Properties

Label 441.4.e.e.226.1
Level $441$
Weight $4$
Character 441.226
Analytic conductor $26.020$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 441 = 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 441.e (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(26.0198423125\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Defining polynomial: \(x^{2} - x + 1\)
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 7)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 226.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 441.226
Dual form 441.4.e.e.361.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.500000 + 0.866025i) q^{2} +(3.50000 + 6.06218i) q^{4} +(-8.00000 + 13.8564i) q^{5} -15.0000 q^{8} +O(q^{10})\) \(q+(-0.500000 + 0.866025i) q^{2} +(3.50000 + 6.06218i) q^{4} +(-8.00000 + 13.8564i) q^{5} -15.0000 q^{8} +(-8.00000 - 13.8564i) q^{10} +(-4.00000 - 6.92820i) q^{11} -28.0000 q^{13} +(-20.5000 + 35.5070i) q^{16} +(-27.0000 - 46.7654i) q^{17} +(-55.0000 + 95.2628i) q^{19} -112.000 q^{20} +8.00000 q^{22} +(24.0000 - 41.5692i) q^{23} +(-65.5000 - 113.449i) q^{25} +(14.0000 - 24.2487i) q^{26} +110.000 q^{29} +(6.00000 + 10.3923i) q^{31} +(-80.5000 - 139.430i) q^{32} +54.0000 q^{34} +(123.000 - 213.042i) q^{37} +(-55.0000 - 95.2628i) q^{38} +(120.000 - 207.846i) q^{40} +182.000 q^{41} +128.000 q^{43} +(28.0000 - 48.4974i) q^{44} +(24.0000 + 41.5692i) q^{46} +(-162.000 + 280.592i) q^{47} +131.000 q^{50} +(-98.0000 - 169.741i) q^{52} +(-81.0000 - 140.296i) q^{53} +128.000 q^{55} +(-55.0000 + 95.2628i) q^{58} +(-405.000 - 701.481i) q^{59} +(-244.000 + 422.620i) q^{61} -12.0000 q^{62} -167.000 q^{64} +(224.000 - 387.979i) q^{65} +(-122.000 - 211.310i) q^{67} +(189.000 - 327.358i) q^{68} +768.000 q^{71} +(-351.000 - 607.950i) q^{73} +(123.000 + 213.042i) q^{74} -770.000 q^{76} +(-220.000 + 381.051i) q^{79} +(-328.000 - 568.113i) q^{80} +(-91.0000 + 157.617i) q^{82} -1302.00 q^{83} +864.000 q^{85} +(-64.0000 + 110.851i) q^{86} +(60.0000 + 103.923i) q^{88} +(-365.000 + 632.199i) q^{89} +336.000 q^{92} +(-162.000 - 280.592i) q^{94} +(-880.000 - 1524.20i) q^{95} -294.000 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q - q^{2} + 7q^{4} - 16q^{5} - 30q^{8} + O(q^{10}) \) \( 2q - q^{2} + 7q^{4} - 16q^{5} - 30q^{8} - 16q^{10} - 8q^{11} - 56q^{13} - 41q^{16} - 54q^{17} - 110q^{19} - 224q^{20} + 16q^{22} + 48q^{23} - 131q^{25} + 28q^{26} + 220q^{29} + 12q^{31} - 161q^{32} + 108q^{34} + 246q^{37} - 110q^{38} + 240q^{40} + 364q^{41} + 256q^{43} + 56q^{44} + 48q^{46} - 324q^{47} + 262q^{50} - 196q^{52} - 162q^{53} + 256q^{55} - 110q^{58} - 810q^{59} - 488q^{61} - 24q^{62} - 334q^{64} + 448q^{65} - 244q^{67} + 378q^{68} + 1536q^{71} - 702q^{73} + 246q^{74} - 1540q^{76} - 440q^{79} - 656q^{80} - 182q^{82} - 2604q^{83} + 1728q^{85} - 128q^{86} + 120q^{88} - 730q^{89} + 672q^{92} - 324q^{94} - 1760q^{95} - 588q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/441\mathbb{Z}\right)^\times\).

\(n\) \(199\) \(344\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.500000 + 0.866025i −0.176777 + 0.306186i −0.940775 0.339032i \(-0.889900\pi\)
0.763998 + 0.645219i \(0.223234\pi\)
\(3\) 0 0
\(4\) 3.50000 + 6.06218i 0.437500 + 0.757772i
\(5\) −8.00000 + 13.8564i −0.715542 + 1.23935i 0.247208 + 0.968962i \(0.420487\pi\)
−0.962750 + 0.270392i \(0.912847\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) −15.0000 −0.662913
\(9\) 0 0
\(10\) −8.00000 13.8564i −0.252982 0.438178i
\(11\) −4.00000 6.92820i −0.109640 0.189903i 0.805984 0.591937i \(-0.201637\pi\)
−0.915625 + 0.402034i \(0.868303\pi\)
\(12\) 0 0
\(13\) −28.0000 −0.597369 −0.298685 0.954352i \(-0.596548\pi\)
−0.298685 + 0.954352i \(0.596548\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) −20.5000 + 35.5070i −0.320312 + 0.554798i
\(17\) −27.0000 46.7654i −0.385204 0.667192i 0.606594 0.795012i \(-0.292535\pi\)
−0.991797 + 0.127820i \(0.959202\pi\)
\(18\) 0 0
\(19\) −55.0000 + 95.2628i −0.664098 + 1.15025i 0.315431 + 0.948949i \(0.397851\pi\)
−0.979529 + 0.201303i \(0.935482\pi\)
\(20\) −112.000 −1.25220
\(21\) 0 0
\(22\) 8.00000 0.0775275
\(23\) 24.0000 41.5692i 0.217580 0.376860i −0.736487 0.676451i \(-0.763517\pi\)
0.954068 + 0.299591i \(0.0968503\pi\)
\(24\) 0 0
\(25\) −65.5000 113.449i −0.524000 0.907595i
\(26\) 14.0000 24.2487i 0.105601 0.182906i
\(27\) 0 0
\(28\) 0 0
\(29\) 110.000 0.704362 0.352181 0.935932i \(-0.385440\pi\)
0.352181 + 0.935932i \(0.385440\pi\)
\(30\) 0 0
\(31\) 6.00000 + 10.3923i 0.0347623 + 0.0602101i 0.882883 0.469593i \(-0.155599\pi\)
−0.848121 + 0.529803i \(0.822266\pi\)
\(32\) −80.5000 139.430i −0.444704 0.770250i
\(33\) 0 0
\(34\) 54.0000 0.272380
\(35\) 0 0
\(36\) 0 0
\(37\) 123.000 213.042i 0.546516 0.946593i −0.451994 0.892021i \(-0.649287\pi\)
0.998510 0.0545719i \(-0.0173794\pi\)
\(38\) −55.0000 95.2628i −0.234794 0.406675i
\(39\) 0 0
\(40\) 120.000 207.846i 0.474342 0.821584i
\(41\) 182.000 0.693259 0.346630 0.938002i \(-0.387326\pi\)
0.346630 + 0.938002i \(0.387326\pi\)
\(42\) 0 0
\(43\) 128.000 0.453949 0.226975 0.973901i \(-0.427117\pi\)
0.226975 + 0.973901i \(0.427117\pi\)
\(44\) 28.0000 48.4974i 0.0959354 0.166165i
\(45\) 0 0
\(46\) 24.0000 + 41.5692i 0.0769262 + 0.133240i
\(47\) −162.000 + 280.592i −0.502769 + 0.870821i 0.497226 + 0.867621i \(0.334352\pi\)
−0.999995 + 0.00319997i \(0.998981\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 131.000 0.370524
\(51\) 0 0
\(52\) −98.0000 169.741i −0.261349 0.452670i
\(53\) −81.0000 140.296i −0.209928 0.363607i 0.741763 0.670662i \(-0.233990\pi\)
−0.951692 + 0.307055i \(0.900656\pi\)
\(54\) 0 0
\(55\) 128.000 0.313809
\(56\) 0 0
\(57\) 0 0
\(58\) −55.0000 + 95.2628i −0.124515 + 0.215666i
\(59\) −405.000 701.481i −0.893670 1.54788i −0.835442 0.549578i \(-0.814789\pi\)
−0.0582271 0.998303i \(-0.518545\pi\)
\(60\) 0 0
\(61\) −244.000 + 422.620i −0.512148 + 0.887066i 0.487753 + 0.872982i \(0.337817\pi\)
−0.999901 + 0.0140840i \(0.995517\pi\)
\(62\) −12.0000 −0.0245807
\(63\) 0 0
\(64\) −167.000 −0.326172
\(65\) 224.000 387.979i 0.427443 0.740353i
\(66\) 0 0
\(67\) −122.000 211.310i −0.222458 0.385308i 0.733096 0.680125i \(-0.238075\pi\)
−0.955554 + 0.294817i \(0.904741\pi\)
\(68\) 189.000 327.358i 0.337053 0.583793i
\(69\) 0 0
\(70\) 0 0
\(71\) 768.000 1.28373 0.641865 0.766818i \(-0.278161\pi\)
0.641865 + 0.766818i \(0.278161\pi\)
\(72\) 0 0
\(73\) −351.000 607.950i −0.562759 0.974728i −0.997254 0.0740537i \(-0.976406\pi\)
0.434495 0.900674i \(-0.356927\pi\)
\(74\) 123.000 + 213.042i 0.193222 + 0.334671i
\(75\) 0 0
\(76\) −770.000 −1.16217
\(77\) 0 0
\(78\) 0 0
\(79\) −220.000 + 381.051i −0.313316 + 0.542679i −0.979078 0.203485i \(-0.934773\pi\)
0.665762 + 0.746164i \(0.268106\pi\)
\(80\) −328.000 568.113i −0.458394 0.793962i
\(81\) 0 0
\(82\) −91.0000 + 157.617i −0.122552 + 0.212266i
\(83\) −1302.00 −1.72184 −0.860922 0.508737i \(-0.830113\pi\)
−0.860922 + 0.508737i \(0.830113\pi\)
\(84\) 0 0
\(85\) 864.000 1.10252
\(86\) −64.0000 + 110.851i −0.0802476 + 0.138993i
\(87\) 0 0
\(88\) 60.0000 + 103.923i 0.0726821 + 0.125889i
\(89\) −365.000 + 632.199i −0.434718 + 0.752954i −0.997273 0.0738062i \(-0.976485\pi\)
0.562554 + 0.826760i \(0.309819\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 336.000 0.380765
\(93\) 0 0
\(94\) −162.000 280.592i −0.177756 0.307882i
\(95\) −880.000 1524.20i −0.950380 1.64611i
\(96\) 0 0
\(97\) −294.000 −0.307744 −0.153872 0.988091i \(-0.549174\pi\)
−0.153872 + 0.988091i \(0.549174\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 458.500 794.145i 0.458500 0.794145i
\(101\) 344.000 + 595.825i 0.338904 + 0.586999i 0.984227 0.176911i \(-0.0566106\pi\)
−0.645323 + 0.763910i \(0.723277\pi\)
\(102\) 0 0
\(103\) 694.000 1202.04i 0.663901 1.14991i −0.315680 0.948866i \(-0.602233\pi\)
0.979582 0.201046i \(-0.0644339\pi\)
\(104\) 420.000 0.396004
\(105\) 0 0
\(106\) 162.000 0.148442
\(107\) 122.000 211.310i 0.110226 0.190917i −0.805635 0.592412i \(-0.798176\pi\)
0.915861 + 0.401495i \(0.131509\pi\)
\(108\) 0 0
\(109\) −45.0000 77.9423i −0.0395433 0.0684910i 0.845576 0.533854i \(-0.179257\pi\)
−0.885120 + 0.465363i \(0.845924\pi\)
\(110\) −64.0000 + 110.851i −0.0554742 + 0.0960841i
\(111\) 0 0
\(112\) 0 0
\(113\) −1318.00 −1.09723 −0.548615 0.836075i \(-0.684845\pi\)
−0.548615 + 0.836075i \(0.684845\pi\)
\(114\) 0 0
\(115\) 384.000 + 665.108i 0.311376 + 0.539318i
\(116\) 385.000 + 666.840i 0.308158 + 0.533746i
\(117\) 0 0
\(118\) 810.000 0.631920
\(119\) 0 0
\(120\) 0 0
\(121\) 633.500 1097.25i 0.475958 0.824383i
\(122\) −244.000 422.620i −0.181071 0.313625i
\(123\) 0 0
\(124\) −42.0000 + 72.7461i −0.0304170 + 0.0526838i
\(125\) 96.0000 0.0686920
\(126\) 0 0
\(127\) −1776.00 −1.24090 −0.620451 0.784245i \(-0.713050\pi\)
−0.620451 + 0.784245i \(0.713050\pi\)
\(128\) 727.500 1260.07i 0.502363 0.870119i
\(129\) 0 0
\(130\) 224.000 + 387.979i 0.151124 + 0.261754i
\(131\) 559.000 968.216i 0.372825 0.645752i −0.617174 0.786827i \(-0.711723\pi\)
0.989999 + 0.141075i \(0.0450559\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 244.000 0.157301
\(135\) 0 0
\(136\) 405.000 + 701.481i 0.255356 + 0.442290i
\(137\) 1137.00 + 1969.34i 0.709054 + 1.22812i 0.965208 + 0.261482i \(0.0842113\pi\)
−0.256154 + 0.966636i \(0.582455\pi\)
\(138\) 0 0
\(139\) 210.000 0.128144 0.0640718 0.997945i \(-0.479591\pi\)
0.0640718 + 0.997945i \(0.479591\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) −384.000 + 665.108i −0.226934 + 0.393060i
\(143\) 112.000 + 193.990i 0.0654959 + 0.113442i
\(144\) 0 0
\(145\) −880.000 + 1524.20i −0.504000 + 0.872954i
\(146\) 702.000 0.397931
\(147\) 0 0
\(148\) 1722.00 0.956402
\(149\) −1005.00 + 1740.71i −0.552569 + 0.957078i 0.445519 + 0.895272i \(0.353019\pi\)
−0.998088 + 0.0618054i \(0.980314\pi\)
\(150\) 0 0
\(151\) −556.000 963.020i −0.299647 0.519003i 0.676408 0.736527i \(-0.263535\pi\)
−0.976055 + 0.217524i \(0.930202\pi\)
\(152\) 825.000 1428.94i 0.440239 0.762516i
\(153\) 0 0
\(154\) 0 0
\(155\) −192.000 −0.0994956
\(156\) 0 0
\(157\) 62.0000 + 107.387i 0.0315168 + 0.0545887i 0.881354 0.472457i \(-0.156633\pi\)
−0.849837 + 0.527046i \(0.823300\pi\)
\(158\) −220.000 381.051i −0.110774 0.191866i
\(159\) 0 0
\(160\) 2576.00 1.27282
\(161\) 0 0
\(162\) 0 0
\(163\) −1004.00 + 1738.98i −0.482450 + 0.835628i −0.999797 0.0201478i \(-0.993586\pi\)
0.517347 + 0.855776i \(0.326920\pi\)
\(164\) 637.000 + 1103.32i 0.303301 + 0.525333i
\(165\) 0 0
\(166\) 651.000 1127.57i 0.304382 0.527205i
\(167\) 2884.00 1.33635 0.668176 0.744004i \(-0.267076\pi\)
0.668176 + 0.744004i \(0.267076\pi\)
\(168\) 0 0
\(169\) −1413.00 −0.643150
\(170\) −432.000 + 748.246i −0.194899 + 0.337576i
\(171\) 0 0
\(172\) 448.000 + 775.959i 0.198603 + 0.343990i
\(173\) −1114.00 + 1929.50i −0.489571 + 0.847963i −0.999928 0.0120003i \(-0.996180\pi\)
0.510357 + 0.859963i \(0.329513\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 328.000 0.140477
\(177\) 0 0
\(178\) −365.000 632.199i −0.153696 0.266209i
\(179\) −410.000 710.141i −0.171200 0.296527i 0.767640 0.640882i \(-0.221431\pi\)
−0.938840 + 0.344354i \(0.888098\pi\)
\(180\) 0 0
\(181\) −3892.00 −1.59829 −0.799144 0.601140i \(-0.794713\pi\)
−0.799144 + 0.601140i \(0.794713\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) −360.000 + 623.538i −0.144237 + 0.249825i
\(185\) 1968.00 + 3408.68i 0.782109 + 1.35465i
\(186\) 0 0
\(187\) −216.000 + 374.123i −0.0844678 + 0.146303i
\(188\) −2268.00 −0.879845
\(189\) 0 0
\(190\) 1760.00 0.672020
\(191\) −2524.00 + 4371.70i −0.956179 + 1.65615i −0.224533 + 0.974466i \(0.572086\pi\)
−0.731646 + 0.681684i \(0.761248\pi\)
\(192\) 0 0
\(193\) 1481.00 + 2565.17i 0.552356 + 0.956709i 0.998104 + 0.0615502i \(0.0196044\pi\)
−0.445748 + 0.895159i \(0.647062\pi\)
\(194\) 147.000 254.611i 0.0544020 0.0942270i
\(195\) 0 0
\(196\) 0 0
\(197\) −3334.00 −1.20577 −0.602887 0.797826i \(-0.705983\pi\)
−0.602887 + 0.797826i \(0.705983\pi\)
\(198\) 0 0
\(199\) 930.000 + 1610.81i 0.331286 + 0.573805i 0.982764 0.184863i \(-0.0591841\pi\)
−0.651478 + 0.758667i \(0.725851\pi\)
\(200\) 982.500 + 1701.74i 0.347366 + 0.601656i
\(201\) 0 0
\(202\) −688.000 −0.239641
\(203\) 0 0
\(204\) 0 0
\(205\) −1456.00 + 2521.87i −0.496056 + 0.859194i
\(206\) 694.000 + 1202.04i 0.234725 + 0.406555i
\(207\) 0 0
\(208\) 574.000 994.197i 0.191345 0.331419i
\(209\) 880.000 0.291248
\(210\) 0 0
\(211\) −4268.00 −1.39252 −0.696259 0.717791i \(-0.745153\pi\)
−0.696259 + 0.717791i \(0.745153\pi\)
\(212\) 567.000 982.073i 0.183687 0.318156i
\(213\) 0 0
\(214\) 122.000 + 211.310i 0.0389708 + 0.0674994i
\(215\) −1024.00 + 1773.62i −0.324820 + 0.562604i
\(216\) 0 0
\(217\) 0 0
\(218\) 90.0000 0.0279613
\(219\) 0 0
\(220\) 448.000 + 775.959i 0.137292 + 0.237796i
\(221\) 756.000 + 1309.43i 0.230109 + 0.398560i
\(222\) 0 0
\(223\) 5432.00 1.63118 0.815591 0.578629i \(-0.196412\pi\)
0.815591 + 0.578629i \(0.196412\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 659.000 1141.42i 0.193965 0.335957i
\(227\) 1023.00 + 1771.89i 0.299114 + 0.518081i 0.975934 0.218068i \(-0.0699756\pi\)
−0.676819 + 0.736149i \(0.736642\pi\)
\(228\) 0 0
\(229\) −1490.00 + 2580.76i −0.429965 + 0.744721i −0.996870 0.0790622i \(-0.974807\pi\)
0.566905 + 0.823783i \(0.308141\pi\)
\(230\) −768.000 −0.220176
\(231\) 0 0
\(232\) −1650.00 −0.466930
\(233\) 2229.00 3860.74i 0.626724 1.08552i −0.361481 0.932379i \(-0.617729\pi\)
0.988205 0.153138i \(-0.0489379\pi\)
\(234\) 0 0
\(235\) −2592.00 4489.48i −0.719504 1.24622i
\(236\) 2835.00 4910.36i 0.781961 1.35440i
\(237\) 0 0
\(238\) 0 0
\(239\) −4440.00 −1.20167 −0.600836 0.799372i \(-0.705166\pi\)
−0.600836 + 0.799372i \(0.705166\pi\)
\(240\) 0 0
\(241\) 1651.00 + 2859.62i 0.441287 + 0.764332i 0.997785 0.0665168i \(-0.0211886\pi\)
−0.556498 + 0.830849i \(0.687855\pi\)
\(242\) 633.500 + 1097.25i 0.168277 + 0.291464i
\(243\) 0 0
\(244\) −3416.00 −0.896258
\(245\) 0 0
\(246\) 0 0
\(247\) 1540.00 2667.36i 0.396712 0.687125i
\(248\) −90.0000 155.885i −0.0230444 0.0399140i
\(249\) 0 0
\(250\) −48.0000 + 83.1384i −0.0121431 + 0.0210325i
\(251\) 1582.00 0.397829 0.198914 0.980017i \(-0.436258\pi\)
0.198914 + 0.980017i \(0.436258\pi\)
\(252\) 0 0
\(253\) −384.000 −0.0954224
\(254\) 888.000 1538.06i 0.219363 0.379947i
\(255\) 0 0
\(256\) 59.5000 + 103.057i 0.0145264 + 0.0251604i
\(257\) −1177.00 + 2038.62i −0.285678 + 0.494809i −0.972773 0.231758i \(-0.925552\pi\)
0.687095 + 0.726567i \(0.258885\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 3136.00 0.748025
\(261\) 0 0
\(262\) 559.000 + 968.216i 0.131813 + 0.228308i
\(263\) −1936.00 3353.25i −0.453912 0.786199i 0.544713 0.838623i \(-0.316639\pi\)
−0.998625 + 0.0524239i \(0.983305\pi\)
\(264\) 0 0
\(265\) 2592.00 0.600850
\(266\) 0 0
\(267\) 0 0
\(268\) 854.000 1479.17i 0.194651 0.337145i
\(269\) −90.0000 155.885i −0.0203992 0.0353325i 0.855646 0.517562i \(-0.173160\pi\)
−0.876045 + 0.482230i \(0.839827\pi\)
\(270\) 0 0
\(271\) 1016.00 1759.76i 0.227740 0.394458i −0.729398 0.684090i \(-0.760200\pi\)
0.957138 + 0.289632i \(0.0935330\pi\)
\(272\) 2214.00 0.493542
\(273\) 0 0
\(274\) −2274.00 −0.501377
\(275\) −524.000 + 907.595i −0.114903 + 0.199018i
\(276\) 0 0
\(277\) 2713.00 + 4699.05i 0.588478 + 1.01927i 0.994432 + 0.105380i \(0.0336059\pi\)
−0.405954 + 0.913893i \(0.633061\pi\)
\(278\) −105.000 + 181.865i −0.0226528 + 0.0392358i
\(279\) 0 0
\(280\) 0 0
\(281\) −842.000 −0.178753 −0.0893764 0.995998i \(-0.528487\pi\)
−0.0893764 + 0.995998i \(0.528487\pi\)
\(282\) 0 0
\(283\) −1891.00 3275.31i −0.397202 0.687975i 0.596177 0.802853i \(-0.296686\pi\)
−0.993380 + 0.114878i \(0.963352\pi\)
\(284\) 2688.00 + 4655.75i 0.561632 + 0.972775i
\(285\) 0 0
\(286\) −224.000 −0.0463126
\(287\) 0 0
\(288\) 0 0
\(289\) 998.500 1729.45i 0.203236 0.352016i
\(290\) −880.000 1524.20i −0.178191 0.308636i
\(291\) 0 0
\(292\) 2457.00 4255.65i 0.492415 0.852887i
\(293\) −4312.00 −0.859760 −0.429880 0.902886i \(-0.641444\pi\)
−0.429880 + 0.902886i \(0.641444\pi\)
\(294\) 0 0
\(295\) 12960.0 2.55783
\(296\) −1845.00 + 3195.63i −0.362292 + 0.627508i
\(297\) 0 0
\(298\) −1005.00 1740.71i −0.195363 0.338378i
\(299\) −672.000 + 1163.94i −0.129976 + 0.225125i
\(300\) 0 0
\(301\) 0 0
\(302\) 1112.00 0.211882
\(303\) 0 0
\(304\) −2255.00 3905.77i −0.425438 0.736880i
\(305\) −3904.00 6761.93i −0.732926 1.26946i
\(306\) 0 0
\(307\) −2674.00 −0.497112 −0.248556 0.968618i \(-0.579956\pi\)
−0.248556 + 0.968618i \(0.579956\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 96.0000 166.277i 0.0175885 0.0304642i
\(311\) 1884.00 + 3263.18i 0.343511 + 0.594978i 0.985082 0.172085i \(-0.0550505\pi\)
−0.641571 + 0.767063i \(0.721717\pi\)
\(312\) 0 0
\(313\) 1219.00 2111.37i 0.220134 0.381283i −0.734714 0.678376i \(-0.762684\pi\)
0.954849 + 0.297093i \(0.0960172\pi\)
\(314\) −124.000 −0.0222857
\(315\) 0 0
\(316\) −3080.00 −0.548302
\(317\) −1593.00 + 2759.16i −0.282245 + 0.488863i −0.971937 0.235239i \(-0.924413\pi\)
0.689692 + 0.724103i \(0.257746\pi\)
\(318\) 0 0
\(319\) −440.000 762.102i −0.0772266 0.133760i
\(320\) 1336.00 2314.02i 0.233390 0.404243i
\(321\) 0 0
\(322\) 0 0
\(323\) 5940.00 1.02325
\(324\) 0 0
\(325\) 1834.00 + 3176.58i 0.313022 + 0.542169i
\(326\) −1004.00 1738.98i −0.170572 0.295439i
\(327\) 0 0
\(328\) −2730.00 −0.459570
\(329\) 0 0
\(330\) 0 0
\(331\) −4336.00 + 7510.17i −0.720025 + 1.24712i 0.240965 + 0.970534i \(0.422536\pi\)
−0.960989 + 0.276585i \(0.910797\pi\)
\(332\) −4557.00 7892.96i −0.753307 1.30477i
\(333\) 0 0
\(334\) −1442.00 + 2497.62i −0.236236 + 0.409172i
\(335\) 3904.00 0.636711
\(336\) 0 0
\(337\) 814.000 0.131577 0.0657884 0.997834i \(-0.479044\pi\)
0.0657884 + 0.997834i \(0.479044\pi\)
\(338\) 706.500 1223.69i 0.113694 0.196924i
\(339\) 0 0
\(340\) 3024.00 + 5237.72i 0.482351 + 0.835457i
\(341\) 48.0000 83.1384i 0.00762271 0.0132029i
\(342\) 0 0
\(343\) 0 0
\(344\) −1920.00 −0.300929
\(345\) 0 0
\(346\) −1114.00 1929.50i −0.173090 0.299800i
\(347\) 4672.00 + 8092.14i 0.722784 + 1.25190i 0.959880 + 0.280413i \(0.0904713\pi\)
−0.237095 + 0.971486i \(0.576195\pi\)
\(348\) 0 0
\(349\) 5180.00 0.794496 0.397248 0.917711i \(-0.369965\pi\)
0.397248 + 0.917711i \(0.369965\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) −644.000 + 1115.44i −0.0975151 + 0.168901i
\(353\) −6089.00 10546.5i −0.918087 1.59017i −0.802317 0.596898i \(-0.796400\pi\)
−0.115770 0.993276i \(-0.536933\pi\)
\(354\) 0 0
\(355\) −6144.00 + 10641.7i −0.918562 + 1.59100i
\(356\) −5110.00 −0.760757
\(357\) 0 0
\(358\) 820.000 0.121057
\(359\) 220.000 381.051i 0.0323431 0.0560198i −0.849401 0.527748i \(-0.823036\pi\)
0.881744 + 0.471729i \(0.156370\pi\)
\(360\) 0 0
\(361\) −2620.50 4538.84i −0.382053 0.661735i
\(362\) 1946.00 3370.57i 0.282540 0.489374i
\(363\) 0 0
\(364\) 0 0
\(365\) 11232.0 1.61071
\(366\) 0 0
\(367\) −4908.00 8500.91i −0.698080 1.20911i −0.969131 0.246546i \(-0.920704\pi\)
0.271051 0.962565i \(-0.412629\pi\)
\(368\) 984.000 + 1704.34i 0.139387 + 0.241426i
\(369\) 0 0
\(370\) −3936.00 −0.553035
\(371\) 0 0
\(372\) 0 0
\(373\) 221.000 382.783i 0.0306781 0.0531361i −0.850279 0.526333i \(-0.823567\pi\)
0.880957 + 0.473197i \(0.156900\pi\)
\(374\) −216.000 374.123i −0.0298639 0.0517258i
\(375\) 0 0
\(376\) 2430.00 4208.88i 0.333292 0.577278i
\(377\) −3080.00 −0.420764
\(378\) 0 0
\(379\) −3960.00 −0.536706 −0.268353 0.963321i \(-0.586479\pi\)
−0.268353 + 0.963321i \(0.586479\pi\)
\(380\) 6160.00 10669.4i 0.831582 1.44034i
\(381\) 0 0
\(382\) −2524.00 4371.70i −0.338060 0.585538i
\(383\) −3354.00 + 5809.30i −0.447471 + 0.775043i −0.998221 0.0596280i \(-0.981009\pi\)
0.550750 + 0.834670i \(0.314342\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) −2962.00 −0.390575
\(387\) 0 0
\(388\) −1029.00 1782.28i −0.134638 0.233200i
\(389\) −6675.00 11561.4i −0.870015 1.50691i −0.861980 0.506943i \(-0.830775\pi\)
−0.00803563 0.999968i \(-0.502558\pi\)
\(390\) 0 0
\(391\) −2592.00 −0.335251
\(392\) 0 0
\(393\) 0 0
\(394\) 1667.00 2887.33i 0.213153 0.369192i
\(395\) −3520.00 6096.82i −0.448381 0.776618i
\(396\) 0 0
\(397\) −678.000 + 1174.33i −0.0857125 + 0.148458i −0.905695 0.423931i \(-0.860650\pi\)
0.819982 + 0.572389i \(0.193983\pi\)
\(398\) −1860.00 −0.234255
\(399\) 0 0
\(400\) 5371.00 0.671375
\(401\) 3111.00 5388.41i 0.387421 0.671033i −0.604681 0.796468i \(-0.706699\pi\)
0.992102 + 0.125435i \(0.0400326\pi\)
\(402\) 0 0
\(403\) −168.000 290.985i −0.0207659 0.0359677i
\(404\) −2408.00 + 4170.78i −0.296541 + 0.513624i
\(405\) 0 0
\(406\) 0 0
\(407\) −1968.00 −0.239681
\(408\) 0 0
\(409\) 2575.00 + 4460.03i 0.311309 + 0.539204i 0.978646 0.205552i \(-0.0658991\pi\)
−0.667337 + 0.744756i \(0.732566\pi\)
\(410\) −1456.00 2521.87i −0.175382 0.303771i
\(411\) 0 0
\(412\) 9716.00 1.16183
\(413\) 0 0
\(414\) 0 0
\(415\) 10416.0 18041.0i 1.23205 2.13398i
\(416\) 2254.00 + 3904.04i 0.265653 + 0.460124i
\(417\) 0 0
\(418\) −440.000 + 762.102i −0.0514859 + 0.0891762i
\(419\) 2310.00 0.269334 0.134667 0.990891i \(-0.457004\pi\)
0.134667 + 0.990891i \(0.457004\pi\)
\(420\) 0 0
\(421\) 1262.00 0.146095 0.0730476 0.997328i \(-0.476727\pi\)
0.0730476 + 0.997328i \(0.476727\pi\)
\(422\) 2134.00 3696.20i 0.246165 0.426370i
\(423\) 0 0
\(424\) 1215.00 + 2104.44i 0.139164 + 0.241039i
\(425\) −3537.00 + 6126.26i −0.403693 + 0.699218i
\(426\) 0 0
\(427\) 0 0
\(428\) 1708.00 0.192896
\(429\) 0 0
\(430\) −1024.00 1773.62i −0.114841 0.198911i
\(431\) −2244.00 3886.72i −0.250788 0.434378i 0.712955 0.701210i \(-0.247356\pi\)
−0.963743 + 0.266832i \(0.914023\pi\)
\(432\) 0 0
\(433\) −17038.0 −1.89098 −0.945490 0.325652i \(-0.894416\pi\)
−0.945490 + 0.325652i \(0.894416\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 315.000 545.596i 0.0346004 0.0599296i
\(437\) 2640.00 + 4572.61i 0.288989 + 0.500544i
\(438\) 0 0
\(439\) 8100.00 14029.6i 0.880619 1.52528i 0.0299658 0.999551i \(-0.490460\pi\)
0.850654 0.525727i \(-0.176206\pi\)
\(440\) −1920.00 −0.208028
\(441\) 0 0
\(442\) −1512.00 −0.162712
\(443\) −4386.00 + 7596.77i −0.470395 + 0.814749i −0.999427 0.0338535i \(-0.989222\pi\)
0.529031 + 0.848602i \(0.322555\pi\)
\(444\) 0 0
\(445\) −5840.00 10115.2i −0.622118 1.07754i
\(446\) −2716.00 + 4704.25i −0.288355 + 0.499446i
\(447\) 0 0
\(448\) 0 0
\(449\) −2130.00 −0.223877 −0.111939 0.993715i \(-0.535706\pi\)
−0.111939 + 0.993715i \(0.535706\pi\)
\(450\) 0 0
\(451\) −728.000 1260.93i −0.0760093 0.131652i
\(452\) −4613.00 7989.95i −0.480038 0.831451i
\(453\) 0 0
\(454\) −2046.00 −0.211506
\(455\) 0 0
\(456\) 0 0
\(457\) −5267.00 + 9122.71i −0.539124 + 0.933791i 0.459827 + 0.888009i \(0.347911\pi\)
−0.998951 + 0.0457824i \(0.985422\pi\)
\(458\) −1490.00 2580.76i −0.152016 0.263299i
\(459\) 0 0
\(460\) −2688.00 + 4655.75i −0.272454 + 0.471903i
\(461\) −9268.00 −0.936342 −0.468171 0.883638i \(-0.655087\pi\)
−0.468171 + 0.883638i \(0.655087\pi\)
\(462\) 0 0
\(463\) −9392.00 −0.942728 −0.471364 0.881939i \(-0.656238\pi\)
−0.471364 + 0.881939i \(0.656238\pi\)
\(464\) −2255.00 + 3905.77i −0.225616 + 0.390778i
\(465\) 0 0
\(466\) 2229.00 + 3860.74i 0.221580 + 0.383788i
\(467\) 5403.00 9358.27i 0.535377 0.927300i −0.463768 0.885957i \(-0.653503\pi\)
0.999145 0.0413434i \(-0.0131638\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 5184.00 0.508766
\(471\) 0 0
\(472\) 6075.00 + 10522.2i 0.592425 + 1.02611i
\(473\) −512.000 886.810i −0.0497712 0.0862063i
\(474\) 0 0
\(475\) 14410.0 1.39195
\(476\) 0 0
\(477\) 0 0
\(478\) 2220.00 3845.15i 0.212428 0.367936i
\(479\) −2470.00 4278.17i −0.235610 0.408088i 0.723840 0.689968i \(-0.242375\pi\)
−0.959450 + 0.281880i \(0.909042\pi\)
\(480\) 0 0
\(481\) −3444.00 + 5965.18i −0.326472 + 0.565466i
\(482\) −3302.00 −0.312037
\(483\) 0 0
\(484\) 8869.00 0.832926
\(485\) 2352.00 4073.78i 0.220204 0.381404i
\(486\) 0 0
\(487\) 2608.00 + 4517.19i 0.242669 + 0.420315i 0.961474 0.274897i \(-0.0886438\pi\)
−0.718805 + 0.695212i \(0.755310\pi\)
\(488\) 3660.00 6339.31i 0.339509 0.588047i
\(489\) 0 0
\(490\) 0 0
\(491\) −4412.00 −0.405521 −0.202760 0.979228i \(-0.564991\pi\)
−0.202760 + 0.979228i \(0.564991\pi\)
\(492\) 0 0
\(493\) −2970.00 5144.19i −0.271323 0.469945i
\(494\) 1540.00 + 2667.36i 0.140259 + 0.242935i
\(495\) 0 0
\(496\) −492.000 −0.0445392
\(497\) 0 0
\(498\) 0 0
\(499\) −9530.00 + 16506.4i −0.854953 + 1.48082i 0.0217362 + 0.999764i \(0.493081\pi\)
−0.876689 + 0.481058i \(0.840253\pi\)
\(500\) 336.000 + 581.969i 0.0300528 + 0.0520529i
\(501\) 0 0
\(502\) −791.000 + 1370.05i −0.0703268 + 0.121810i
\(503\) 12768.0 1.13180 0.565902 0.824473i \(-0.308528\pi\)
0.565902 + 0.824473i \(0.308528\pi\)
\(504\) 0 0
\(505\) −11008.0 −0.969999
\(506\) 192.000 332.554i 0.0168685 0.0292170i
\(507\) 0 0
\(508\) −6216.00 10766.4i −0.542894 0.940321i
\(509\) 2750.00 4763.14i 0.239473 0.414779i −0.721090 0.692841i \(-0.756359\pi\)
0.960563 + 0.278062i \(0.0896921\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 11521.0 0.994455
\(513\) 0 0
\(514\) −1177.00 2038.62i −0.101002 0.174941i
\(515\) 11104.0 + 19232.7i 0.950098 + 1.64562i
\(516\) 0 0
\(517\) 2592.00 0.220495
\(518\) 0 0
\(519\) 0 0
\(520\) −3360.00 + 5819.69i −0.283357 + 0.490789i
\(521\) 3669.00 + 6354.89i 0.308526 + 0.534382i 0.978040 0.208417i \(-0.0668311\pi\)
−0.669514 + 0.742799i \(0.733498\pi\)
\(522\) 0 0
\(523\) −8791.00 + 15226.5i −0.734997 + 1.27305i 0.219727 + 0.975561i \(0.429483\pi\)
−0.954725 + 0.297491i \(0.903850\pi\)
\(524\) 7826.00 0.652444
\(525\) 0 0
\(526\) 3872.00 0.320964
\(527\) 324.000 561.184i 0.0267811 0.0463863i
\(528\) 0 0
\(529\) 4931.50 + 8541.61i 0.405318 + 0.702031i
\(530\) −1296.00 + 2244.74i −0.106216 + 0.183972i
\(531\) 0 0
\(532\) 0 0
\(533\) −5096.00 −0.414132
\(534\) 0 0
\(535\) 1952.00 + 3380.96i 0.157743 + 0.273218i
\(536\) 1830.00 + 3169.65i 0.147470 + 0.255426i
\(537\) 0 0
\(538\) 180.000 0.0144244
\(539\) 0 0
\(540\) 0 0
\(541\) 809.000 1401.23i 0.0642914 0.111356i −0.832088 0.554644i \(-0.812855\pi\)
0.896379 + 0.443288i \(0.146188\pi\)
\(542\) 1016.00 + 1759.76i 0.0805183 + 0.139462i
\(543\) 0 0
\(544\) −4347.00 + 7529.22i −0.342603 + 0.593406i
\(545\) 1440.00 0.113179
\(546\) 0 0
\(547\) 16144.0 1.26192 0.630958 0.775817i \(-0.282662\pi\)
0.630958 + 0.775817i \(0.282662\pi\)
\(548\) −7959.00 + 13785.4i −0.620423 + 1.07460i
\(549\) 0 0
\(550\) −524.000 907.595i −0.0406244 0.0703636i
\(551\) −6050.00 + 10478.9i −0.467765 + 0.810193i
\(552\) 0 0
\(553\) 0 0
\(554\) −5426.00 −0.416117
\(555\) 0 0
\(556\) 735.000 + 1273.06i 0.0560628 + 0.0971037i
\(557\) 2327.00 + 4030.48i 0.177016 + 0.306601i 0.940857 0.338803i \(-0.110022\pi\)
−0.763841 + 0.645405i \(0.776689\pi\)
\(558\) 0 0
\(559\) −3584.00 −0.271175
\(560\) 0 0
\(561\) 0 0
\(562\) 421.000 729.193i 0.0315993 0.0547316i
\(563\) −5039.00 8727.80i −0.377209 0.653345i 0.613446 0.789736i \(-0.289783\pi\)
−0.990655 + 0.136392i \(0.956449\pi\)
\(564\) 0 0
\(565\) 10544.0 18262.7i 0.785114 1.35986i
\(566\) 3782.00 0.280865
\(567\) 0 0
\(568\) −11520.0 −0.851001
\(569\) −2965.00 + 5135.53i −0.218452 + 0.378370i −0.954335 0.298739i \(-0.903434\pi\)
0.735883 + 0.677109i \(0.236767\pi\)
\(570\) 0 0
\(571\) 9524.00 + 16496.1i 0.698016 + 1.20900i 0.969153 + 0.246458i \(0.0792668\pi\)
−0.271138 + 0.962541i \(0.587400\pi\)
\(572\) −784.000 + 1357.93i −0.0573089 + 0.0992619i
\(573\) 0 0
\(574\) 0 0
\(575\) −6288.00 −0.456048
\(576\) 0 0
\(577\) −7183.00 12441.3i −0.518253 0.897641i −0.999775 0.0212070i \(-0.993249\pi\)
0.481522 0.876434i \(-0.340084\pi\)
\(578\) 998.500 + 1729.45i 0.0718549 + 0.124456i
\(579\) 0 0
\(580\) −12320.0 −0.882000
\(581\) 0 0
\(582\) 0 0
\(583\) −648.000 + 1122.37i −0.0460333 + 0.0797320i
\(584\) 5265.00 + 9119.25i 0.373060 + 0.646159i
\(585\) 0 0
\(586\) 2156.00 3734.30i 0.151986 0.263247i
\(587\) −3626.00 −0.254959 −0.127480 0.991841i \(-0.540689\pi\)
−0.127480 + 0.991841i \(0.540689\pi\)
\(588\) 0 0
\(589\) −1320.00 −0.0923424
\(590\) −6480.00 + 11223.7i −0.452165 + 0.783173i
\(591\) 0 0
\(592\) 5043.00 + 8734.73i 0.350112 + 0.606411i
\(593\) 531.000 919.719i 0.0367716 0.0636903i −0.847054 0.531507i \(-0.821626\pi\)
0.883826 + 0.467817i \(0.154959\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) −14070.0 −0.966996
\(597\) 0 0
\(598\) −672.000 1163.94i −0.0459534 0.0795936i
\(599\) −5100.00 8833.46i −0.347880 0.602547i 0.637992 0.770043i \(-0.279765\pi\)
−0.985873 + 0.167496i \(0.946432\pi\)
\(600\) 0 0
\(601\) 25158.0 1.70751 0.853757 0.520671i \(-0.174318\pi\)
0.853757 + 0.520671i \(0.174318\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 3892.00 6741.14i 0.262191 0.454128i
\(605\) 10136.0 + 17556.1i 0.681136 + 1.17976i
\(606\) 0 0
\(607\) 12832.0 22225.7i 0.858047 1.48618i −0.0157413 0.999876i \(-0.505011\pi\)
0.873789 0.486306i \(-0.161656\pi\)
\(608\) 17710.0 1.18131
\(609\) 0 0
\(610\) 7808.00 0.518257
\(611\) 4536.00 7856.58i 0.300339 0.520202i
\(612\) 0 0
\(613\) −9509.00 16470.1i −0.626533 1.08519i −0.988242 0.152896i \(-0.951140\pi\)
0.361709 0.932291i \(-0.382193\pi\)
\(614\) 1337.00 2315.75i 0.0878777 0.152209i
\(615\) 0 0
\(616\) 0 0
\(617\) −17334.0 −1.13102 −0.565511 0.824741i \(-0.691321\pi\)
−0.565511 + 0.824741i \(0.691321\pi\)
\(618\) 0 0
\(619\) 9365.00 + 16220.7i 0.608096 + 1.05325i 0.991554 + 0.129694i \(0.0413996\pi\)
−0.383459 + 0.923558i \(0.625267\pi\)
\(620\) −672.000 1163.94i −0.0435293 0.0753950i
\(621\) 0 0
\(622\) −3768.00 −0.242899
\(623\) 0 0
\(624\) 0 0
\(625\) 7419.50 12851.0i 0.474848 0.822461i
\(626\) 1219.00 + 2111.37i 0.0778291 + 0.134804i
\(627\) 0 0
\(628\) −434.000 + 751.710i −0.0275772 + 0.0477651i
\(629\) −13284.0 −0.842079
\(630\) 0 0
\(631\) −6928.00 −0.437083 −0.218541 0.975828i \(-0.570130\pi\)
−0.218541 + 0.975828i \(0.570130\pi\)
\(632\) 3300.00 5715.77i 0.207701 0.359748i
\(633\) 0 0
\(634\) −1593.00 2759.16i −0.0997888 0.172839i
\(635\) 14208.0 24609.0i 0.887917 1.53792i
\(636\) 0 0
\(637\) 0 0
\(638\) 880.000 0.0546074
\(639\) 0 0
\(640\) 11640.0 + 20161.1i 0.718924 + 1.24521i
\(641\) 8151.00 + 14117.9i 0.502255 + 0.869930i 0.999997 + 0.00260525i \(0.000829277\pi\)
−0.497742 + 0.867325i \(0.665837\pi\)
\(642\) 0 0
\(643\) −4718.00 −0.289362 −0.144681 0.989478i \(-0.546216\pi\)
−0.144681 + 0.989478i \(0.546216\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) −2970.00 + 5144.19i −0.180887 + 0.313306i
\(647\) 10718.0 + 18564.1i 0.651264 + 1.12802i 0.982816 + 0.184586i \(0.0590944\pi\)
−0.331552 + 0.943437i \(0.607572\pi\)
\(648\) 0 0
\(649\) −3240.00 + 5611.84i −0.195965 + 0.339421i
\(650\) −3668.00 −0.221340
\(651\) 0 0
\(652\) −14056.0 −0.844287
\(653\) 2229.00 3860.74i 0.133580 0.231367i −0.791474 0.611202i \(-0.790686\pi\)
0.925054 + 0.379836i \(0.124019\pi\)
\(654\) 0 0
\(655\) 8944.00 + 15491.5i 0.533544 + 0.924124i
\(656\) −3731.00 + 6462.28i −0.222060 + 0.384618i
\(657\) 0 0
\(658\) 0 0
\(659\) 26640.0 1.57473 0.787365 0.616487i \(-0.211445\pi\)
0.787365 + 0.616487i \(0.211445\pi\)
\(660\) 0 0
\(661\) 3716.00 + 6436.30i 0.218662 + 0.378734i 0.954399 0.298533i \(-0.0964974\pi\)
−0.735737 + 0.677267i \(0.763164\pi\)
\(662\) −4336.00 7510.17i −0.254567 0.440923i
\(663\) 0 0
\(664\) 19530.0 1.14143
\(665\) 0 0
\(666\) 0 0
\(667\) 2640.00 4572.61i 0.153255 0.265446i
\(668\) 10094.0 + 17483.3i 0.584654 + 1.01265i
\(669\) 0 0
\(670\) −1952.00 + 3380.96i −0.112556 + 0.194952i
\(671\) 3904.00 0.224608
\(672\) 0 0
\(673\) 58.0000 0.00332204 0.00166102 0.999999i \(-0.499471\pi\)
0.00166102 + 0.999999i \(0.499471\pi\)
\(674\) −407.000 + 704.945i −0.0232597 + 0.0402870i
\(675\) 0 0
\(676\) −4945.50 8565.86i −0.281378 0.487361i
\(677\) 10758.0 18633.4i 0.610729 1.05781i −0.380389 0.924827i \(-0.624210\pi\)
0.991118 0.132987i \(-0.0424568\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) −12960.0 −0.730873
\(681\) 0 0
\(682\) 48.0000 + 83.1384i 0.00269504 + 0.00466794i
\(683\) 9054.00 + 15682.0i 0.507235 + 0.878557i 0.999965 + 0.00837480i \(0.00266581\pi\)
−0.492730 + 0.870182i \(0.664001\pi\)
\(684\) 0 0
\(685\) −36384.0 −2.02943
\(686\) 0 0
\(687\) 0 0
\(688\) −2624.00 + 4544.90i −0.145406 + 0.251850i
\(689\) 2268.00 + 3928.29i 0.125405 + 0.217208i
\(690\) 0 0
\(691\) −5039.00 + 8727.80i −0.277413 + 0.480494i −0.970741 0.240128i \(-0.922810\pi\)
0.693328 + 0.720622i \(0.256144\pi\)
\(692\) −15596.0 −0.856750
\(693\) 0 0
\(694\) −9344.00 −0.511086
\(695\) −1680.00 + 2909.85i −0.0916921 + 0.158815i
\(696\) 0 0
\(697\) −4914.00 8511.30i −0.267046 0.462537i
\(698\) −2590.00 + 4486.01i −0.140448 + 0.243264i
\(699\) 0 0
\(700\) 0 0
\(701\) −18762.0 −1.01089 −0.505443 0.862860i \(-0.668671\pi\)
−0.505443 + 0.862860i \(0.668671\pi\)
\(702\) 0 0
\(703\) 13530.0 + 23434.6i 0.725880 + 1.25726i
\(704\) 668.000 + 1157.01i 0.0357616 + 0.0619410i
\(705\) 0 0
\(706\) 12178.0 0.649186
\(707\) 0 0
\(708\) 0 0
\(709\) −3405.00 + 5897.63i −0.180363 + 0.312398i −0.942004 0.335601i \(-0.891061\pi\)
0.761641 + 0.647999i \(0.224394\pi\)
\(710\) −6144.00 10641.7i −0.324761 0.562502i
\(711\) 0 0
\(712\) 5475.00 9482.98i 0.288180 0.499143i
\(713\) 576.000 0.0302544
\(714\) 0 0
\(715\) −3584.00 −0.187460
\(716\) 2870.00 4970.99i 0.149800 0.259462i
\(717\) 0 0
\(718\) 220.000 + 381.051i 0.0114350 + 0.0198060i
\(719\) −2430.00 + 4208.88i −0.126041 + 0.218310i −0.922140 0.386858i \(-0.873561\pi\)
0.796098 + 0.605167i \(0.206894\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 5241.00 0.270152
\(723\) 0 0
\(724\) −13622.0 23594.0i −0.699251 1.21114i
\(725\) −7205.00 12479.4i −0.369085 0.639275i
\(726\) 0 0
\(727\) 13636.0 0.695641 0.347821 0.937561i \(-0.386922\pi\)
0.347821 + 0.937561i \(0.386922\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) −5616.00 + 9727.20i −0.284736 + 0.493178i
\(731\) −3456.00 5985.97i −0.174863 0.302871i
\(732\) 0 0
\(733\) 1044.00 1808.26i 0.0526071 0.0911182i −0.838523 0.544867i \(-0.816580\pi\)
0.891130 + 0.453749i \(0.149914\pi\)
\(734\) 9816.00 0.493617
\(735\) 0 0
\(736\) −7728.00 −0.387035
\(737\) −976.000 + 1690.48i −0.0487808 + 0.0844908i
\(738\) 0 0
\(739\) 2580.00 + 4468.69i 0.128426 + 0.222440i 0.923067 0.384639i \(-0.125674\pi\)
−0.794641 + 0.607080i \(0.792341\pi\)
\(740\) −13776.0 + 23860.7i −0.684346 + 1.18532i
\(741\) 0 0
\(742\) 0 0
\(743\) 28152.0 1.39004 0.695018 0.718992i \(-0.255396\pi\)
0.695018 + 0.718992i \(0.255396\pi\)
\(744\) 0 0
\(745\) −16080.0 27851.4i −0.790773 1.36966i
\(746\) 221.000 + 382.783i 0.0108464 + 0.0187864i
\(747\) 0 0
\(748\) −3024.00 −0.147819
\(749\) 0 0
\(750\) 0 0
\(751\) 8404.00 14556.2i 0.408344 0.707272i −0.586360 0.810050i \(-0.699440\pi\)
0.994704 + 0.102778i \(0.0327731\pi\)
\(752\) −6642.00 11504.3i −0.322086 0.557870i
\(753\) 0 0
\(754\) 1540.00 2667.36i 0.0743813 0.128832i
\(755\) 17792.0 0.857639
\(756\) 0 0
\(757\) 21674.0 1.04063 0.520314 0.853975i \(-0.325815\pi\)
0.520314 + 0.853975i \(0.325815\pi\)
\(758\) 1980.00 3429.46i 0.0948771 0.164332i
\(759\) 0 0
\(760\) 13200.0 + 22863.1i 0.630019 + 1.09122i
\(761\) −3711.00 + 6427.64i −0.176772 + 0.306178i −0.940773 0.339037i \(-0.889899\pi\)
0.764001 + 0.645215i \(0.223232\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) −35336.0 −1.67331
\(765\) 0 0
\(766\) −3354.00 5809.30i −0.158205 0.274019i
\(767\) 11340.0 + 19641.5i 0.533851 + 0.924657i
\(768\) 0 0
\(769\) −13790.0 −0.646658 −0.323329 0.946287i \(-0.604802\pi\)
−0.323329 + 0.946287i \(0.604802\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −10367.0 + 17956.2i −0.483312 + 0.837120i
\(773\) 3116.00 + 5397.07i 0.144987 + 0.251124i 0.929368 0.369155i \(-0.120353\pi\)
−0.784381 + 0.620279i \(0.787019\pi\)
\(774\) 0 0
\(775\) 786.000 1361.39i 0.0364309 0.0631002i
\(776\) 4410.00 0.204007
\(777\) 0 0
\(778\) 13350.0 0.615194
\(779\) −10010.0 + 17337.8i −0.460392 + 0.797423i
\(780\) 0 0
\(781\) −3072.00 5320.86i −0.140749 0.243784i
\(782\) 1296.00 2244.74i 0.0592645 0.102649i
\(783\) 0 0
\(784\) 0 0
\(785\) −1984.00 −0.0902064
\(786\) 0 0
\(787\) −883.000 1529.40i −0.0399943 0.0692722i 0.845335 0.534236i \(-0.179401\pi\)
−0.885330 + 0.464964i \(0.846067\pi\)
\(788\) −11669.0 20211.3i −0.527527 0.913703i
\(789\) 0 0
\(790\) 7040.00 0.317053