Properties

Label 882.4.g.be.361.2
Level $882$
Weight $4$
Character 882.361
Analytic conductor $52.040$
Analytic rank $0$
Dimension $4$
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: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\sqrt{2}, \sqrt{-3})\)
Defining polynomial: \(x^{4} + 2 x^{2} + 4\)
Coefficient ring: \(\Z[a_1, \ldots, a_{25}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 294)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 361.2
Root \(0.707107 - 1.22474i\) of defining polynomial
Character \(\chi\) \(=\) 882.361
Dual form 882.4.g.be.667.2

$q$-expansion

\(f(q)\) \(=\) \(q+(1.00000 + 1.73205i) q^{2} +(-2.00000 + 3.46410i) q^{4} +(-2.29289 - 3.97141i) q^{5} -8.00000 q^{8} +O(q^{10})\) \(q+(1.00000 + 1.73205i) q^{2} +(-2.00000 + 3.46410i) q^{4} +(-2.29289 - 3.97141i) q^{5} -8.00000 q^{8} +(4.58579 - 7.94282i) q^{10} +(-3.24264 + 5.61642i) q^{11} -45.2132 q^{13} +(-8.00000 - 13.8564i) q^{16} +(-40.7782 + 70.6299i) q^{17} +(-2.52691 - 4.37674i) q^{19} +18.3431 q^{20} -12.9706 q^{22} +(53.1249 + 92.0150i) q^{23} +(51.9853 - 90.0411i) q^{25} +(-45.2132 - 78.3116i) q^{26} +268.132 q^{29} +(146.184 - 253.198i) q^{31} +(16.0000 - 27.7128i) q^{32} -163.113 q^{34} +(-57.2792 - 99.2105i) q^{37} +(5.05382 - 8.75348i) q^{38} +(18.3431 + 31.7713i) q^{40} -161.605 q^{41} -471.294 q^{43} +(-12.9706 - 22.4657i) q^{44} +(-106.250 + 184.030i) q^{46} +(-173.002 - 299.648i) q^{47} +207.941 q^{50} +(90.4264 - 156.623i) q^{52} +(202.765 - 351.198i) q^{53} +29.7401 q^{55} +(268.132 + 464.418i) q^{58} +(126.718 - 219.482i) q^{59} +(-375.609 - 650.573i) q^{61} +584.735 q^{62} +64.0000 q^{64} +(103.669 + 179.560i) q^{65} +(-5.82338 + 10.0864i) q^{67} +(-163.113 - 282.519i) q^{68} +681.661 q^{71} +(342.729 - 593.623i) q^{73} +(114.558 - 198.421i) q^{74} +20.2153 q^{76} +(-0.132034 - 0.228690i) q^{79} +(-36.6863 + 63.5425i) q^{80} +(-161.605 - 279.908i) q^{82} -437.137 q^{83} +374.000 q^{85} +(-471.294 - 816.304i) q^{86} +(25.9411 - 44.9313i) q^{88} +(29.2563 + 50.6734i) q^{89} -424.999 q^{92} +(346.004 - 599.297i) q^{94} +(-11.5879 + 20.0708i) q^{95} +1280.09 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q + 4q^{2} - 8q^{4} - 12q^{5} - 32q^{8} + O(q^{10}) \) \( 4q + 4q^{2} - 8q^{4} - 12q^{5} - 32q^{8} + 24q^{10} + 4q^{11} - 96q^{13} - 32q^{16} - 132q^{17} + 120q^{19} + 96q^{20} + 16q^{22} - 76q^{23} + 174q^{25} - 96q^{26} + 224q^{29} + 432q^{31} + 64q^{32} - 528q^{34} + 280q^{37} - 240q^{38} + 96q^{40} + 72q^{41} - 256q^{43} + 16q^{44} + 152q^{46} + 264q^{47} + 696q^{50} + 192q^{52} + 268q^{53} - 96q^{55} + 224q^{58} - 336q^{59} - 504q^{61} + 1728q^{62} + 256q^{64} + 228q^{65} + 384q^{67} - 528q^{68} + 792q^{71} - 312q^{73} - 560q^{74} - 960q^{76} + 848q^{79} - 192q^{80} + 72q^{82} - 1296q^{83} + 1496q^{85} - 256q^{86} - 32q^{88} + 612q^{89} + 608q^{92} - 528q^{94} + 904q^{95} + 4368q^{97} + O(q^{100}) \)

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
\(5\) −2.29289 3.97141i −0.205083 0.355213i 0.745076 0.666979i \(-0.232413\pi\)
−0.950159 + 0.311766i \(0.899080\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) −8.00000 −0.353553
\(9\) 0 0
\(10\) 4.58579 7.94282i 0.145015 0.251174i
\(11\) −3.24264 + 5.61642i −0.0888812 + 0.153947i −0.907038 0.421048i \(-0.861662\pi\)
0.818157 + 0.574994i \(0.194996\pi\)
\(12\) 0 0
\(13\) −45.2132 −0.964607 −0.482303 0.876004i \(-0.660200\pi\)
−0.482303 + 0.876004i \(0.660200\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) −8.00000 13.8564i −0.125000 0.216506i
\(17\) −40.7782 + 70.6299i −0.581774 + 1.00766i 0.413495 + 0.910506i \(0.364308\pi\)
−0.995269 + 0.0971560i \(0.969025\pi\)
\(18\) 0 0
\(19\) −2.52691 4.37674i −0.0305112 0.0528470i 0.850367 0.526191i \(-0.176380\pi\)
−0.880878 + 0.473344i \(0.843047\pi\)
\(20\) 18.3431 0.205083
\(21\) 0 0
\(22\) −12.9706 −0.125697
\(23\) 53.1249 + 92.0150i 0.481622 + 0.834194i 0.999778 0.0210927i \(-0.00671450\pi\)
−0.518156 + 0.855286i \(0.673381\pi\)
\(24\) 0 0
\(25\) 51.9853 90.0411i 0.415882 0.720329i
\(26\) −45.2132 78.3116i −0.341040 0.590699i
\(27\) 0 0
\(28\) 0 0
\(29\) 268.132 1.71693 0.858463 0.512875i \(-0.171420\pi\)
0.858463 + 0.512875i \(0.171420\pi\)
\(30\) 0 0
\(31\) 146.184 253.198i 0.846948 1.46696i −0.0369712 0.999316i \(-0.511771\pi\)
0.883919 0.467640i \(-0.154896\pi\)
\(32\) 16.0000 27.7128i 0.0883883 0.153093i
\(33\) 0 0
\(34\) −163.113 −0.822753
\(35\) 0 0
\(36\) 0 0
\(37\) −57.2792 99.2105i −0.254504 0.440814i 0.710257 0.703943i \(-0.248579\pi\)
−0.964761 + 0.263129i \(0.915246\pi\)
\(38\) 5.05382 8.75348i 0.0215747 0.0373685i
\(39\) 0 0
\(40\) 18.3431 + 31.7713i 0.0725077 + 0.125587i
\(41\) −161.605 −0.615573 −0.307786 0.951456i \(-0.599588\pi\)
−0.307786 + 0.951456i \(0.599588\pi\)
\(42\) 0 0
\(43\) −471.294 −1.67143 −0.835716 0.549162i \(-0.814947\pi\)
−0.835716 + 0.549162i \(0.814947\pi\)
\(44\) −12.9706 22.4657i −0.0444406 0.0769734i
\(45\) 0 0
\(46\) −106.250 + 184.030i −0.340558 + 0.589864i
\(47\) −173.002 299.648i −0.536914 0.929962i −0.999068 0.0431624i \(-0.986257\pi\)
0.462154 0.886800i \(-0.347077\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 207.941 0.588146
\(51\) 0 0
\(52\) 90.4264 156.623i 0.241152 0.417687i
\(53\) 202.765 351.198i 0.525507 0.910204i −0.474052 0.880497i \(-0.657209\pi\)
0.999559 0.0297072i \(-0.00945750\pi\)
\(54\) 0 0
\(55\) 29.7401 0.0729119
\(56\) 0 0
\(57\) 0 0
\(58\) 268.132 + 464.418i 0.607025 + 1.05140i
\(59\) 126.718 219.482i 0.279614 0.484307i −0.691674 0.722209i \(-0.743127\pi\)
0.971289 + 0.237903i \(0.0764600\pi\)
\(60\) 0 0
\(61\) −375.609 650.573i −0.788390 1.36553i −0.926953 0.375177i \(-0.877582\pi\)
0.138563 0.990354i \(-0.455752\pi\)
\(62\) 584.735 1.19776
\(63\) 0 0
\(64\) 64.0000 0.125000
\(65\) 103.669 + 179.560i 0.197824 + 0.342641i
\(66\) 0 0
\(67\) −5.82338 + 10.0864i −0.0106185 + 0.0183918i −0.871286 0.490776i \(-0.836713\pi\)
0.860667 + 0.509168i \(0.170047\pi\)
\(68\) −163.113 282.519i −0.290887 0.503831i
\(69\) 0 0
\(70\) 0 0
\(71\) 681.661 1.13941 0.569706 0.821848i \(-0.307057\pi\)
0.569706 + 0.821848i \(0.307057\pi\)
\(72\) 0 0
\(73\) 342.729 593.623i 0.549498 0.951758i −0.448811 0.893627i \(-0.648152\pi\)
0.998309 0.0581315i \(-0.0185143\pi\)
\(74\) 114.558 198.421i 0.179961 0.311702i
\(75\) 0 0
\(76\) 20.2153 0.0305112
\(77\) 0 0
\(78\) 0 0
\(79\) −0.132034 0.228690i −0.000188038 0.000325692i 0.865931 0.500163i \(-0.166727\pi\)
−0.866119 + 0.499837i \(0.833393\pi\)
\(80\) −36.6863 + 63.5425i −0.0512707 + 0.0888034i
\(81\) 0 0
\(82\) −161.605 279.908i −0.217638 0.376960i
\(83\) −437.137 −0.578097 −0.289048 0.957314i \(-0.593339\pi\)
−0.289048 + 0.957314i \(0.593339\pi\)
\(84\) 0 0
\(85\) 374.000 0.477247
\(86\) −471.294 816.304i −0.590941 1.02354i
\(87\) 0 0
\(88\) 25.9411 44.9313i 0.0314242 0.0544284i
\(89\) 29.2563 + 50.6734i 0.0348445 + 0.0603525i 0.882922 0.469520i \(-0.155573\pi\)
−0.848077 + 0.529873i \(0.822240\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) −424.999 −0.481622
\(93\) 0 0
\(94\) 346.004 599.297i 0.379655 0.657582i
\(95\) −11.5879 + 20.0708i −0.0125146 + 0.0216760i
\(96\) 0 0
\(97\) 1280.09 1.33993 0.669966 0.742391i \(-0.266308\pi\)
0.669966 + 0.742391i \(0.266308\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 207.941 + 360.165i 0.207941 + 0.360165i
\(101\) 653.194 1131.37i 0.643518 1.11461i −0.341124 0.940018i \(-0.610808\pi\)
0.984642 0.174587i \(-0.0558590\pi\)
\(102\) 0 0
\(103\) −379.487 657.291i −0.363029 0.628785i 0.625429 0.780281i \(-0.284924\pi\)
−0.988458 + 0.151496i \(0.951591\pi\)
\(104\) 361.706 0.341040
\(105\) 0 0
\(106\) 811.058 0.743178
\(107\) 631.257 + 1093.37i 0.570336 + 0.987850i 0.996531 + 0.0832192i \(0.0265202\pi\)
−0.426196 + 0.904631i \(0.640146\pi\)
\(108\) 0 0
\(109\) 1052.76 1823.44i 0.925105 1.60233i 0.133713 0.991020i \(-0.457310\pi\)
0.791392 0.611309i \(-0.209357\pi\)
\(110\) 29.7401 + 51.5114i 0.0257783 + 0.0446493i
\(111\) 0 0
\(112\) 0 0
\(113\) −1535.76 −1.27852 −0.639258 0.768992i \(-0.720759\pi\)
−0.639258 + 0.768992i \(0.720759\pi\)
\(114\) 0 0
\(115\) 243.619 421.961i 0.197545 0.342157i
\(116\) −536.264 + 928.837i −0.429232 + 0.743451i
\(117\) 0 0
\(118\) 506.871 0.395435
\(119\) 0 0
\(120\) 0 0
\(121\) 644.471 + 1116.26i 0.484200 + 0.838659i
\(122\) 751.217 1301.15i 0.557476 0.965576i
\(123\) 0 0
\(124\) 584.735 + 1012.79i 0.423474 + 0.733478i
\(125\) −1050.01 −0.751326
\(126\) 0 0
\(127\) 24.1749 0.0168911 0.00844557 0.999964i \(-0.497312\pi\)
0.00844557 + 0.999964i \(0.497312\pi\)
\(128\) 64.0000 + 110.851i 0.0441942 + 0.0765466i
\(129\) 0 0
\(130\) −207.338 + 359.120i −0.139883 + 0.242284i
\(131\) −790.764 1369.64i −0.527400 0.913483i −0.999490 0.0319327i \(-0.989834\pi\)
0.472090 0.881550i \(-0.343500\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) −23.2935 −0.0150168
\(135\) 0 0
\(136\) 326.225 565.039i 0.205688 0.356262i
\(137\) −372.594 + 645.352i −0.232357 + 0.402454i −0.958501 0.285089i \(-0.907977\pi\)
0.726144 + 0.687542i \(0.241310\pi\)
\(138\) 0 0
\(139\) 1373.60 0.838179 0.419090 0.907945i \(-0.362349\pi\)
0.419090 + 0.907945i \(0.362349\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 681.661 + 1180.67i 0.402843 + 0.697745i
\(143\) 146.610 253.936i 0.0857354 0.148498i
\(144\) 0 0
\(145\) −614.798 1064.86i −0.352112 0.609875i
\(146\) 1370.91 0.777107
\(147\) 0 0
\(148\) 458.234 0.254504
\(149\) 310.265 + 537.395i 0.170590 + 0.295470i 0.938626 0.344936i \(-0.112099\pi\)
−0.768036 + 0.640406i \(0.778766\pi\)
\(150\) 0 0
\(151\) 969.632 1679.45i 0.522567 0.905112i −0.477089 0.878855i \(-0.658308\pi\)
0.999655 0.0262568i \(-0.00835877\pi\)
\(152\) 20.2153 + 35.0139i 0.0107873 + 0.0186842i
\(153\) 0 0
\(154\) 0 0
\(155\) −1340.74 −0.694777
\(156\) 0 0
\(157\) −206.422 + 357.533i −0.104931 + 0.181747i −0.913710 0.406366i \(-0.866796\pi\)
0.808779 + 0.588113i \(0.200129\pi\)
\(158\) 0.264069 0.457380i 0.000132963 0.000230299i
\(159\) 0 0
\(160\) −146.745 −0.0725077
\(161\) 0 0
\(162\) 0 0
\(163\) 1953.72 + 3383.94i 0.938817 + 1.62608i 0.767682 + 0.640831i \(0.221410\pi\)
0.171135 + 0.985248i \(0.445257\pi\)
\(164\) 323.210 559.817i 0.153893 0.266551i
\(165\) 0 0
\(166\) −437.137 757.144i −0.204388 0.354011i
\(167\) −1286.41 −0.596082 −0.298041 0.954553i \(-0.596333\pi\)
−0.298041 + 0.954553i \(0.596333\pi\)
\(168\) 0 0
\(169\) −152.766 −0.0695340
\(170\) 374.000 + 647.787i 0.168732 + 0.292253i
\(171\) 0 0
\(172\) 942.587 1632.61i 0.417858 0.723751i
\(173\) 625.628 + 1083.62i 0.274946 + 0.476220i 0.970121 0.242620i \(-0.0780068\pi\)
−0.695176 + 0.718840i \(0.744673\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 103.765 0.0444406
\(177\) 0 0
\(178\) −58.5126 + 101.347i −0.0246388 + 0.0426757i
\(179\) 1811.76 3138.05i 0.756520 1.31033i −0.188095 0.982151i \(-0.560231\pi\)
0.944615 0.328180i \(-0.106435\pi\)
\(180\) 0 0
\(181\) −181.727 −0.0746280 −0.0373140 0.999304i \(-0.511880\pi\)
−0.0373140 + 0.999304i \(0.511880\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) −424.999 736.120i −0.170279 0.294932i
\(185\) −262.670 + 454.958i −0.104389 + 0.180806i
\(186\) 0 0
\(187\) −264.458 458.055i −0.103418 0.179124i
\(188\) 1384.02 0.536914
\(189\) 0 0
\(190\) −46.3515 −0.0176984
\(191\) 740.640 + 1282.83i 0.280580 + 0.485979i 0.971528 0.236926i \(-0.0761398\pi\)
−0.690948 + 0.722905i \(0.742806\pi\)
\(192\) 0 0
\(193\) 178.354 308.918i 0.0665192 0.115215i −0.830848 0.556500i \(-0.812144\pi\)
0.897367 + 0.441285i \(0.145477\pi\)
\(194\) 1280.09 + 2217.18i 0.473738 + 0.820538i
\(195\) 0 0
\(196\) 0 0
\(197\) −4890.53 −1.76871 −0.884355 0.466816i \(-0.845401\pi\)
−0.884355 + 0.466816i \(0.845401\pi\)
\(198\) 0 0
\(199\) 1771.43 3068.20i 0.631020 1.09296i −0.356323 0.934363i \(-0.615970\pi\)
0.987344 0.158596i \(-0.0506969\pi\)
\(200\) −415.882 + 720.329i −0.147037 + 0.254675i
\(201\) 0 0
\(202\) 2612.78 0.910071
\(203\) 0 0
\(204\) 0 0
\(205\) 370.543 + 641.800i 0.126243 + 0.218660i
\(206\) 758.975 1314.58i 0.256700 0.444618i
\(207\) 0 0
\(208\) 361.706 + 626.493i 0.120576 + 0.208843i
\(209\) 32.7755 0.0108475
\(210\) 0 0
\(211\) −4289.50 −1.39953 −0.699765 0.714373i \(-0.746712\pi\)
−0.699765 + 0.714373i \(0.746712\pi\)
\(212\) 811.058 + 1404.79i 0.262753 + 0.455102i
\(213\) 0 0
\(214\) −1262.51 + 2186.74i −0.403288 + 0.698516i
\(215\) 1080.63 + 1871.70i 0.342782 + 0.593715i
\(216\) 0 0
\(217\) 0 0
\(218\) 4211.05 1.30830
\(219\) 0 0
\(220\) −59.4802 + 103.023i −0.0182280 + 0.0315718i
\(221\) 1843.71 3193.40i 0.561183 0.971998i
\(222\) 0 0
\(223\) −5795.73 −1.74041 −0.870204 0.492692i \(-0.836013\pi\)
−0.870204 + 0.492692i \(0.836013\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) −1535.76 2660.02i −0.452024 0.782929i
\(227\) −2052.02 + 3554.21i −0.599989 + 1.03921i 0.392833 + 0.919610i \(0.371495\pi\)
−0.992822 + 0.119601i \(0.961838\pi\)
\(228\) 0 0
\(229\) −648.416 1123.09i −0.187111 0.324086i 0.757175 0.653213i \(-0.226579\pi\)
−0.944286 + 0.329126i \(0.893246\pi\)
\(230\) 974.478 0.279370
\(231\) 0 0
\(232\) −2145.06 −0.607025
\(233\) −739.167 1280.27i −0.207830 0.359972i 0.743201 0.669069i \(-0.233307\pi\)
−0.951031 + 0.309096i \(0.899973\pi\)
\(234\) 0 0
\(235\) −793.351 + 1374.12i −0.220223 + 0.381438i
\(236\) 506.871 + 877.927i 0.139807 + 0.242153i
\(237\) 0 0
\(238\) 0 0
\(239\) 3776.92 1.02221 0.511106 0.859518i \(-0.329236\pi\)
0.511106 + 0.859518i \(0.329236\pi\)
\(240\) 0 0
\(241\) −1998.19 + 3460.97i −0.534086 + 0.925065i 0.465121 + 0.885247i \(0.346011\pi\)
−0.999207 + 0.0398173i \(0.987322\pi\)
\(242\) −1288.94 + 2232.51i −0.342381 + 0.593022i
\(243\) 0 0
\(244\) 3004.87 0.788390
\(245\) 0 0
\(246\) 0 0
\(247\) 114.250 + 197.886i 0.0294313 + 0.0509766i
\(248\) −1169.47 + 2025.58i −0.299441 + 0.518647i
\(249\) 0 0
\(250\) −1050.01 1818.67i −0.265634 0.460091i
\(251\) 5423.58 1.36388 0.681939 0.731409i \(-0.261137\pi\)
0.681939 + 0.731409i \(0.261137\pi\)
\(252\) 0 0
\(253\) −689.060 −0.171229
\(254\) 24.1749 + 41.8721i 0.00597192 + 0.0103437i
\(255\) 0 0
\(256\) −128.000 + 221.703i −0.0312500 + 0.0541266i
\(257\) −2982.11 5165.17i −0.723809 1.25367i −0.959462 0.281837i \(-0.909056\pi\)
0.235653 0.971837i \(-0.424277\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) −829.352 −0.197824
\(261\) 0 0
\(262\) 1581.53 2739.29i 0.372928 0.645930i
\(263\) 2583.00 4473.89i 0.605608 1.04894i −0.386347 0.922353i \(-0.626263\pi\)
0.991955 0.126590i \(-0.0404033\pi\)
\(264\) 0 0
\(265\) −1859.67 −0.431089
\(266\) 0 0
\(267\) 0 0
\(268\) −23.2935 40.3455i −0.00530924 0.00919588i
\(269\) −1941.65 + 3363.03i −0.440090 + 0.762259i −0.997696 0.0678474i \(-0.978387\pi\)
0.557605 + 0.830106i \(0.311720\pi\)
\(270\) 0 0
\(271\) 2763.83 + 4787.09i 0.619522 + 1.07304i 0.989573 + 0.144032i \(0.0460069\pi\)
−0.370051 + 0.929011i \(0.620660\pi\)
\(272\) 1304.90 0.290887
\(273\) 0 0
\(274\) −1490.38 −0.328602
\(275\) 337.139 + 583.942i 0.0739282 + 0.128047i
\(276\) 0 0
\(277\) −1134.06 + 1964.25i −0.245989 + 0.426066i −0.962409 0.271603i \(-0.912446\pi\)
0.716420 + 0.697669i \(0.245779\pi\)
\(278\) 1373.60 + 2379.14i 0.296341 + 0.513278i
\(279\) 0 0
\(280\) 0 0
\(281\) −725.656 −0.154053 −0.0770267 0.997029i \(-0.524543\pi\)
−0.0770267 + 0.997029i \(0.524543\pi\)
\(282\) 0 0
\(283\) 2118.50 3669.35i 0.444988 0.770742i −0.553063 0.833139i \(-0.686541\pi\)
0.998051 + 0.0623972i \(0.0198745\pi\)
\(284\) −1363.32 + 2361.34i −0.284853 + 0.493380i
\(285\) 0 0
\(286\) 586.441 0.121248
\(287\) 0 0
\(288\) 0 0
\(289\) −869.219 1505.53i −0.176922 0.306438i
\(290\) 1229.60 2129.72i 0.248981 0.431247i
\(291\) 0 0
\(292\) 1370.91 + 2374.49i 0.274749 + 0.475879i
\(293\) −4373.78 −0.872079 −0.436039 0.899928i \(-0.643619\pi\)
−0.436039 + 0.899928i \(0.643619\pi\)
\(294\) 0 0
\(295\) −1162.20 −0.229376
\(296\) 458.234 + 793.684i 0.0899807 + 0.155851i
\(297\) 0 0
\(298\) −620.530 + 1074.79i −0.120625 + 0.208929i
\(299\) −2401.95 4160.29i −0.464576 0.804669i
\(300\) 0 0
\(301\) 0 0
\(302\) 3878.53 0.739021
\(303\) 0 0
\(304\) −40.4306 + 70.0278i −0.00762781 + 0.0132117i
\(305\) −1722.46 + 2983.39i −0.323370 + 0.560093i
\(306\) 0 0
\(307\) −4133.47 −0.768435 −0.384217 0.923243i \(-0.625529\pi\)
−0.384217 + 0.923243i \(0.625529\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) −1340.74 2322.22i −0.245641 0.425462i
\(311\) −2531.62 + 4384.89i −0.461591 + 0.799499i −0.999040 0.0437972i \(-0.986054\pi\)
0.537450 + 0.843296i \(0.319388\pi\)
\(312\) 0 0
\(313\) 3705.78 + 6418.60i 0.669211 + 1.15911i 0.978125 + 0.208017i \(0.0667011\pi\)
−0.308914 + 0.951090i \(0.599966\pi\)
\(314\) −825.686 −0.148395
\(315\) 0 0
\(316\) 1.05627 0.000188038
\(317\) −3368.53 5834.46i −0.596831 1.03374i −0.993286 0.115687i \(-0.963093\pi\)
0.396455 0.918054i \(-0.370240\pi\)
\(318\) 0 0
\(319\) −869.456 + 1505.94i −0.152602 + 0.264315i
\(320\) −146.745 254.170i −0.0256353 0.0444017i
\(321\) 0 0
\(322\) 0 0
\(323\) 412.171 0.0710026
\(324\) 0 0
\(325\) −2350.42 + 4071.05i −0.401163 + 0.694834i
\(326\) −3907.44 + 6767.88i −0.663844 + 1.14981i
\(327\) 0 0
\(328\) 1292.84 0.217638
\(329\) 0 0
\(330\) 0 0
\(331\) −5587.97 9678.65i −0.927923 1.60721i −0.786791 0.617219i \(-0.788259\pi\)
−0.141132 0.989991i \(-0.545074\pi\)
\(332\) 874.274 1514.29i 0.144524 0.250323i
\(333\) 0 0
\(334\) −1286.41 2228.14i −0.210747 0.365024i
\(335\) 53.4095 0.00871067
\(336\) 0 0
\(337\) 9379.78 1.51617 0.758085 0.652156i \(-0.226135\pi\)
0.758085 + 0.652156i \(0.226135\pi\)
\(338\) −152.766 264.599i −0.0245840 0.0425807i
\(339\) 0 0
\(340\) −748.000 + 1295.57i −0.119312 + 0.206654i
\(341\) 948.043 + 1642.06i 0.150555 + 0.260770i
\(342\) 0 0
\(343\) 0 0
\(344\) 3770.35 0.590941
\(345\) 0 0
\(346\) −1251.26 + 2167.24i −0.194416 + 0.336738i
\(347\) 2840.73 4920.29i 0.439476 0.761195i −0.558173 0.829725i \(-0.688497\pi\)
0.997649 + 0.0685293i \(0.0218307\pi\)
\(348\) 0 0
\(349\) 704.250 0.108016 0.0540080 0.998541i \(-0.482800\pi\)
0.0540080 + 0.998541i \(0.482800\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 103.765 + 179.725i 0.0157121 + 0.0272142i
\(353\) 2142.48 3710.89i 0.323039 0.559520i −0.658074 0.752953i \(-0.728629\pi\)
0.981114 + 0.193433i \(0.0619622\pi\)
\(354\) 0 0
\(355\) −1562.98 2707.15i −0.233674 0.404735i
\(356\) −234.051 −0.0348445
\(357\) 0 0
\(358\) 7247.03 1.06988
\(359\) 2330.64 + 4036.78i 0.342636 + 0.593463i 0.984921 0.173003i \(-0.0553470\pi\)
−0.642285 + 0.766465i \(0.722014\pi\)
\(360\) 0 0
\(361\) 3416.73 5917.95i 0.498138 0.862801i
\(362\) −181.727 314.760i −0.0263850 0.0457001i
\(363\) 0 0
\(364\) 0 0
\(365\) −3143.36 −0.450770
\(366\) 0 0
\(367\) −3467.65 + 6006.15i −0.493215 + 0.854274i −0.999969 0.00781688i \(-0.997512\pi\)
0.506754 + 0.862091i \(0.330845\pi\)
\(368\) 849.998 1472.24i 0.120405 0.208548i
\(369\) 0 0
\(370\) −1050.68 −0.147628
\(371\) 0 0
\(372\) 0 0
\(373\) 1540.55 + 2668.31i 0.213852 + 0.370402i 0.952917 0.303232i \(-0.0980657\pi\)
−0.739065 + 0.673634i \(0.764732\pi\)
\(374\) 528.916 916.109i 0.0731272 0.126660i
\(375\) 0 0
\(376\) 1384.02 + 2397.19i 0.189828 + 0.328791i
\(377\) −12123.1 −1.65616
\(378\) 0 0
\(379\) 941.827 0.127647 0.0638237 0.997961i \(-0.479670\pi\)
0.0638237 + 0.997961i \(0.479670\pi\)
\(380\) −46.3515 80.2832i −0.00625732 0.0108380i
\(381\) 0 0
\(382\) −1481.28 + 2565.65i −0.198400 + 0.343639i
\(383\) 338.763 + 586.755i 0.0451958 + 0.0782814i 0.887738 0.460348i \(-0.152276\pi\)
−0.842543 + 0.538630i \(0.818942\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 713.416 0.0940724
\(387\) 0 0
\(388\) −2560.18 + 4434.36i −0.334983 + 0.580208i
\(389\) −5932.71 + 10275.8i −0.773266 + 1.33934i 0.162498 + 0.986709i \(0.448045\pi\)
−0.935764 + 0.352627i \(0.885289\pi\)
\(390\) 0 0
\(391\) −8665.34 −1.12078
\(392\) 0 0
\(393\) 0 0
\(394\) −4890.53 8470.64i −0.625333 1.08311i
\(395\) −0.605481 + 1.04872i −7.71268e−5 + 0.000133587i
\(396\) 0 0
\(397\) −2570.38 4452.03i −0.324947 0.562824i 0.656555 0.754278i \(-0.272013\pi\)
−0.981502 + 0.191454i \(0.938680\pi\)
\(398\) 7085.70 0.892397
\(399\) 0 0
\(400\) −1663.53 −0.207941
\(401\) −6190.99 10723.1i −0.770981 1.33538i −0.937026 0.349260i \(-0.886433\pi\)
0.166045 0.986118i \(-0.446900\pi\)
\(402\) 0 0
\(403\) −6609.44 + 11447.9i −0.816971 + 1.41504i
\(404\) 2612.78 + 4525.46i 0.321759 + 0.557303i
\(405\) 0 0
\(406\) 0 0
\(407\) 742.944 0.0904824
\(408\) 0 0
\(409\) −7937.82 + 13748.7i −0.959657 + 1.66217i −0.236326 + 0.971674i \(0.575943\pi\)
−0.723331 + 0.690501i \(0.757390\pi\)
\(410\) −741.087 + 1283.60i −0.0892675 + 0.154616i
\(411\) 0 0
\(412\) 3035.90 0.363029
\(413\) 0 0
\(414\) 0 0
\(415\) 1002.31 + 1736.05i 0.118558 + 0.205348i
\(416\) −723.411 + 1252.99i −0.0852600 + 0.147675i
\(417\) 0 0
\(418\) 32.7755 + 56.7688i 0.00383517 + 0.00664271i
\(419\) −16111.9 −1.87857 −0.939283 0.343145i \(-0.888508\pi\)
−0.939283 + 0.343145i \(0.888508\pi\)
\(420\) 0 0
\(421\) 8691.58 1.00618 0.503090 0.864234i \(-0.332197\pi\)
0.503090 + 0.864234i \(0.332197\pi\)
\(422\) −4289.50 7429.62i −0.494809 0.857034i
\(423\) 0 0
\(424\) −1622.12 + 2809.59i −0.185795 + 0.321806i
\(425\) 4239.73 + 7343.43i 0.483899 + 0.838138i
\(426\) 0 0
\(427\) 0 0
\(428\) −5050.06 −0.570336
\(429\) 0 0
\(430\) −2161.25 + 3743.40i −0.242383 + 0.419820i
\(431\) −2097.55 + 3633.07i −0.234421 + 0.406029i −0.959104 0.283053i \(-0.908653\pi\)
0.724683 + 0.689082i \(0.241986\pi\)
\(432\) 0 0
\(433\) 5426.54 0.602270 0.301135 0.953582i \(-0.402635\pi\)
0.301135 + 0.953582i \(0.402635\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 4211.05 + 7293.76i 0.462553 + 0.801165i
\(437\) 268.484 465.028i 0.0293898 0.0509046i
\(438\) 0 0
\(439\) −1885.62 3265.99i −0.205002 0.355073i 0.745132 0.666917i \(-0.232387\pi\)
−0.950133 + 0.311844i \(0.899053\pi\)
\(440\) −237.921 −0.0257783
\(441\) 0 0
\(442\) 7374.85 0.793633
\(443\) −2965.15 5135.79i −0.318010 0.550810i 0.662063 0.749449i \(-0.269681\pi\)
−0.980073 + 0.198639i \(0.936348\pi\)
\(444\) 0 0
\(445\) 134.163 232.377i 0.0142920 0.0247545i
\(446\) −5795.73 10038.5i −0.615327 1.06578i
\(447\) 0 0
\(448\) 0 0
\(449\) 529.065 0.0556083 0.0278041 0.999613i \(-0.491149\pi\)
0.0278041 + 0.999613i \(0.491149\pi\)
\(450\) 0 0
\(451\) 524.027 907.642i 0.0547128 0.0947654i
\(452\) 3071.53 5320.04i 0.319629 0.553614i
\(453\) 0 0
\(454\) −8208.09 −0.848512
\(455\) 0 0
\(456\) 0 0
\(457\) −5028.59 8709.77i −0.514721 0.891523i −0.999854 0.0170824i \(-0.994562\pi\)
0.485133 0.874440i \(-0.338771\pi\)
\(458\) 1296.83 2246.18i 0.132308 0.229164i
\(459\) 0 0
\(460\) 974.478 + 1687.84i 0.0987723 + 0.171079i
\(461\) −5010.31 −0.506190 −0.253095 0.967441i \(-0.581448\pi\)
−0.253095 + 0.967441i \(0.581448\pi\)
\(462\) 0 0
\(463\) −7124.38 −0.715114 −0.357557 0.933891i \(-0.616390\pi\)
−0.357557 + 0.933891i \(0.616390\pi\)
\(464\) −2145.06 3715.35i −0.214616 0.371725i
\(465\) 0 0
\(466\) 1478.33 2560.55i 0.146958 0.254539i
\(467\) −3750.72 6496.44i −0.371654 0.643724i 0.618166 0.786048i \(-0.287876\pi\)
−0.989820 + 0.142323i \(0.954543\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) −3173.40 −0.311443
\(471\) 0 0
\(472\) −1013.74 + 1755.85i −0.0988587 + 0.171228i
\(473\) 1528.24 2646.98i 0.148559 0.257312i
\(474\) 0 0
\(475\) −525.449 −0.0507563
\(476\) 0 0
\(477\) 0 0
\(478\) 3776.92 + 6541.82i 0.361406 + 0.625974i
\(479\) 4086.90 7078.72i 0.389844 0.675230i −0.602584 0.798055i \(-0.705862\pi\)
0.992428 + 0.122826i \(0.0391956\pi\)
\(480\) 0 0
\(481\) 2589.78 + 4485.63i 0.245496 + 0.425212i
\(482\) −7992.76 −0.755312
\(483\) 0 0
\(484\) −5155.76 −0.484200
\(485\) −2935.11 5083.76i −0.274797 0.475962i
\(486\) 0 0
\(487\) 5984.39 10365.3i 0.556835 0.964467i −0.440923 0.897545i \(-0.645349\pi\)
0.997758 0.0669221i \(-0.0213179\pi\)
\(488\) 3004.87 + 5204.59i 0.278738 + 0.482788i
\(489\) 0 0
\(490\) 0 0
\(491\) −2079.96 −0.191176 −0.0955878 0.995421i \(-0.530473\pi\)
−0.0955878 + 0.995421i \(0.530473\pi\)
\(492\) 0 0
\(493\) −10933.9 + 18938.1i −0.998863 + 1.73008i
\(494\) −228.500 + 395.773i −0.0208111 + 0.0360459i
\(495\) 0 0
\(496\) −4677.88 −0.423474
\(497\) 0 0
\(498\) 0 0
\(499\) −6417.21 11114.9i −0.575699 0.997140i −0.995965 0.0897390i \(-0.971397\pi\)
0.420266 0.907401i \(-0.361937\pi\)
\(500\) 2100.02 3637.34i 0.187832 0.325334i
\(501\) 0 0
\(502\) 5423.58 + 9393.92i 0.482204 + 0.835202i
\(503\) 16808.8 1.48999 0.744997 0.667068i \(-0.232451\pi\)
0.744997 + 0.667068i \(0.232451\pi\)
\(504\) 0 0
\(505\) −5990.82 −0.527897
\(506\) −689.060 1193.49i −0.0605384 0.104856i
\(507\) 0 0
\(508\) −48.3498 + 83.7443i −0.00422278 + 0.00731408i
\(509\) 2135.13 + 3698.16i 0.185929 + 0.322039i 0.943889 0.330262i \(-0.107137\pi\)
−0.757960 + 0.652301i \(0.773804\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) −512.000 −0.0441942
\(513\) 0 0
\(514\) 5964.22 10330.3i 0.511811 0.886482i
\(515\) −1740.25 + 3014.20i −0.148902 + 0.257906i
\(516\) 0 0
\(517\) 2243.93 0.190886
\(518\) 0 0
\(519\) 0 0
\(520\) −829.352 1436.48i −0.0699414 0.121142i
\(521\) −7641.64 + 13235.7i −0.642584 + 1.11299i 0.342270 + 0.939602i \(0.388804\pi\)
−0.984854 + 0.173386i \(0.944529\pi\)
\(522\) 0 0
\(523\) −2249.66 3896.53i −0.188090 0.325781i 0.756524 0.653966i \(-0.226896\pi\)
−0.944613 + 0.328185i \(0.893563\pi\)
\(524\) 6326.11 0.527400
\(525\) 0 0
\(526\) 10332.0 0.856459
\(527\) 11922.2 + 20649.9i 0.985465 + 1.70687i
\(528\) 0 0
\(529\) 438.992 760.356i 0.0360805 0.0624933i
\(530\) −1859.67 3221.04i −0.152413 0.263987i
\(531\) 0 0
\(532\) 0 0
\(533\) 7306.69 0.593785
\(534\) 0 0
\(535\) 2894.81 5013.96i 0.233932 0.405182i
\(536\) 46.5870 80.6911i 0.00375420 0.00650247i
\(537\) 0 0
\(538\) −7766.59 −0.622382
\(539\) 0 0
\(540\) 0 0
\(541\) −1985.41 3438.83i −0.157781 0.273284i 0.776287 0.630379i \(-0.217101\pi\)
−0.934068 + 0.357095i \(0.883767\pi\)
\(542\) −5527.65 + 9574.18i −0.438068 + 0.758757i
\(543\) 0 0
\(544\) 1304.90 + 2260.16i 0.102844 + 0.178131i
\(545\) −9655.50 −0.758892
\(546\) 0 0
\(547\) −2703.90 −0.211353 −0.105677 0.994401i \(-0.533701\pi\)
−0.105677 + 0.994401i \(0.533701\pi\)
\(548\) −1490.38 2581.41i −0.116178 0.201227i
\(549\) 0 0
\(550\) −674.278 + 1167.88i −0.0522751 + 0.0905432i
\(551\) −677.546 1173.54i −0.0523855 0.0907344i
\(552\) 0 0
\(553\) 0 0
\(554\) −4536.24 −0.347881
\(555\) 0 0
\(556\) −2747.19 + 4758.28i −0.209545 + 0.362942i
\(557\) 395.412 684.874i 0.0300793 0.0520988i −0.850594 0.525823i \(-0.823757\pi\)
0.880673 + 0.473724i \(0.157091\pi\)
\(558\) 0 0
\(559\) 21308.7 1.61227
\(560\) 0 0
\(561\) 0 0
\(562\) −725.656 1256.87i −0.0544661 0.0943380i
\(563\) −3758.58 + 6510.05i −0.281359 + 0.487328i −0.971720 0.236137i \(-0.924119\pi\)
0.690361 + 0.723465i \(0.257452\pi\)
\(564\) 0 0
\(565\) 3521.34 + 6099.14i 0.262202 + 0.454146i
\(566\) 8473.99 0.629308
\(567\) 0 0
\(568\) −5453.29 −0.402843
\(569\) 6972.72 + 12077.1i 0.513728 + 0.889804i 0.999873 + 0.0159254i \(0.00506942\pi\)
−0.486145 + 0.873878i \(0.661597\pi\)
\(570\) 0 0
\(571\) 1059.25 1834.67i 0.0776323 0.134463i −0.824596 0.565723i \(-0.808597\pi\)
0.902228 + 0.431259i \(0.141931\pi\)
\(572\) 586.441 + 1015.75i 0.0428677 + 0.0742490i
\(573\) 0 0
\(574\) 0 0
\(575\) 11046.8 0.801192
\(576\) 0 0
\(577\) 11428.9 19795.4i 0.824592 1.42823i −0.0776391 0.996982i \(-0.524738\pi\)
0.902231 0.431253i \(-0.141928\pi\)
\(578\) 1738.44 3011.06i 0.125103 0.216685i
\(579\) 0 0
\(580\) 4918.38 0.352112
\(581\) 0 0
\(582\) 0 0
\(583\) 1314.98 + 2277.62i 0.0934153 + 0.161800i
\(584\) −2741.83 + 4748.99i −0.194277 + 0.336497i
\(585\) 0 0
\(586\) −4373.78 7575.61i −0.308326 0.534037i
\(587\) 23955.3 1.68440 0.842199 0.539167i \(-0.181261\pi\)
0.842199 + 0.539167i \(0.181261\pi\)
\(588\) 0 0
\(589\) −1477.57 −0.103366
\(590\) −1162.20 2012.99i −0.0810968 0.140464i
\(591\) 0 0
\(592\) −916.468 + 1587.37i −0.0636260 + 0.110203i
\(593\) 5388.99 + 9334.01i 0.373186 + 0.646378i 0.990054 0.140689i \(-0.0449319\pi\)
−0.616867 + 0.787067i \(0.711599\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) −2482.12 −0.170590
\(597\) 0 0
\(598\) 4803.89 8320.59i 0.328505 0.568987i
\(599\) 3798.79 6579.69i 0.259122 0.448813i −0.706885 0.707329i \(-0.749900\pi\)
0.966007 + 0.258516i \(0.0832334\pi\)
\(600\) 0 0
\(601\) −19956.1 −1.35445 −0.677225 0.735776i \(-0.736818\pi\)
−0.677225 + 0.735776i \(0.736818\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 3878.53 + 6717.81i 0.261283 + 0.452556i
\(605\) 2955.40 5118.91i 0.198602 0.343989i
\(606\) 0 0
\(607\) −118.155 204.651i −0.00790079 0.0136846i 0.862048 0.506827i \(-0.169182\pi\)
−0.869949 + 0.493142i \(0.835848\pi\)
\(608\) −161.722 −0.0107873
\(609\) 0 0
\(610\) −6889.85 −0.457314
\(611\) 7821.98 + 13548.1i 0.517911 + 0.897048i
\(612\) 0 0
\(613\) −13207.5 + 22876.0i −0.870219 + 1.50726i −0.00844986 + 0.999964i \(0.502690\pi\)
−0.861770 + 0.507300i \(0.830644\pi\)
\(614\) −4133.47 7159.38i −0.271683 0.470568i
\(615\) 0 0
\(616\) 0 0
\(617\) −18473.6 −1.20538 −0.602689 0.797976i \(-0.705904\pi\)
−0.602689 + 0.797976i \(0.705904\pi\)
\(618\) 0 0
\(619\) 8023.96 13897.9i 0.521018 0.902430i −0.478683 0.877988i \(-0.658886\pi\)
0.999701 0.0244421i \(-0.00778093\pi\)
\(620\) 2681.47 4644.44i 0.173694 0.300847i
\(621\) 0 0
\(622\) −10126.5 −0.652788
\(623\) 0 0
\(624\) 0 0
\(625\) −4090.60 7085.13i −0.261798 0.453448i
\(626\) −7411.56 + 12837.2i −0.473204 + 0.819613i
\(627\) 0 0
\(628\) −825.686 1430.13i −0.0524657 0.0908733i
\(629\) 9342.97 0.592255
\(630\) 0 0
\(631\) −15065.7 −0.950487 −0.475243 0.879854i \(-0.657640\pi\)
−0.475243 + 0.879854i \(0.657640\pi\)
\(632\) 1.05627 + 1.82952i 6.64816e−5 + 0.000115149i
\(633\) 0 0
\(634\) 6737.05 11668.9i 0.422023 0.730965i
\(635\) −55.4304 96.0083i −0.00346408 0.00599996i
\(636\) 0 0
\(637\) 0 0
\(638\) −3477.82 −0.215812
\(639\) 0 0
\(640\) 293.490 508.340i 0.0181269 0.0313967i
\(641\) −15599.2 + 27018.6i −0.961203 + 1.66485i −0.241715 + 0.970347i \(0.577710\pi\)
−0.719488 + 0.694505i \(0.755623\pi\)
\(642\) 0 0
\(643\) 12497.9 0.766517 0.383259 0.923641i \(-0.374802\pi\)
0.383259 + 0.923641i \(0.374802\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 412.171 + 713.902i 0.0251032 + 0.0434800i
\(647\) 4964.86 8599.39i 0.301683 0.522530i −0.674834 0.737969i \(-0.735785\pi\)
0.976517 + 0.215439i \(0.0691183\pi\)
\(648\) 0 0
\(649\) 821.801 + 1423.40i 0.0497049 + 0.0860915i
\(650\) −9401.68 −0.567330
\(651\) 0 0
\(652\) −15629.8 −0.938817
\(653\) −4072.79 7054.28i −0.244075 0.422750i 0.717796 0.696253i \(-0.245151\pi\)
−0.961871 + 0.273503i \(0.911817\pi\)
\(654\) 0 0
\(655\) −3626.27 + 6280.89i −0.216321 + 0.374679i
\(656\) 1292.84 + 2239.27i 0.0769466 + 0.133275i
\(657\) 0 0
\(658\) 0 0
\(659\) 16975.8 1.00347 0.501733 0.865022i \(-0.332696\pi\)
0.501733 + 0.865022i \(0.332696\pi\)
\(660\) 0 0
\(661\) 10318.9 17872.8i 0.607199 1.05170i −0.384501 0.923124i \(-0.625627\pi\)
0.991700 0.128574i \(-0.0410401\pi\)
\(662\) 11175.9 19357.3i 0.656141 1.13647i
\(663\) 0 0
\(664\) 3497.10 0.204388
\(665\) 0 0
\(666\) 0 0
\(667\) 14244.5 + 24672.2i 0.826910 + 1.43225i
\(668\) 2572.83 4456.27i 0.149021 0.258111i
\(669\) 0 0
\(670\) 53.4095 + 92.5080i 0.00307969 + 0.00533417i
\(671\) 4871.86 0.280292
\(672\) 0 0
\(673\) −2150.29 −0.123161 −0.0615807 0.998102i \(-0.519614\pi\)
−0.0615807 + 0.998102i \(0.519614\pi\)
\(674\) 9379.78 + 16246.3i 0.536047 + 0.928461i
\(675\) 0 0
\(676\) 305.532 529.198i 0.0173835 0.0301091i
\(677\) 13891.7 + 24061.1i 0.788628 + 1.36594i 0.926808 + 0.375536i \(0.122541\pi\)
−0.138180 + 0.990407i \(0.544125\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) −2992.00 −0.168732
\(681\) 0 0
\(682\) −1896.09 + 3284.12i −0.106459 + 0.184392i
\(683\) 9090.89 15745.9i 0.509302 0.882137i −0.490640 0.871362i \(-0.663237\pi\)
0.999942 0.0107743i \(-0.00342962\pi\)
\(684\) 0 0
\(685\) 3417.27 0.190609
\(686\) 0 0
\(687\) 0 0
\(688\) 3770.35 + 6530.43i 0.208929 + 0.361876i
\(689\) −9167.63 + 15878.8i −0.506907 + 0.877989i
\(690\) 0 0
\(691\) 11967.6 + 20728.4i 0.658853 + 1.14117i 0.980913 + 0.194447i \(0.0622912\pi\)
−0.322060 + 0.946719i \(0.604375\pi\)
\(692\) −5005.02 −0.274946
\(693\) 0 0
\(694\) 11362.9 0.621513
\(695\) −3149.51 5455.11i −0.171896 0.297733i
\(696\) 0 0
\(697\) 6589.96 11414.1i 0.358124 0.620289i
\(698\) 704.250 + 1219.80i 0.0381895 + 0.0661461i
\(699\) 0 0
\(700\) 0 0
\(701\) 20627.2 1.11138 0.555691 0.831389i \(-0.312454\pi\)
0.555691 + 0.831389i \(0.312454\pi\)
\(702\) 0 0
\(703\) −289.479 + 501.392i −0.0155305 + 0.0268995i
\(704\) −207.529 + 359.451i −0.0111101 + 0.0192433i
\(705\) 0 0
\(706\) 8569.93 0.456846
\(707\) 0 0
\(708\) 0 0
\(709\) 3292.32 + 5702.46i 0.174394 + 0.302060i 0.939952 0.341308i \(-0.110870\pi\)
−0.765557 + 0.643368i \(0.777537\pi\)
\(710\) 3125.95 5414.31i 0.165232 0.286191i
\(711\) 0 0
\(712\) −234.051 405.387i −0.0123194 0.0213378i
\(713\) 31064.0 1.63163
\(714\) 0 0
\(715\) −1344.65 −0.0703313
\(716\) 7247.03 + 12552.2i 0.378260 + 0.655165i
\(717\) 0 0
\(718\) −4661.27 + 8073.56i −0.242280 + 0.419642i
\(719\) −85.4430 147.992i −0.00443183 0.00767616i 0.863801 0.503833i \(-0.168077\pi\)
−0.868233 + 0.496157i \(0.834744\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 13666.9 0.704474
\(723\) 0 0
\(724\) 363.454 629.521i 0.0186570 0.0323149i
\(725\) 13938.9 24142.9i 0.714039 1.23675i
\(726\) 0 0
\(727\) 11127.5 0.567671 0.283836 0.958873i \(-0.408393\pi\)
0.283836 + 0.958873i \(0.408393\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) −3143.36 5444.46i −0.159371 0.276039i
\(731\) 19218.5 33287.4i 0.972396 1.68424i
\(732\) 0 0
\(733\) −11288.0 19551.3i −0.568800 0.985191i −0.996685 0.0813578i \(-0.974074\pi\)
0.427885 0.903833i \(-0.359259\pi\)
\(734\) −13870.6 −0.697511
\(735\) 0 0
\(736\) 3399.99 0.170279
\(737\) −37.7662 65.4130i −0.00188757 0.00326936i
\(738\) 0 0
\(739\) 11468.2 19863.5i 0.570860 0.988758i −0.425618 0.904903i \(-0.639943\pi\)
0.996478 0.0838550i \(-0.0267233\pi\)
\(740\) −1050.68 1819.83i −0.0521943 0.0904032i
\(741\) 0 0
\(742\) 0 0
\(743\) −16973.4 −0.838081 −0.419041 0.907967i \(-0.637634\pi\)
−0.419041 + 0.907967i \(0.637634\pi\)
\(744\) 0 0
\(745\) 1422.81 2464.38i 0.0699700 0.121192i
\(746\) −3081.10 + 5336.63i −0.151216 + 0.261914i
\(747\) 0 0
\(748\) 2115.66 0.103418
\(749\) 0 0
\(750\) 0 0
\(751\) 10598.9 + 18357.9i 0.514994 + 0.891995i 0.999849 + 0.0174007i \(0.00553909\pi\)
−0.484855 + 0.874595i \(0.661128\pi\)
\(752\) −2768.03 + 4794.37i −0.134228 + 0.232490i
\(753\) 0 0
\(754\) −12123.1 20997.8i −0.585541 1.01419i
\(755\) −8893.05 −0.428677
\(756\) 0 0
\(757\) −7962.24 −0.382289 −0.191144 0.981562i \(-0.561220\pi\)
−0.191144 + 0.981562i \(0.561220\pi\)
\(758\) 941.827 + 1631.29i 0.0451302 + 0.0781678i
\(759\) 0 0
\(760\) 92.7030 160.566i 0.00442460 0.00766362i
\(761\) −13428.1 23258.1i −0.639642 1.10789i −0.985511 0.169610i \(-0.945749\pi\)
0.345869 0.938283i \(-0.387584\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) −5925.12 −0.280580
\(765\) 0 0
\(766\) −677.526 + 1173.51i −0.0319582 + 0.0553533i
\(767\) −5729.32 + 9923.47i −0.269718 + 0.467165i
\(768\) 0 0
\(769\) 12183.6 0.571331 0.285666 0.958329i \(-0.407785\pi\)
0.285666 + 0.958329i \(0.407785\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 713.416 + 1235.67i 0.0332596 + 0.0576073i
\(773\) 8727.61 15116.7i 0.406093 0.703374i −0.588355 0.808603i \(-0.700224\pi\)
0.994448 + 0.105229i \(0.0335574\pi\)
\(774\) 0 0
\(775\) −15198.8 26325.1i −0.704461 1.22016i
\(776\) −10240.7 −0.473738
\(777\) 0 0
\(778\) −23730.8 −1.09356
\(779\) 408.362 + 707.304i 0.0187819 + 0.0325312i
\(780\) 0 0
\(781\) −2210.38 + 3828.49i −0.101272 + 0.175409i
\(782\) −8665.34 15008.8i −0.396256 0.686335i
\(783\) 0 0
\(784\) 0 0
\(785\) 1893.21 0.0860785
\(786\) 0 0
\(787\) 15490.5 26830.3i 0.701622 1.21524i −0.266275 0.963897i \(-0.585793\pi\)
0.967897 0.251348i \(-0.0808738\pi\)
\(788\) 9781.06 16941.3i 0.442177 0.765874i
\(789\) 0 0
\(790\) −2.42193 −0.000109074