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 2832.00 + 4905.17i 0.518861 + 0.898693i
\(311\) 4404.00 7627.95i 0.802984 1.39081i −0.114660 0.993405i \(-0.536578\pi\)
0.917644 0.397404i \(-0.130089\pi\)
\(312\) 0 0
\(313\) −1385.00 2398.89i −0.250111 0.433205i 0.713445 0.700711i \(-0.247134\pi\)
−0.963556 + 0.267506i \(0.913801\pi\)
\(314\) −1040.00 −0.186913
\(315\) 0 0
\(316\) 3104.00 0.552575
\(317\) 3783.00 + 6552.35i 0.670266 + 1.16094i 0.977828 + 0.209407i \(0.0671535\pi\)
−0.307562 + 0.951528i \(0.599513\pi\)
\(318\) 0 0
\(319\) 1296.00 2244.74i 0.227467 0.393985i
\(320\) 384.000 + 665.108i 0.0670820 + 0.116190i
\(321\) 0 0
\(322\) 0 0
\(323\) 228.000 0.0392763
\(324\) 0 0
\(325\) 532.000 921.451i 0.0908002 0.157270i
\(326\) 1280.00 2217.03i 0.217462 0.376655i
\(327\) 0 0
\(328\) −1008.00 −0.169687
\(329\) 0 0
\(330\) 0 0
\(331\) 5660.00 + 9803.41i 0.939884 + 1.62793i 0.765684 + 0.643217i \(0.222401\pi\)
0.174201 + 0.984710i \(0.444266\pi\)
\(332\) −756.000 + 1309.43i −0.124973 + 0.216459i
\(333\) 0 0
\(334\) 1764.00 + 3055.34i 0.288987 + 0.500541i
\(335\) 5808.00 0.947239
\(336\) 0 0
\(337\) −4786.00 −0.773620 −0.386810 0.922159i \(-0.626423\pi\)
−0.386810 + 0.922159i \(0.626423\pi\)
\(338\) 939.000 + 1626.40i 0.151109 + 0.261729i
\(339\) 0 0
\(340\) −2736.00 + 4738.89i −0.436413 + 0.755890i
\(341\) −5664.00 9810.34i −0.899480 1.55795i
\(342\) 0 0
\(343\) 0 0
\(344\) 3008.00 0.471455
\(345\) 0 0
\(346\) −768.000 + 1330.22i −0.119329 + 0.206684i
\(347\) 6324.00 10953.5i 0.978358 1.69457i 0.309980 0.950743i \(-0.399678\pi\)
0.668378 0.743822i \(-0.266989\pi\)
\(348\) 0 0
\(349\) −9632.00 −1.47733 −0.738666 0.674071i \(-0.764544\pi\)
−0.738666 + 0.674071i \(0.764544\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) −768.000 1330.22i −0.116291 0.201422i
\(353\) 1695.00 2935.83i 0.255569 0.442658i −0.709481 0.704724i \(-0.751071\pi\)
0.965050 + 0.262066i \(0.0844040\pi\)
\(354\) 0 0
\(355\) −3456.00 5985.97i −0.516691 0.894936i
\(356\) −1560.00 −0.232247
\(357\) 0 0
\(358\) 3624.00 0.535012
\(359\) −5352.00 9269.94i −0.786818 1.36281i −0.927907 0.372812i \(-0.878394\pi\)
0.141089 0.989997i \(-0.454940\pi\)
\(360\) 0 0
\(361\) 3427.50 5936.60i 0.499708 0.865520i
\(362\) 448.000 + 775.959i 0.0650452 + 0.112662i
\(363\) 0 0
\(364\) 0 0
\(365\) −13800.0 −1.97897
\(366\) 0 0
\(367\) −4292.00 + 7433.96i −0.610465 + 1.05736i 0.380697 + 0.924700i \(0.375684\pi\)
−0.991162 + 0.132656i \(0.957649\pi\)
\(368\) −960.000 + 1662.77i −0.135988 + 0.235538i
\(369\) 0 0
\(370\) 3504.00 0.492336
\(371\) 0 0
\(372\) 0 0
\(373\) 1061.00 + 1837.71i 0.147283 + 0.255101i 0.930222 0.366997i \(-0.119614\pi\)
−0.782939 + 0.622098i \(0.786281\pi\)
\(374\) 5472.00 9477.78i 0.756552 1.31039i
\(375\) 0 0
\(376\) −48.0000 83.1384i −0.00658354 0.0114030i
\(377\) −3024.00 −0.413114
\(378\) 0 0
\(379\) −4912.00 −0.665732 −0.332866 0.942974i \(-0.608016\pi\)
−0.332866 + 0.942974i \(0.608016\pi\)
\(380\) −48.0000 83.1384i −0.00647986 0.0112235i
\(381\) 0 0
\(382\) 2136.00 3699.66i 0.286092 0.495526i
\(383\) −4530.00 7846.19i −0.604366 1.04679i −0.992151 0.125043i \(-0.960093\pi\)
0.387785 0.921750i \(-0.373240\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) −8860.00 −1.16830
\(387\) 0 0
\(388\) −2660.00 + 4607.26i −0.348044 + 0.602830i
\(389\) 4497.00 7789.03i 0.586136 1.01522i −0.408597 0.912715i \(-0.633982\pi\)
0.994733 0.102502i \(-0.0326850\pi\)
\(390\) 0 0
\(391\) −13680.0 −1.76938
\(392\) 0 0
\(393\) 0 0
\(394\) −198.000 342.946i −0.0253175 0.0438512i
\(395\) 4656.00 8064.43i 0.593086 1.02725i
\(396\) 0 0
\(397\) −6488.00 11237.5i −0.820210 1.42065i −0.905526 0.424291i \(-0.860523\pi\)
0.0853156 0.996354i \(-0.472810\pi\)
\(398\) −4568.00 −0.575309
\(399\) 0 0
\(400\) 304.000 0.0380000
\(401\) −1761.00 3050.14i −0.219302 0.379842i 0.735293 0.677750i \(-0.237045\pi\)
−0.954595 + 0.297907i \(0.903711\pi\)
\(402\) 0 0
\(403\) −6608.00 + 11445.4i −0.816794 + 1.41473i
\(404\) 3000.00 + 5196.15i 0.369445 + 0.639897i
\(405\) 0 0
\(406\) 0 0
\(407\) −7008.00 −0.853498
\(408\) 0 0
\(409\) 6355.00 11007.2i 0.768300 1.33073i −0.170185 0.985412i \(-0.554436\pi\)
0.938484 0.345322i \(-0.112230\pi\)
\(410\) −1512.00 + 2618.86i −0.182128 + 0.315454i
\(411\) 0 0
\(412\) −1520.00 −0.181760
\(413\) 0 0
\(414\) 0 0
\(415\) 2268.00 + 3928.29i 0.268269 + 0.464656i
\(416\) −896.000 + 1551.92i −0.105601 + 0.182906i
\(417\) 0 0
\(418\) 96.0000 + 166.277i 0.0112333 + 0.0194566i
\(419\) 1638.00 0.190982 0.0954911 0.995430i \(-0.469558\pi\)
0.0954911 + 0.995430i \(0.469558\pi\)
\(420\) 0 0
\(421\) −12850.0 −1.48758 −0.743789 0.668414i \(-0.766973\pi\)
−0.743789 + 0.668414i \(0.766973\pi\)
\(422\) 4412.00 + 7641.81i 0.508940 + 0.881510i
\(423\) 0 0
\(424\) −696.000 + 1205.51i −0.0797187 + 0.138077i
\(425\) 1083.00 + 1875.81i 0.123608 + 0.214095i
\(426\) 0 0
\(427\) 0 0
\(428\) −2544.00 −0.287310
\(429\) 0 0
\(430\) 4512.00 7815.01i 0.506019 0.876450i
\(431\) −4008.00 + 6942.06i −0.447932 + 0.775840i −0.998251 0.0591136i \(-0.981173\pi\)
0.550320 + 0.834954i \(0.314506\pi\)
\(432\) 0 0
\(433\) −2198.00 −0.243947 −0.121974 0.992533i \(-0.538922\pi\)
−0.121974 + 0.992533i \(0.538922\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) −292.000 505.759i −0.0320740 0.0555538i
\(437\) 120.000 207.846i 0.0131359 0.0227520i
\(438\) 0 0
\(439\) −188.000 325.626i −0.0204391 0.0354015i 0.855625 0.517596i \(-0.173173\pi\)
−0.876064 + 0.482195i \(0.839840\pi\)
\(440\) −4608.00 −0.499268
\(441\) 0 0
\(442\) −12768.0 −1.37401
\(443\) 3594.00 + 6224.99i 0.385454 + 0.667626i 0.991832 0.127551i \(-0.0407115\pi\)
−0.606378 + 0.795176i \(0.707378\pi\)
\(444\) 0 0
\(445\) −2340.00 + 4053.00i −0.249273 + 0.431754i
\(446\) −2072.00 3588.81i −0.219982 0.381020i
\(447\) 0 0
\(448\) 0 0
\(449\) 14670.0 1.54192 0.770958 0.636886i \(-0.219778\pi\)
0.770958 + 0.636886i \(0.219778\pi\)
\(450\) 0 0
\(451\) 3024.00 5237.72i 0.315731 0.546862i
\(452\) 396.000 685.892i 0.0412086 0.0713753i
\(453\) 0 0
\(454\) 732.000 0.0756706
\(455\) 0 0
\(456\) 0 0
\(457\) 2573.00 + 4456.57i 0.263370 + 0.456169i 0.967135 0.254263i \(-0.0818328\pi\)
−0.703766 + 0.710432i \(0.748499\pi\)
\(458\) 376.000 651.251i 0.0383610 0.0664432i
\(459\) 0 0
\(460\) 2880.00 + 4988.31i 0.291915 + 0.505611i
\(461\) −1512.00 −0.152757 −0.0763784 0.997079i \(-0.524336\pi\)
−0.0763784 + 0.997079i \(0.524336\pi\)
\(462\) 0 0
\(463\) 7184.00 0.721099 0.360549 0.932740i \(-0.382589\pi\)
0.360549 + 0.932740i \(0.382589\pi\)
\(464\) −432.000 748.246i −0.0432222 0.0748630i
\(465\) 0 0
\(466\) 2262.00 3917.90i 0.224861 0.389470i
\(467\) 8259.00 + 14305.0i 0.818375 + 1.41747i 0.906879 + 0.421391i \(0.138458\pi\)
−0.0885046 + 0.996076i \(0.528209\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) −288.000 −0.0282648
\(471\) 0 0
\(472\) 552.000 956.092i 0.0538302 0.0932367i
\(473\) −9024.00 + 15630.0i −0.877218 + 1.51939i
\(474\) 0 0
\(475\) −38.0000 −0.00367065
\(476\) 0 0
\(477\) 0 0
\(478\) −2592.00 4489.48i −0.248024 0.429590i
\(479\) −5046.00 + 8739.93i −0.481331 + 0.833690i −0.999770 0.0214244i \(-0.993180\pi\)
0.518439 + 0.855114i \(0.326513\pi\)
\(480\) 0 0
\(481\) 4088.00 + 7080.62i 0.387519 + 0.671203i
\(482\) 220.000 0.0207899
\(483\) 0 0
\(484\) 3892.00 0.365515
\(485\) 7980.00 + 13821.8i 0.747120 + 1.29405i
\(486\) 0 0
\(487\) −3916.00 + 6782.71i −0.364376 + 0.631117i −0.988676 0.150068i \(-0.952051\pi\)
0.624300 + 0.781185i \(0.285384\pi\)
\(488\) −1520.00 2632.72i −0.140998 0.244216i
\(489\) 0 0
\(490\) 0 0
\(491\) 6732.00 0.618759 0.309380 0.950939i \(-0.399879\pi\)
0.309380 + 0.950939i \(0.399879\pi\)
\(492\) 0 0
\(493\) 3078.00 5331.25i 0.281189 0.487034i
\(494\) 112.000 193.990i 0.0102006 0.0176680i
\(495\) 0 0
\(496\) −3776.00 −0.341829
\(497\) 0 0
\(498\) 0 0
\(499\) −9334.00 16167.0i −0.837369 1.45037i −0.892087 0.451864i \(-0.850759\pi\)
0.0547176 0.998502i \(-0.482574\pi\)
\(500\) −2544.00 + 4406.34i −0.227542 + 0.394115i
\(501\) 0 0
\(502\) −1890.00 3273.58i −0.168038 0.291049i
\(503\) −6048.00 −0.536117 −0.268059 0.963403i \(-0.586382\pi\)
−0.268059 + 0.963403i \(0.586382\pi\)
\(504\) 0 0
\(505\) 18000.0 1.58612
\(506\) −5760.00 9976.61i −0.506054 0.876511i
\(507\) 0 0
\(508\) 752.000 1302.50i 0.0656784 0.113758i
\(509\) −5664.00 9810.34i −0.493227 0.854294i 0.506743 0.862097i \(-0.330849\pi\)
−0.999970 + 0.00780356i \(0.997516\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) −512.000 −0.0441942
\(513\) 0 0
\(514\) 2130.00 3689.27i 0.182783 0.316589i
\(515\) −2280.00 + 3949.08i −0.195085 + 0.337897i
\(516\) 0 0
\(517\) 576.000 0.0489989
\(518\) 0 0
\(519\) 0 0
\(520\) 2688.00 + 4655.75i 0.226686 + 0.392631i
\(521\) 2073.00 3590.54i 0.174318 0.301928i −0.765607 0.643309i \(-0.777561\pi\)
0.939925 + 0.341381i \(0.110895\pi\)
\(522\) 0 0
\(523\) −503.000 871.222i −0.0420548 0.0728410i 0.844232 0.535978i \(-0.180057\pi\)
−0.886287 + 0.463137i \(0.846724\pi\)
\(524\) 8520.00 0.710301
\(525\) 0 0
\(526\) −9984.00 −0.827610
\(527\) −13452.0 23299.5i −1.11191 1.92589i
\(528\) 0 0
\(529\) −1116.50 + 1933.83i −0.0917646 + 0.158941i
\(530\) 2088.00 + 3616.52i 0.171126 + 0.296399i
\(531\) 0 0
\(532\) 0 0
\(533\) −7056.00 −0.573413
\(534\) 0 0
\(535\) −3816.00 + 6609.51i −0.308374 + 0.534119i
\(536\) −1936.00 + 3353.25i −0.156012 + 0.270221i
\(537\) 0 0
\(538\) −13632.0 −1.09241
\(539\) 0 0
\(540\) 0 0
\(541\) 7361.00 + 12749.6i 0.584980 + 1.01321i 0.994878 + 0.101084i \(0.0322309\pi\)
−0.409898 + 0.912131i \(0.634436\pi\)
\(542\) −8192.00 + 14189.0i −0.649219 + 1.12448i
\(543\) 0 0
\(544\) −1824.00 3159.26i −0.143756 0.248993i
\(545\) −1752.00 −0.137702
\(546\) 0 0
\(547\) −13480.0 −1.05368 −0.526840 0.849964i \(-0.676623\pi\)
−0.526840 + 0.849964i \(0.676623\pi\)
\(548\) −156.000 270.200i −0.0121606 0.0210627i
\(549\) 0 0
\(550\) −912.000 + 1579.63i −0.0707051 + 0.122465i
\(551\) 54.0000 + 93.5307i 0.00417509 + 0.00723148i
\(552\) 0 0
\(553\) 0 0
\(554\) −4828.00 −0.370256
\(555\) 0 0
\(556\) −4676.00 + 8099.07i −0.356666 + 0.617764i
\(557\) 3111.00 5388.41i 0.236656 0.409900i −0.723097 0.690747i \(-0.757282\pi\)
0.959753 + 0.280847i \(0.0906153\pi\)
\(558\) 0 0
\(559\) 21056.0 1.59316
\(560\) 0 0
\(561\) 0 0
\(562\) −1962.00 3398.28i −0.147263 0.255068i
\(563\) −2463.00 + 4266.04i −0.184375 + 0.319347i −0.943366 0.331755i \(-0.892359\pi\)
0.758991 + 0.651101i \(0.225693\pi\)
\(564\) 0 0
\(565\) −1188.00 2057.68i −0.0884594 0.153216i
\(566\) 10804.0 0.802343
\(567\) 0 0
\(568\) 4608.00 0.340400
\(569\) 11091.0 + 19210.2i 0.817151 + 1.41535i 0.907773 + 0.419462i \(0.137781\pi\)
−0.0906221 + 0.995885i \(0.528886\pi\)
\(570\) 0 0
\(571\) −1648.00 + 2854.42i −0.120782 + 0.209201i −0.920076 0.391739i \(-0.871874\pi\)
0.799294 + 0.600940i \(0.205207\pi\)
\(572\) −5376.00 9311.51i −0.392975 0.680653i
\(573\) 0 0
\(574\) 0 0
\(575\) 2280.00 0.165361
\(576\) 0 0
\(577\) −12167.0 + 21073.9i −0.877849 + 1.52048i −0.0241523 + 0.999708i \(0.507689\pi\)
−0.853697 + 0.520771i \(0.825645\pi\)
\(578\) 8083.00 14000.2i 0.581676 1.00749i
\(579\) 0 0
\(580\) −2592.00 −0.185564
\(581\) 0 0
\(582\) 0 0
\(583\) −4176.00 7233.04i −0.296659 0.513829i
\(584\) 4600.00 7967.43i 0.325941 0.564546i
\(585\) 0 0
\(586\) −4788.00 8293.06i −0.337526 0.584613i
\(587\) 1638.00 0.115175 0.0575873 0.998340i \(-0.481659\pi\)
0.0575873 + 0.998340i \(0.481659\pi\)
\(588\) 0 0
\(589\) 472.000 0.0330194
\(590\) −1656.00 2868.28i −0.115553 0.200144i
\(591\) 0 0
\(592\) −1168.00 + 2023.04i −0.0810887 + 0.140450i
\(593\) 3723.00 + 6448.43i 0.257817 + 0.446552i 0.965657 0.259821i \(-0.0836636\pi\)
−0.707840 + 0.706373i \(0.750330\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 4008.00 0.275460
\(597\) 0 0
\(598\) −6720.00 + 11639.4i −0.459534 + 0.795936i
\(599\) −3252.00 + 5632.63i −0.221825 + 0.384212i −0.955362 0.295437i \(-0.904535\pi\)
0.733537 + 0.679649i \(0.237868\pi\)
\(600\) 0 0
\(601\) −16058.0 −1.08988 −0.544941 0.838474i \(-0.683448\pi\)
−0.544941 + 0.838474i \(0.683448\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 5504.00 + 9533.21i 0.370786 + 0.642220i
\(605\) 5838.00 10111.7i 0.392311 0.679503i
\(606\) 0 0
\(607\) 5104.00 + 8840.39i 0.341293 + 0.591137i 0.984673 0.174410i \(-0.0558018\pi\)
−0.643380 + 0.765547i \(0.722468\pi\)
\(608\) 64.0000 0.00426898
\(609\) 0 0
\(610\) −9120.00 −0.605341
\(611\) −336.000 581.969i −0.0222473 0.0385335i
\(612\) 0 0
\(613\) 7487.00 12967.9i 0.493307 0.854432i −0.506663 0.862144i \(-0.669121\pi\)
0.999970 + 0.00771145i \(0.00245465\pi\)
\(614\) 574.000 + 994.197i 0.0377276 + 0.0653461i
\(615\) 0 0
\(616\) 0 0
\(617\) −7254.00 −0.473314 −0.236657 0.971593i \(-0.576052\pi\)
−0.236657 + 0.971593i \(0.576052\pi\)
\(618\) 0 0
\(619\) 6229.00 10788.9i 0.404466 0.700556i −0.589793 0.807555i \(-0.700791\pi\)
0.994259 + 0.106998i \(0.0341240\pi\)
\(620\) −5664.00 + 9810.34i −0.366890 + 0.635472i
\(621\) 0 0
\(622\) 17616.0 1.13559
\(623\) 0 0
\(624\) 0 0
\(625\) 8819.50 + 15275.8i 0.564448 + 0.977653i
\(626\) 2770.00 4797.78i 0.176855 0.306322i
\(627\) 0 0
\(628\) −1040.00 1801.33i −0.0660836 0.114460i
\(629\) −16644.0 −1.05507
\(630\) 0 0
\(631\) 28352.0 1.78871 0.894354 0.447359i \(-0.147635\pi\)
0.894354 + 0.447359i \(0.147635\pi\)
\(632\) 3104.00 + 5376.29i 0.195365 + 0.338382i
\(633\) 0 0
\(634\) −7566.00 + 13104.7i −0.473950 + 0.820905i
\(635\) −2256.00 3907.51i −0.140987 0.244196i
\(636\) 0 0
\(637\) 0 0
\(638\) 5184.00 0.321687
\(639\) 0 0
\(640\) −768.000 + 1330.22i −0.0474342 + 0.0821584i
\(641\) 13695.0 23720.4i 0.843869 1.46162i −0.0427309 0.999087i \(-0.513606\pi\)
0.886600 0.462537i \(-0.153061\pi\)
\(642\) 0 0
\(643\) 21490.0 1.31801 0.659007 0.752137i \(-0.270977\pi\)
0.659007 + 0.752137i \(0.270977\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 228.000 + 394.908i 0.0138863 + 0.0240518i
\(647\) −8826.00 + 15287.1i −0.536300 + 0.928898i 0.462800 + 0.886463i \(0.346845\pi\)
−0.999099 + 0.0424353i \(0.986488\pi\)
\(648\) 0 0
\(649\) 3312.00 + 5736.55i 0.200320 + 0.346964i
\(650\) 2128.00 0.128411
\(651\) 0 0
\(652\) 5120.00 0.307538
\(653\) −2391.00 4141.33i −0.143288 0.248182i 0.785445 0.618932i \(-0.212434\pi\)
−0.928733 + 0.370749i \(0.879101\pi\)
\(654\) 0 0
\(655\) 12780.0 22135.6i 0.762375 1.32047i
\(656\) −1008.00 1745.91i −0.0599936 0.103912i
\(657\) 0 0
\(658\) 0 0
\(659\) 27144.0 1.60452 0.802261 0.596973i \(-0.203630\pi\)
0.802261 + 0.596973i \(0.203630\pi\)
\(660\) 0 0
\(661\) −5930.00 + 10271.1i −0.348941 + 0.604384i −0.986062 0.166380i \(-0.946792\pi\)
0.637120 + 0.770764i \(0.280125\pi\)
\(662\) −11320.0 + 19606.8i −0.664599 + 1.15112i
\(663\) 0 0
\(664\) −3024.00 −0.176738
\(665\) 0 0
\(666\) 0 0
\(667\) −3240.00 5611.84i −0.188086 0.325774i
\(668\) −3528.00 + 6110.68i −0.204345 + 0.353936i
\(669\) 0 0
\(670\) 5808.00 + 10059.8i 0.334899 + 0.580063i
\(671\) 18240.0 1.04940
\(672\) 0 0
\(673\) 5546.00 0.317656 0.158828 0.987306i \(-0.449228\pi\)
0.158828 + 0.987306i \(0.449228\pi\)
\(674\) −4786.00 8289.60i −0.273516 0.473744i
\(675\) 0 0
\(676\) −1878.00 + 3252.79i −0.106850 + 0.185070i
\(677\) 7440.00 + 12886.5i 0.422367 + 0.731561i 0.996170 0.0874320i \(-0.0278660\pi\)
−0.573804 + 0.818993i \(0.694533\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) −10944.0 −0.617181
\(681\) 0 0
\(682\) 11328.0 19620.7i 0.636029 1.10163i
\(683\) 10482.0 18155.4i 0.587237 1.01712i −0.407356 0.913269i \(-0.633549\pi\)
0.994593 0.103854i \(-0.0331175\pi\)
\(684\) 0 0
\(685\) −936.000 −0.0522084
\(686\) 0 0
\(687\) 0 0
\(688\) 3008.00 + 5210.01i 0.166684 + 0.288706i
\(689\) −4872.00 + 8438.55i −0.269388 + 0.466594i
\(690\) 0 0
\(691\) 6553.00 + 11350.1i 0.360764 + 0.624861i 0.988087 0.153898i \(-0.0491827\pi\)
−0.627323 + 0.778759i \(0.715849\pi\)
\(692\) −3072.00 −0.168757
\(693\) 0 0
\(694\) 25296.0 1.38361
\(695\) 14028.0 + 24297.2i 0.765629 + 1.32611i
\(696\) 0 0
\(697\) 7182.00 12439.6i 0.390298 0.676016i
\(698\) −9632.00 16683.1i −0.522316 0.904678i
\(699\) 0 0
\(700\) 0 0
\(701\) 4590.00 0.247307 0.123653 0.992325i \(-0.460539\pi\)
0.123653 + 0.992325i \(0.460539\pi\)
\(702\) 0 0
\(703\) 146.000 252.879i 0.00783285 0.0135669i
\(704\) 1536.00 2660.43i 0.0822304 0.142427i
\(705\) 0 0
\(706\) 6780.00 0.361429
\(707\) 0 0
\(708\) 0 0
\(709\) 431.000 + 746.514i 0.0228301 + 0.0395429i 0.877215 0.480098i \(-0.159399\pi\)
−0.854385 + 0.519641i \(0.826066\pi\)
\(710\) 6912.00 11971.9i 0.365356 0.632815i
\(711\) 0 0
\(712\) −1560.00 2702.00i −0.0821116 0.142221i
\(713\) −28320.0 −1.48751
\(714\) 0 0
\(715\) −32256.0 −1.68714
\(716\) 3624.00 + 6276.95i 0.189155 + 0.327627i
\(717\) 0 0
\(718\) 10704.0 18539.9i 0.556365 0.963652i
\(719\) 1770.00 + 3065.73i 0.0918079 + 0.159016i 0.908272 0.418380i \(-0.137402\pi\)
−0.816464 + 0.577396i \(0.804069\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 13710.0 0.706694
\(723\) 0 0
\(724\) −896.000 + 1551.92i −0.0459939 + 0.0796638i
\(725\) −513.000 + 888.542i −0.0262791 + 0.0455167i
\(726\) 0 0
\(727\) 4228.00 0.215692 0.107846 0.994168i \(-0.465605\pi\)
0.107846 + 0.994168i \(0.465605\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) −13800.0 23902.3i −0.699672 1.21187i
\(731\) −21432.0 + 37121.3i −1.08439 + 1.87822i
\(732\) 0 0
\(733\) 2710.00 + 4693.86i 0.136557 + 0.236523i 0.926191 0.377054i \(-0.123063\pi\)
−0.789634 + 0.613578i \(0.789730\pi\)
\(734\) −17168.0 −0.863328
\(735\) 0 0
\(736\) −3840.00 −0.192316
\(737\) −11616.0 20119.5i −0.580571 1.00558i
\(738\) 0 0
\(739\) −640.000 + 1108.51i −0.0318576 + 0.0551790i −0.881515 0.472157i \(-0.843476\pi\)
0.849657 + 0.527336i \(0.176809\pi\)
\(740\) 3504.00 + 6069.11i 0.174067 + 0.301493i
\(741\) 0 0
\(742\) 0 0
\(743\) 35712.0 1.76332 0.881660 0.471886i \(-0.156427\pi\)
0.881660 + 0.471886i \(0.156427\pi\)
\(744\) 0 0
\(745\) 6012.00 10413.1i 0.295655 0.512089i
\(746\) −2122.00 + 3675.41i −0.104145 + 0.180384i
\(747\) 0 0
\(748\) 21888.0 1.06993
\(749\) 0 0
\(750\) 0 0
\(751\) −12232.0 21186.4i −0.594344 1.02943i −0.993639 0.112611i \(-0.964079\pi\)
0.399296 0.916822i \(-0.369255\pi\)
\(752\) 96.0000 166.277i 0.00465527 0.00806316i
\(753\) 0 0
\(754\) −3024.00 5237.72i −0.146058 0.252980i
\(755\) 33024.0 1.59188
\(756\) 0 0
\(757\) 30242.0 1.45200 0.726000 0.687695i \(-0.241377\pi\)
0.726000 + 0.687695i \(0.241377\pi\)
\(758\) −4912.00 8507.83i −0.235372 0.407676i
\(759\) 0 0
\(760\) 96.0000 166.277i 0.00458196 0.00793618i
\(761\) 1077.00 + 1865.42i 0.0513025 + 0.0888586i 0.890536 0.454912i \(-0.150329\pi\)
−0.839234 + 0.543771i \(0.816996\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 8544.00 0.404596
\(765\) 0 0
\(766\) 9060.00 15692.4i 0.427351 0.740194i
\(767\) 3864.00 6692.64i 0.181905 0.315068i
\(768\) 0 0
\(769\) −10262.0 −0.481219 −0.240609 0.970622i \(-0.577347\pi\)
−0.240609 + 0.970622i \(0.577347\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −8860.00 15346.0i −0.413055 0.715432i
\(773\) −4542.00 + 7866.97i −0.211338 + 0.366048i −0.952134 0.305682i \(-0.901115\pi\)
0.740795 + 0.671731i \(0.234449\pi\)
\(774\) 0 0
\(775\) 2242.00 + 3883.26i 0.103916 + 0.179988i
\(776\) −10640.0 −0.492208
\(777\) 0 0
\(778\) 17988.0 0.828922
\(779\) 126.000 + 218.238i 0.00579515 + 0.0100375i
\(780\) 0 0
\(781\) −13824.0 + 23943.9i −0.633370 + 1.09703i
\(782\) −13680.0 23694.5i −0.625570 1.08352i
\(783\) 0 0
\(784\) 0 0
\(785\) −6240.00 −0.283714
\(786\) 0 0
\(787\) −9899.00 + 17145.6i −0.448362 + 0.776587i −0.998280 0.0586327i \(-0.981326\pi\)
0.549917 + 0.835219i \(0.314659\pi\)
\(788\) 396.000 685.892i 0.0179022 0.0310075i
\(789\) 0 0
\(790\) 18624.0 0.838750