Properties

Label 441.4.e.w.226.1
Level $441$
Weight $4$
Character 441.226
Analytic conductor $26.020$
Analytic rank $0$
Dimension $6$
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: \(6\)
Relative dimension: \(3\) over \(\Q(\zeta_{3})\)
Coefficient field: 6.0.9924270768.1
Defining polynomial: \(x^{6} - x^{5} + 25 x^{4} + 12 x^{3} + 582 x^{2} - 144 x + 36\)
Coefficient ring: \(\Z[a_1, \ldots, a_{19}]\)
Coefficient ring index: \( 3 \)
Twist minimal: no (minimal twist has level 21)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 226.1
Root \(-2.27818 + 3.94593i\) of defining polynomial
Character \(\chi\) \(=\) 441.226
Dual form 441.4.e.w.361.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-2.27818 + 3.94593i) q^{2} +(-6.38024 - 11.0509i) q^{4} +(-8.93660 + 15.4786i) q^{5} +21.6905 q^{8} +O(q^{10})\) \(q+(-2.27818 + 3.94593i) q^{2} +(-6.38024 - 11.0509i) q^{4} +(-8.93660 + 15.4786i) q^{5} +21.6905 q^{8} +(-40.7184 - 70.5264i) q^{10} +(-5.69708 - 9.86762i) q^{11} +13.0987 q^{13} +(1.62706 - 2.81815i) q^{16} +(-26.6337 - 46.1309i) q^{17} +(-21.2111 + 36.7388i) q^{19} +228.071 q^{20} +51.9159 q^{22} +(76.0427 - 131.710i) q^{23} +(-97.2257 - 168.400i) q^{25} +(-29.8412 + 51.6864i) q^{26} -186.493 q^{29} +(-78.9369 - 136.723i) q^{31} +(94.1753 + 163.116i) q^{32} +242.706 q^{34} +(-1.87294 + 3.24403i) q^{37} +(-96.6457 - 167.395i) q^{38} +(-193.839 + 335.739i) q^{40} -39.3230 q^{41} +429.439 q^{43} +(-72.6974 + 125.916i) q^{44} +(346.478 + 600.118i) q^{46} +(-10.5934 + 18.3484i) q^{47} +885.992 q^{50} +(-83.5726 - 144.752i) q^{52} +(182.952 + 316.882i) q^{53} +203.650 q^{55} +(424.866 - 735.889i) q^{58} +(113.289 + 196.222i) q^{59} +(325.987 - 564.626i) q^{61} +719.331 q^{62} -832.161 q^{64} +(-117.058 + 202.750i) q^{65} +(-72.7166 - 125.949i) q^{67} +(-339.858 + 588.652i) q^{68} +368.962 q^{71} +(304.453 + 527.328i) q^{73} +(-8.53380 - 14.7810i) q^{74} +541.328 q^{76} +(-455.119 + 788.289i) q^{79} +(29.0808 + 50.3694i) q^{80} +(89.5850 - 155.166i) q^{82} -327.929 q^{83} +952.058 q^{85} +(-978.340 + 1694.53i) q^{86} +(-123.572 - 214.033i) q^{88} +(18.8059 - 32.5728i) q^{89} -1940.68 q^{92} +(-48.2676 - 83.6019i) q^{94} +(-379.111 - 656.640i) q^{95} -722.013 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6q + q^{2} - 25q^{4} - 11q^{5} - 78q^{8} + O(q^{10}) \) \( 6q + q^{2} - 25q^{4} - 11q^{5} - 78q^{8} - 55q^{10} + 35q^{11} - 124q^{13} - 241q^{16} - 48q^{17} - 202q^{19} + 878q^{20} - 14q^{22} + 216q^{23} - 130q^{25} - 274q^{26} - 106q^{29} - 95q^{31} + 683q^{32} + 48q^{34} - 262q^{37} + 398q^{38} + 21q^{40} + 488q^{41} + 720q^{43} - 905q^{44} + 1056q^{46} + 210q^{47} + 2756q^{50} + 324q^{52} + 393q^{53} + 2062q^{55} + 1249q^{58} - 1143q^{59} - 70q^{61} + 2118q^{62} - 798q^{64} - 472q^{65} + 628q^{67} - 1944q^{68} - 636q^{71} + 988q^{73} + 1002q^{74} + 4680q^{76} - 861q^{79} - 175q^{80} + 124q^{82} + 1038q^{83} + 3600q^{85} - 3208q^{86} + 891q^{88} - 1766q^{89} + 1344q^{92} - 3294q^{94} - 736q^{95} - 38q^{97} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.27818 + 3.94593i −0.805459 + 1.39510i 0.110521 + 0.993874i \(0.464748\pi\)
−0.915981 + 0.401223i \(0.868585\pi\)
\(3\) 0 0
\(4\) −6.38024 11.0509i −0.797530 1.38136i
\(5\) −8.93660 + 15.4786i −0.799314 + 1.38445i 0.120749 + 0.992683i \(0.461470\pi\)
−0.920063 + 0.391769i \(0.871863\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 21.6905 0.958592
\(9\) 0 0
\(10\) −40.7184 70.5264i −1.28763 2.23024i
\(11\) −5.69708 9.86762i −0.156158 0.270473i 0.777322 0.629102i \(-0.216577\pi\)
−0.933480 + 0.358630i \(0.883244\pi\)
\(12\) 0 0
\(13\) 13.0987 0.279455 0.139728 0.990190i \(-0.455377\pi\)
0.139728 + 0.990190i \(0.455377\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 1.62706 2.81815i 0.0254228 0.0440336i
\(17\) −26.6337 46.1309i −0.379977 0.658140i 0.611081 0.791568i \(-0.290735\pi\)
−0.991059 + 0.133428i \(0.957402\pi\)
\(18\) 0 0
\(19\) −21.2111 + 36.7388i −0.256114 + 0.443603i −0.965198 0.261522i \(-0.915776\pi\)
0.709083 + 0.705125i \(0.249109\pi\)
\(20\) 228.071 2.54991
\(21\) 0 0
\(22\) 51.9159 0.503114
\(23\) 76.0427 131.710i 0.689391 1.19406i −0.282644 0.959225i \(-0.591211\pi\)
0.972035 0.234836i \(-0.0754553\pi\)
\(24\) 0 0
\(25\) −97.2257 168.400i −0.777806 1.34720i
\(26\) −29.8412 + 51.6864i −0.225090 + 0.389867i
\(27\) 0 0
\(28\) 0 0
\(29\) −186.493 −1.19417 −0.597085 0.802178i \(-0.703675\pi\)
−0.597085 + 0.802178i \(0.703675\pi\)
\(30\) 0 0
\(31\) −78.9369 136.723i −0.457338 0.792133i 0.541481 0.840713i \(-0.317864\pi\)
−0.998819 + 0.0485801i \(0.984530\pi\)
\(32\) 94.1753 + 163.116i 0.520250 + 0.901099i
\(33\) 0 0
\(34\) 242.706 1.22423
\(35\) 0 0
\(36\) 0 0
\(37\) −1.87294 + 3.24403i −0.00832188 + 0.0144139i −0.870156 0.492776i \(-0.835982\pi\)
0.861834 + 0.507190i \(0.169316\pi\)
\(38\) −96.6457 167.395i −0.412579 0.714608i
\(39\) 0 0
\(40\) −193.839 + 335.739i −0.766216 + 1.32712i
\(41\) −39.3230 −0.149786 −0.0748930 0.997192i \(-0.523862\pi\)
−0.0748930 + 0.997192i \(0.523862\pi\)
\(42\) 0 0
\(43\) 429.439 1.52300 0.761498 0.648168i \(-0.224464\pi\)
0.761498 + 0.648168i \(0.224464\pi\)
\(44\) −72.6974 + 125.916i −0.249080 + 0.431420i
\(45\) 0 0
\(46\) 346.478 + 600.118i 1.11055 + 1.92354i
\(47\) −10.5934 + 18.3484i −0.0328768 + 0.0569444i −0.881996 0.471258i \(-0.843800\pi\)
0.849119 + 0.528202i \(0.177134\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 885.992 2.50596
\(51\) 0 0
\(52\) −83.5726 144.752i −0.222874 0.386029i
\(53\) 182.952 + 316.882i 0.474158 + 0.821266i 0.999562 0.0295866i \(-0.00941909\pi\)
−0.525404 + 0.850853i \(0.676086\pi\)
\(54\) 0 0
\(55\) 203.650 0.499276
\(56\) 0 0
\(57\) 0 0
\(58\) 424.866 735.889i 0.961856 1.66598i
\(59\) 113.289 + 196.222i 0.249982 + 0.432982i 0.963521 0.267634i \(-0.0862419\pi\)
−0.713538 + 0.700616i \(0.752909\pi\)
\(60\) 0 0
\(61\) 325.987 564.626i 0.684235 1.18513i −0.289442 0.957196i \(-0.593470\pi\)
0.973677 0.227934i \(-0.0731970\pi\)
\(62\) 719.331 1.47347
\(63\) 0 0
\(64\) −832.161 −1.62532
\(65\) −117.058 + 202.750i −0.223372 + 0.386892i
\(66\) 0 0
\(67\) −72.7166 125.949i −0.132593 0.229658i 0.792082 0.610414i \(-0.208997\pi\)
−0.924675 + 0.380756i \(0.875664\pi\)
\(68\) −339.858 + 588.652i −0.606086 + 1.04977i
\(69\) 0 0
\(70\) 0 0
\(71\) 368.962 0.616728 0.308364 0.951268i \(-0.400218\pi\)
0.308364 + 0.951268i \(0.400218\pi\)
\(72\) 0 0
\(73\) 304.453 + 527.328i 0.488130 + 0.845466i 0.999907 0.0136522i \(-0.00434576\pi\)
−0.511777 + 0.859119i \(0.671012\pi\)
\(74\) −8.53380 14.7810i −0.0134059 0.0232197i
\(75\) 0 0
\(76\) 541.328 0.817034
\(77\) 0 0
\(78\) 0 0
\(79\) −455.119 + 788.289i −0.648163 + 1.12265i 0.335399 + 0.942076i \(0.391129\pi\)
−0.983561 + 0.180574i \(0.942204\pi\)
\(80\) 29.0808 + 50.3694i 0.0406416 + 0.0703933i
\(81\) 0 0
\(82\) 89.5850 155.166i 0.120646 0.208966i
\(83\) −327.929 −0.433674 −0.216837 0.976208i \(-0.569574\pi\)
−0.216837 + 0.976208i \(0.569574\pi\)
\(84\) 0 0
\(85\) 952.058 1.21489
\(86\) −978.340 + 1694.53i −1.22671 + 2.12473i
\(87\) 0 0
\(88\) −123.572 214.033i −0.149691 0.259273i
\(89\) 18.8059 32.5728i 0.0223980 0.0387945i −0.854609 0.519272i \(-0.826203\pi\)
0.877007 + 0.480477i \(0.159537\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) −1940.68 −2.19924
\(93\) 0 0
\(94\) −48.2676 83.6019i −0.0529619 0.0917327i
\(95\) −379.111 656.640i −0.409431 0.709156i
\(96\) 0 0
\(97\) −722.013 −0.755766 −0.377883 0.925853i \(-0.623348\pi\)
−0.377883 + 0.925853i \(0.623348\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) −1240.65 + 2148.86i −1.24065 + 2.14886i
\(101\) −759.336 1315.21i −0.748087 1.29572i −0.948739 0.316062i \(-0.897639\pi\)
0.200652 0.979663i \(-0.435694\pi\)
\(102\) 0 0
\(103\) −525.942 + 910.957i −0.503132 + 0.871450i 0.496862 + 0.867830i \(0.334486\pi\)
−0.999993 + 0.00361990i \(0.998848\pi\)
\(104\) 284.116 0.267883
\(105\) 0 0
\(106\) −1667.19 −1.52766
\(107\) 383.260 663.826i 0.346273 0.599762i −0.639312 0.768948i \(-0.720781\pi\)
0.985584 + 0.169186i \(0.0541139\pi\)
\(108\) 0 0
\(109\) 713.524 + 1235.86i 0.627002 + 1.08600i 0.988150 + 0.153491i \(0.0490516\pi\)
−0.361148 + 0.932509i \(0.617615\pi\)
\(110\) −463.952 + 803.588i −0.402146 + 0.696538i
\(111\) 0 0
\(112\) 0 0
\(113\) −362.564 −0.301833 −0.150917 0.988546i \(-0.548222\pi\)
−0.150917 + 0.988546i \(0.548222\pi\)
\(114\) 0 0
\(115\) 1359.13 + 2354.08i 1.10208 + 1.90886i
\(116\) 1189.87 + 2060.92i 0.952386 + 1.64958i
\(117\) 0 0
\(118\) −1032.37 −0.805402
\(119\) 0 0
\(120\) 0 0
\(121\) 600.587 1040.25i 0.451230 0.781553i
\(122\) 1485.31 + 2572.64i 1.10225 + 1.90915i
\(123\) 0 0
\(124\) −1007.27 + 1744.65i −0.729481 + 1.26350i
\(125\) 1241.32 0.888216
\(126\) 0 0
\(127\) 974.777 0.681082 0.340541 0.940230i \(-0.389390\pi\)
0.340541 + 0.940230i \(0.389390\pi\)
\(128\) 1142.41 1978.72i 0.788875 1.36637i
\(129\) 0 0
\(130\) −533.357 923.802i −0.359835 0.623252i
\(131\) 896.351 1552.53i 0.597821 1.03546i −0.395321 0.918543i \(-0.629367\pi\)
0.993142 0.116914i \(-0.0373001\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 662.647 0.427194
\(135\) 0 0
\(136\) −577.697 1000.60i −0.364243 0.630888i
\(137\) 842.208 + 1458.75i 0.525217 + 0.909702i 0.999569 + 0.0293665i \(0.00934900\pi\)
−0.474352 + 0.880335i \(0.657318\pi\)
\(138\) 0 0
\(139\) −315.089 −0.192270 −0.0961350 0.995368i \(-0.530648\pi\)
−0.0961350 + 0.995368i \(0.530648\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) −840.563 + 1455.90i −0.496750 + 0.860396i
\(143\) −74.6241 129.253i −0.0436390 0.0755850i
\(144\) 0 0
\(145\) 1666.62 2886.67i 0.954517 1.65327i
\(146\) −2774.40 −1.57268
\(147\) 0 0
\(148\) 47.7992 0.0265478
\(149\) 946.887 1640.06i 0.520617 0.901736i −0.479095 0.877763i \(-0.659035\pi\)
0.999713 0.0239729i \(-0.00763155\pi\)
\(150\) 0 0
\(151\) 1005.92 + 1742.31i 0.542124 + 0.938986i 0.998782 + 0.0493434i \(0.0157129\pi\)
−0.456658 + 0.889642i \(0.650954\pi\)
\(152\) −460.079 + 796.881i −0.245509 + 0.425234i
\(153\) 0 0
\(154\) 0 0
\(155\) 2821.71 1.46223
\(156\) 0 0
\(157\) −1914.25 3315.58i −0.973082 1.68543i −0.686125 0.727483i \(-0.740690\pi\)
−0.286956 0.957944i \(-0.592643\pi\)
\(158\) −2073.69 3591.73i −1.04414 1.80850i
\(159\) 0 0
\(160\) −3366.43 −1.66337
\(161\) 0 0
\(162\) 0 0
\(163\) 1754.63 3039.11i 0.843148 1.46038i −0.0440718 0.999028i \(-0.514033\pi\)
0.887220 0.461347i \(-0.152634\pi\)
\(164\) 250.890 + 434.554i 0.119459 + 0.206909i
\(165\) 0 0
\(166\) 747.083 1293.99i 0.349307 0.605017i
\(167\) −343.008 −0.158939 −0.0794694 0.996837i \(-0.525323\pi\)
−0.0794694 + 0.996837i \(0.525323\pi\)
\(168\) 0 0
\(169\) −2025.42 −0.921905
\(170\) −2168.96 + 3756.75i −0.978541 + 1.69488i
\(171\) 0 0
\(172\) −2739.92 4745.68i −1.21463 2.10381i
\(173\) 2093.61 3626.23i 0.920081 1.59363i 0.120793 0.992678i \(-0.461456\pi\)
0.799288 0.600949i \(-0.205210\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) −37.0779 −0.0158798
\(177\) 0 0
\(178\) 85.6866 + 148.413i 0.0360813 + 0.0624947i
\(179\) −985.143 1706.32i −0.411358 0.712493i 0.583681 0.811983i \(-0.301612\pi\)
−0.995039 + 0.0994906i \(0.968279\pi\)
\(180\) 0 0
\(181\) 3613.10 1.48376 0.741878 0.670535i \(-0.233935\pi\)
0.741878 + 0.670535i \(0.233935\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 1649.40 2856.85i 0.660845 1.14462i
\(185\) −33.4755 57.9812i −0.0133036 0.0230425i
\(186\) 0 0
\(187\) −303.468 + 525.622i −0.118673 + 0.205547i
\(188\) 270.355 0.104881
\(189\) 0 0
\(190\) 3454.74 1.31912
\(191\) 953.884 1652.18i 0.361365 0.625902i −0.626821 0.779163i \(-0.715644\pi\)
0.988186 + 0.153261i \(0.0489776\pi\)
\(192\) 0 0
\(193\) −1199.96 2078.40i −0.447540 0.775162i 0.550685 0.834713i \(-0.314366\pi\)
−0.998225 + 0.0595509i \(0.981033\pi\)
\(194\) 1644.88 2849.01i 0.608738 1.05437i
\(195\) 0 0
\(196\) 0 0
\(197\) −1514.32 −0.547668 −0.273834 0.961777i \(-0.588292\pi\)
−0.273834 + 0.961777i \(0.588292\pi\)
\(198\) 0 0
\(199\) 683.889 + 1184.53i 0.243616 + 0.421955i 0.961742 0.273958i \(-0.0883330\pi\)
−0.718126 + 0.695914i \(0.755000\pi\)
\(200\) −2108.87 3652.67i −0.745598 1.29141i
\(201\) 0 0
\(202\) 6919.63 2.41021
\(203\) 0 0
\(204\) 0 0
\(205\) 351.414 608.667i 0.119726 0.207371i
\(206\) −2396.38 4150.66i −0.810504 1.40383i
\(207\) 0 0
\(208\) 21.3123 36.9140i 0.00710453 0.0123054i
\(209\) 483.366 0.159977
\(210\) 0 0
\(211\) 4302.52 1.40378 0.701891 0.712285i \(-0.252339\pi\)
0.701891 + 0.712285i \(0.252339\pi\)
\(212\) 2334.55 4043.57i 0.756311 1.30997i
\(213\) 0 0
\(214\) 1746.27 + 3024.64i 0.557817 + 0.966167i
\(215\) −3837.72 + 6647.13i −1.21735 + 2.10851i
\(216\) 0 0
\(217\) 0 0
\(218\) −6502.16 −2.02010
\(219\) 0 0
\(220\) −1299.34 2250.51i −0.398187 0.689680i
\(221\) −348.866 604.253i −0.106187 0.183921i
\(222\) 0 0
\(223\) 1497.19 0.449592 0.224796 0.974406i \(-0.427828\pi\)
0.224796 + 0.974406i \(0.427828\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 825.987 1430.65i 0.243114 0.421086i
\(227\) −801.662 1388.52i −0.234397 0.405988i 0.724700 0.689065i \(-0.241978\pi\)
−0.959097 + 0.283076i \(0.908645\pi\)
\(228\) 0 0
\(229\) 505.261 875.137i 0.145802 0.252536i −0.783870 0.620925i \(-0.786757\pi\)
0.929672 + 0.368389i \(0.120091\pi\)
\(230\) −12385.4 −3.55072
\(231\) 0 0
\(232\) −4045.13 −1.14472
\(233\) 99.1084 171.661i 0.0278661 0.0482656i −0.851756 0.523939i \(-0.824462\pi\)
0.879622 + 0.475673i \(0.157795\pi\)
\(234\) 0 0
\(235\) −189.339 327.944i −0.0525578 0.0910329i
\(236\) 1445.62 2503.88i 0.398736 0.690631i
\(237\) 0 0
\(238\) 0 0
\(239\) 1201.19 0.325098 0.162549 0.986700i \(-0.448028\pi\)
0.162549 + 0.986700i \(0.448028\pi\)
\(240\) 0 0
\(241\) −1366.35 2366.58i −0.365204 0.632551i 0.623605 0.781739i \(-0.285667\pi\)
−0.988809 + 0.149188i \(0.952334\pi\)
\(242\) 2736.49 + 4739.74i 0.726894 + 1.25902i
\(243\) 0 0
\(244\) −8319.49 −2.18279
\(245\) 0 0
\(246\) 0 0
\(247\) −277.838 + 481.229i −0.0715724 + 0.123967i
\(248\) −1712.18 2965.58i −0.438401 0.759332i
\(249\) 0 0
\(250\) −2827.95 + 4898.16i −0.715422 + 1.23915i
\(251\) 7565.82 1.90259 0.951295 0.308281i \(-0.0997537\pi\)
0.951295 + 0.308281i \(0.0997537\pi\)
\(252\) 0 0
\(253\) −1732.88 −0.430615
\(254\) −2220.72 + 3846.40i −0.548584 + 0.950175i
\(255\) 0 0
\(256\) 1876.61 + 3250.38i 0.458156 + 0.793550i
\(257\) −2504.34 + 4337.64i −0.607846 + 1.05282i 0.383749 + 0.923437i \(0.374633\pi\)
−0.991595 + 0.129382i \(0.958701\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 2987.42 0.712584
\(261\) 0 0
\(262\) 4084.10 + 7073.88i 0.963041 + 1.66804i
\(263\) −3124.40 5411.63i −0.732544 1.26880i −0.955793 0.294042i \(-0.905000\pi\)
0.223249 0.974761i \(-0.428334\pi\)
\(264\) 0 0
\(265\) −6539.88 −1.51601
\(266\) 0 0
\(267\) 0 0
\(268\) −927.898 + 1607.17i −0.211494 + 0.366318i
\(269\) 1794.22 + 3107.69i 0.406676 + 0.704383i 0.994515 0.104595i \(-0.0333546\pi\)
−0.587839 + 0.808978i \(0.700021\pi\)
\(270\) 0 0
\(271\) −991.571 + 1717.45i −0.222264 + 0.384973i −0.955495 0.295007i \(-0.904678\pi\)
0.733231 + 0.679980i \(0.238012\pi\)
\(272\) −173.338 −0.0386404
\(273\) 0 0
\(274\) −7674.81 −1.69216
\(275\) −1107.80 + 1918.77i −0.242920 + 0.420751i
\(276\) 0 0
\(277\) −3681.96 6377.33i −0.798654 1.38331i −0.920493 0.390760i \(-0.872212\pi\)
0.121838 0.992550i \(-0.461121\pi\)
\(278\) 717.831 1243.32i 0.154866 0.268235i
\(279\) 0 0
\(280\) 0 0
\(281\) 5312.05 1.12772 0.563861 0.825869i \(-0.309315\pi\)
0.563861 + 0.825869i \(0.309315\pi\)
\(282\) 0 0
\(283\) −545.882 945.495i −0.114662 0.198600i 0.802983 0.596002i \(-0.203245\pi\)
−0.917645 + 0.397402i \(0.869912\pi\)
\(284\) −2354.06 4077.36i −0.491859 0.851925i
\(285\) 0 0
\(286\) 680.030 0.140598
\(287\) 0 0
\(288\) 0 0
\(289\) 1037.79 1797.51i 0.211234 0.365869i
\(290\) 7593.72 + 13152.7i 1.53765 + 2.66329i
\(291\) 0 0
\(292\) 3884.96 6728.95i 0.778597 1.34857i
\(293\) −7191.86 −1.43397 −0.716985 0.697089i \(-0.754478\pi\)
−0.716985 + 0.697089i \(0.754478\pi\)
\(294\) 0 0
\(295\) −4049.67 −0.799257
\(296\) −40.6249 + 70.3645i −0.00797729 + 0.0138171i
\(297\) 0 0
\(298\) 4314.36 + 7472.70i 0.838672 + 1.45262i
\(299\) 996.058 1725.22i 0.192654 0.333687i
\(300\) 0 0
\(301\) 0 0
\(302\) −9166.69 −1.74663
\(303\) 0 0
\(304\) 69.0236 + 119.552i 0.0130223 + 0.0225552i
\(305\) 5826.43 + 10091.7i 1.09384 + 1.89458i
\(306\) 0 0
\(307\) −541.355 −0.100641 −0.0503204 0.998733i \(-0.516024\pi\)
−0.0503204 + 0.998733i \(0.516024\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) −6428.37 + 11134.3i −1.17776 + 2.03995i
\(311\) −27.0084 46.7799i −0.00492446 0.00852941i 0.863553 0.504259i \(-0.168234\pi\)
−0.868477 + 0.495729i \(0.834901\pi\)
\(312\) 0 0
\(313\) 1886.47 3267.46i 0.340670 0.590058i −0.643887 0.765120i \(-0.722679\pi\)
0.984557 + 0.175063i \(0.0560128\pi\)
\(314\) 17444.1 3.13511
\(315\) 0 0
\(316\) 11615.1 2.06772
\(317\) 859.618 1488.90i 0.152306 0.263802i −0.779769 0.626068i \(-0.784663\pi\)
0.932075 + 0.362266i \(0.117997\pi\)
\(318\) 0 0
\(319\) 1062.47 + 1840.25i 0.186479 + 0.322991i
\(320\) 7436.70 12880.7i 1.29914 2.25017i
\(321\) 0 0
\(322\) 0 0
\(323\) 2259.72 0.389270
\(324\) 0 0
\(325\) −1273.53 2205.81i −0.217362 0.376482i
\(326\) 7994.73 + 13847.3i 1.35824 + 2.35255i
\(327\) 0 0
\(328\) −852.934 −0.143584
\(329\) 0 0
\(330\) 0 0
\(331\) −4204.11 + 7281.73i −0.698123 + 1.20918i 0.270994 + 0.962581i \(0.412648\pi\)
−0.969117 + 0.246603i \(0.920686\pi\)
\(332\) 2092.27 + 3623.91i 0.345868 + 0.599060i
\(333\) 0 0
\(334\) 781.436 1353.49i 0.128019 0.221735i
\(335\) 2599.36 0.423935
\(336\) 0 0
\(337\) 2789.46 0.450894 0.225447 0.974255i \(-0.427616\pi\)
0.225447 + 0.974255i \(0.427616\pi\)
\(338\) 4614.29 7992.18i 0.742557 1.28615i
\(339\) 0 0
\(340\) −6074.36 10521.1i −0.968907 1.67820i
\(341\) −899.419 + 1557.84i −0.142834 + 0.247395i
\(342\) 0 0
\(343\) 0 0
\(344\) 9314.72 1.45993
\(345\) 0 0
\(346\) 9539.24 + 16522.4i 1.48217 + 2.56720i
\(347\) −1735.98 3006.81i −0.268566 0.465170i 0.699926 0.714216i \(-0.253216\pi\)
−0.968492 + 0.249046i \(0.919883\pi\)
\(348\) 0 0
\(349\) 6626.12 1.01630 0.508149 0.861269i \(-0.330330\pi\)
0.508149 + 0.861269i \(0.330330\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 1073.05 1858.57i 0.162482 0.281427i
\(353\) −4734.20 8199.87i −0.713813 1.23636i −0.963416 0.268012i \(-0.913633\pi\)
0.249603 0.968348i \(-0.419700\pi\)
\(354\) 0 0
\(355\) −3297.27 + 5711.03i −0.492960 + 0.853831i
\(356\) −479.944 −0.0714522
\(357\) 0 0
\(358\) 8977.35 1.32533
\(359\) −3139.78 + 5438.25i −0.461591 + 0.799499i −0.999040 0.0437971i \(-0.986054\pi\)
0.537450 + 0.843296i \(0.319388\pi\)
\(360\) 0 0
\(361\) 2529.68 + 4381.53i 0.368811 + 0.638800i
\(362\) −8231.31 + 14257.0i −1.19510 + 2.06998i
\(363\) 0 0
\(364\) 0 0
\(365\) −10883.1 −1.56068
\(366\) 0 0
\(367\) −5413.91 9377.17i −0.770038 1.33374i −0.937542 0.347873i \(-0.886904\pi\)
0.167504 0.985871i \(-0.446429\pi\)
\(368\) −247.452 428.599i −0.0350525 0.0607127i
\(369\) 0 0
\(370\) 305.053 0.0428620
\(371\) 0 0
\(372\) 0 0
\(373\) −2619.61 + 4537.30i −0.363642 + 0.629846i −0.988557 0.150846i \(-0.951800\pi\)
0.624915 + 0.780693i \(0.285134\pi\)
\(374\) −1382.71 2394.93i −0.191172 0.331120i
\(375\) 0 0
\(376\) −229.777 + 397.985i −0.0315155 + 0.0545864i
\(377\) −2442.81 −0.333717
\(378\) 0 0
\(379\) −11050.4 −1.49768 −0.748839 0.662751i \(-0.769389\pi\)
−0.748839 + 0.662751i \(0.769389\pi\)
\(380\) −4837.64 + 8379.03i −0.653067 + 1.13115i
\(381\) 0 0
\(382\) 4346.25 + 7527.92i 0.582129 + 1.00828i
\(383\) 5234.02 9065.59i 0.698292 1.20948i −0.270766 0.962645i \(-0.587277\pi\)
0.969058 0.246832i \(-0.0793897\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 10934.9 1.44190
\(387\) 0 0
\(388\) 4606.61 + 7978.88i 0.602745 + 1.04399i
\(389\) −5807.02 10058.1i −0.756884 1.31096i −0.944432 0.328705i \(-0.893388\pi\)
0.187549 0.982255i \(-0.439946\pi\)
\(390\) 0 0
\(391\) −8101.19 −1.04781
\(392\) 0 0
\(393\) 0 0
\(394\) 3449.89 5975.38i 0.441124 0.764049i
\(395\) −8134.43 14089.2i −1.03617 1.79470i
\(396\) 0 0
\(397\) −3353.65 + 5808.69i −0.423967 + 0.734332i −0.996323 0.0856726i \(-0.972696\pi\)
0.572356 + 0.820005i \(0.306029\pi\)
\(398\) −6232.10 −0.784892
\(399\) 0 0
\(400\) −632.768 −0.0790960
\(401\) 2763.19 4785.98i 0.344107 0.596011i −0.641084 0.767471i \(-0.721515\pi\)
0.985191 + 0.171459i \(0.0548482\pi\)
\(402\) 0 0
\(403\) −1033.97 1790.89i −0.127805 0.221366i
\(404\) −9689.49 + 16782.7i −1.19324 + 2.06676i
\(405\) 0 0
\(406\) 0 0
\(407\) 42.6811 0.00519810
\(408\) 0 0
\(409\) −659.453 1142.21i −0.0797258 0.138089i 0.823406 0.567453i \(-0.192071\pi\)
−0.903132 + 0.429364i \(0.858738\pi\)
\(410\) 1601.17 + 2773.31i 0.192869 + 0.334059i
\(411\) 0 0
\(412\) 13422.5 1.60505
\(413\) 0 0
\(414\) 0 0
\(415\) 2930.57 5075.90i 0.346641 0.600401i
\(416\) 1233.57 + 2136.61i 0.145387 + 0.251817i
\(417\) 0 0
\(418\) −1101.20 + 1907.33i −0.128855 + 0.223183i
\(419\) 3656.13 0.426286 0.213143 0.977021i \(-0.431630\pi\)
0.213143 + 0.977021i \(0.431630\pi\)
\(420\) 0 0
\(421\) −135.389 −0.0156733 −0.00783663 0.999969i \(-0.502495\pi\)
−0.00783663 + 0.999969i \(0.502495\pi\)
\(422\) −9801.93 + 16977.4i −1.13069 + 1.95841i
\(423\) 0 0
\(424\) 3968.31 + 6873.32i 0.454524 + 0.787259i
\(425\) −5178.96 + 8970.22i −0.591097 + 1.02381i
\(426\) 0 0
\(427\) 0 0
\(428\) −9781.16 −1.10465
\(429\) 0 0
\(430\) −17486.1 30286.8i −1.96105 3.39665i
\(431\) 4194.58 + 7265.23i 0.468784 + 0.811958i 0.999363 0.0356776i \(-0.0113589\pi\)
−0.530579 + 0.847635i \(0.678026\pi\)
\(432\) 0 0
\(433\) 8243.02 0.914859 0.457430 0.889246i \(-0.348770\pi\)
0.457430 + 0.889246i \(0.348770\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 9104.91 15770.2i 1.00011 1.73223i
\(437\) 3225.91 + 5587.43i 0.353126 + 0.611632i
\(438\) 0 0
\(439\) −9141.59 + 15833.7i −0.993859 + 1.72142i −0.401104 + 0.916032i \(0.631374\pi\)
−0.592755 + 0.805383i \(0.701960\pi\)
\(440\) 4417.26 0.478602
\(441\) 0 0
\(442\) 3179.12 0.342116
\(443\) 605.218 1048.27i 0.0649092 0.112426i −0.831745 0.555159i \(-0.812658\pi\)
0.896654 + 0.442733i \(0.145991\pi\)
\(444\) 0 0
\(445\) 336.122 + 582.180i 0.0358061 + 0.0620179i
\(446\) −3410.86 + 5907.79i −0.362128 + 0.627224i
\(447\) 0 0
\(448\) 0 0
\(449\) 8301.16 0.872508 0.436254 0.899824i \(-0.356305\pi\)
0.436254 + 0.899824i \(0.356305\pi\)
\(450\) 0 0
\(451\) 224.026 + 388.025i 0.0233902 + 0.0405130i
\(452\) 2313.24 + 4006.66i 0.240721 + 0.416941i
\(453\) 0 0
\(454\) 7305.34 0.755190
\(455\) 0 0
\(456\) 0 0
\(457\) 6146.88 10646.7i 0.629188 1.08979i −0.358527 0.933519i \(-0.616721\pi\)
0.987715 0.156266i \(-0.0499458\pi\)
\(458\) 2302.15 + 3987.45i 0.234875 + 0.406815i
\(459\) 0 0
\(460\) 17343.1 30039.1i 1.75788 3.04474i
\(461\) 19434.2 1.96343 0.981717 0.190346i \(-0.0609609\pi\)
0.981717 + 0.190346i \(0.0609609\pi\)
\(462\) 0 0
\(463\) −12491.1 −1.25380 −0.626902 0.779098i \(-0.715678\pi\)
−0.626902 + 0.779098i \(0.715678\pi\)
\(464\) −303.436 + 525.566i −0.0303592 + 0.0525836i
\(465\) 0 0
\(466\) 451.574 + 782.150i 0.0448901 + 0.0777519i
\(467\) −1692.59 + 2931.65i −0.167716 + 0.290493i −0.937617 0.347671i \(-0.886973\pi\)
0.769900 + 0.638164i \(0.220306\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 1725.39 0.169333
\(471\) 0 0
\(472\) 2457.29 + 4256.14i 0.239631 + 0.415053i
\(473\) −2446.54 4237.54i −0.237827 0.411929i
\(474\) 0 0
\(475\) 8249.07 0.796828
\(476\) 0 0
\(477\) 0 0
\(478\) −2736.53 + 4739.80i −0.261853 + 0.453543i
\(479\) −2989.71 5178.32i −0.285184 0.493953i 0.687470 0.726213i \(-0.258721\pi\)
−0.972654 + 0.232260i \(0.925388\pi\)
\(480\) 0 0
\(481\) −24.5330 + 42.4925i −0.00232559 + 0.00402804i
\(482\) 12451.1 1.17663
\(483\) 0 0
\(484\) −15327.5 −1.43948
\(485\) 6452.34 11175.8i 0.604094 1.04632i
\(486\) 0 0
\(487\) 557.481 + 965.586i 0.0518725 + 0.0898457i 0.890796 0.454404i \(-0.150148\pi\)
−0.838923 + 0.544250i \(0.816814\pi\)
\(488\) 7070.80 12247.0i 0.655902 1.13606i
\(489\) 0 0
\(490\) 0 0
\(491\) −1086.23 −0.0998387 −0.0499194 0.998753i \(-0.515896\pi\)
−0.0499194 + 0.998753i \(0.515896\pi\)
\(492\) 0 0
\(493\) 4967.00 + 8603.10i 0.453758 + 0.785932i
\(494\) −1265.93 2192.66i −0.115297 0.199701i
\(495\) 0 0
\(496\) −513.740 −0.0465073
\(497\) 0 0
\(498\) 0 0
\(499\) 1106.75 1916.95i 0.0992884 0.171973i −0.812102 0.583516i \(-0.801677\pi\)
0.911390 + 0.411543i \(0.135010\pi\)
\(500\) −7919.92 13717.7i −0.708379 1.22695i
\(501\) 0 0
\(502\) −17236.3 + 29854.2i −1.53246 + 2.65430i
\(503\) −2643.32 −0.234314 −0.117157 0.993113i \(-0.537378\pi\)
−0.117157 + 0.993113i \(0.537378\pi\)
\(504\) 0 0
\(505\) 27143.5 2.39183
\(506\) 3947.83 6837.84i 0.346843 0.600749i
\(507\) 0 0
\(508\) −6219.31 10772.2i −0.543183 0.940821i
\(509\) 332.584 576.053i 0.0289618 0.0501633i −0.851181 0.524872i \(-0.824113\pi\)
0.880143 + 0.474709i \(0.157447\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 1177.58 0.101645
\(513\) 0 0
\(514\) −11410.7 19763.9i −0.979190 1.69601i
\(515\) −9400.26 16281.7i −0.804320 1.39312i
\(516\) 0 0
\(517\) 241.406 0.0205359
\(518\) 0 0
\(519\) 0 0
\(520\) −2539.03 + 4397.73i −0.214123 + 0.370872i
\(521\) 5880.99 + 10186.2i 0.494531 + 0.856554i 0.999980 0.00630307i \(-0.00200634\pi\)
−0.505449 + 0.862857i \(0.668673\pi\)
\(522\) 0 0
\(523\) 5061.30 8766.43i 0.423165 0.732943i −0.573082 0.819498i \(-0.694252\pi\)
0.996247 + 0.0865547i \(0.0275857\pi\)
\(524\) −22875.7 −1.90712
\(525\) 0 0
\(526\) 28471.9 2.36014
\(527\) −4204.76 + 7282.85i −0.347556 + 0.601985i
\(528\) 0 0
\(529\) −5481.49 9494.22i −0.450521 0.780325i
\(530\) 14899.0 25805.9i 1.22108 2.11497i
\(531\) 0 0
\(532\) 0 0
\(533\) −515.079 −0.0418585
\(534\) 0 0
\(535\) 6850.09 + 11864.7i 0.553561 + 0.958796i
\(536\) −1577.26 2731.89i −0.127103 0.220148i
\(537\) 0 0
\(538\) −16350.3 −1.31024
\(539\) 0 0
\(540\) 0 0
\(541\) −8058.98 + 13958.6i −0.640449 + 1.10929i 0.344884 + 0.938645i \(0.387918\pi\)
−0.985333 + 0.170644i \(0.945415\pi\)
\(542\) −4517.96 7825.34i −0.358050 0.620161i
\(543\) 0 0
\(544\) 5016.47 8688.78i 0.395366 0.684795i
\(545\) −25505.9 −2.00469
\(546\) 0 0
\(547\) −626.100 −0.0489399 −0.0244699 0.999701i \(-0.507790\pi\)
−0.0244699 + 0.999701i \(0.507790\pi\)
\(548\) 10747.0 18614.3i 0.837751 1.45103i
\(549\) 0 0
\(550\) −5047.56 8742.64i −0.391325 0.677795i
\(551\) 3955.74 6851.54i 0.305844 0.529737i
\(552\) 0 0
\(553\) 0 0
\(554\) 33552.7 2.57313
\(555\) 0 0
\(556\) 2010.34 + 3482.02i 0.153341 + 0.265594i
\(557\) 10385.6 + 17988.4i 0.790039 + 1.36839i 0.925942 + 0.377665i \(0.123273\pi\)
−0.135903 + 0.990722i \(0.543394\pi\)
\(558\) 0 0
\(559\) 5625.08 0.425609
\(560\) 0 0
\(561\) 0 0
\(562\) −12101.8 + 20961.0i −0.908335 + 1.57328i
\(563\) 2760.86 + 4781.95i 0.206672 + 0.357966i 0.950664 0.310222i \(-0.100403\pi\)
−0.743992 + 0.668188i \(0.767070\pi\)
\(564\) 0 0
\(565\) 3240.09 5612.00i 0.241260 0.417874i
\(566\) 4974.48 0.369422
\(567\) 0 0
\(568\) 8002.95 0.591191
\(569\) 3787.40 6559.97i 0.279044 0.483319i −0.692103 0.721799i \(-0.743316\pi\)
0.971147 + 0.238480i \(0.0766491\pi\)
\(570\) 0 0
\(571\) 165.624 + 286.869i 0.0121386 + 0.0210247i 0.872031 0.489451i \(-0.162803\pi\)
−0.859892 + 0.510476i \(0.829469\pi\)
\(572\) −952.239 + 1649.33i −0.0696068 + 0.120563i
\(573\) 0 0
\(574\) 0 0
\(575\) −29573.2 −2.14485
\(576\) 0 0
\(577\) 1019.06 + 1765.06i 0.0735248 + 0.127349i 0.900444 0.434972i \(-0.143242\pi\)
−0.826919 + 0.562321i \(0.809909\pi\)
\(578\) 4728.57 + 8190.13i 0.340281 + 0.589385i
\(579\) 0 0
\(580\) −42533.6 −3.04502
\(581\) 0 0
\(582\) 0 0
\(583\) 2084.58 3610.60i 0.148087 0.256494i
\(584\) 6603.72 + 11438.0i 0.467918 + 0.810457i
\(585\) 0 0
\(586\) 16384.4 28378.6i 1.15500 2.00053i
\(587\) 5232.90 0.367947 0.183973 0.982931i \(-0.441104\pi\)
0.183973 + 0.982931i \(0.441104\pi\)
\(588\) 0 0
\(589\) 6697.36 0.468523
\(590\) 9225.88 15979.7i 0.643769 1.11504i
\(591\) 0 0
\(592\) 6.09477 + 10.5565i 0.000423131 + 0.000732884i
\(593\) 2860.12 4953.87i 0.198062 0.343054i −0.749838 0.661622i \(-0.769868\pi\)
0.947900 + 0.318568i \(0.103202\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) −24165.5 −1.66083
\(597\) 0 0
\(598\) 4538.41 + 7860.75i 0.310350 + 0.537542i
\(599\) 9044.21 + 15665.0i 0.616922 + 1.06854i 0.990044 + 0.140758i \(0.0449540\pi\)
−0.373122 + 0.927782i \(0.621713\pi\)
\(600\) 0 0
\(601\) 1821.43 0.123623 0.0618117 0.998088i \(-0.480312\pi\)
0.0618117 + 0.998088i \(0.480312\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 12836.0 22232.6i 0.864719 1.49774i
\(605\) 10734.4 + 18592.5i 0.721348 + 1.24941i
\(606\) 0 0
\(607\) 1186.10 2054.39i 0.0793120 0.137372i −0.823641 0.567111i \(-0.808061\pi\)
0.902953 + 0.429739i \(0.141394\pi\)
\(608\) −7990.26 −0.532974
\(609\) 0 0
\(610\) −53094.7 −3.52416
\(611\) −138.760 + 240.339i −0.00918760 + 0.0159134i
\(612\) 0 0
\(613\) −4862.54 8422.16i −0.320385 0.554923i 0.660182 0.751105i \(-0.270479\pi\)
−0.980567 + 0.196182i \(0.937146\pi\)
\(614\) 1233.30 2136.15i 0.0810621 0.140404i
\(615\) 0 0
\(616\) 0 0
\(617\) 5329.51 0.347744 0.173872 0.984768i \(-0.444372\pi\)
0.173872 + 0.984768i \(0.444372\pi\)
\(618\) 0 0
\(619\) −7988.29 13836.1i −0.518702 0.898418i −0.999764 0.0217314i \(-0.993082\pi\)
0.481062 0.876687i \(-0.340251\pi\)
\(620\) −18003.2 31182.4i −1.16617 2.01986i
\(621\) 0 0
\(622\) 246.120 0.0158658
\(623\) 0 0
\(624\) 0 0
\(625\) 1060.03 1836.03i 0.0678420 0.117506i
\(626\) 8595.45 + 14887.8i 0.548791 + 0.950535i
\(627\) 0 0
\(628\) −24426.7 + 42308.4i −1.55212 + 2.68836i
\(629\) 199.533 0.0126485
\(630\) 0 0
\(631\) −4199.98 −0.264974 −0.132487 0.991185i \(-0.542296\pi\)
−0.132487 + 0.991185i \(0.542296\pi\)
\(632\) −9871.73 + 17098.3i −0.621324 + 1.07616i
\(633\) 0 0
\(634\) 3916.74 + 6783.99i 0.245352 + 0.424963i
\(635\) −8711.19 + 15088.2i −0.544399 + 0.942926i
\(636\) 0 0
\(637\) 0 0
\(638\) −9681.97 −0.600804
\(639\) 0 0
\(640\) 20418.6 + 35366.0i 1.26112 + 2.18432i
\(641\) 1324.25 + 2293.67i 0.0815988 + 0.141333i 0.903937 0.427666i \(-0.140664\pi\)
−0.822338 + 0.568999i \(0.807331\pi\)
\(642\) 0 0
\(643\) −13.4305 −0.000823715 −0.000411857 1.00000i \(-0.500131\pi\)
−0.000411857 1.00000i \(0.500131\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) −5148.06 + 8916.70i −0.313541 + 0.543070i
\(647\) −5812.07 10066.8i −0.353162 0.611695i 0.633639 0.773628i \(-0.281560\pi\)
−0.986802 + 0.161934i \(0.948227\pi\)
\(648\) 0 0
\(649\) 1290.83 2235.78i 0.0780732 0.135227i
\(650\) 11605.3 0.700305
\(651\) 0 0
\(652\) −44779.8 −2.68974
\(653\) −14258.3 + 24696.1i −0.854471 + 1.47999i 0.0226638 + 0.999743i \(0.492785\pi\)
−0.877135 + 0.480244i \(0.840548\pi\)
\(654\) 0 0
\(655\) 16020.7 + 27748.6i 0.955694 + 1.65531i
\(656\) −63.9809 + 110.818i −0.00380798 + 0.00659561i
\(657\) 0 0
\(658\) 0 0
\(659\) −18048.6 −1.06688 −0.533440 0.845838i \(-0.679101\pi\)
−0.533440 + 0.845838i \(0.679101\pi\)
\(660\) 0 0
\(661\) 8920.72 + 15451.1i 0.524926 + 0.909198i 0.999579 + 0.0290250i \(0.00924023\pi\)
−0.474653 + 0.880173i \(0.657426\pi\)
\(662\) −19155.5 33178.2i −1.12462 1.94790i
\(663\) 0 0
\(664\) −7112.94 −0.415716
\(665\) 0 0
\(666\) 0 0
\(667\) −14181.5 + 24563.0i −0.823251 + 1.42591i
\(668\) 2188.47 + 3790.55i 0.126758 + 0.219552i
\(669\) 0 0
\(670\) −5921.81 + 10256.9i −0.341462 + 0.591430i
\(671\) −7428.68 −0.427394
\(672\) 0 0
\(673\) −6826.13 −0.390978 −0.195489 0.980706i \(-0.562629\pi\)
−0.195489 + 0.980706i \(0.562629\pi\)
\(674\) −6354.89 + 11007.0i −0.363177 + 0.629041i
\(675\) 0 0
\(676\) 12922.7 + 22382.8i 0.735246 + 1.27348i
\(677\) 10643.4 18435.0i 0.604225 1.04655i −0.387949 0.921681i \(-0.626816\pi\)
0.992173 0.124867i \(-0.0398505\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 20650.6 1.16458
\(681\) 0 0
\(682\) −4098.08 7098.08i −0.230093 0.398533i
\(683\) −10348.4 17924.0i −0.579753 1.00416i −0.995507 0.0946842i \(-0.969816\pi\)
0.415755 0.909477i \(-0.363517\pi\)
\(684\) 0 0
\(685\) −30105.9 −1.67925
\(686\) 0 0
\(687\) 0 0
\(688\) 698.722 1210.22i 0.0387188 0.0670629i
\(689\) 2396.43 + 4150.74i 0.132506 + 0.229507i
\(690\) 0 0
\(691\) 15671.0 27142.9i 0.862738 1.49431i −0.00653825 0.999979i \(-0.502081\pi\)
0.869276 0.494327i \(-0.164585\pi\)
\(692\) −53430.8 −2.93517
\(693\) 0 0
\(694\) 15819.5 0.865276
\(695\) 2815.83 4877.16i 0.153684 0.266189i
\(696\) 0 0
\(697\) 1047.32 + 1814.01i 0.0569153 + 0.0985801i
\(698\) −15095.5 + 26146.2i −0.818587 + 1.41783i
\(699\) 0 0
\(700\) 0 0
\(701\) 9213.32 0.496408 0.248204 0.968708i \(-0.420160\pi\)
0.248204 + 0.968708i \(0.420160\pi\)
\(702\) 0 0
\(703\) −79.4544 137.619i −0.00426270 0.00738322i
\(704\) 4740.89 + 8211.46i 0.253805 + 0.439604i
\(705\) 0 0
\(706\) 43141.5 2.29979
\(707\) 0 0
\(708\) 0 0
\(709\) −7258.27 + 12571.7i −0.384471 + 0.665923i −0.991696 0.128607i \(-0.958949\pi\)
0.607225 + 0.794530i \(0.292283\pi\)
\(710\) −15023.5 26021.6i −0.794118 1.37545i
\(711\) 0 0
\(712\) 407.908 706.518i 0.0214705 0.0371880i
\(713\) −24010.3 −1.26114
\(714\) 0 0
\(715\) 2667.54 0.139525
\(716\) −12570.9 + 21773.4i −0.656140 + 1.13647i
\(717\) 0 0
\(718\) −14306.0 24778.7i −0.743585 1.28793i
\(719\) −12941.2 + 22414.8i −0.671246 + 1.16263i 0.306306 + 0.951933i \(0.400907\pi\)
−0.977551 + 0.210698i \(0.932426\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) −23052.3 −1.18825
\(723\) 0 0
\(724\) −23052.4 39928.0i −1.18334 2.04960i
\(725\) 18132.0 + 31405.5i 0.928833 + 1.60879i
\(726\) 0 0
\(727\) −32181.2 −1.64172 −0.820862 0.571127i \(-0.806506\pi\)
−0.820862 + 0.571127i \(0.806506\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 24793.7 42943.9i 1.25706 2.17730i
\(731\) −11437.5 19810.4i −0.578704 1.00234i
\(732\) 0 0
\(733\) 10418.1 18044.6i 0.524966 0.909268i −0.474611 0.880195i \(-0.657411\pi\)
0.999577 0.0290722i \(-0.00925528\pi\)
\(734\) 49335.5 2.48094
\(735\) 0 0
\(736\) 28645.4 1.43462
\(737\) −828.544 + 1435.08i −0.0414109 + 0.0717257i
\(738\) 0 0
\(739\) −13217.4 22893.3i −0.657931 1.13957i −0.981150 0.193246i \(-0.938098\pi\)
0.323219 0.946324i \(-0.395235\pi\)
\(740\) −427.163 + 739.867i −0.0212200 + 0.0367541i
\(741\) 0 0
\(742\) 0 0
\(743\) −9954.69 −0.491524 −0.245762 0.969330i \(-0.579038\pi\)
−0.245762 + 0.969330i \(0.579038\pi\)
\(744\) 0 0
\(745\) 16923.9 + 29313.1i 0.832274 + 1.44154i
\(746\) −11935.9 20673.6i −0.585798 1.01463i
\(747\) 0 0
\(748\) 7744.79 0.378580
\(749\) 0 0
\(750\) 0 0
\(751\) 16602.3 28756.0i 0.806692 1.39723i −0.108451 0.994102i \(-0.534589\pi\)
0.915143 0.403129i \(-0.132077\pi\)
\(752\) 34.4723 + 59.7078i 0.00167164 + 0.00289537i
\(753\) 0 0
\(754\) 5565.18 9639.17i 0.268796 0.465568i
\(755\) −35958.1 −1.73331
\(756\) 0 0
\(757\) 1964.06 0.0942998 0.0471499 0.998888i \(-0.484986\pi\)
0.0471499 + 0.998888i \(0.484986\pi\)
\(758\) 25174.8 43604.0i 1.20632 2.08941i
\(759\) 0 0
\(760\) −8223.09 14242.8i −0.392477 0.679791i
\(761\) 19276.9 33388.6i 0.918248 1.59045i 0.116174 0.993229i \(-0.462937\pi\)
0.802075 0.597224i \(-0.203730\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) −24344.0 −1.15280
\(765\) 0 0
\(766\) 23848.1 + 41306.1i 1.12489 + 1.94837i
\(767\) 1483.93 + 2570.25i 0.0698588 + 0.120999i
\(768\) 0 0
\(769\) 19715.0 0.924501 0.462251 0.886749i \(-0.347042\pi\)
0.462251 + 0.886749i \(0.347042\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −15312.1 + 26521.3i −0.713853 + 1.23643i
\(773\) 7350.34 + 12731.2i 0.342010 + 0.592378i 0.984806 0.173659i \(-0.0555591\pi\)
−0.642796 + 0.766037i \(0.722226\pi\)
\(774\) 0 0
\(775\) −15349.4 + 26585.9i −0.711440 + 1.23225i
\(776\) −15660.8 −0.724471
\(777\) 0 0
\(778\) 52917.8 2.43856
\(779\) 834.086 1444.68i 0.0383623 0.0664454i
\(780\) 0 0
\(781\) −2102.00 3640.78i −0.0963068 0.166808i
\(782\) 18456.0 31966.7i 0.843970 1.46180i
\(783\) 0 0
\(784\) 0 0
\(785\) 68427.6 3.11119
\(786\) 0 0
\(787\) −11959.3 20714.1i −0.541681 0.938218i −0.998808 0.0488169i \(-0.984455\pi\)
0.457127 0.889401i \(-0.348878\pi\)
\(788\) 9661.69 + 16734.5i 0.436781 + 0.756527i
\(789\) 0 0
\(790\) 74126.9 3.33837