Properties

Label 441.4.e.w.361.3
Level $441$
Weight $4$
Character 441.361
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 361.3
Root \(2.65415 + 4.59712i\) of defining polynomial
Character \(\chi\) \(=\) 441.361
Dual form 441.4.e.w.226.3

$q$-expansion

\(f(q)\) \(=\) \(q+(2.65415 + 4.59712i) q^{2} +(-10.0890 + 17.4746i) q^{4} +(-2.78070 - 4.81631i) q^{5} -64.6443 q^{8} +O(q^{10})\) \(q+(2.65415 + 4.59712i) q^{2} +(-10.0890 + 17.4746i) q^{4} +(-2.78070 - 4.81631i) q^{5} -64.6443 q^{8} +(14.7608 - 25.5664i) q^{10} +(-6.95869 + 12.0528i) q^{11} -38.6718 q^{13} +(-90.8636 - 157.380i) q^{16} +(-21.7394 + 37.6537i) q^{17} +(-54.5139 - 94.4208i) q^{19} +112.218 q^{20} -73.8775 q^{22} +(-37.4389 - 64.8461i) q^{23} +(47.0354 - 81.4677i) q^{25} +(-102.641 - 177.779i) q^{26} +72.3589 q^{29} +(32.0215 - 55.4629i) q^{31} +(223.754 - 387.553i) q^{32} -230.798 q^{34} +(-94.3636 - 163.443i) q^{37} +(289.376 - 501.213i) q^{38} +(179.756 + 311.347i) q^{40} -24.7923 q^{41} -243.881 q^{43} +(-140.412 - 243.201i) q^{44} +(198.737 - 344.222i) q^{46} +(310.274 + 537.411i) q^{47} +499.356 q^{50} +(390.159 - 675.776i) q^{52} +(-143.919 + 249.276i) q^{53} +77.4001 q^{55} +(192.051 + 332.642i) q^{58} +(-262.526 + 454.708i) q^{59} +(-191.718 - 332.065i) q^{61} +339.960 q^{62} +921.681 q^{64} +(107.535 + 186.255i) q^{65} +(-99.0583 + 171.574i) q^{67} +(-438.657 - 759.776i) q^{68} -785.432 q^{71} +(-165.570 + 286.776i) q^{73} +(500.910 - 867.602i) q^{74} +2199.96 q^{76} +(-218.823 - 379.013i) q^{79} +(-505.329 + 875.255i) q^{80} +(-65.8024 - 113.973i) q^{82} +241.241 q^{83} +241.803 q^{85} +(-647.297 - 1121.15i) q^{86} +(449.840 - 779.145i) q^{88} +(-792.772 - 1373.12i) q^{89} +1510.88 q^{92} +(-1647.03 + 2852.73i) q^{94} +(-303.173 + 525.112i) q^{95} -79.2754 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6q + q^{2} - 25q^{4} - 11q^{5} - 78q^{8} + O(q^{10}) \) \( 6q + q^{2} - 25q^{4} - 11q^{5} - 78q^{8} - 55q^{10} + 35q^{11} - 124q^{13} - 241q^{16} - 48q^{17} - 202q^{19} + 878q^{20} - 14q^{22} + 216q^{23} - 130q^{25} - 274q^{26} - 106q^{29} - 95q^{31} + 683q^{32} + 48q^{34} - 262q^{37} + 398q^{38} + 21q^{40} + 488q^{41} + 720q^{43} - 905q^{44} + 1056q^{46} + 210q^{47} + 2756q^{50} + 324q^{52} + 393q^{53} + 2062q^{55} + 1249q^{58} - 1143q^{59} - 70q^{61} + 2118q^{62} - 798q^{64} - 472q^{65} + 628q^{67} - 1944q^{68} - 636q^{71} + 988q^{73} + 1002q^{74} + 4680q^{76} - 861q^{79} - 175q^{80} + 124q^{82} + 1038q^{83} + 3600q^{85} - 3208q^{86} + 891q^{88} - 1766q^{89} + 1344q^{92} - 3294q^{94} - 736q^{95} - 38q^{97} + O(q^{100}) \)

Character values

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

\(n\) \(199\) \(344\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.65415 + 4.59712i 0.938383 + 1.62533i 0.768488 + 0.639864i \(0.221009\pi\)
0.169895 + 0.985462i \(0.445657\pi\)
\(3\) 0 0
\(4\) −10.0890 + 17.4746i −1.26112 + 2.18433i
\(5\) −2.78070 4.81631i −0.248713 0.430784i 0.714456 0.699681i \(-0.246674\pi\)
−0.963169 + 0.268897i \(0.913341\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) −64.6443 −2.85690
\(9\) 0 0
\(10\) 14.7608 25.5664i 0.466777 0.808481i
\(11\) −6.95869 + 12.0528i −0.190738 + 0.330369i −0.945495 0.325636i \(-0.894422\pi\)
0.754757 + 0.656005i \(0.227755\pi\)
\(12\) 0 0
\(13\) −38.6718 −0.825048 −0.412524 0.910947i \(-0.635353\pi\)
−0.412524 + 0.910947i \(0.635353\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) −90.8636 157.380i −1.41974 2.45907i
\(17\) −21.7394 + 37.6537i −0.310152 + 0.537198i −0.978395 0.206744i \(-0.933713\pi\)
0.668243 + 0.743943i \(0.267046\pi\)
\(18\) 0 0
\(19\) −54.5139 94.4208i −0.658228 1.14009i −0.981074 0.193633i \(-0.937973\pi\)
0.322845 0.946452i \(-0.395361\pi\)
\(20\) 112.218 1.25463
\(21\) 0 0
\(22\) −73.8775 −0.715943
\(23\) −37.4389 64.8461i −0.339415 0.587885i 0.644907 0.764261i \(-0.276896\pi\)
−0.984323 + 0.176376i \(0.943563\pi\)
\(24\) 0 0
\(25\) 47.0354 81.4677i 0.376283 0.651742i
\(26\) −102.641 177.779i −0.774211 1.34097i
\(27\) 0 0
\(28\) 0 0
\(29\) 72.3589 0.463335 0.231667 0.972795i \(-0.425582\pi\)
0.231667 + 0.972795i \(0.425582\pi\)
\(30\) 0 0
\(31\) 32.0215 55.4629i 0.185524 0.321337i −0.758229 0.651988i \(-0.773935\pi\)
0.943753 + 0.330652i \(0.107268\pi\)
\(32\) 223.754 387.553i 1.23608 2.14095i
\(33\) 0 0
\(34\) −230.798 −1.16416
\(35\) 0 0
\(36\) 0 0
\(37\) −94.3636 163.443i −0.419278 0.726211i 0.576589 0.817034i \(-0.304383\pi\)
−0.995867 + 0.0908235i \(0.971050\pi\)
\(38\) 289.376 501.213i 1.23534 2.13967i
\(39\) 0 0
\(40\) 179.756 + 311.347i 0.710550 + 1.23071i
\(41\) −24.7923 −0.0944367 −0.0472184 0.998885i \(-0.515036\pi\)
−0.0472184 + 0.998885i \(0.515036\pi\)
\(42\) 0 0
\(43\) −243.881 −0.864920 −0.432460 0.901653i \(-0.642354\pi\)
−0.432460 + 0.901653i \(0.642354\pi\)
\(44\) −140.412 243.201i −0.481090 0.833272i
\(45\) 0 0
\(46\) 198.737 344.222i 0.637003 1.10332i
\(47\) 310.274 + 537.411i 0.962940 + 1.66786i 0.715052 + 0.699071i \(0.246403\pi\)
0.247888 + 0.968789i \(0.420264\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 499.356 1.41239
\(51\) 0 0
\(52\) 390.159 675.776i 1.04049 1.80218i
\(53\) −143.919 + 249.276i −0.372997 + 0.646050i −0.990025 0.140891i \(-0.955003\pi\)
0.617028 + 0.786941i \(0.288337\pi\)
\(54\) 0 0
\(55\) 77.4001 0.189757
\(56\) 0 0
\(57\) 0 0
\(58\) 192.051 + 332.642i 0.434785 + 0.753070i
\(59\) −262.526 + 454.708i −0.579287 + 1.00335i 0.416275 + 0.909239i \(0.363336\pi\)
−0.995561 + 0.0941152i \(0.969998\pi\)
\(60\) 0 0
\(61\) −191.718 332.065i −0.402409 0.696993i 0.591607 0.806226i \(-0.298494\pi\)
−0.994016 + 0.109234i \(0.965160\pi\)
\(62\) 339.960 0.696369
\(63\) 0 0
\(64\) 921.681 1.80016
\(65\) 107.535 + 186.255i 0.205200 + 0.355417i
\(66\) 0 0
\(67\) −99.0583 + 171.574i −0.180625 + 0.312852i −0.942094 0.335350i \(-0.891145\pi\)
0.761468 + 0.648202i \(0.224479\pi\)
\(68\) −438.657 759.776i −0.782279 1.35495i
\(69\) 0 0
\(70\) 0 0
\(71\) −785.432 −1.31287 −0.656434 0.754384i \(-0.727936\pi\)
−0.656434 + 0.754384i \(0.727936\pi\)
\(72\) 0 0
\(73\) −165.570 + 286.776i −0.265459 + 0.459789i −0.967684 0.252166i \(-0.918857\pi\)
0.702224 + 0.711956i \(0.252190\pi\)
\(74\) 500.910 867.602i 0.786887 1.36293i
\(75\) 0 0
\(76\) 2199.96 3.32043
\(77\) 0 0
\(78\) 0 0
\(79\) −218.823 379.013i −0.311640 0.539776i 0.667078 0.744988i \(-0.267545\pi\)
−0.978718 + 0.205212i \(0.934212\pi\)
\(80\) −505.329 + 875.255i −0.706219 + 1.22321i
\(81\) 0 0
\(82\) −65.8024 113.973i −0.0886178 0.153491i
\(83\) 241.241 0.319032 0.159516 0.987195i \(-0.449007\pi\)
0.159516 + 0.987195i \(0.449007\pi\)
\(84\) 0 0
\(85\) 241.803 0.308555
\(86\) −647.297 1121.15i −0.811626 1.40578i
\(87\) 0 0
\(88\) 449.840 779.145i 0.544921 0.943831i
\(89\) −792.772 1373.12i −0.944198 1.63540i −0.757349 0.653010i \(-0.773506\pi\)
−0.186849 0.982389i \(-0.559828\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 1510.88 1.71218
\(93\) 0 0
\(94\) −1647.03 + 2852.73i −1.80721 + 3.13018i
\(95\) −303.173 + 525.112i −0.327420 + 0.567109i
\(96\) 0 0
\(97\) −79.2754 −0.0829814 −0.0414907 0.999139i \(-0.513211\pi\)
−0.0414907 + 0.999139i \(0.513211\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 949.080 + 1643.85i 0.949080 + 1.64385i
\(101\) −577.487 + 1000.24i −0.568931 + 0.985418i 0.427741 + 0.903902i \(0.359310\pi\)
−0.996672 + 0.0815165i \(0.974024\pi\)
\(102\) 0 0
\(103\) −722.430 1251.28i −0.691098 1.19702i −0.971478 0.237128i \(-0.923794\pi\)
0.280380 0.959889i \(-0.409539\pi\)
\(104\) 2499.91 2.35708
\(105\) 0 0
\(106\) −1527.93 −1.40006
\(107\) 495.480 + 858.197i 0.447662 + 0.775374i 0.998233 0.0594143i \(-0.0189233\pi\)
−0.550571 + 0.834788i \(0.685590\pi\)
\(108\) 0 0
\(109\) −976.585 + 1691.49i −0.858164 + 1.48638i 0.0155145 + 0.999880i \(0.495061\pi\)
−0.873678 + 0.486504i \(0.838272\pi\)
\(110\) 205.431 + 355.817i 0.178064 + 0.308417i
\(111\) 0 0
\(112\) 0 0
\(113\) −672.882 −0.560172 −0.280086 0.959975i \(-0.590363\pi\)
−0.280086 + 0.959975i \(0.590363\pi\)
\(114\) 0 0
\(115\) −208.213 + 360.635i −0.168834 + 0.292430i
\(116\) −730.028 + 1264.45i −0.584323 + 1.01208i
\(117\) 0 0
\(118\) −2787.13 −2.17437
\(119\) 0 0
\(120\) 0 0
\(121\) 568.653 + 984.936i 0.427238 + 0.739997i
\(122\) 1017.69 1762.70i 0.755227 1.30809i
\(123\) 0 0
\(124\) 646.130 + 1119.13i 0.467937 + 0.810491i
\(125\) −1218.34 −0.871773
\(126\) 0 0
\(127\) 175.815 0.122843 0.0614216 0.998112i \(-0.480437\pi\)
0.0614216 + 0.998112i \(0.480437\pi\)
\(128\) 656.249 + 1136.66i 0.453163 + 0.784900i
\(129\) 0 0
\(130\) −570.825 + 988.698i −0.385113 + 0.667035i
\(131\) −562.965 975.085i −0.375470 0.650332i 0.614928 0.788584i \(-0.289185\pi\)
−0.990397 + 0.138251i \(0.955852\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) −1051.66 −0.677983
\(135\) 0 0
\(136\) 1405.33 2434.10i 0.886073 1.53472i
\(137\) 934.350 1618.34i 0.582678 1.00923i −0.412483 0.910966i \(-0.635338\pi\)
0.995161 0.0982624i \(-0.0313285\pi\)
\(138\) 0 0
\(139\) 2817.19 1.71907 0.859537 0.511074i \(-0.170752\pi\)
0.859537 + 0.511074i \(0.170752\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) −2084.65 3610.72i −1.23197 2.13384i
\(143\) 269.105 466.103i 0.157368 0.272570i
\(144\) 0 0
\(145\) −201.208 348.503i −0.115238 0.199597i
\(146\) −1757.79 −0.996410
\(147\) 0 0
\(148\) 3808.14 2.11505
\(149\) 900.163 + 1559.13i 0.494928 + 0.857240i 0.999983 0.00584714i \(-0.00186121\pi\)
−0.505055 + 0.863087i \(0.668528\pi\)
\(150\) 0 0
\(151\) 226.492 392.296i 0.122064 0.211421i −0.798517 0.601972i \(-0.794382\pi\)
0.920581 + 0.390551i \(0.127715\pi\)
\(152\) 3524.01 + 6103.77i 1.88050 + 3.25711i
\(153\) 0 0
\(154\) 0 0
\(155\) −356.169 −0.184569
\(156\) 0 0
\(157\) −931.829 + 1613.98i −0.473682 + 0.820441i −0.999546 0.0301273i \(-0.990409\pi\)
0.525864 + 0.850569i \(0.323742\pi\)
\(158\) 1161.58 2011.91i 0.584875 1.01303i
\(159\) 0 0
\(160\) −2488.77 −1.22971
\(161\) 0 0
\(162\) 0 0
\(163\) −1160.57 2010.16i −0.557686 0.965940i −0.997689 0.0679437i \(-0.978356\pi\)
0.440004 0.897996i \(-0.354977\pi\)
\(164\) 250.129 433.237i 0.119096 0.206281i
\(165\) 0 0
\(166\) 640.290 + 1109.01i 0.299374 + 0.518531i
\(167\) 3211.62 1.48816 0.744079 0.668092i \(-0.232889\pi\)
0.744079 + 0.668092i \(0.232889\pi\)
\(168\) 0 0
\(169\) −701.494 −0.319296
\(170\) 641.780 + 1111.60i 0.289543 + 0.501503i
\(171\) 0 0
\(172\) 2460.52 4261.74i 1.09077 1.88927i
\(173\) −107.139 185.569i −0.0470844 0.0815525i 0.841523 0.540222i \(-0.181660\pi\)
−0.888607 + 0.458669i \(0.848326\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 2529.17 1.08320
\(177\) 0 0
\(178\) 4208.27 7288.93i 1.77204 3.06926i
\(179\) −1218.61 + 2110.70i −0.508845 + 0.881345i 0.491102 + 0.871102i \(0.336594\pi\)
−0.999948 + 0.0102437i \(0.996739\pi\)
\(180\) 0 0
\(181\) 248.631 0.102103 0.0510514 0.998696i \(-0.483743\pi\)
0.0510514 + 0.998696i \(0.483743\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 2420.21 + 4191.93i 0.969677 + 1.67953i
\(185\) −524.794 + 908.970i −0.208560 + 0.361237i
\(186\) 0 0
\(187\) −302.555 524.041i −0.118316 0.204929i
\(188\) −12521.4 −4.85755
\(189\) 0 0
\(190\) −3218.67 −1.22898
\(191\) −2156.54 3735.24i −0.816972 1.41504i −0.907903 0.419180i \(-0.862317\pi\)
0.0909306 0.995857i \(-0.471016\pi\)
\(192\) 0 0
\(193\) −1030.43 + 1784.75i −0.384309 + 0.665643i −0.991673 0.128781i \(-0.958894\pi\)
0.607364 + 0.794424i \(0.292227\pi\)
\(194\) −210.409 364.438i −0.0778683 0.134872i
\(195\) 0 0
\(196\) 0 0
\(197\) 1666.09 0.602557 0.301279 0.953536i \(-0.402587\pi\)
0.301279 + 0.953536i \(0.402587\pi\)
\(198\) 0 0
\(199\) −543.767 + 941.832i −0.193702 + 0.335501i −0.946474 0.322780i \(-0.895383\pi\)
0.752773 + 0.658281i \(0.228716\pi\)
\(200\) −3040.57 + 5266.43i −1.07501 + 1.86196i
\(201\) 0 0
\(202\) −6130.94 −2.13550
\(203\) 0 0
\(204\) 0 0
\(205\) 68.9399 + 119.407i 0.0234877 + 0.0406818i
\(206\) 3834.87 6642.19i 1.29703 2.24652i
\(207\) 0 0
\(208\) 3513.86 + 6086.18i 1.17136 + 2.02885i
\(209\) 1517.38 0.502198
\(210\) 0 0
\(211\) −4676.47 −1.52579 −0.762895 0.646522i \(-0.776223\pi\)
−0.762895 + 0.646522i \(0.776223\pi\)
\(212\) −2904.01 5029.88i −0.940792 1.62950i
\(213\) 0 0
\(214\) −2630.15 + 4555.56i −0.840157 + 1.45520i
\(215\) 678.161 + 1174.61i 0.215117 + 0.372594i
\(216\) 0 0
\(217\) 0 0
\(218\) −10368.0 −3.22114
\(219\) 0 0
\(220\) −780.889 + 1352.54i −0.239307 + 0.414492i
\(221\) 840.701 1456.14i 0.255890 0.443214i
\(222\) 0 0
\(223\) −3246.03 −0.974754 −0.487377 0.873192i \(-0.662046\pi\)
−0.487377 + 0.873192i \(0.662046\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) −1785.93 3093.32i −0.525656 0.910463i
\(227\) −2569.08 + 4449.77i −0.751171 + 1.30107i 0.196085 + 0.980587i \(0.437177\pi\)
−0.947256 + 0.320479i \(0.896156\pi\)
\(228\) 0 0
\(229\) 307.403 + 532.438i 0.0887064 + 0.153644i 0.906965 0.421207i \(-0.138393\pi\)
−0.818258 + 0.574851i \(0.805060\pi\)
\(230\) −2210.51 −0.633725
\(231\) 0 0
\(232\) −4677.59 −1.32370
\(233\) 1413.71 + 2448.61i 0.397490 + 0.688472i 0.993415 0.114567i \(-0.0365482\pi\)
−0.595926 + 0.803039i \(0.703215\pi\)
\(234\) 0 0
\(235\) 1725.56 2988.76i 0.478992 0.829638i
\(236\) −5297.24 9175.09i −1.46111 2.53071i
\(237\) 0 0
\(238\) 0 0
\(239\) 3432.45 0.928983 0.464491 0.885578i \(-0.346237\pi\)
0.464491 + 0.885578i \(0.346237\pi\)
\(240\) 0 0
\(241\) −1318.06 + 2282.94i −0.352296 + 0.610195i −0.986651 0.162847i \(-0.947932\pi\)
0.634355 + 0.773042i \(0.281266\pi\)
\(242\) −3018.58 + 5228.33i −0.801825 + 1.38880i
\(243\) 0 0
\(244\) 7736.96 2.02995
\(245\) 0 0
\(246\) 0 0
\(247\) 2108.15 + 3651.42i 0.543070 + 0.940625i
\(248\) −2070.01 + 3585.37i −0.530024 + 0.918028i
\(249\) 0 0
\(250\) −3233.65 5600.85i −0.818057 1.41692i
\(251\) 2057.57 0.517422 0.258711 0.965955i \(-0.416702\pi\)
0.258711 + 0.965955i \(0.416702\pi\)
\(252\) 0 0
\(253\) 1042.10 0.258958
\(254\) 466.639 + 808.243i 0.115274 + 0.199660i
\(255\) 0 0
\(256\) 203.161 351.885i 0.0495998 0.0859093i
\(257\) −1075.10 1862.13i −0.260946 0.451972i 0.705548 0.708663i \(-0.250701\pi\)
−0.966494 + 0.256691i \(0.917368\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) −4339.66 −1.03513
\(261\) 0 0
\(262\) 2988.39 5176.04i 0.704668 1.22052i
\(263\) −2295.08 + 3975.19i −0.538100 + 0.932017i 0.460906 + 0.887449i \(0.347525\pi\)
−0.999006 + 0.0445683i \(0.985809\pi\)
\(264\) 0 0
\(265\) 1600.79 0.371078
\(266\) 0 0
\(267\) 0 0
\(268\) −1998.80 3462.02i −0.455582 0.789091i
\(269\) 189.689 328.551i 0.0429945 0.0744687i −0.843727 0.536772i \(-0.819644\pi\)
0.886722 + 0.462303i \(0.152977\pi\)
\(270\) 0 0
\(271\) −2684.42 4649.55i −0.601723 1.04221i −0.992560 0.121755i \(-0.961148\pi\)
0.390837 0.920460i \(-0.372185\pi\)
\(272\) 7901.28 1.76134
\(273\) 0 0
\(274\) 9919.61 2.18710
\(275\) 654.610 + 1133.82i 0.143543 + 0.248624i
\(276\) 0 0
\(277\) 2390.80 4140.99i 0.518590 0.898224i −0.481177 0.876624i \(-0.659791\pi\)
0.999767 0.0216003i \(-0.00687613\pi\)
\(278\) 7477.25 + 12951.0i 1.61315 + 2.79406i
\(279\) 0 0
\(280\) 0 0
\(281\) 2076.57 0.440845 0.220423 0.975404i \(-0.429256\pi\)
0.220423 + 0.975404i \(0.429256\pi\)
\(282\) 0 0
\(283\) 1278.81 2214.96i 0.268612 0.465250i −0.699892 0.714249i \(-0.746768\pi\)
0.968504 + 0.248999i \(0.0801017\pi\)
\(284\) 7924.21 13725.1i 1.65569 2.86774i
\(285\) 0 0
\(286\) 2856.97 0.590687
\(287\) 0 0
\(288\) 0 0
\(289\) 1511.30 + 2617.65i 0.307612 + 0.532800i
\(290\) 1068.07 1849.96i 0.216274 0.374597i
\(291\) 0 0
\(292\) −3340.88 5786.57i −0.669555 1.15970i
\(293\) 560.049 0.111667 0.0558335 0.998440i \(-0.482218\pi\)
0.0558335 + 0.998440i \(0.482218\pi\)
\(294\) 0 0
\(295\) 2920.02 0.576305
\(296\) 6100.08 + 10565.6i 1.19784 + 2.07471i
\(297\) 0 0
\(298\) −4778.33 + 8276.31i −0.928863 + 1.60884i
\(299\) 1447.83 + 2507.71i 0.280034 + 0.485033i
\(300\) 0 0
\(301\) 0 0
\(302\) 2404.57 0.458171
\(303\) 0 0
\(304\) −9906.66 + 17158.8i −1.86903 + 3.23726i
\(305\) −1066.22 + 1846.75i −0.200169 + 0.346703i
\(306\) 0 0
\(307\) −3653.02 −0.679117 −0.339558 0.940585i \(-0.610278\pi\)
−0.339558 + 0.940585i \(0.610278\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) −945.325 1637.35i −0.173196 0.299985i
\(311\) −1746.13 + 3024.39i −0.318374 + 0.551439i −0.980149 0.198263i \(-0.936470\pi\)
0.661775 + 0.749702i \(0.269803\pi\)
\(312\) 0 0
\(313\) 4356.05 + 7544.90i 0.786640 + 1.36250i 0.928014 + 0.372544i \(0.121515\pi\)
−0.141374 + 0.989956i \(0.545152\pi\)
\(314\) −9892.85 −1.77798
\(315\) 0 0
\(316\) 8830.83 1.57207
\(317\) 970.165 + 1680.37i 0.171892 + 0.297726i 0.939081 0.343695i \(-0.111679\pi\)
−0.767189 + 0.641421i \(0.778345\pi\)
\(318\) 0 0
\(319\) −503.523 + 872.127i −0.0883758 + 0.153071i
\(320\) −2562.92 4439.11i −0.447724 0.775480i
\(321\) 0 0
\(322\) 0 0
\(323\) 4740.39 0.816602
\(324\) 0 0
\(325\) −1818.94 + 3150.50i −0.310452 + 0.537718i
\(326\) 6160.64 10670.5i 1.04665 1.81284i
\(327\) 0 0
\(328\) 1602.68 0.269797
\(329\) 0 0
\(330\) 0 0
\(331\) 2865.75 + 4963.63i 0.475879 + 0.824247i 0.999618 0.0276315i \(-0.00879650\pi\)
−0.523739 + 0.851879i \(0.675463\pi\)
\(332\) −2433.88 + 4215.61i −0.402339 + 0.696872i
\(333\) 0 0
\(334\) 8524.10 + 14764.2i 1.39646 + 2.41874i
\(335\) 1101.81 0.179696
\(336\) 0 0
\(337\) 2403.74 0.388547 0.194273 0.980947i \(-0.437765\pi\)
0.194273 + 0.980947i \(0.437765\pi\)
\(338\) −1861.87 3224.85i −0.299622 0.518960i
\(339\) 0 0
\(340\) −2439.55 + 4225.42i −0.389127 + 0.673987i
\(341\) 445.656 + 771.898i 0.0707731 + 0.122583i
\(342\) 0 0
\(343\) 0 0
\(344\) 15765.6 2.47099
\(345\) 0 0
\(346\) 568.723 985.057i 0.0883663 0.153055i
\(347\) −1668.22 + 2889.45i −0.258083 + 0.447013i −0.965728 0.259555i \(-0.916424\pi\)
0.707645 + 0.706568i \(0.249758\pi\)
\(348\) 0 0
\(349\) 2424.54 0.371870 0.185935 0.982562i \(-0.440469\pi\)
0.185935 + 0.982562i \(0.440469\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 3114.06 + 5393.71i 0.471534 + 0.816721i
\(353\) 6201.56 10741.4i 0.935059 1.61957i 0.160531 0.987031i \(-0.448679\pi\)
0.774528 0.632540i \(-0.217987\pi\)
\(354\) 0 0
\(355\) 2184.05 + 3782.88i 0.326528 + 0.565562i
\(356\) 31993.1 4.76300
\(357\) 0 0
\(358\) −12937.5 −1.90997
\(359\) 676.921 + 1172.46i 0.0995168 + 0.172368i 0.911485 0.411334i \(-0.134937\pi\)
−0.811968 + 0.583702i \(0.801604\pi\)
\(360\) 0 0
\(361\) −2514.03 + 4354.42i −0.366529 + 0.634848i
\(362\) 659.903 + 1142.99i 0.0958114 + 0.165950i
\(363\) 0 0
\(364\) 0 0
\(365\) 1841.61 0.264093
\(366\) 0 0
\(367\) −689.031 + 1193.44i −0.0980031 + 0.169746i −0.910858 0.412720i \(-0.864579\pi\)
0.812855 + 0.582466i \(0.197912\pi\)
\(368\) −6803.67 + 11784.3i −0.963766 + 1.66929i
\(369\) 0 0
\(370\) −5571.52 −0.782837
\(371\) 0 0
\(372\) 0 0
\(373\) −2728.46 4725.83i −0.378752 0.656017i 0.612129 0.790758i \(-0.290313\pi\)
−0.990881 + 0.134741i \(0.956980\pi\)
\(374\) 1606.05 2781.76i 0.222051 0.384603i
\(375\) 0 0
\(376\) −20057.5 34740.6i −2.75103 4.76492i
\(377\) −2798.25 −0.382273
\(378\) 0 0
\(379\) 554.675 0.0751761 0.0375881 0.999293i \(-0.488033\pi\)
0.0375881 + 0.999293i \(0.488033\pi\)
\(380\) −6117.43 10595.7i −0.825836 1.43039i
\(381\) 0 0
\(382\) 11447.5 19827.7i 1.53327 2.65569i
\(383\) −2930.33 5075.48i −0.390948 0.677141i 0.601627 0.798777i \(-0.294519\pi\)
−0.992575 + 0.121636i \(0.961186\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) −10939.6 −1.44252
\(387\) 0 0
\(388\) 799.809 1385.31i 0.104650 0.181259i
\(389\) 3889.43 6736.69i 0.506946 0.878056i −0.493022 0.870017i \(-0.664108\pi\)
0.999968 0.00803932i \(-0.00255902\pi\)
\(390\) 0 0
\(391\) 3255.60 0.421081
\(392\) 0 0
\(393\) 0 0
\(394\) 4422.04 + 7659.20i 0.565429 + 0.979352i
\(395\) −1216.96 + 2107.84i −0.155018 + 0.268499i
\(396\) 0 0
\(397\) 4013.94 + 6952.35i 0.507440 + 0.878912i 0.999963 + 0.00861270i \(0.00274154\pi\)
−0.492523 + 0.870300i \(0.663925\pi\)
\(398\) −5772.95 −0.727065
\(399\) 0 0
\(400\) −17095.2 −2.13690
\(401\) 389.990 + 675.482i 0.0485665 + 0.0841196i 0.889287 0.457350i \(-0.151201\pi\)
−0.840720 + 0.541470i \(0.817868\pi\)
\(402\) 0 0
\(403\) −1238.33 + 2144.85i −0.153066 + 0.265118i
\(404\) −11652.5 20182.8i −1.43499 2.48547i
\(405\) 0 0
\(406\) 0 0
\(407\) 2626.59 0.319890
\(408\) 0 0
\(409\) 7346.25 12724.1i 0.888139 1.53830i 0.0460654 0.998938i \(-0.485332\pi\)
0.842073 0.539363i \(-0.181335\pi\)
\(410\) −365.953 + 633.850i −0.0440809 + 0.0763503i
\(411\) 0 0
\(412\) 29154.4 3.48624
\(413\) 0 0
\(414\) 0 0
\(415\) −670.820 1161.89i −0.0793476 0.137434i
\(416\) −8652.95 + 14987.3i −1.01982 + 1.76638i
\(417\) 0 0
\(418\) 4027.35 + 6975.57i 0.471254 + 0.816236i
\(419\) 3370.31 0.392960 0.196480 0.980508i \(-0.437049\pi\)
0.196480 + 0.980508i \(0.437049\pi\)
\(420\) 0 0
\(421\) 15651.0 1.81184 0.905919 0.423450i \(-0.139181\pi\)
0.905919 + 0.423450i \(0.139181\pi\)
\(422\) −12412.0 21498.3i −1.43178 2.47991i
\(423\) 0 0
\(424\) 9303.58 16114.3i 1.06562 1.84570i
\(425\) 2045.04 + 3542.12i 0.233410 + 0.404277i
\(426\) 0 0
\(427\) 0 0
\(428\) −19995.6 −2.25823
\(429\) 0 0
\(430\) −3599.88 + 6235.17i −0.403724 + 0.699271i
\(431\) 2444.06 4233.24i 0.273147 0.473104i −0.696519 0.717538i \(-0.745269\pi\)
0.969666 + 0.244434i \(0.0786022\pi\)
\(432\) 0 0
\(433\) 5255.73 0.583313 0.291656 0.956523i \(-0.405794\pi\)
0.291656 + 0.956523i \(0.405794\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) −19705.5 34131.0i −2.16450 3.74903i
\(437\) −4081.88 + 7070.03i −0.446826 + 0.773925i
\(438\) 0 0
\(439\) −412.488 714.451i −0.0448451 0.0776740i 0.842732 0.538334i \(-0.180946\pi\)
−0.887577 + 0.460660i \(0.847613\pi\)
\(440\) −5003.48 −0.542117
\(441\) 0 0
\(442\) 8925.37 0.960490
\(443\) 6513.64 + 11281.9i 0.698583 + 1.20998i 0.968958 + 0.247226i \(0.0795190\pi\)
−0.270375 + 0.962755i \(0.587148\pi\)
\(444\) 0 0
\(445\) −4408.92 + 7636.47i −0.469669 + 0.813491i
\(446\) −8615.44 14922.4i −0.914693 1.58429i
\(447\) 0 0
\(448\) 0 0
\(449\) −16526.1 −1.73700 −0.868500 0.495689i \(-0.834916\pi\)
−0.868500 + 0.495689i \(0.834916\pi\)
\(450\) 0 0
\(451\) 172.522 298.817i 0.0180127 0.0311989i
\(452\) 6788.71 11758.4i 0.706447 1.22360i
\(453\) 0 0
\(454\) −27274.9 −2.81954
\(455\) 0 0
\(456\) 0 0
\(457\) 1855.41 + 3213.67i 0.189918 + 0.328947i 0.945223 0.326426i \(-0.105844\pi\)
−0.755305 + 0.655374i \(0.772511\pi\)
\(458\) −1631.79 + 2826.34i −0.166481 + 0.288354i
\(459\) 0 0
\(460\) −4201.31 7276.89i −0.425842 0.737580i
\(461\) −9714.00 −0.981401 −0.490701 0.871328i \(-0.663259\pi\)
−0.490701 + 0.871328i \(0.663259\pi\)
\(462\) 0 0
\(463\) −43.2780 −0.00434406 −0.00217203 0.999998i \(-0.500691\pi\)
−0.00217203 + 0.999998i \(0.500691\pi\)
\(464\) −6574.79 11387.9i −0.657817 1.13937i
\(465\) 0 0
\(466\) −7504.38 + 12998.0i −0.745995 + 1.29210i
\(467\) 766.618 + 1327.82i 0.0759633 + 0.131572i 0.901505 0.432769i \(-0.142463\pi\)
−0.825541 + 0.564341i \(0.809130\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 18319.6 1.79791
\(471\) 0 0
\(472\) 16970.8 29394.3i 1.65497 2.86649i
\(473\) 1697.09 2939.45i 0.164974 0.285743i
\(474\) 0 0
\(475\) −10256.3 −0.990722
\(476\) 0 0
\(477\) 0 0
\(478\) 9110.23 + 15779.4i 0.871741 + 1.50990i
\(479\) 3517.69 6092.81i 0.335547 0.581185i −0.648042 0.761604i \(-0.724412\pi\)
0.983590 + 0.180419i \(0.0577454\pi\)
\(480\) 0 0
\(481\) 3649.21 + 6320.62i 0.345924 + 0.599159i
\(482\) −13993.3 −1.32236
\(483\) 0 0
\(484\) −22948.6 −2.15520
\(485\) 220.441 + 381.815i 0.0206386 + 0.0357471i
\(486\) 0 0
\(487\) 7685.64 13311.9i 0.715132 1.23865i −0.247776 0.968817i \(-0.579700\pi\)
0.962908 0.269828i \(-0.0869669\pi\)
\(488\) 12393.5 + 21466.1i 1.14964 + 1.99124i
\(489\) 0 0
\(490\) 0 0
\(491\) 2393.35 0.219980 0.109990 0.993933i \(-0.464918\pi\)
0.109990 + 0.993933i \(0.464918\pi\)
\(492\) 0 0
\(493\) −1573.04 + 2724.58i −0.143704 + 0.248903i
\(494\) −11190.7 + 19382.8i −1.01921 + 1.76533i
\(495\) 0 0
\(496\) −11638.4 −1.05359
\(497\) 0 0
\(498\) 0 0
\(499\) −346.760 600.606i −0.0311084 0.0538814i 0.850052 0.526699i \(-0.176570\pi\)
−0.881160 + 0.472817i \(0.843237\pi\)
\(500\) 12291.8 21290.1i 1.09941 1.90424i
\(501\) 0 0
\(502\) 5461.10 + 9458.91i 0.485540 + 0.840979i
\(503\) −8646.95 −0.766498 −0.383249 0.923645i \(-0.625195\pi\)
−0.383249 + 0.923645i \(0.625195\pi\)
\(504\) 0 0
\(505\) 6423.27 0.566003
\(506\) 2765.89 + 4790.67i 0.243002 + 0.420892i
\(507\) 0 0
\(508\) −1773.80 + 3072.31i −0.154920 + 0.268330i
\(509\) 7750.44 + 13424.1i 0.674916 + 1.16899i 0.976494 + 0.215546i \(0.0691533\pi\)
−0.301578 + 0.953441i \(0.597513\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 12656.9 1.09250
\(513\) 0 0
\(514\) 5706.96 9884.75i 0.489734 0.848245i
\(515\) −4017.72 + 6958.89i −0.343771 + 0.595428i
\(516\) 0 0
\(517\) −8636.41 −0.734678
\(518\) 0 0
\(519\) 0 0
\(520\) −6951.50 12040.4i −0.586238 1.01539i
\(521\) −432.354 + 748.858i −0.0363565 + 0.0629714i −0.883631 0.468184i \(-0.844909\pi\)
0.847275 + 0.531155i \(0.178242\pi\)
\(522\) 0 0
\(523\) −3127.81 5417.52i −0.261509 0.452947i 0.705134 0.709074i \(-0.250887\pi\)
−0.966643 + 0.256127i \(0.917554\pi\)
\(524\) 22719.0 1.89406
\(525\) 0 0
\(526\) −24365.9 −2.01978
\(527\) 1392.26 + 2411.46i 0.115081 + 0.199326i
\(528\) 0 0
\(529\) 3280.15 5681.39i 0.269594 0.466951i
\(530\) 4248.72 + 7359.01i 0.348213 + 0.603122i
\(531\) 0 0
\(532\) 0 0
\(533\) 958.762 0.0779148
\(534\) 0 0
\(535\) 2755.56 4772.78i 0.222679 0.385692i
\(536\) 6403.56 11091.3i 0.516029 0.893789i
\(537\) 0 0
\(538\) 2013.85 0.161381
\(539\) 0 0
\(540\) 0 0
\(541\) −71.9353 124.596i −0.00571671 0.00990164i 0.863153 0.504943i \(-0.168486\pi\)
−0.868870 + 0.495041i \(0.835153\pi\)
\(542\) 14249.7 24681.2i 1.12929 1.95599i
\(543\) 0 0
\(544\) 9728.53 + 16850.3i 0.766741 + 1.32804i
\(545\) 10862.4 0.853747
\(546\) 0 0
\(547\) 5455.65 0.426448 0.213224 0.977003i \(-0.431604\pi\)
0.213224 + 0.977003i \(0.431604\pi\)
\(548\) 18853.3 + 32654.9i 1.46966 + 2.54552i
\(549\) 0 0
\(550\) −3474.86 + 6018.63i −0.269397 + 0.466610i
\(551\) −3944.56 6832.18i −0.304980 0.528241i
\(552\) 0 0
\(553\) 0 0
\(554\) 25382.2 1.94654
\(555\) 0 0
\(556\) −28422.7 + 49229.5i −2.16797 + 3.75503i
\(557\) 12404.9 21486.0i 0.943652 1.63445i 0.185223 0.982696i \(-0.440699\pi\)
0.758428 0.651756i \(-0.225968\pi\)
\(558\) 0 0
\(559\) 9431.33 0.713600
\(560\) 0 0
\(561\) 0 0
\(562\) 5511.51 + 9546.22i 0.413682 + 0.716517i
\(563\) −8184.91 + 14176.7i −0.612705 + 1.06124i 0.378077 + 0.925774i \(0.376585\pi\)
−0.990782 + 0.135462i \(0.956748\pi\)
\(564\) 0 0
\(565\) 1871.08 + 3240.81i 0.139322 + 0.241313i
\(566\) 13576.6 1.00824
\(567\) 0 0
\(568\) 50773.7 3.75074
\(569\) −9225.29 15978.7i −0.679691 1.17726i −0.975074 0.221881i \(-0.928781\pi\)
0.295383 0.955379i \(-0.404553\pi\)
\(570\) 0 0
\(571\) 3554.34 6156.30i 0.260499 0.451197i −0.705876 0.708335i \(-0.749446\pi\)
0.966374 + 0.257139i \(0.0827797\pi\)
\(572\) 5429.99 + 9405.02i 0.396922 + 0.687489i
\(573\) 0 0
\(574\) 0 0
\(575\) −7043.82 −0.510865
\(576\) 0 0
\(577\) 3797.09 6576.75i 0.273960 0.474512i −0.695912 0.718127i \(-0.745000\pi\)
0.969872 + 0.243615i \(0.0783332\pi\)
\(578\) −8022.42 + 13895.2i −0.577316 + 0.999940i
\(579\) 0 0
\(580\) 8119.96 0.581315
\(581\) 0 0
\(582\) 0 0
\(583\) −2002.98 3469.26i −0.142290 0.246453i
\(584\) 10703.2 18538.5i 0.758392 1.31357i
\(585\) 0 0
\(586\) 1486.45 + 2574.61i 0.104786 + 0.181495i
\(587\) −1763.34 −0.123988 −0.0619939 0.998077i \(-0.519746\pi\)
−0.0619939 + 0.998077i \(0.519746\pi\)
\(588\) 0 0
\(589\) −6982.47 −0.488468
\(590\) 7750.16 + 13423.7i 0.540795 + 0.936684i
\(591\) 0 0
\(592\) −17148.4 + 29702.0i −1.19054 + 2.06207i
\(593\) 6158.07 + 10666.1i 0.426445 + 0.738624i 0.996554 0.0829448i \(-0.0264325\pi\)
−0.570109 + 0.821569i \(0.693099\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) −36327.0 −2.49666
\(597\) 0 0
\(598\) −7685.50 + 13311.7i −0.525558 + 0.910293i
\(599\) −4451.70 + 7710.57i −0.303659 + 0.525952i −0.976962 0.213414i \(-0.931542\pi\)
0.673303 + 0.739367i \(0.264875\pi\)
\(600\) 0 0
\(601\) 19157.1 1.30022 0.650112 0.759838i \(-0.274722\pi\)
0.650112 + 0.759838i \(0.274722\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 4570.15 + 7915.74i 0.307876 + 0.533256i
\(605\) 3162.51 5477.62i 0.212519 0.368094i
\(606\) 0 0
\(607\) −3784.96 6555.75i −0.253092 0.438369i 0.711283 0.702905i \(-0.248114\pi\)
−0.964376 + 0.264537i \(0.914781\pi\)
\(608\) −48790.7 −3.25448
\(609\) 0 0
\(610\) −11319.6 −0.751340
\(611\) −11998.9 20782.6i −0.794471 1.37606i
\(612\) 0 0
\(613\) −1453.56 + 2517.65i −0.0957730 + 0.165884i −0.909931 0.414760i \(-0.863866\pi\)
0.814158 + 0.580643i \(0.197199\pi\)
\(614\) −9695.65 16793.4i −0.637272 1.10379i
\(615\) 0 0
\(616\) 0 0
\(617\) 12510.9 0.816320 0.408160 0.912910i \(-0.366171\pi\)
0.408160 + 0.912910i \(0.366171\pi\)
\(618\) 0 0
\(619\) 5032.78 8717.03i 0.326792 0.566021i −0.655081 0.755558i \(-0.727366\pi\)
0.981873 + 0.189538i \(0.0606989\pi\)
\(620\) 3593.39 6223.93i 0.232764 0.403160i
\(621\) 0 0
\(622\) −18538.0 −1.19503
\(623\) 0 0
\(624\) 0 0
\(625\) −2491.59 4315.56i −0.159462 0.276196i
\(626\) −23123.2 + 40050.5i −1.47634 + 2.55709i
\(627\) 0 0
\(628\) −18802.4 32566.8i −1.19474 2.06936i
\(629\) 8205.63 0.520159
\(630\) 0 0
\(631\) −25146.6 −1.58648 −0.793242 0.608907i \(-0.791608\pi\)
−0.793242 + 0.608907i \(0.791608\pi\)
\(632\) 14145.7 + 24501.1i 0.890325 + 1.54209i
\(633\) 0 0
\(634\) −5149.92 + 8919.92i −0.322602 + 0.558762i
\(635\) −488.889 846.781i −0.0305527 0.0529189i
\(636\) 0 0
\(637\) 0 0
\(638\) −5345.70 −0.331721
\(639\) 0 0
\(640\) 3649.66 6321.41i 0.225415 0.390430i
\(641\) −14479.5 + 25079.1i −0.892206 + 1.54535i −0.0549809 + 0.998487i \(0.517510\pi\)
−0.837225 + 0.546859i \(0.815824\pi\)
\(642\) 0 0
\(643\) −7341.90 −0.450290 −0.225145 0.974325i \(-0.572286\pi\)
−0.225145 + 0.974325i \(0.572286\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 12581.7 + 21792.1i 0.766285 + 1.32725i
\(647\) −3035.99 + 5258.49i −0.184478 + 0.319525i −0.943400 0.331656i \(-0.892393\pi\)
0.758923 + 0.651181i \(0.225726\pi\)
\(648\) 0 0
\(649\) −3653.67 6328.34i −0.220985 0.382756i
\(650\) −19311.0 −1.16529
\(651\) 0 0
\(652\) 46835.9 2.81324
\(653\) 13131.1 + 22743.7i 0.786920 + 1.36298i 0.927846 + 0.372965i \(0.121659\pi\)
−0.140926 + 0.990020i \(0.545008\pi\)
\(654\) 0 0
\(655\) −3130.88 + 5422.84i −0.186769 + 0.323493i
\(656\) 2252.72 + 3901.82i 0.134076 + 0.232226i
\(657\) 0 0
\(658\) 0 0
\(659\) −26130.1 −1.54459 −0.772296 0.635263i \(-0.780892\pi\)
−0.772296 + 0.635263i \(0.780892\pi\)
\(660\) 0 0
\(661\) −5962.75 + 10327.8i −0.350868 + 0.607722i −0.986402 0.164351i \(-0.947447\pi\)
0.635533 + 0.772073i \(0.280780\pi\)
\(662\) −15212.3 + 26348.4i −0.893114 + 1.54692i
\(663\) 0 0
\(664\) −15594.9 −0.911444
\(665\) 0 0
\(666\) 0 0
\(667\) −2709.04 4692.19i −0.157263 0.272387i
\(668\) −32402.0 + 56121.9i −1.87675 + 3.25063i
\(669\) 0 0
\(670\) 2924.35 + 5065.13i 0.168623 + 0.292064i
\(671\) 5336.42 0.307019
\(672\) 0 0
\(673\) −6359.85 −0.364271 −0.182135 0.983273i \(-0.558301\pi\)
−0.182135 + 0.983273i \(0.558301\pi\)
\(674\) 6379.89 + 11050.3i 0.364606 + 0.631516i
\(675\) 0 0
\(676\) 7077.36 12258.4i 0.402672 0.697449i
\(677\) −4280.81 7414.57i −0.243020 0.420924i 0.718553 0.695472i \(-0.244805\pi\)
−0.961573 + 0.274549i \(0.911472\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) −15631.2 −0.881513
\(681\) 0 0
\(682\) −2365.67 + 4097.46i −0.132824 + 0.230059i
\(683\) −3352.94 + 5807.47i −0.187843 + 0.325354i −0.944531 0.328423i \(-0.893483\pi\)
0.756688 + 0.653776i \(0.226816\pi\)
\(684\) 0 0
\(685\) −10392.6 −0.579679
\(686\) 0 0
\(687\) 0 0
\(688\) 22160.0 + 38382.2i 1.22797 + 2.12690i
\(689\) 5565.62 9639.94i 0.307741 0.533022i
\(690\) 0 0
\(691\) −12665.3 21937.0i −0.697267 1.20770i −0.969410 0.245445i \(-0.921066\pi\)
0.272143 0.962257i \(-0.412268\pi\)
\(692\) 4323.68 0.237517
\(693\) 0 0
\(694\) −17710.8 −0.968723
\(695\) −7833.77 13568.5i −0.427557 0.740550i
\(696\) 0 0
\(697\) 538.969 933.522i 0.0292897 0.0507312i
\(698\) 6435.08 + 11145.9i 0.348956 + 0.604410i
\(699\) 0 0
\(700\) 0 0
\(701\) 27184.1 1.46467 0.732333 0.680947i \(-0.238432\pi\)
0.732333 + 0.680947i \(0.238432\pi\)
\(702\) 0 0
\(703\) −10288.3 + 17819.8i −0.551961 + 0.956025i
\(704\) −6413.69 + 11108.8i −0.343360 + 0.594716i
\(705\) 0 0
\(706\) 65839.5 3.50977
\(707\) 0 0
\(708\) 0 0
\(709\) −8072.75 13982.4i −0.427614 0.740649i 0.569047 0.822305i \(-0.307312\pi\)
−0.996661 + 0.0816561i \(0.973979\pi\)
\(710\) −11593.6 + 20080.7i −0.612816 + 1.06143i
\(711\) 0 0
\(712\) 51248.2 + 88764.5i 2.69748 + 4.67218i
\(713\) −4795.41 −0.251879
\(714\) 0 0
\(715\) −2993.20 −0.156558
\(716\) −24589.1 42589.6i −1.28343 2.22297i
\(717\) 0 0
\(718\) −3593.30 + 6223.77i −0.186770 + 0.323494i
\(719\) −8648.74 14980.0i −0.448600 0.776998i 0.549695 0.835365i \(-0.314744\pi\)
−0.998295 + 0.0583673i \(0.981411\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) −26690.4 −1.37578
\(723\) 0 0
\(724\) −2508.44 + 4344.74i −0.128764 + 0.223026i
\(725\) 3403.43 5894.91i 0.174345 0.301975i
\(726\) 0 0
\(727\) −3514.71 −0.179303 −0.0896516 0.995973i \(-0.528575\pi\)
−0.0896516 + 0.995973i \(0.528575\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 4887.89 + 8466.08i 0.247821 + 0.429238i
\(731\) 5301.83 9183.04i 0.268256 0.464633i
\(732\) 0 0
\(733\) −13755.6 23825.4i −0.693144 1.20056i −0.970802 0.239881i \(-0.922892\pi\)
0.277658 0.960680i \(-0.410442\pi\)
\(734\) −7315.16 −0.367858
\(735\) 0 0
\(736\) −33508.4 −1.67817
\(737\) −1378.63 2387.86i −0.0689044 0.119346i
\(738\) 0 0
\(739\) −8050.80 + 13944.4i −0.400749 + 0.694117i −0.993816 0.111035i \(-0.964583\pi\)
0.593068 + 0.805153i \(0.297917\pi\)
\(740\) −10589.3 18341.2i −0.526040 0.911129i
\(741\) 0 0
\(742\) 0 0
\(743\) −14682.4 −0.724961 −0.362480 0.931991i \(-0.618070\pi\)
−0.362480 + 0.931991i \(0.618070\pi\)
\(744\) 0 0
\(745\) 5006.17 8670.93i 0.246190 0.426414i
\(746\) 14483.5 25086.1i 0.710828 1.23119i
\(747\) 0 0
\(748\) 12209.9 0.596843
\(749\) 0 0
\(750\) 0 0
\(751\) 3636.53 + 6298.66i 0.176696 + 0.306047i 0.940747 0.339109i \(-0.110126\pi\)
−0.764051 + 0.645156i \(0.776792\pi\)
\(752\) 56385.3 97662.2i 2.73426 4.73587i
\(753\) 0 0
\(754\) −7426.96 12863.9i −0.358719 0.621319i
\(755\) −2519.23 −0.121436
\(756\) 0 0
\(757\) 8505.93 0.408393 0.204196 0.978930i \(-0.434542\pi\)
0.204196 + 0.978930i \(0.434542\pi\)
\(758\) 1472.19 + 2549.91i 0.0705440 + 0.122186i
\(759\) 0 0
\(760\) 19598.4 33945.5i 0.935408 1.62017i
\(761\) −7108.86 12312.9i −0.338628 0.586521i 0.645547 0.763721i \(-0.276630\pi\)
−0.984175 + 0.177200i \(0.943296\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 87029.3 4.12121
\(765\) 0 0
\(766\) 15555.1 26942.2i 0.733717 1.27084i
\(767\) 10152.3 17584.4i 0.477939 0.827815i
\(768\) 0 0
\(769\) −16379.1 −0.768068 −0.384034 0.923319i \(-0.625466\pi\)
−0.384034 + 0.923319i \(0.625466\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −20791.9 36012.6i −0.969323 1.67892i
\(773\) 19948.3 34551.6i 0.928192 1.60768i 0.141846 0.989889i \(-0.454696\pi\)
0.786346 0.617787i \(-0.211970\pi\)
\(774\) 0 0
\(775\) −3012.29 5217.45i −0.139619 0.241827i
\(776\) 5124.70 0.237070
\(777\) 0 0
\(778\) 41292.5 1.90284
\(779\) 1351.52 + 2340.91i 0.0621609 + 0.107666i
\(780\) 0 0
\(781\) 5465.57 9466.65i 0.250414 0.433730i
\(782\) 8640.83 + 14966.4i 0.395135 + 0.684394i
\(783\) 0 0
\(784\) 0 0
\(785\) 10364.5 0.471244
\(786\) 0 0
\(787\) −16564.3 + 28690.2i −0.750257 + 1.29948i 0.197440 + 0.980315i \(0.436737\pi\)
−0.947698 + 0.319169i \(0.896596\pi\)
\(788\) −16809.1 + 29114.3i −0.759899 + 1.31618i
\(789\) 0 0
\(790\) −12920.0