Properties

Label 648.4.i.p.217.1
Level $648$
Weight $4$
Character 648.217
Analytic conductor $38.233$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 648 = 2^{3} \cdot 3^{4} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 648.i (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(38.2332376837\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\sqrt{-3}, \sqrt{-43})\)
Defining polynomial: \(x^{4} - x^{3} - 10 x^{2} - 11 x + 121\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{2}\cdot 3 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 217.1
Root \(-2.58945 - 2.07237i\) of defining polynomial
Character \(\chi\) \(=\) 648.217
Dual form 648.4.i.p.433.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-6.67891 - 11.5682i) q^{5} +(7.17891 - 12.4342i) q^{7} +O(q^{10})\) \(q+(-6.67891 - 11.5682i) q^{5} +(7.17891 - 12.4342i) q^{7} +(-19.5367 + 33.8386i) q^{11} +(38.3945 + 66.5013i) q^{13} -62.4313 q^{17} -39.7891 q^{19} +(64.2524 + 111.288i) q^{23} +(-26.7156 + 46.2728i) q^{25} +(-32.4680 + 56.2362i) q^{29} +(4.56873 + 7.91328i) q^{31} -191.789 q^{35} +319.505 q^{37} +(-8.78908 - 15.2231i) q^{41} +(225.473 - 390.530i) q^{43} +(290.799 - 503.678i) q^{47} +(68.4265 + 118.518i) q^{49} +329.450 q^{53} +521.936 q^{55} +(120.927 + 209.451i) q^{59} +(-248.762 + 430.868i) q^{61} +(512.867 - 888.312i) q^{65} +(289.032 + 500.618i) q^{67} -660.927 q^{71} +696.559 q^{73} +(280.505 + 485.848i) q^{77} +(-365.134 + 632.430i) q^{79} +(-545.239 + 944.382i) q^{83} +(416.973 + 722.218i) q^{85} -317.588 q^{89} +1102.52 q^{91} +(265.748 + 460.288i) q^{95} +(742.827 - 1286.61i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q - 4q^{5} + 6q^{7} + O(q^{10}) \) \( 4q - 4q^{5} + 6q^{7} - 10q^{11} + 40q^{13} - 68q^{17} + 68q^{19} + 98q^{23} - 16q^{25} + 120q^{29} + 200q^{31} - 540q^{35} + 960q^{37} + 192q^{41} + 334q^{43} + 300q^{47} + 410q^{49} - 136q^{53} + 1588q^{55} + 620q^{59} - 200q^{61} + 1370q^{65} + 1406q^{67} - 2780q^{71} + 3604q^{73} + 804q^{77} + 334q^{79} - 500q^{83} + 1100q^{85} - 180q^{89} + 2820q^{91} + 1222q^{95} + 200q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/648\mathbb{Z}\right)^\times\).

\(n\) \(325\) \(487\) \(569\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{2}{3}\right)\)

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
\(3\) 0 0
\(4\) 0 0
\(5\) −6.67891 11.5682i −0.597380 1.03469i −0.993206 0.116367i \(-0.962875\pi\)
0.395827 0.918325i \(-0.370458\pi\)
\(6\) 0 0
\(7\) 7.17891 12.4342i 0.387625 0.671386i −0.604505 0.796601i \(-0.706629\pi\)
0.992130 + 0.125216i \(0.0399624\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −19.5367 + 33.8386i −0.535504 + 0.927520i 0.463635 + 0.886026i \(0.346545\pi\)
−0.999139 + 0.0414937i \(0.986788\pi\)
\(12\) 0 0
\(13\) 38.3945 + 66.5013i 0.819133 + 1.41878i 0.906322 + 0.422588i \(0.138878\pi\)
−0.0871887 + 0.996192i \(0.527788\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −62.4313 −0.890694 −0.445347 0.895358i \(-0.646920\pi\)
−0.445347 + 0.895358i \(0.646920\pi\)
\(18\) 0 0
\(19\) −39.7891 −0.480434 −0.240217 0.970719i \(-0.577219\pi\)
−0.240217 + 0.970719i \(0.577219\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 64.2524 + 111.288i 0.582502 + 1.00892i 0.995182 + 0.0980467i \(0.0312595\pi\)
−0.412680 + 0.910876i \(0.635407\pi\)
\(24\) 0 0
\(25\) −26.7156 + 46.2728i −0.213725 + 0.370183i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −32.4680 + 56.2362i −0.207902 + 0.360097i −0.951053 0.309027i \(-0.899997\pi\)
0.743152 + 0.669123i \(0.233330\pi\)
\(30\) 0 0
\(31\) 4.56873 + 7.91328i 0.0264700 + 0.0458473i 0.878957 0.476901i \(-0.158240\pi\)
−0.852487 + 0.522748i \(0.824907\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −191.789 −0.926236
\(36\) 0 0
\(37\) 319.505 1.41963 0.709814 0.704389i \(-0.248779\pi\)
0.709814 + 0.704389i \(0.248779\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −8.78908 15.2231i −0.0334786 0.0579867i 0.848801 0.528713i \(-0.177325\pi\)
−0.882279 + 0.470726i \(0.843992\pi\)
\(42\) 0 0
\(43\) 225.473 390.530i 0.799634 1.38501i −0.120220 0.992747i \(-0.538360\pi\)
0.919855 0.392260i \(-0.128307\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 290.799 503.678i 0.902496 1.56317i 0.0782529 0.996934i \(-0.475066\pi\)
0.824243 0.566236i \(-0.191601\pi\)
\(48\) 0 0
\(49\) 68.4265 + 118.518i 0.199494 + 0.345534i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 329.450 0.853839 0.426919 0.904290i \(-0.359599\pi\)
0.426919 + 0.904290i \(0.359599\pi\)
\(54\) 0 0
\(55\) 521.936 1.27960
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 120.927 + 209.451i 0.266836 + 0.462173i 0.968043 0.250785i \(-0.0806886\pi\)
−0.701207 + 0.712957i \(0.747355\pi\)
\(60\) 0 0
\(61\) −248.762 + 430.868i −0.522142 + 0.904377i 0.477526 + 0.878618i \(0.341534\pi\)
−0.999668 + 0.0257594i \(0.991800\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 512.867 888.312i 0.978667 1.69510i
\(66\) 0 0
\(67\) 289.032 + 500.618i 0.527028 + 0.912839i 0.999504 + 0.0314957i \(0.0100271\pi\)
−0.472476 + 0.881344i \(0.656640\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −660.927 −1.10475 −0.552377 0.833594i \(-0.686279\pi\)
−0.552377 + 0.833594i \(0.686279\pi\)
\(72\) 0 0
\(73\) 696.559 1.11680 0.558398 0.829573i \(-0.311416\pi\)
0.558398 + 0.829573i \(0.311416\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 280.505 + 485.848i 0.415149 + 0.719059i
\(78\) 0 0
\(79\) −365.134 + 632.430i −0.520010 + 0.900683i 0.479720 + 0.877422i \(0.340738\pi\)
−0.999729 + 0.0232613i \(0.992595\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −545.239 + 944.382i −0.721058 + 1.24891i 0.239519 + 0.970892i \(0.423010\pi\)
−0.960576 + 0.278017i \(0.910323\pi\)
\(84\) 0 0
\(85\) 416.973 + 722.218i 0.532083 + 0.921594i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −317.588 −0.378250 −0.189125 0.981953i \(-0.560565\pi\)
−0.189125 + 0.981953i \(0.560565\pi\)
\(90\) 0 0
\(91\) 1102.52 1.27006
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 265.748 + 460.288i 0.287001 + 0.497101i
\(96\) 0 0
\(97\) 742.827 1286.61i 0.777553 1.34676i −0.155795 0.987789i \(-0.549794\pi\)
0.933348 0.358972i \(-0.116873\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 501.633 868.853i 0.494201 0.855982i −0.505776 0.862665i \(-0.668794\pi\)
0.999978 + 0.00668295i \(0.00212727\pi\)
\(102\) 0 0
\(103\) 858.799 + 1487.48i 0.821553 + 1.42297i 0.904526 + 0.426419i \(0.140225\pi\)
−0.0829729 + 0.996552i \(0.526441\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −1006.27 −0.909161 −0.454581 0.890706i \(-0.650211\pi\)
−0.454581 + 0.890706i \(0.650211\pi\)
\(108\) 0 0
\(109\) 1724.94 1.51577 0.757885 0.652388i \(-0.226233\pi\)
0.757885 + 0.652388i \(0.226233\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 313.509 + 543.014i 0.260995 + 0.452057i 0.966507 0.256641i \(-0.0826159\pi\)
−0.705511 + 0.708699i \(0.749283\pi\)
\(114\) 0 0
\(115\) 858.271 1486.57i 0.695950 1.20542i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −448.188 + 776.285i −0.345255 + 0.597999i
\(120\) 0 0
\(121\) −97.8673 169.511i −0.0735291 0.127356i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −956.002 −0.684059
\(126\) 0 0
\(127\) −1990.05 −1.39046 −0.695230 0.718788i \(-0.744697\pi\)
−0.695230 + 0.718788i \(0.744697\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −78.2072 135.459i −0.0521603 0.0903442i 0.838766 0.544491i \(-0.183277\pi\)
−0.890927 + 0.454147i \(0.849944\pi\)
\(132\) 0 0
\(133\) −285.642 + 494.747i −0.186228 + 0.322556i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 1059.66 1835.38i 0.660822 1.14458i −0.319579 0.947560i \(-0.603541\pi\)
0.980400 0.197017i \(-0.0631253\pi\)
\(138\) 0 0
\(139\) 1343.39 + 2326.81i 0.819745 + 1.41984i 0.905870 + 0.423555i \(0.139218\pi\)
−0.0861255 + 0.996284i \(0.527449\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −3000.41 −1.75460
\(144\) 0 0
\(145\) 867.403 0.496785
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 775.781 + 1343.69i 0.426540 + 0.738789i 0.996563 0.0828401i \(-0.0263991\pi\)
−0.570023 + 0.821629i \(0.693066\pi\)
\(150\) 0 0
\(151\) 9.05458 15.6830i 0.00487981 0.00845208i −0.863575 0.504220i \(-0.831780\pi\)
0.868455 + 0.495768i \(0.165113\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 61.0283 105.704i 0.0316252 0.0547765i
\(156\) 0 0
\(157\) −1870.75 3240.24i −0.950971 1.64713i −0.743330 0.668925i \(-0.766755\pi\)
−0.207641 0.978205i \(-0.566579\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 1845.05 0.903168
\(162\) 0 0
\(163\) 2608.90 1.25365 0.626826 0.779160i \(-0.284354\pi\)
0.626826 + 0.779160i \(0.284354\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 781.446 + 1353.50i 0.362097 + 0.627170i 0.988306 0.152485i \(-0.0487277\pi\)
−0.626209 + 0.779655i \(0.715394\pi\)
\(168\) 0 0
\(169\) −1849.78 + 3203.92i −0.841958 + 1.45831i
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 751.385 1301.44i 0.330212 0.571945i −0.652341 0.757926i \(-0.726213\pi\)
0.982553 + 0.185981i \(0.0595463\pi\)
\(174\) 0 0
\(175\) 383.578 + 664.377i 0.165690 + 0.286984i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 4126.50 1.72307 0.861534 0.507700i \(-0.169504\pi\)
0.861534 + 0.507700i \(0.169504\pi\)
\(180\) 0 0
\(181\) 1582.33 0.649800 0.324900 0.945748i \(-0.394669\pi\)
0.324900 + 0.945748i \(0.394669\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −2133.94 3696.10i −0.848057 1.46888i
\(186\) 0 0
\(187\) 1219.70 2112.59i 0.476970 0.826137i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −1287.94 + 2230.78i −0.487916 + 0.845096i −0.999903 0.0138971i \(-0.995576\pi\)
0.511987 + 0.858993i \(0.328910\pi\)
\(192\) 0 0
\(193\) 697.649 + 1208.36i 0.260196 + 0.450673i 0.966294 0.257441i \(-0.0828794\pi\)
−0.706098 + 0.708114i \(0.749546\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 5047.62 1.82552 0.912761 0.408494i \(-0.133946\pi\)
0.912761 + 0.408494i \(0.133946\pi\)
\(198\) 0 0
\(199\) −2441.47 −0.869704 −0.434852 0.900502i \(-0.643199\pi\)
−0.434852 + 0.900502i \(0.643199\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 466.169 + 807.429i 0.161176 + 0.279165i
\(204\) 0 0
\(205\) −117.403 + 203.348i −0.0399989 + 0.0692802i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 777.348 1346.41i 0.257274 0.445612i
\(210\) 0 0
\(211\) −2133.08 3694.61i −0.695959 1.20544i −0.969856 0.243678i \(-0.921646\pi\)
0.273897 0.961759i \(-0.411687\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −6023.65 −1.91074
\(216\) 0 0
\(217\) 131.194 0.0410416
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −2397.02 4151.76i −0.729597 1.26370i
\(222\) 0 0
\(223\) −875.574 + 1516.54i −0.262927 + 0.455404i −0.967019 0.254706i \(-0.918021\pi\)
0.704091 + 0.710110i \(0.251355\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −1100.02 + 1905.29i −0.321635 + 0.557088i −0.980825 0.194888i \(-0.937566\pi\)
0.659191 + 0.751976i \(0.270899\pi\)
\(228\) 0 0
\(229\) 595.645 + 1031.69i 0.171884 + 0.297711i 0.939078 0.343703i \(-0.111681\pi\)
−0.767195 + 0.641414i \(0.778348\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 2644.52 0.743555 0.371778 0.928322i \(-0.378748\pi\)
0.371778 + 0.928322i \(0.378748\pi\)
\(234\) 0 0
\(235\) −7768.87 −2.15653
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −718.761 1244.93i −0.194530 0.336937i 0.752216 0.658917i \(-0.228985\pi\)
−0.946746 + 0.321980i \(0.895652\pi\)
\(240\) 0 0
\(241\) −1633.54 + 2829.37i −0.436620 + 0.756248i −0.997426 0.0716990i \(-0.977158\pi\)
0.560806 + 0.827947i \(0.310491\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 914.029 1583.15i 0.238348 0.412830i
\(246\) 0 0
\(247\) −1527.68 2646.03i −0.393539 0.681630i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −1871.89 −0.470727 −0.235364 0.971907i \(-0.575628\pi\)
−0.235364 + 0.971907i \(0.575628\pi\)
\(252\) 0 0
\(253\) −5021.12 −1.24773
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 2345.41 + 4062.37i 0.569271 + 0.986007i 0.996638 + 0.0819287i \(0.0261080\pi\)
−0.427367 + 0.904078i \(0.640559\pi\)
\(258\) 0 0
\(259\) 2293.70 3972.80i 0.550283 0.953118i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −2296.69 + 3977.98i −0.538479 + 0.932673i 0.460507 + 0.887656i \(0.347667\pi\)
−0.998986 + 0.0450168i \(0.985666\pi\)
\(264\) 0 0
\(265\) −2200.37 3811.15i −0.510066 0.883460i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 83.0074 0.0188143 0.00940716 0.999956i \(-0.497006\pi\)
0.00940716 + 0.999956i \(0.497006\pi\)
\(270\) 0 0
\(271\) −3464.08 −0.776487 −0.388244 0.921557i \(-0.626918\pi\)
−0.388244 + 0.921557i \(0.626918\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −1043.87 1808.04i −0.228901 0.396469i
\(276\) 0 0
\(277\) 635.350 1100.46i 0.137814 0.238701i −0.788855 0.614580i \(-0.789326\pi\)
0.926669 + 0.375879i \(0.122659\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −3825.90 + 6626.65i −0.812221 + 1.40681i 0.0990857 + 0.995079i \(0.468408\pi\)
−0.911306 + 0.411729i \(0.864925\pi\)
\(282\) 0 0
\(283\) 3.72507 + 6.45201i 0.000782446 + 0.00135524i 0.866416 0.499322i \(-0.166418\pi\)
−0.865634 + 0.500677i \(0.833084\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −252.384 −0.0519086
\(288\) 0 0
\(289\) −1015.34 −0.206663
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 1407.01 + 2437.02i 0.280541 + 0.485911i 0.971518 0.236965i \(-0.0761528\pi\)
−0.690977 + 0.722877i \(0.742819\pi\)
\(294\) 0 0
\(295\) 1615.31 2797.81i 0.318804 0.552185i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −4933.88 + 8545.73i −0.954293 + 1.65288i
\(300\) 0 0
\(301\) −3237.30 5607.16i −0.619916 1.07373i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 6645.83 1.24767
\(306\) 0 0
\(307\) −5096.55 −0.947477 −0.473739 0.880666i \(-0.657096\pi\)
−0.473739 + 0.880666i \(0.657096\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −3892.41 6741.85i −0.709705 1.22924i −0.964967 0.262373i \(-0.915495\pi\)
0.255262 0.966872i \(-0.417838\pi\)
\(312\) 0 0
\(313\) 123.235 213.448i 0.0222544 0.0385457i −0.854684 0.519149i \(-0.826249\pi\)
0.876938 + 0.480603i \(0.159582\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 29.6600 51.3727i 0.00525512 0.00910214i −0.863386 0.504544i \(-0.831661\pi\)
0.868641 + 0.495442i \(0.164994\pi\)
\(318\) 0 0
\(319\) −1268.64 2197.34i −0.222665 0.385666i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 2484.08 0.427920
\(324\) 0 0
\(325\) −4102.94 −0.700277
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −4175.23 7231.71i −0.699660 1.21185i
\(330\) 0 0
\(331\) −2204.55 + 3818.39i −0.366082 + 0.634072i −0.988949 0.148255i \(-0.952634\pi\)
0.622867 + 0.782327i \(0.285968\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 3860.84 6687.17i 0.629672 1.09062i
\(336\) 0 0
\(337\) −3016.15 5224.12i −0.487537 0.844440i 0.512360 0.858771i \(-0.328771\pi\)
−0.999897 + 0.0143313i \(0.995438\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −357.032 −0.0566991
\(342\) 0 0
\(343\) 6889.64 1.08456
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 3120.39 + 5404.68i 0.482742 + 0.836133i 0.999804 0.0198147i \(-0.00630762\pi\)
−0.517062 + 0.855948i \(0.672974\pi\)
\(348\) 0 0
\(349\) −2817.31 + 4879.72i −0.432111 + 0.748439i −0.997055 0.0766906i \(-0.975565\pi\)
0.564943 + 0.825130i \(0.308898\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 1720.66 2980.27i 0.259437 0.449359i −0.706654 0.707559i \(-0.749796\pi\)
0.966091 + 0.258201i \(0.0831296\pi\)
\(354\) 0 0
\(355\) 4414.27 + 7645.74i 0.659958 + 1.14308i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 7808.79 1.14800 0.574000 0.818855i \(-0.305391\pi\)
0.574000 + 0.818855i \(0.305391\pi\)
\(360\) 0 0
\(361\) −5275.83 −0.769183
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −4652.26 8057.94i −0.667151 1.15554i
\(366\) 0 0
\(367\) −6804.06 + 11785.0i −0.967763 + 1.67621i −0.265763 + 0.964038i \(0.585624\pi\)
−0.702001 + 0.712176i \(0.747710\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 2365.09 4096.46i 0.330969 0.573255i
\(372\) 0 0
\(373\) 1874.08 + 3246.01i 0.260151 + 0.450595i 0.966282 0.257486i \(-0.0828942\pi\)
−0.706131 + 0.708082i \(0.749561\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −4986.37 −0.681197
\(378\) 0 0
\(379\) −10210.3 −1.38382 −0.691909 0.721985i \(-0.743230\pi\)
−0.691909 + 0.721985i \(0.743230\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −3064.75 5308.30i −0.408880 0.708202i 0.585884 0.810395i \(-0.300747\pi\)
−0.994765 + 0.102193i \(0.967414\pi\)
\(384\) 0 0
\(385\) 3746.93 6489.87i 0.496003 0.859103i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 2432.99 4214.05i 0.317114 0.549257i −0.662771 0.748822i \(-0.730620\pi\)
0.979885 + 0.199565i \(0.0639530\pi\)
\(390\) 0 0
\(391\) −4011.36 6947.87i −0.518831 0.898642i
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 9754.78 1.24257
\(396\) 0 0
\(397\) −438.311 −0.0554110 −0.0277055 0.999616i \(-0.508820\pi\)
−0.0277055 + 0.999616i \(0.508820\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 5876.83 + 10179.0i 0.731857 + 1.26761i 0.956089 + 0.293078i \(0.0946796\pi\)
−0.224231 + 0.974536i \(0.571987\pi\)
\(402\) 0 0
\(403\) −350.829 + 607.653i −0.0433648 + 0.0751101i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −6242.08 + 10811.6i −0.760217 + 1.31673i
\(408\) 0 0
\(409\) −5623.24 9739.75i −0.679833 1.17750i −0.975031 0.222069i \(-0.928719\pi\)
0.295198 0.955436i \(-0.404614\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 3472.48 0.413728
\(414\) 0 0
\(415\) 14566.4 1.72298
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 6158.18 + 10666.3i 0.718012 + 1.24363i 0.961786 + 0.273801i \(0.0882810\pi\)
−0.243774 + 0.969832i \(0.578386\pi\)
\(420\) 0 0
\(421\) 2351.30 4072.57i 0.272198 0.471461i −0.697226 0.716851i \(-0.745583\pi\)
0.969424 + 0.245390i \(0.0789160\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 1667.89 2888.87i 0.190364 0.329720i
\(426\) 0 0
\(427\) 3571.68 + 6186.32i 0.404790 + 0.701118i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −2204.89 −0.246417 −0.123208 0.992381i \(-0.539318\pi\)
−0.123208 + 0.992381i \(0.539318\pi\)
\(432\) 0 0
\(433\) 9426.46 1.04620 0.523102 0.852270i \(-0.324775\pi\)
0.523102 + 0.852270i \(0.324775\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −2556.54 4428.06i −0.279854 0.484721i
\(438\) 0 0
\(439\) 3842.29 6655.05i 0.417728 0.723527i −0.577982 0.816049i \(-0.696160\pi\)
0.995711 + 0.0925227i \(0.0294931\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 6197.15 10733.8i 0.664640 1.15119i −0.314743 0.949177i \(-0.601918\pi\)
0.979383 0.202013i \(-0.0647483\pi\)
\(444\) 0 0
\(445\) 2121.14 + 3673.92i 0.225959 + 0.391372i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −14568.7 −1.53127 −0.765635 0.643275i \(-0.777575\pi\)
−0.765635 + 0.643275i \(0.777575\pi\)
\(450\) 0 0
\(451\) 686.840 0.0717118
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −7363.65 12754.2i −0.758711 1.31413i
\(456\) 0 0
\(457\) 323.024 559.493i 0.0330643 0.0572691i −0.849020 0.528361i \(-0.822807\pi\)
0.882084 + 0.471092i \(0.156140\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −9500.49 + 16455.3i −0.959831 + 1.66248i −0.236927 + 0.971528i \(0.576140\pi\)
−0.722904 + 0.690948i \(0.757193\pi\)
\(462\) 0 0
\(463\) −6832.86 11834.9i −0.685853 1.18793i −0.973168 0.230096i \(-0.926096\pi\)
0.287315 0.957836i \(-0.407237\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 3762.83 0.372855 0.186427 0.982469i \(-0.440309\pi\)
0.186427 + 0.982469i \(0.440309\pi\)
\(468\) 0 0
\(469\) 8299.74 0.817156
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 8810.00 + 15259.4i 0.856415 + 1.48335i
\(474\) 0 0
\(475\) 1062.99 1841.15i 0.102681 0.177848i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 3381.94 5857.68i 0.322598 0.558757i −0.658425 0.752646i \(-0.728777\pi\)
0.981023 + 0.193890i \(0.0621104\pi\)
\(480\) 0 0
\(481\) 12267.2 + 21247.5i 1.16286 + 2.01414i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −19845.1 −1.85798
\(486\) 0 0
\(487\) −1447.72 −0.134708 −0.0673538 0.997729i \(-0.521456\pi\)
−0.0673538 + 0.997729i \(0.521456\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 3919.14 + 6788.15i 0.360220 + 0.623920i 0.987997 0.154474i \(-0.0493682\pi\)
−0.627777 + 0.778394i \(0.716035\pi\)
\(492\) 0 0
\(493\) 2027.02 3510.90i 0.185177 0.320736i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −4744.73 + 8218.12i −0.428230 + 0.741716i
\(498\) 0 0
\(499\) 2122.67 + 3676.57i 0.190428 + 0.329832i 0.945392 0.325935i \(-0.105679\pi\)
−0.754964 + 0.655766i \(0.772346\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −17914.9 −1.58804 −0.794021 0.607891i \(-0.792016\pi\)
−0.794021 + 0.607891i \(0.792016\pi\)
\(504\) 0 0
\(505\) −13401.4 −1.18090
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 7260.14 + 12574.9i 0.632220 + 1.09504i 0.987097 + 0.160124i \(0.0511896\pi\)
−0.354877 + 0.934913i \(0.615477\pi\)
\(510\) 0 0
\(511\) 5000.54 8661.18i 0.432898 0.749801i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 11471.7 19869.5i 0.981558 1.70011i
\(516\) 0 0
\(517\) 11362.5 + 19680.4i 0.966581 + 1.67417i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 3372.49 0.283592 0.141796 0.989896i \(-0.454712\pi\)
0.141796 + 0.989896i \(0.454712\pi\)
\(522\) 0 0
\(523\) 4339.40 0.362808 0.181404 0.983409i \(-0.441936\pi\)
0.181404 + 0.983409i \(0.441936\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −285.232 494.036i −0.0235766 0.0408359i
\(528\) 0 0
\(529\) −2173.23 + 3764.15i −0.178617 + 0.309373i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 674.906 1168.97i 0.0548469 0.0949977i
\(534\) 0 0
\(535\) 6720.82 + 11640.8i 0.543115 + 0.940702i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −5347.32 −0.427320
\(540\) 0 0
\(541\) −3831.98 −0.304528 −0.152264 0.988340i \(-0.548656\pi\)
−0.152264 + 0.988340i \(0.548656\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −11520.7 19954.4i −0.905490 1.56835i
\(546\) 0 0
\(547\) −6701.34 + 11607.1i −0.523818 + 0.907280i 0.475797 + 0.879555i \(0.342160\pi\)
−0.999616 + 0.0277247i \(0.991174\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 1291.87 2237.59i 0.0998831 0.173003i
\(552\) 0 0
\(553\) 5242.52 + 9080.32i 0.403137 + 0.698254i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 14810.0 1.12661 0.563304 0.826249i \(-0.309530\pi\)
0.563304 + 0.826249i \(0.309530\pi\)
\(558\) 0 0
\(559\) 34627.7 2.62003
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 6116.61 + 10594.3i 0.457877 + 0.793066i 0.998849 0.0479751i \(-0.0152768\pi\)
−0.540972 + 0.841041i \(0.681943\pi\)
\(564\) 0 0
\(565\) 4187.80 7253.49i 0.311827 0.540100i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −4855.84 + 8410.56i −0.357763 + 0.619664i −0.987587 0.157074i \(-0.949794\pi\)
0.629823 + 0.776738i \(0.283127\pi\)
\(570\) 0 0
\(571\) −4264.81 7386.86i −0.312568 0.541384i 0.666349 0.745640i \(-0.267856\pi\)
−0.978918 + 0.204255i \(0.934523\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −6866.17 −0.497981
\(576\) 0 0
\(577\) 15314.0 1.10491 0.552453 0.833544i \(-0.313692\pi\)
0.552453 + 0.833544i \(0.313692\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 7828.44 + 13559.3i 0.558999 + 0.968215i
\(582\) 0 0
\(583\) −6436.38 + 11148.1i −0.457234 + 0.791953i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 9837.53 17039.1i 0.691717 1.19809i −0.279557 0.960129i \(-0.590188\pi\)
0.971275 0.237961i \(-0.0764790\pi\)
\(588\) 0 0
\(589\) −181.786 314.862i −0.0127171 0.0220266i
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −15635.9 −1.08278 −0.541391 0.840771i \(-0.682102\pi\)
−0.541391 + 0.840771i \(0.682102\pi\)
\(594\) 0 0
\(595\) 11973.6 0.824994
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −242.594 420.186i −0.0165478 0.0286616i 0.857633 0.514262i \(-0.171934\pi\)
−0.874181 + 0.485601i \(0.838601\pi\)
\(600\) 0 0
\(601\) 7398.12 12813.9i 0.502123 0.869702i −0.497874 0.867249i \(-0.665886\pi\)
0.999997 0.00245282i \(-0.000780759\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −1307.29 + 2264.30i −0.0878496 + 0.152160i
\(606\) 0 0
\(607\) −1773.99 3072.64i −0.118623 0.205461i 0.800599 0.599200i \(-0.204515\pi\)
−0.919222 + 0.393739i \(0.871181\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 44660.3 2.95706
\(612\) 0 0
\(613\) 20450.9 1.34748 0.673740 0.738968i \(-0.264687\pi\)
0.673740 + 0.738968i \(0.264687\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −7652.60 13254.7i −0.499323 0.864853i 0.500677 0.865634i \(-0.333085\pi\)
−1.00000 0.000781625i \(0.999751\pi\)
\(618\) 0 0
\(619\) 2075.59 3595.03i 0.134774 0.233435i −0.790737 0.612156i \(-0.790302\pi\)
0.925511 + 0.378720i \(0.123636\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −2279.93 + 3948.96i −0.146619 + 0.253951i
\(624\) 0 0
\(625\) 9724.50 + 16843.3i 0.622368 + 1.07797i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −19947.1 −1.26446
\(630\) 0 0
\(631\) 25954.4 1.63745 0.818724 0.574187i \(-0.194682\pi\)
0.818724 + 0.574187i \(0.194682\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 13291.4 + 23021.3i 0.830632 + 1.43870i
\(636\) 0 0
\(637\) −5254.41 + 9100.91i −0.326825 + 0.566077i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 8630.66 14948.7i 0.531811 0.921123i −0.467500 0.883993i \(-0.654845\pi\)
0.999310 0.0371297i \(-0.0118215\pi\)
\(642\) 0 0
\(643\) −1430.18 2477.15i −0.0877152 0.151927i 0.818830 0.574036i \(-0.194623\pi\)
−0.906545 + 0.422109i \(0.861290\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −28384.9 −1.72477 −0.862384 0.506255i \(-0.831029\pi\)
−0.862384 + 0.506255i \(0.831029\pi\)
\(648\) 0 0
\(649\) −9450.04 −0.571566
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 5518.22 + 9557.84i 0.330696 + 0.572783i 0.982649 0.185477i \(-0.0593831\pi\)
−0.651952 + 0.758260i \(0.726050\pi\)
\(654\) 0 0
\(655\) −1044.68 + 1809.43i −0.0623190 + 0.107940i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 10647.5 18441.9i 0.629387 1.09013i −0.358288 0.933611i \(-0.616639\pi\)
0.987675 0.156519i \(-0.0500273\pi\)
\(660\) 0 0
\(661\) −6162.37 10673.5i −0.362615 0.628067i 0.625776 0.780003i \(-0.284783\pi\)
−0.988390 + 0.151936i \(0.951449\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 7631.11 0.444995
\(666\) 0 0
\(667\) −8344.58 −0.484413
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −9719.98 16835.5i −0.559219 0.968595i
\(672\) 0 0
\(673\) −1525.47 + 2642.19i −0.0873738 + 0.151336i −0.906400 0.422420i \(-0.861181\pi\)
0.819027 + 0.573756i \(0.194514\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 842.733 1459.66i 0.0478418 0.0828643i −0.841113 0.540860i \(-0.818099\pi\)
0.888955 + 0.457995i \(0.151432\pi\)
\(678\) 0 0
\(679\) −10665.4 18473.0i −0.602797 1.04408i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 34715.5 1.94488 0.972440 0.233155i \(-0.0749050\pi\)
0.972440 + 0.233155i \(0.0749050\pi\)
\(684\) 0 0
\(685\) −28309.4 −1.57905
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 12649.1 + 21908.9i 0.699408 + 1.21141i
\(690\) 0 0
\(691\) 4147.68 7184.00i 0.228343 0.395502i −0.728974 0.684542i \(-0.760002\pi\)
0.957317 + 0.289039i \(0.0933358\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 17944.7 31081.1i 0.979398 1.69637i
\(696\) 0 0
\(697\) 548.714 + 950.400i 0.0298192 + 0.0516484i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −23420.5 −1.26188 −0.630942 0.775830i \(-0.717331\pi\)
−0.630942 + 0.775830i \(0.717331\pi\)
\(702\) 0 0
\(703\) −12712.8 −0.682037
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −7202.35 12474.8i −0.383129 0.663599i
\(708\) 0 0
\(709\) 2641.33 4574.92i 0.139912 0.242334i −0.787551 0.616249i \(-0.788651\pi\)
0.927463 + 0.373915i \(0.121985\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −587.104 + 1016.89i −0.0308376 + 0.0534123i
\(714\) 0 0
\(715\) 20039.5 + 34709.4i 1.04816 + 1.81547i
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −714.975 −0.0370849 −0.0185425 0.999828i \(-0.505903\pi\)
−0.0185425 + 0.999828i \(0.505903\pi\)
\(720\) 0 0
\(721\) 24660.9 1.27382
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −1734.81 3004.77i −0.0888677 0.153923i
\(726\) 0 0
\(727\) −12897.7 + 22339.5i −0.657979 + 1.13965i 0.323159 + 0.946345i \(0.395255\pi\)
−0.981138 + 0.193308i \(0.938078\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −14076.5 + 24381.3i −0.712230 + 1.23362i
\(732\) 0 0
\(733\) −1815.78 3145.02i −0.0914969 0.158477i 0.816644 0.577141i \(-0.195832\pi\)
−0.908141 + 0.418664i \(0.862498\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −22587.0 −1.12890
\(738\) 0 0
\(739\) −24758.3 −1.23241 −0.616203 0.787588i \(-0.711330\pi\)
−0.616203 + 0.787588i \(0.711330\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −4422.66 7660.28i −0.218374 0.378235i 0.735937 0.677050i \(-0.236742\pi\)
−0.954311 + 0.298815i \(0.903409\pi\)
\(744\) 0 0
\(745\) 10362.7 17948.8i 0.509612 0.882675i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −7223.96 + 12512.3i −0.352413 + 0.610398i
\(750\) 0 0
\(751\) −830.199 1437.95i −0.0403387 0.0698688i 0.845151 0.534527i \(-0.179510\pi\)
−0.885490 + 0.464659i \(0.846177\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −241.899 −0.0116604
\(756\) 0 0
\(757\) 19937.2 0.957239 0.478619 0.878022i \(-0.341137\pi\)
0.478619 + 0.878022i \(0.341137\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −4221.87 7312.50i −0.201107 0.348328i 0.747778 0.663949i \(-0.231121\pi\)
−0.948886 + 0.315620i \(0.897787\pi\)
\(762\) 0 0
\(763\) 12383.2 21448.3i 0.587550 1.01767i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −9285.84 + 16083.5i −0.437148 + 0.757162i
\(768\) 0 0
\(769\) −8553.93 14815.8i −0.401122 0.694763i 0.592740 0.805394i \(-0.298046\pi\)
−0.993862 + 0.110631i \(0.964713\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −9821.05 −0.456971 −0.228486 0.973547i \(-0.573377\pi\)
−0.228486 + 0.973547i \(0.573377\pi\)
\(774\) 0 0
\(775\) −488.226 −0.0226292
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 349.710 + 605.715i 0.0160843 + 0.0278588i
\(780\) 0 0
\(781\) 12912.3 22364.8i 0.591600 1.02468i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −24989.2 + 43282.6i −1.13618 + 1.96792i
\(786\) 0 0
\(787\) 2622.78 + 4542.80i 0.118796 + 0.205760i 0.919291 0.393579i \(-0.128763\pi\)
−0.800495 + 0.599339i \(0.795430\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 9002.62 0.404673
\(792\) 0 0
\(793\) −38204.4 −1.71082
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 4609.26 + 7983.47i 0.204854 + 0.354817i 0.950086 0.311988i \(-0.100995\pi\)
−0.745232 + 0.666805i \(0.767661\pi\)
\(798\) 0 0
\(799\) −18154.9 + 31445.2i −0.803848 + 1.39231i
\(800\) 0 0
\(801\) 0 0
\(802\) 0