Properties

Label 588.4.i.k.373.4
Level $588$
Weight $4$
Character 588.373
Analytic conductor $34.693$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 588 = 2^{2} \cdot 3 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 588.i (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(34.6931230834\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{8} - \cdots)\)
Defining polynomial: \(x^{8} - 2 x^{7} + 27 x^{6} + 10 x^{5} + 446 x^{4} + 62 x^{3} + 3061 x^{2} + 2142 x + 14161\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2^{8}\cdot 7^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 373.4
Root \(1.44795 + 2.50793i\) of defining polynomial
Character \(\chi\) \(=\) 588.373
Dual form 588.4.i.k.361.4

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.50000 - 2.59808i) q^{3} +(8.32734 - 14.4234i) q^{5} +(-4.50000 + 7.79423i) q^{9} +O(q^{10})\) \(q+(-1.50000 - 2.59808i) q^{3} +(8.32734 - 14.4234i) q^{5} +(-4.50000 + 7.79423i) q^{9} +(35.8800 + 62.1460i) q^{11} -65.3878 q^{13} -49.9641 q^{15} +(-45.2158 - 78.3160i) q^{17} +(-81.9092 + 141.871i) q^{19} +(-39.6144 + 68.6142i) q^{23} +(-76.1893 - 131.964i) q^{25} +27.0000 q^{27} -43.2995 q^{29} +(-67.8179 - 117.464i) q^{31} +(107.640 - 186.438i) q^{33} +(-135.370 + 234.468i) q^{37} +(98.0817 + 169.882i) q^{39} +152.241 q^{41} -177.641 q^{43} +(74.9461 + 129.810i) q^{45} +(22.8166 - 39.5194i) q^{47} +(-135.647 + 234.948i) q^{51} +(79.2188 + 137.211i) q^{53} +1195.14 q^{55} +491.455 q^{57} +(195.884 + 339.282i) q^{59} +(-275.647 + 477.435i) q^{61} +(-544.506 + 943.113i) q^{65} +(-229.315 - 397.185i) q^{67} +237.687 q^{69} -486.786 q^{71} +(-287.446 - 497.871i) q^{73} +(-228.568 + 395.891i) q^{75} +(334.160 - 578.782i) q^{79} +(-40.5000 - 70.1481i) q^{81} +76.2450 q^{83} -1506.11 q^{85} +(64.9493 + 112.495i) q^{87} +(-683.401 + 1183.69i) q^{89} +(-203.454 + 352.392i) q^{93} +(1364.17 + 2362.82i) q^{95} +242.655 q^{97} -645.840 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q - 12q^{3} - 36q^{9} + O(q^{10}) \) \( 8q - 12q^{3} - 36q^{9} - 48q^{17} - 192q^{19} - 192q^{23} - 324q^{25} + 216q^{27} + 192q^{29} - 48q^{31} - 256q^{37} + 2016q^{41} - 224q^{43} - 864q^{47} - 144q^{51} + 648q^{53} + 4704q^{55} + 1152q^{57} - 336q^{59} - 960q^{61} + 360q^{65} - 720q^{67} + 1152q^{69} - 2688q^{71} - 672q^{73} - 972q^{75} + 1984q^{79} - 324q^{81} + 6240q^{83} + 1360q^{85} - 288q^{87} - 2160q^{89} - 144q^{93} + 3744q^{95} + 4032q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/588\mathbb{Z}\right)^\times\).

\(n\) \(197\) \(295\) \(493\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{1}{3}\right)\)

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 0
\(3\) −1.50000 2.59808i −0.288675 0.500000i
\(4\) 0 0
\(5\) 8.32734 14.4234i 0.744820 1.29007i −0.205459 0.978666i \(-0.565869\pi\)
0.950279 0.311401i \(-0.100798\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 0 0
\(9\) −4.50000 + 7.79423i −0.166667 + 0.288675i
\(10\) 0 0
\(11\) 35.8800 + 62.1460i 0.983475 + 1.70343i 0.648526 + 0.761192i \(0.275386\pi\)
0.334949 + 0.942236i \(0.391281\pi\)
\(12\) 0 0
\(13\) −65.3878 −1.39502 −0.697512 0.716573i \(-0.745709\pi\)
−0.697512 + 0.716573i \(0.745709\pi\)
\(14\) 0 0
\(15\) −49.9641 −0.860044
\(16\) 0 0
\(17\) −45.2158 78.3160i −0.645085 1.11732i −0.984282 0.176604i \(-0.943489\pi\)
0.339197 0.940715i \(-0.389845\pi\)
\(18\) 0 0
\(19\) −81.9092 + 141.871i −0.989014 + 1.71302i −0.366488 + 0.930423i \(0.619440\pi\)
−0.622526 + 0.782599i \(0.713893\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −39.6144 + 68.6142i −0.359138 + 0.622045i −0.987817 0.155619i \(-0.950263\pi\)
0.628679 + 0.777665i \(0.283596\pi\)
\(24\) 0 0
\(25\) −76.1893 131.964i −0.609514 1.05571i
\(26\) 0 0
\(27\) 27.0000 0.192450
\(28\) 0 0
\(29\) −43.2995 −0.277259 −0.138630 0.990344i \(-0.544270\pi\)
−0.138630 + 0.990344i \(0.544270\pi\)
\(30\) 0 0
\(31\) −67.8179 117.464i −0.392918 0.680554i 0.599915 0.800064i \(-0.295201\pi\)
−0.992833 + 0.119510i \(0.961868\pi\)
\(32\) 0 0
\(33\) 107.640 186.438i 0.567810 0.983475i
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) −135.370 + 234.468i −0.601479 + 1.04179i 0.391118 + 0.920340i \(0.372088\pi\)
−0.992597 + 0.121452i \(0.961245\pi\)
\(38\) 0 0
\(39\) 98.0817 + 169.882i 0.402709 + 0.697512i
\(40\) 0 0
\(41\) 152.241 0.579902 0.289951 0.957041i \(-0.406361\pi\)
0.289951 + 0.957041i \(0.406361\pi\)
\(42\) 0 0
\(43\) −177.641 −0.630001 −0.315001 0.949091i \(-0.602005\pi\)
−0.315001 + 0.949091i \(0.602005\pi\)
\(44\) 0 0
\(45\) 74.9461 + 129.810i 0.248273 + 0.430022i
\(46\) 0 0
\(47\) 22.8166 39.5194i 0.0708114 0.122649i −0.828446 0.560069i \(-0.810774\pi\)
0.899257 + 0.437420i \(0.144108\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 0 0
\(51\) −135.647 + 234.948i −0.372440 + 0.645085i
\(52\) 0 0
\(53\) 79.2188 + 137.211i 0.205312 + 0.355611i 0.950232 0.311543i \(-0.100846\pi\)
−0.744920 + 0.667154i \(0.767512\pi\)
\(54\) 0 0
\(55\) 1195.14 2.93005
\(56\) 0 0
\(57\) 491.455 1.14201
\(58\) 0 0
\(59\) 195.884 + 339.282i 0.432237 + 0.748656i 0.997066 0.0765519i \(-0.0243911\pi\)
−0.564829 + 0.825208i \(0.691058\pi\)
\(60\) 0 0
\(61\) −275.647 + 477.435i −0.578574 + 1.00212i 0.417069 + 0.908875i \(0.363057\pi\)
−0.995643 + 0.0932450i \(0.970276\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −544.506 + 943.113i −1.03904 + 1.79967i
\(66\) 0 0
\(67\) −229.315 397.185i −0.418139 0.724237i 0.577614 0.816310i \(-0.303984\pi\)
−0.995752 + 0.0920729i \(0.970651\pi\)
\(68\) 0 0
\(69\) 237.687 0.414697
\(70\) 0 0
\(71\) −486.786 −0.813674 −0.406837 0.913501i \(-0.633368\pi\)
−0.406837 + 0.913501i \(0.633368\pi\)
\(72\) 0 0
\(73\) −287.446 497.871i −0.460863 0.798238i 0.538141 0.842855i \(-0.319127\pi\)
−0.999004 + 0.0446164i \(0.985793\pi\)
\(74\) 0 0
\(75\) −228.568 + 395.891i −0.351903 + 0.609514i
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) 334.160 578.782i 0.475897 0.824279i −0.523721 0.851890i \(-0.675457\pi\)
0.999619 + 0.0276111i \(0.00878999\pi\)
\(80\) 0 0
\(81\) −40.5000 70.1481i −0.0555556 0.0962250i
\(82\) 0 0
\(83\) 76.2450 0.100831 0.0504155 0.998728i \(-0.483945\pi\)
0.0504155 + 0.998728i \(0.483945\pi\)
\(84\) 0 0
\(85\) −1506.11 −1.92189
\(86\) 0 0
\(87\) 64.9493 + 112.495i 0.0800379 + 0.138630i
\(88\) 0 0
\(89\) −683.401 + 1183.69i −0.813937 + 1.40978i 0.0961518 + 0.995367i \(0.469347\pi\)
−0.910089 + 0.414413i \(0.863987\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) −203.454 + 352.392i −0.226851 + 0.392918i
\(94\) 0 0
\(95\) 1364.17 + 2362.82i 1.47327 + 2.55179i
\(96\) 0 0
\(97\) 242.655 0.253999 0.127000 0.991903i \(-0.459465\pi\)
0.127000 + 0.991903i \(0.459465\pi\)
\(98\) 0 0
\(99\) −645.840 −0.655650
\(100\) 0 0
\(101\) −347.371 601.665i −0.342225 0.592751i 0.642620 0.766185i \(-0.277847\pi\)
−0.984846 + 0.173433i \(0.944514\pi\)
\(102\) 0 0
\(103\) 87.1089 150.877i 0.0833310 0.144334i −0.821348 0.570428i \(-0.806777\pi\)
0.904679 + 0.426094i \(0.140111\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −23.8025 + 41.2272i −0.0215054 + 0.0372485i −0.876578 0.481260i \(-0.840179\pi\)
0.855072 + 0.518509i \(0.173513\pi\)
\(108\) 0 0
\(109\) 816.549 + 1414.30i 0.717534 + 1.24281i 0.961974 + 0.273141i \(0.0880626\pi\)
−0.244440 + 0.969664i \(0.578604\pi\)
\(110\) 0 0
\(111\) 812.221 0.694528
\(112\) 0 0
\(113\) −1127.29 −0.938464 −0.469232 0.883075i \(-0.655469\pi\)
−0.469232 + 0.883075i \(0.655469\pi\)
\(114\) 0 0
\(115\) 659.766 + 1142.75i 0.534987 + 0.926624i
\(116\) 0 0
\(117\) 294.245 509.647i 0.232504 0.402709i
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) −1909.25 + 3306.91i −1.43445 + 2.48453i
\(122\) 0 0
\(123\) −228.361 395.533i −0.167403 0.289951i
\(124\) 0 0
\(125\) −455.982 −0.326274
\(126\) 0 0
\(127\) 2398.66 1.67596 0.837979 0.545702i \(-0.183737\pi\)
0.837979 + 0.545702i \(0.183737\pi\)
\(128\) 0 0
\(129\) 266.462 + 461.526i 0.181866 + 0.315001i
\(130\) 0 0
\(131\) −774.482 + 1341.44i −0.516541 + 0.894675i 0.483275 + 0.875469i \(0.339447\pi\)
−0.999816 + 0.0192062i \(0.993886\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) 224.838 389.431i 0.143341 0.248273i
\(136\) 0 0
\(137\) −761.634 1319.19i −0.474969 0.822671i 0.524620 0.851337i \(-0.324207\pi\)
−0.999589 + 0.0286657i \(0.990874\pi\)
\(138\) 0 0
\(139\) 551.445 0.336496 0.168248 0.985745i \(-0.446189\pi\)
0.168248 + 0.985745i \(0.446189\pi\)
\(140\) 0 0
\(141\) −136.899 −0.0817660
\(142\) 0 0
\(143\) −2346.11 4063.59i −1.37197 2.37632i
\(144\) 0 0
\(145\) −360.570 + 624.526i −0.206508 + 0.357683i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 1200.12 2078.67i 0.659851 1.14290i −0.320803 0.947146i \(-0.603953\pi\)
0.980654 0.195749i \(-0.0627139\pi\)
\(150\) 0 0
\(151\) −310.780 538.287i −0.167490 0.290100i 0.770047 0.637987i \(-0.220233\pi\)
−0.937537 + 0.347887i \(0.886899\pi\)
\(152\) 0 0
\(153\) 813.884 0.430056
\(154\) 0 0
\(155\) −2258.97 −1.17061
\(156\) 0 0
\(157\) 1345.79 + 2330.97i 0.684112 + 1.18492i 0.973715 + 0.227770i \(0.0731433\pi\)
−0.289603 + 0.957147i \(0.593523\pi\)
\(158\) 0 0
\(159\) 237.657 411.633i 0.118537 0.205312i
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) −528.653 + 915.654i −0.254032 + 0.439997i −0.964632 0.263599i \(-0.915090\pi\)
0.710600 + 0.703596i \(0.248424\pi\)
\(164\) 0 0
\(165\) −1792.71 3105.06i −0.845832 1.46502i
\(166\) 0 0
\(167\) −243.840 −0.112987 −0.0564937 0.998403i \(-0.517992\pi\)
−0.0564937 + 0.998403i \(0.517992\pi\)
\(168\) 0 0
\(169\) 2078.56 0.946090
\(170\) 0 0
\(171\) −737.183 1276.84i −0.329671 0.571007i
\(172\) 0 0
\(173\) 843.632 1461.21i 0.370753 0.642162i −0.618929 0.785447i \(-0.712433\pi\)
0.989682 + 0.143285i \(0.0457665\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 587.653 1017.85i 0.249552 0.432237i
\(178\) 0 0
\(179\) 179.570 + 311.024i 0.0749814 + 0.129872i 0.901078 0.433657i \(-0.142777\pi\)
−0.826097 + 0.563528i \(0.809444\pi\)
\(180\) 0 0
\(181\) 2982.58 1.22483 0.612413 0.790538i \(-0.290199\pi\)
0.612413 + 0.790538i \(0.290199\pi\)
\(182\) 0 0
\(183\) 1653.88 0.668080
\(184\) 0 0
\(185\) 2254.55 + 3904.99i 0.895988 + 1.55190i
\(186\) 0 0
\(187\) 3244.68 5619.96i 1.26885 2.19771i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −1745.39 + 3023.10i −0.661213 + 1.14525i 0.319084 + 0.947726i \(0.396625\pi\)
−0.980297 + 0.197528i \(0.936709\pi\)
\(192\) 0 0
\(193\) −802.114 1389.30i −0.299158 0.518156i 0.676786 0.736180i \(-0.263372\pi\)
−0.975943 + 0.218024i \(0.930039\pi\)
\(194\) 0 0
\(195\) 3267.04 1.19978
\(196\) 0 0
\(197\) −455.935 −0.164893 −0.0824467 0.996595i \(-0.526273\pi\)
−0.0824467 + 0.996595i \(0.526273\pi\)
\(198\) 0 0
\(199\) −1042.08 1804.94i −0.371212 0.642958i 0.618541 0.785753i \(-0.287724\pi\)
−0.989752 + 0.142795i \(0.954391\pi\)
\(200\) 0 0
\(201\) −687.945 + 1191.56i −0.241412 + 0.418139i
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 1267.76 2195.83i 0.431923 0.748113i
\(206\) 0 0
\(207\) −356.530 617.528i −0.119713 0.207348i
\(208\) 0 0
\(209\) −11755.6 −3.89068
\(210\) 0 0
\(211\) 2568.06 0.837880 0.418940 0.908014i \(-0.362402\pi\)
0.418940 + 0.908014i \(0.362402\pi\)
\(212\) 0 0
\(213\) 730.178 + 1264.71i 0.234887 + 0.406837i
\(214\) 0 0
\(215\) −1479.28 + 2562.19i −0.469238 + 0.812743i
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) −862.338 + 1493.61i −0.266079 + 0.460863i
\(220\) 0 0
\(221\) 2956.56 + 5120.91i 0.899908 + 1.55869i
\(222\) 0 0
\(223\) −4659.55 −1.39922 −0.699612 0.714523i \(-0.746644\pi\)
−0.699612 + 0.714523i \(0.746644\pi\)
\(224\) 0 0
\(225\) 1371.41 0.406343
\(226\) 0 0
\(227\) −2414.39 4181.84i −0.705940 1.22272i −0.966351 0.257227i \(-0.917191\pi\)
0.260411 0.965498i \(-0.416142\pi\)
\(228\) 0 0
\(229\) 1611.29 2790.84i 0.464966 0.805345i −0.534234 0.845337i \(-0.679400\pi\)
0.999200 + 0.0399917i \(0.0127331\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 2851.21 4938.44i 0.801670 1.38853i −0.116847 0.993150i \(-0.537279\pi\)
0.918517 0.395383i \(-0.129388\pi\)
\(234\) 0 0
\(235\) −380.003 658.184i −0.105484 0.182703i
\(236\) 0 0
\(237\) −2004.96 −0.549519
\(238\) 0 0
\(239\) 1994.47 0.539796 0.269898 0.962889i \(-0.413010\pi\)
0.269898 + 0.962889i \(0.413010\pi\)
\(240\) 0 0
\(241\) 710.443 + 1230.52i 0.189891 + 0.328900i 0.945214 0.326452i \(-0.105853\pi\)
−0.755323 + 0.655353i \(0.772520\pi\)
\(242\) 0 0
\(243\) −121.500 + 210.444i −0.0320750 + 0.0555556i
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 5355.86 9276.62i 1.37970 2.38971i
\(248\) 0 0
\(249\) −114.367 198.090i −0.0291074 0.0504155i
\(250\) 0 0
\(251\) −3855.44 −0.969534 −0.484767 0.874643i \(-0.661096\pi\)
−0.484767 + 0.874643i \(0.661096\pi\)
\(252\) 0 0
\(253\) −5685.46 −1.41281
\(254\) 0 0
\(255\) 2259.16 + 3912.99i 0.554801 + 0.960944i
\(256\) 0 0
\(257\) −2026.64 + 3510.24i −0.491900 + 0.851996i −0.999956 0.00932793i \(-0.997031\pi\)
0.508056 + 0.861324i \(0.330364\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) 194.848 337.486i 0.0462099 0.0800379i
\(262\) 0 0
\(263\) 250.393 + 433.694i 0.0587069 + 0.101683i 0.893885 0.448296i \(-0.147969\pi\)
−0.835178 + 0.549979i \(0.814636\pi\)
\(264\) 0 0
\(265\) 2638.73 0.611683
\(266\) 0 0
\(267\) 4100.41 0.939853
\(268\) 0 0
\(269\) −1640.87 2842.07i −0.371917 0.644179i 0.617943 0.786223i \(-0.287966\pi\)
−0.989860 + 0.142043i \(0.954633\pi\)
\(270\) 0 0
\(271\) −1662.18 + 2878.98i −0.372584 + 0.645334i −0.989962 0.141332i \(-0.954861\pi\)
0.617378 + 0.786666i \(0.288195\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 5467.34 9469.71i 1.19888 2.07653i
\(276\) 0 0
\(277\) −4309.87 7464.92i −0.934856 1.61922i −0.774890 0.632096i \(-0.782195\pi\)
−0.159966 0.987122i \(-0.551139\pi\)
\(278\) 0 0
\(279\) 1220.72 0.261945
\(280\) 0 0
\(281\) −7710.80 −1.63697 −0.818484 0.574529i \(-0.805185\pi\)
−0.818484 + 0.574529i \(0.805185\pi\)
\(282\) 0 0
\(283\) 69.6354 + 120.612i 0.0146268 + 0.0253344i 0.873246 0.487279i \(-0.162011\pi\)
−0.858619 + 0.512614i \(0.828677\pi\)
\(284\) 0 0
\(285\) 4092.52 7088.45i 0.850596 1.47327i
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) −1632.43 + 2827.46i −0.332268 + 0.575506i
\(290\) 0 0
\(291\) −363.983 630.437i −0.0733232 0.127000i
\(292\) 0 0
\(293\) −4437.09 −0.884702 −0.442351 0.896842i \(-0.645855\pi\)
−0.442351 + 0.896842i \(0.645855\pi\)
\(294\) 0 0
\(295\) 6524.79 1.28776
\(296\) 0 0
\(297\) 968.760 + 1677.94i 0.189270 + 0.327825i
\(298\) 0 0
\(299\) 2590.30 4486.53i 0.501006 0.867768i
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) −1042.11 + 1804.99i −0.197584 + 0.342225i
\(304\) 0 0
\(305\) 4590.82 + 7951.53i 0.861867 + 1.49280i
\(306\) 0 0
\(307\) −299.480 −0.0556749 −0.0278375 0.999612i \(-0.508862\pi\)
−0.0278375 + 0.999612i \(0.508862\pi\)
\(308\) 0 0
\(309\) −522.654 −0.0962224
\(310\) 0 0
\(311\) −456.972 791.498i −0.0833199 0.144314i 0.821354 0.570419i \(-0.193219\pi\)
−0.904674 + 0.426104i \(0.859886\pi\)
\(312\) 0 0
\(313\) −1943.69 + 3366.57i −0.351002 + 0.607954i −0.986425 0.164210i \(-0.947492\pi\)
0.635423 + 0.772164i \(0.280826\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −1439.65 + 2493.55i −0.255075 + 0.441803i −0.964916 0.262559i \(-0.915434\pi\)
0.709841 + 0.704362i \(0.248767\pi\)
\(318\) 0 0
\(319\) −1553.59 2690.89i −0.272678 0.472291i
\(320\) 0 0
\(321\) 142.815 0.0248323
\(322\) 0 0
\(323\) 14814.4 2.55199
\(324\) 0 0
\(325\) 4981.85 + 8628.81i 0.850287 + 1.47274i
\(326\) 0 0
\(327\) 2449.65 4242.91i 0.414269 0.717534i
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) 1405.39 2434.21i 0.233376 0.404219i −0.725424 0.688303i \(-0.758356\pi\)
0.958799 + 0.284084i \(0.0916894\pi\)
\(332\) 0 0
\(333\) −1218.33 2110.21i −0.200493 0.347264i
\(334\) 0 0
\(335\) −7638.34 −1.24575
\(336\) 0 0
\(337\) 2960.90 0.478607 0.239303 0.970945i \(-0.423081\pi\)
0.239303 + 0.970945i \(0.423081\pi\)
\(338\) 0 0
\(339\) 1690.93 + 2928.78i 0.270911 + 0.469232i
\(340\) 0 0
\(341\) 4866.61 8429.22i 0.772850 1.33862i
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) 1979.30 3428.24i 0.308875 0.534987i
\(346\) 0 0
\(347\) 2142.26 + 3710.50i 0.331419 + 0.574034i 0.982790 0.184725i \(-0.0591393\pi\)
−0.651371 + 0.758759i \(0.725806\pi\)
\(348\) 0 0
\(349\) 3295.36 0.505434 0.252717 0.967540i \(-0.418676\pi\)
0.252717 + 0.967540i \(0.418676\pi\)
\(350\) 0 0
\(351\) −1765.47 −0.268472
\(352\) 0 0
\(353\) 5314.83 + 9205.56i 0.801360 + 1.38800i 0.918721 + 0.394906i \(0.129223\pi\)
−0.117362 + 0.993089i \(0.537444\pi\)
\(354\) 0 0
\(355\) −4053.63 + 7021.09i −0.606040 + 1.04969i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −1592.51 + 2758.30i −0.234121 + 0.405509i −0.959017 0.283349i \(-0.908554\pi\)
0.724896 + 0.688858i \(0.241888\pi\)
\(360\) 0 0
\(361\) −9988.74 17301.0i −1.45630 2.52238i
\(362\) 0 0
\(363\) 11455.5 1.65636
\(364\) 0 0
\(365\) −9574.65 −1.37304
\(366\) 0 0
\(367\) −3801.52 6584.42i −0.540702 0.936523i −0.998864 0.0476544i \(-0.984825\pi\)
0.458162 0.888869i \(-0.348508\pi\)
\(368\) 0 0
\(369\) −685.083 + 1186.60i −0.0966504 + 0.167403i
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) −755.978 + 1309.39i −0.104941 + 0.181763i −0.913714 0.406358i \(-0.866799\pi\)
0.808773 + 0.588121i \(0.200132\pi\)
\(374\) 0 0
\(375\) 683.972 + 1184.67i 0.0941871 + 0.163137i
\(376\) 0 0
\(377\) 2831.26 0.386783
\(378\) 0 0
\(379\) 8848.36 1.19923 0.599617 0.800287i \(-0.295320\pi\)
0.599617 + 0.800287i \(0.295320\pi\)
\(380\) 0 0
\(381\) −3597.99 6231.90i −0.483807 0.837979i
\(382\) 0 0
\(383\) −2067.05 + 3580.24i −0.275774 + 0.477654i −0.970330 0.241784i \(-0.922267\pi\)
0.694556 + 0.719438i \(0.255601\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 799.386 1384.58i 0.105000 0.181866i
\(388\) 0 0
\(389\) −3815.30 6608.30i −0.497284 0.861322i 0.502711 0.864455i \(-0.332336\pi\)
−0.999995 + 0.00313295i \(0.999003\pi\)
\(390\) 0 0
\(391\) 7164.79 0.926698
\(392\) 0 0
\(393\) 4646.89 0.596450
\(394\) 0 0
\(395\) −5565.32 9639.43i −0.708916 1.22788i
\(396\) 0 0
\(397\) 5809.25 10061.9i 0.734403 1.27202i −0.220582 0.975368i \(-0.570796\pi\)
0.954985 0.296654i \(-0.0958709\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −1523.51 + 2638.79i −0.189726 + 0.328616i −0.945159 0.326611i \(-0.894093\pi\)
0.755433 + 0.655226i \(0.227427\pi\)
\(402\) 0 0
\(403\) 4434.46 + 7680.71i 0.548130 + 0.949388i
\(404\) 0 0
\(405\) −1349.03 −0.165516
\(406\) 0 0
\(407\) −19428.3 −2.36616
\(408\) 0 0
\(409\) −5791.42 10031.0i −0.700164 1.21272i −0.968408 0.249369i \(-0.919777\pi\)
0.268244 0.963351i \(-0.413557\pi\)
\(410\) 0 0
\(411\) −2284.90 + 3957.57i −0.274224 + 0.474969i
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) 634.918 1099.71i 0.0751010 0.130079i
\(416\) 0 0
\(417\) −827.167 1432.70i −0.0971380 0.168248i
\(418\) 0 0
\(419\) −1318.83 −0.153768 −0.0768841 0.997040i \(-0.524497\pi\)
−0.0768841 + 0.997040i \(0.524497\pi\)
\(420\) 0 0
\(421\) −9733.56 −1.12680 −0.563402 0.826183i \(-0.690508\pi\)
−0.563402 + 0.826183i \(0.690508\pi\)
\(422\) 0 0
\(423\) 205.349 + 355.675i 0.0236038 + 0.0408830i
\(424\) 0 0
\(425\) −6889.92 + 11933.7i −0.786377 + 1.36204i
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) −7038.34 + 12190.8i −0.792108 + 1.37197i
\(430\) 0 0
\(431\) 7214.47 + 12495.8i 0.806284 + 1.39653i 0.915421 + 0.402499i \(0.131858\pi\)
−0.109136 + 0.994027i \(0.534808\pi\)
\(432\) 0 0
\(433\) −16620.3 −1.84463 −0.922313 0.386444i \(-0.873703\pi\)
−0.922313 + 0.386444i \(0.873703\pi\)
\(434\) 0 0
\(435\) 2163.42 0.238455
\(436\) 0 0
\(437\) −6489.57 11240.3i −0.710385 1.23042i
\(438\) 0 0
\(439\) 257.783 446.493i 0.0280257 0.0485420i −0.851672 0.524075i \(-0.824411\pi\)
0.879698 + 0.475533i \(0.157745\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −4488.05 + 7773.52i −0.481340 + 0.833705i −0.999771 0.0214146i \(-0.993183\pi\)
0.518431 + 0.855120i \(0.326516\pi\)
\(444\) 0 0
\(445\) 11381.8 + 19713.9i 1.21247 + 2.10007i
\(446\) 0 0
\(447\) −7200.73 −0.761930
\(448\) 0 0
\(449\) 2106.83 0.221442 0.110721 0.993852i \(-0.464684\pi\)
0.110721 + 0.993852i \(0.464684\pi\)
\(450\) 0 0
\(451\) 5462.39 + 9461.14i 0.570319 + 0.987822i
\(452\) 0 0
\(453\) −932.340 + 1614.86i −0.0967001 + 0.167490i
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −7863.08 + 13619.3i −0.804857 + 1.39405i 0.111531 + 0.993761i \(0.464425\pi\)
−0.916388 + 0.400292i \(0.868909\pi\)
\(458\) 0 0
\(459\) −1220.83 2114.53i −0.124147 0.215028i
\(460\) 0 0
\(461\) −7921.16 −0.800272 −0.400136 0.916456i \(-0.631037\pi\)
−0.400136 + 0.916456i \(0.631037\pi\)
\(462\) 0 0
\(463\) −5821.20 −0.584306 −0.292153 0.956372i \(-0.594372\pi\)
−0.292153 + 0.956372i \(0.594372\pi\)
\(464\) 0 0
\(465\) 3388.46 + 5868.98i 0.337927 + 0.585306i
\(466\) 0 0
\(467\) −5893.94 + 10208.6i −0.584024 + 1.01156i 0.410973 + 0.911648i \(0.365189\pi\)
−0.994996 + 0.0999112i \(0.968144\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) 4037.36 6992.92i 0.394972 0.684112i
\(472\) 0 0
\(473\) −6373.77 11039.7i −0.619590 1.07316i
\(474\) 0 0
\(475\) 24962.4 2.41127
\(476\) 0 0
\(477\) −1425.94 −0.136875
\(478\) 0 0
\(479\) 2657.21 + 4602.43i 0.253468 + 0.439020i 0.964478 0.264162i \(-0.0850954\pi\)
−0.711010 + 0.703182i \(0.751762\pi\)
\(480\) 0 0
\(481\) 8851.56 15331.3i 0.839078 1.45332i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 2020.67 3499.91i 0.189184 0.327676i
\(486\) 0 0
\(487\) 9331.34 + 16162.4i 0.868261 + 1.50387i 0.863772 + 0.503883i \(0.168096\pi\)
0.00448933 + 0.999990i \(0.498571\pi\)
\(488\) 0 0
\(489\) 3171.92 0.293331
\(490\) 0 0
\(491\) 13519.1 1.24259 0.621293 0.783578i \(-0.286608\pi\)
0.621293 + 0.783578i \(0.286608\pi\)
\(492\) 0 0
\(493\) 1957.82 + 3391.05i 0.178856 + 0.309787i
\(494\) 0 0
\(495\) −5378.13 + 9315.19i −0.488341 + 0.845832i
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) −6916.17 + 11979.2i −0.620462 + 1.07467i 0.368938 + 0.929454i \(0.379721\pi\)
−0.989400 + 0.145217i \(0.953612\pi\)
\(500\) 0 0
\(501\) 365.760 + 633.515i 0.0326167 + 0.0564937i
\(502\) 0 0
\(503\) 13469.0 1.19394 0.596970 0.802264i \(-0.296371\pi\)
0.596970 + 0.802264i \(0.296371\pi\)
\(504\) 0 0
\(505\) −11570.7 −1.01958
\(506\) 0 0
\(507\) −3117.84 5400.26i −0.273113 0.473045i
\(508\) 0 0
\(509\) −4387.62 + 7599.59i −0.382079 + 0.661779i −0.991359 0.131175i \(-0.958125\pi\)
0.609281 + 0.792955i \(0.291458\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) −2211.55 + 3830.51i −0.190336 + 0.329671i
\(514\) 0 0
\(515\) −1450.77 2512.81i −0.124133 0.215005i
\(516\) 0 0
\(517\) 3274.63 0.278565
\(518\) 0 0
\(519\) −5061.79 −0.428108
\(520\) 0 0
\(521\) 830.382 + 1438.26i 0.0698267 + 0.120943i 0.898825 0.438308i \(-0.144422\pi\)
−0.828998 + 0.559251i \(0.811089\pi\)
\(522\) 0 0
\(523\) −3162.41 + 5477.45i −0.264402 + 0.457958i −0.967407 0.253227i \(-0.918508\pi\)
0.703005 + 0.711185i \(0.251841\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −6132.88 + 10622.5i −0.506931 + 0.878030i
\(528\) 0 0
\(529\) 2944.90 + 5100.71i 0.242040 + 0.419225i
\(530\) 0 0
\(531\) −3525.92 −0.288158
\(532\) 0 0
\(533\) −9954.68 −0.808977
\(534\) 0 0
\(535\) 396.424 + 686.626i 0.0320353 + 0.0554868i
\(536\) 0 0
\(537\) 538.709 933.071i 0.0432905 0.0749814i
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) −2233.94 + 3869.30i −0.177532 + 0.307494i −0.941034 0.338311i \(-0.890145\pi\)
0.763503 + 0.645804i \(0.223478\pi\)
\(542\) 0 0
\(543\) −4473.87 7748.97i −0.353577 0.612413i
\(544\) 0 0
\(545\) 27198.7 2.13774
\(546\) 0 0
\(547\) −10939.0 −0.855063 −0.427531 0.904000i \(-0.640617\pi\)
−0.427531 + 0.904000i \(0.640617\pi\)
\(548\) 0 0
\(549\) −2480.83 4296.92i −0.192858 0.334040i
\(550\) 0 0
\(551\) 3546.63 6142.94i 0.274213 0.474951i
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) 6763.65 11715.0i 0.517299 0.895988i
\(556\) 0 0
\(557\) 7162.57 + 12405.9i 0.544862 + 0.943728i 0.998616 + 0.0526011i \(0.0167512\pi\)
−0.453754 + 0.891127i \(0.649915\pi\)
\(558\) 0 0
\(559\) 11615.6 0.878867
\(560\) 0 0
\(561\) −19468.1 −1.46514
\(562\) 0 0
\(563\) −10201.4 17669.4i −0.763656 1.32269i −0.940954 0.338533i \(-0.890069\pi\)
0.177299 0.984157i \(-0.443264\pi\)
\(564\) 0 0
\(565\) −9387.32 + 16259.3i −0.698987 + 1.21068i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 3625.21 6279.05i 0.267095 0.462622i −0.701016 0.713146i \(-0.747270\pi\)
0.968110 + 0.250524i \(0.0806030\pi\)
\(570\) 0 0
\(571\) −12447.4 21559.5i −0.912272 1.58010i −0.810847 0.585258i \(-0.800993\pi\)
−0.101424 0.994843i \(-0.532340\pi\)
\(572\) 0 0
\(573\) 10472.3 0.763503
\(574\) 0 0
\(575\) 12072.8 0.875599
\(576\) 0 0
\(577\) −681.723 1180.78i −0.0491863 0.0851932i 0.840384 0.541991i \(-0.182329\pi\)
−0.889570 + 0.456798i \(0.848996\pi\)
\(578\) 0 0
\(579\) −2406.34 + 4167.90i −0.172719 + 0.299158i
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) −5684.74 + 9846.26i −0.403839 + 0.699469i
\(584\) 0 0
\(585\) −4900.56 8488.01i −0.346347 0.599891i
\(586\) 0 0
\(587\) 23854.8 1.67733 0.838666 0.544647i \(-0.183336\pi\)
0.838666 + 0.544647i \(0.183336\pi\)
\(588\) 0 0
\(589\) 22219.6 1.55440
\(590\) 0 0
\(591\) 683.902 + 1184.55i 0.0476006 + 0.0824467i
\(592\) 0 0
\(593\) −1718.60 + 2976.71i −0.119013 + 0.206136i −0.919377 0.393378i \(-0.871306\pi\)
0.800364 + 0.599514i \(0.204640\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) −3126.24 + 5414.81i −0.214319 + 0.371212i
\(598\) 0 0
\(599\) −8255.87 14299.6i −0.563148 0.975401i −0.997219 0.0745226i \(-0.976257\pi\)
0.434071 0.900879i \(-0.357077\pi\)
\(600\) 0 0
\(601\) −11148.3 −0.756656 −0.378328 0.925672i \(-0.623501\pi\)
−0.378328 + 0.925672i \(0.623501\pi\)
\(602\) 0 0
\(603\) 4127.67 0.278759
\(604\) 0 0
\(605\) 31797.9 + 55075.6i 2.13681 + 3.70106i
\(606\) 0 0
\(607\) 195.791 339.121i 0.0130921 0.0226763i −0.859405 0.511295i \(-0.829166\pi\)
0.872497 + 0.488619i \(0.162499\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −1491.92 + 2584.09i −0.0987836 + 0.171098i
\(612\) 0 0
\(613\) 5870.25 + 10167.6i 0.386782 + 0.669925i 0.992015 0.126123i \(-0.0402534\pi\)
−0.605233 + 0.796048i \(0.706920\pi\)
\(614\) 0 0
\(615\) −7606.56 −0.498742
\(616\) 0 0
\(617\) −8818.95 −0.575426 −0.287713 0.957717i \(-0.592895\pi\)
−0.287713 + 0.957717i \(0.592895\pi\)
\(618\) 0 0
\(619\) 7962.35 + 13791.2i 0.517018 + 0.895501i 0.999805 + 0.0197631i \(0.00629120\pi\)
−0.482787 + 0.875738i \(0.660375\pi\)
\(620\) 0 0
\(621\) −1069.59 + 1852.58i −0.0691162 + 0.119713i
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) 5726.55 9918.67i 0.366499 0.634795i
\(626\) 0 0
\(627\) 17633.4 + 30542.0i 1.12314 + 1.94534i
\(628\) 0 0
\(629\) 24483.5 1.55202
\(630\) 0 0
\(631\) 29206.4 1.84261 0.921307 0.388836i \(-0.127123\pi\)
0.921307 + 0.388836i \(0.127123\pi\)
\(632\) 0 0
\(633\) −3852.09 6672.02i −0.241875 0.418940i
\(634\) 0 0
\(635\) 19974.5 34596.8i 1.24829 2.16210i
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 2190.54 3794.12i 0.135612 0.234887i
\(640\) 0 0
\(641\) −2806.51 4861.01i −0.172933 0.299530i 0.766511 0.642232i \(-0.221991\pi\)
−0.939444 + 0.342702i \(0.888658\pi\)
\(642\) 0 0
\(643\) −18995.0 −1.16499 −0.582496 0.812834i \(-0.697924\pi\)
−0.582496 + 0.812834i \(0.697924\pi\)
\(644\) 0 0
\(645\) 8875.68 0.541829
\(646\) 0 0
\(647\) −11332.5 19628.5i −0.688604 1.19270i −0.972290 0.233779i \(-0.924891\pi\)
0.283686 0.958917i \(-0.408443\pi\)
\(648\) 0 0
\(649\) −14056.7 + 24346.9i −0.850188 + 1.47257i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −13263.9 + 22973.7i −0.794879 + 1.37677i 0.128037 + 0.991769i \(0.459132\pi\)
−0.922916 + 0.385001i \(0.874201\pi\)
\(654\) 0 0
\(655\) 12898.8 + 22341.3i 0.769460 + 1.33274i
\(656\) 0 0
\(657\) 5174.03 0.307242
\(658\) 0 0
\(659\) −17114.8 −1.01168 −0.505839 0.862628i \(-0.668817\pi\)
−0.505839 + 0.862628i \(0.668817\pi\)
\(660\) 0 0
\(661\) 595.908 + 1032.14i 0.0350653 + 0.0607348i 0.883025 0.469325i \(-0.155503\pi\)
−0.847960 + 0.530060i \(0.822169\pi\)
\(662\) 0 0
\(663\) 8869.68 15362.7i 0.519562 0.899908i
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 1715.29 2970.96i 0.0995744 0.172468i
\(668\) 0 0
\(669\) 6989.33 + 12105.9i 0.403921 + 0.699612i
\(670\) 0 0
\(671\) −39560.9 −2.27605
\(672\) 0 0
\(673\) −9415.20 −0.539271 −0.269636 0.962962i \(-0.586903\pi\)
−0.269636 + 0.962962i \(0.586903\pi\)
\(674\) 0 0
\(675\) −2057.11 3563.02i −0.117301 0.203171i
\(676\) 0 0
\(677\) −3958.56 + 6856.43i −0.224727 + 0.389238i −0.956237 0.292592i \(-0.905482\pi\)
0.731511 + 0.681830i \(0.238816\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) −7243.16 + 12545.5i −0.407575 + 0.705940i
\(682\) 0 0
\(683\) −14617.2 25317.7i −0.818904 1.41838i −0.906490 0.422227i \(-0.861249\pi\)
0.0875859 0.996157i \(-0.472085\pi\)
\(684\) 0 0
\(685\) −25369.6 −1.41507
\(686\) 0 0
\(687\) −9667.76 −0.536897
\(688\) 0 0
\(689\) −5179.94 8971.93i −0.286415 0.496086i
\(690\) 0 0
\(691\) 611.228 1058.68i 0.0336501 0.0582836i −0.848710 0.528859i \(-0.822620\pi\)
0.882360 + 0.470575i \(0.155953\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 4592.07 7953.70i 0.250629 0.434102i
\(696\) 0 0
\(697\) −6883.68 11922.9i −0.374086 0.647936i
\(698\) 0 0
\(699\) −17107.3 −0.925688
\(700\) 0 0
\(701\) 13054.6 0.703372 0.351686 0.936118i \(-0.385608\pi\)
0.351686 + 0.936118i \(0.385608\pi\)
\(702\) 0 0
\(703\) −22176.1 38410.2i −1.18974 2.06069i
\(704\) 0 0
\(705\) −1140.01 + 1974.55i −0.0609010 + 0.105484i
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) 9987.87 17299.5i 0.529058 0.916356i −0.470367 0.882471i \(-0.655879\pi\)
0.999426 0.0338854i \(-0.0107881\pi\)
\(710\) 0 0
\(711\) 3007.44 + 5209.03i 0.158632 + 0.274760i
\(712\) 0 0
\(713\) 10746.3 0.564447
\(714\) 0 0
\(715\) −78147.5 −4.08749
\(716\) 0 0
\(717\) −2991.70 5181.77i −0.155826 0.269898i
\(718\) 0 0
\(719\) −3256.13 + 5639.78i −0.168892 + 0.292529i −0.938030 0.346553i \(-0.887352\pi\)
0.769139 + 0.639082i \(0.220685\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0 0
\(723\) 2131.33 3691.57i 0.109633 0.189891i
\(724\) 0 0
\(725\) 3298.96 + 5713.97i 0.168994 + 0.292705i
\(726\) 0 0
\(727\) 11437.1 0.583467 0.291733 0.956500i \(-0.405768\pi\)
0.291733 + 0.956500i \(0.405768\pi\)
\(728\) 0 0
\(729\) 729.000 0.0370370
\(730\) 0 0
\(731\) 8032.19 + 13912.2i 0.406404 + 0.703913i
\(732\) 0 0
\(733\) 6138.02 10631.4i 0.309295 0.535714i −0.668914 0.743340i \(-0.733240\pi\)
0.978208 + 0.207626i \(0.0665738\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 16455.6 28502.0i 0.822458 1.42454i
\(738\) 0 0
\(739\) −6046.91 10473.5i −0.301000 0.521347i 0.675363 0.737486i \(-0.263987\pi\)
−0.976363 + 0.216138i \(0.930654\pi\)
\(740\) 0 0
\(741\) −32135.2 −1.59314
\(742\) 0 0
\(743\) 34331.6 1.69516 0.847580 0.530668i \(-0.178059\pi\)
0.847580 + 0.530668i \(0.178059\pi\)
\(744\) 0 0
\(745\) −19987.6 34619.6i −0.982940 1.70250i
\(746\) 0 0
\(747\) −343.102 + 594.271i −0.0168052 + 0.0291074i
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) 7278.96 12607.5i 0.353679 0.612590i −0.633212 0.773979i \(-0.718264\pi\)
0.986891 + 0.161388i \(0.0515971\pi\)
\(752\) 0 0
\(753\) 5783.16 + 10016.7i 0.279880 + 0.484767i
\(754\) 0 0
\(755\) −10351.9 −0.498998
\(756\) 0 0
\(757\) 27115.5 1.30189 0.650944 0.759126i \(-0.274373\pi\)
0.650944 + 0.759126i \(0.274373\pi\)
\(758\) 0 0
\(759\) 8528.19 + 14771.3i 0.407844 + 0.706407i
\(760\) 0 0
\(761\) 5481.98 9495.06i 0.261132 0.452294i −0.705411 0.708799i \(-0.749238\pi\)
0.966543 + 0.256504i \(0.0825708\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) 6777.49 11739.0i 0.320315 0.554801i
\(766\) 0 0
\(767\) −12808.4 22184.9i −0.602981 1.04439i
\(768\) 0 0
\(769\) −7835.53 −0.367434 −0.183717 0.982979i \(-0.558813\pi\)
−0.183717 + 0.982979i \(0.558813\pi\)
\(770\) 0 0
\(771\) 12159.8 0.567997
\(772\) 0 0
\(773\) 14383.9 + 24913.6i 0.669278 + 1.15922i 0.978106 + 0.208106i \(0.0667298\pi\)
−0.308828 + 0.951118i \(0.599937\pi\)
\(774\) 0 0
\(775\) −10334.0 + 17899.0i −0.478978 + 0.829614i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −12469.9 + 21598.5i −0.573531 + 0.993386i
\(780\) 0 0
\(781\) −17465.9 30251.8i −0.800228 1.38603i
\(782\) 0 0
\(783\) −1169.09 −0.0533586
\(784\) 0 0
\(785\) 44827.3 2.03816
\(786\) 0 0
\(787\) 1347.91 + 2334.65i 0.0610520 + 0.105745i 0.894936 0.446195i \(-0.147221\pi\)
−0.833884 + 0.551940i \(0.813888\pi\)
\(788\) 0 0
\(789\) 751.180 1301.08i 0.0338944 0.0587069i
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) 18024.0 31218.4i 0.807125 1.39798i
\(794\) 0 0
\(795\) −3958.09 6855.62i −0.176578 0.305841i
\(796\) 0 0
\(797\) 12592.1 0.559643 0.279822 0.960052i \(-0.409725\pi\)