Properties

Label 120.3.l.a.41.5
Level $120$
Weight $3$
Character 120.41
Analytic conductor $3.270$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 120 = 2^{3} \cdot 3 \cdot 5 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 120.l (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.26976317232\)
Analytic rank: \(0\)
Dimension: \(8\)
Coefficient field: 8.0.681615360000.5
Defining polynomial: \( x^{8} - 4x^{7} - 2x^{6} + 20x^{5} + 49x^{4} - 136x^{3} + 168x^{2} - 96x + 864 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{5}\cdot 3 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 41.5
Root \(-2.22255 - 1.41421i\) of defining polynomial
Character \(\chi\) \(=\) 120.41
Dual form 120.3.l.a.41.6

$q$-expansion

\(f(q)\) \(=\) \(q+(0.291610 - 2.98579i) q^{3} -2.23607i q^{5} +4.46268 q^{7} +(-8.82993 - 1.74137i) q^{9} +O(q^{10})\) \(q+(0.291610 - 2.98579i) q^{3} -2.23607i q^{5} +4.46268 q^{7} +(-8.82993 - 1.74137i) q^{9} -17.8696i q^{11} -11.0107 q^{13} +(-6.67644 - 0.652060i) q^{15} +0.794055i q^{17} +26.5852 q^{19} +(1.30136 - 13.3246i) q^{21} +14.9276i q^{23} -5.00000 q^{25} +(-7.77428 + 25.8565i) q^{27} +5.58545i q^{29} +53.1074 q^{31} +(-53.3549 - 5.21095i) q^{33} -9.97885i q^{35} +51.7565 q^{37} +(-3.21084 + 32.8758i) q^{39} +67.8236i q^{41} -40.8243 q^{43} +(-3.89383 + 19.7443i) q^{45} +12.3483i q^{47} -29.0845 q^{49} +(2.37088 + 0.231554i) q^{51} +37.0351i q^{53} -39.9576 q^{55} +(7.75251 - 79.3779i) q^{57} -61.0932i q^{59} +97.8289 q^{61} +(-39.4051 - 7.77119i) q^{63} +24.6208i q^{65} +3.02541 q^{67} +(44.5708 + 4.35305i) q^{69} -57.0787i q^{71} -31.4690 q^{73} +(-1.45805 + 14.9290i) q^{75} -79.7461i q^{77} -2.16053 q^{79} +(74.9352 + 30.7524i) q^{81} -13.0710i q^{83} +1.77556 q^{85} +(16.6770 + 1.62877i) q^{87} -173.692i q^{89} -49.1374 q^{91} +(15.4866 - 158.568i) q^{93} -59.4463i q^{95} -91.6381 q^{97} +(-31.1176 + 157.787i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q - 4 q^{3} + 16 q^{7} + 20 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q - 4 q^{3} + 16 q^{7} + 20 q^{9} - 8 q^{13} - 8 q^{19} + 28 q^{21} - 40 q^{25} + 20 q^{27} + 120 q^{31} - 112 q^{33} + 8 q^{37} - 72 q^{39} - 328 q^{43} - 60 q^{45} + 64 q^{49} + 64 q^{51} - 40 q^{55} + 72 q^{57} + 8 q^{61} + 88 q^{63} + 152 q^{67} + 100 q^{69} + 32 q^{73} + 20 q^{75} + 88 q^{79} + 224 q^{81} - 152 q^{87} + 560 q^{91} - 368 q^{93} + 144 q^{97} + 32 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/120\mathbb{Z}\right)^\times\).

\(n\) \(31\) \(41\) \(61\) \(97\)
\(\chi(n)\) \(1\) \(-1\) \(1\) \(1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 0.291610 2.98579i 0.0972033 0.995265i
\(4\) 0 0
\(5\) 2.23607i 0.447214i
\(6\) 0 0
\(7\) 4.46268 0.637525 0.318763 0.947835i \(-0.396733\pi\)
0.318763 + 0.947835i \(0.396733\pi\)
\(8\) 0 0
\(9\) −8.82993 1.74137i −0.981103 0.193486i
\(10\) 0 0
\(11\) 17.8696i 1.62451i −0.583305 0.812253i \(-0.698241\pi\)
0.583305 0.812253i \(-0.301759\pi\)
\(12\) 0 0
\(13\) −11.0107 −0.846980 −0.423490 0.905901i \(-0.639195\pi\)
−0.423490 + 0.905901i \(0.639195\pi\)
\(14\) 0 0
\(15\) −6.67644 0.652060i −0.445096 0.0434707i
\(16\) 0 0
\(17\) 0.794055i 0.0467091i 0.999727 + 0.0233546i \(0.00743466\pi\)
−0.999727 + 0.0233546i \(0.992565\pi\)
\(18\) 0 0
\(19\) 26.5852 1.39922 0.699611 0.714524i \(-0.253357\pi\)
0.699611 + 0.714524i \(0.253357\pi\)
\(20\) 0 0
\(21\) 1.30136 13.3246i 0.0619696 0.634506i
\(22\) 0 0
\(23\) 14.9276i 0.649027i 0.945881 + 0.324514i \(0.105201\pi\)
−0.945881 + 0.324514i \(0.894799\pi\)
\(24\) 0 0
\(25\) −5.00000 −0.200000
\(26\) 0 0
\(27\) −7.77428 + 25.8565i −0.287936 + 0.957650i
\(28\) 0 0
\(29\) 5.58545i 0.192602i 0.995352 + 0.0963008i \(0.0307011\pi\)
−0.995352 + 0.0963008i \(0.969299\pi\)
\(30\) 0 0
\(31\) 53.1074 1.71314 0.856571 0.516030i \(-0.172591\pi\)
0.856571 + 0.516030i \(0.172591\pi\)
\(32\) 0 0
\(33\) −53.3549 5.21095i −1.61681 0.157907i
\(34\) 0 0
\(35\) 9.97885i 0.285110i
\(36\) 0 0
\(37\) 51.7565 1.39882 0.699412 0.714719i \(-0.253445\pi\)
0.699412 + 0.714719i \(0.253445\pi\)
\(38\) 0 0
\(39\) −3.21084 + 32.8758i −0.0823293 + 0.842969i
\(40\) 0 0
\(41\) 67.8236i 1.65423i 0.562030 + 0.827117i \(0.310020\pi\)
−0.562030 + 0.827117i \(0.689980\pi\)
\(42\) 0 0
\(43\) −40.8243 −0.949403 −0.474701 0.880147i \(-0.657444\pi\)
−0.474701 + 0.880147i \(0.657444\pi\)
\(44\) 0 0
\(45\) −3.89383 + 19.7443i −0.0865296 + 0.438763i
\(46\) 0 0
\(47\) 12.3483i 0.262729i 0.991334 + 0.131365i \(0.0419359\pi\)
−0.991334 + 0.131365i \(0.958064\pi\)
\(48\) 0 0
\(49\) −29.0845 −0.593562
\(50\) 0 0
\(51\) 2.37088 + 0.231554i 0.0464879 + 0.00454028i
\(52\) 0 0
\(53\) 37.0351i 0.698775i 0.936978 + 0.349387i \(0.113610\pi\)
−0.936978 + 0.349387i \(0.886390\pi\)
\(54\) 0 0
\(55\) −39.9576 −0.726502
\(56\) 0 0
\(57\) 7.75251 79.3779i 0.136009 1.39260i
\(58\) 0 0
\(59\) 61.0932i 1.03548i −0.855539 0.517739i \(-0.826774\pi\)
0.855539 0.517739i \(-0.173226\pi\)
\(60\) 0 0
\(61\) 97.8289 1.60375 0.801876 0.597490i \(-0.203835\pi\)
0.801876 + 0.597490i \(0.203835\pi\)
\(62\) 0 0
\(63\) −39.4051 7.77119i −0.625478 0.123352i
\(64\) 0 0
\(65\) 24.6208i 0.378781i
\(66\) 0 0
\(67\) 3.02541 0.0451553 0.0225777 0.999745i \(-0.492813\pi\)
0.0225777 + 0.999745i \(0.492813\pi\)
\(68\) 0 0
\(69\) 44.5708 + 4.35305i 0.645954 + 0.0630876i
\(70\) 0 0
\(71\) 57.0787i 0.803926i −0.915656 0.401963i \(-0.868328\pi\)
0.915656 0.401963i \(-0.131672\pi\)
\(72\) 0 0
\(73\) −31.4690 −0.431082 −0.215541 0.976495i \(-0.569152\pi\)
−0.215541 + 0.976495i \(0.569152\pi\)
\(74\) 0 0
\(75\) −1.45805 + 14.9290i −0.0194407 + 0.199053i
\(76\) 0 0
\(77\) 79.7461i 1.03566i
\(78\) 0 0
\(79\) −2.16053 −0.0273485 −0.0136743 0.999907i \(-0.504353\pi\)
−0.0136743 + 0.999907i \(0.504353\pi\)
\(80\) 0 0
\(81\) 74.9352 + 30.7524i 0.925126 + 0.379660i
\(82\) 0 0
\(83\) 13.0710i 0.157482i −0.996895 0.0787411i \(-0.974910\pi\)
0.996895 0.0787411i \(-0.0250900\pi\)
\(84\) 0 0
\(85\) 1.77556 0.0208890
\(86\) 0 0
\(87\) 16.6770 + 1.62877i 0.191690 + 0.0187215i
\(88\) 0 0
\(89\) 173.692i 1.95160i −0.218667 0.975800i \(-0.570171\pi\)
0.218667 0.975800i \(-0.429829\pi\)
\(90\) 0 0
\(91\) −49.1374 −0.539971
\(92\) 0 0
\(93\) 15.4866 158.568i 0.166523 1.70503i
\(94\) 0 0
\(95\) 59.4463i 0.625751i
\(96\) 0 0
\(97\) −91.6381 −0.944722 −0.472361 0.881405i \(-0.656598\pi\)
−0.472361 + 0.881405i \(0.656598\pi\)
\(98\) 0 0
\(99\) −31.1176 + 157.787i −0.314319 + 1.59381i
\(100\) 0 0
\(101\) 116.353i 1.15201i 0.817446 + 0.576005i \(0.195389\pi\)
−0.817446 + 0.576005i \(0.804611\pi\)
\(102\) 0 0
\(103\) −182.071 −1.76768 −0.883842 0.467786i \(-0.845052\pi\)
−0.883842 + 0.467786i \(0.845052\pi\)
\(104\) 0 0
\(105\) −29.7948 2.90993i −0.283760 0.0277136i
\(106\) 0 0
\(107\) 102.828i 0.961013i 0.876991 + 0.480506i \(0.159547\pi\)
−0.876991 + 0.480506i \(0.840453\pi\)
\(108\) 0 0
\(109\) 75.4257 0.691979 0.345990 0.938238i \(-0.387543\pi\)
0.345990 + 0.938238i \(0.387543\pi\)
\(110\) 0 0
\(111\) 15.0927 154.534i 0.135970 1.39220i
\(112\) 0 0
\(113\) 141.923i 1.25596i 0.778230 + 0.627980i \(0.216118\pi\)
−0.778230 + 0.627980i \(0.783882\pi\)
\(114\) 0 0
\(115\) 33.3792 0.290254
\(116\) 0 0
\(117\) 97.2241 + 19.1738i 0.830975 + 0.163879i
\(118\) 0 0
\(119\) 3.54361i 0.0297782i
\(120\) 0 0
\(121\) −198.322 −1.63902
\(122\) 0 0
\(123\) 202.507 + 19.7780i 1.64640 + 0.160797i
\(124\) 0 0
\(125\) 11.1803i 0.0894427i
\(126\) 0 0
\(127\) 112.920 0.889132 0.444566 0.895746i \(-0.353358\pi\)
0.444566 + 0.895746i \(0.353358\pi\)
\(128\) 0 0
\(129\) −11.9048 + 121.893i −0.0922851 + 0.944907i
\(130\) 0 0
\(131\) 107.233i 0.818570i −0.912407 0.409285i \(-0.865778\pi\)
0.912407 0.409285i \(-0.134222\pi\)
\(132\) 0 0
\(133\) 118.641 0.892039
\(134\) 0 0
\(135\) 57.8170 + 17.3838i 0.428274 + 0.128769i
\(136\) 0 0
\(137\) 67.7434i 0.494477i 0.968955 + 0.247239i \(0.0795232\pi\)
−0.968955 + 0.247239i \(0.920477\pi\)
\(138\) 0 0
\(139\) −141.204 −1.01586 −0.507928 0.861399i \(-0.669589\pi\)
−0.507928 + 0.861399i \(0.669589\pi\)
\(140\) 0 0
\(141\) 36.8694 + 3.60088i 0.261485 + 0.0255382i
\(142\) 0 0
\(143\) 196.757i 1.37593i
\(144\) 0 0
\(145\) 12.4894 0.0861341
\(146\) 0 0
\(147\) −8.48134 + 86.8404i −0.0576962 + 0.590751i
\(148\) 0 0
\(149\) 55.0831i 0.369685i 0.982768 + 0.184843i \(0.0591775\pi\)
−0.982768 + 0.184843i \(0.940822\pi\)
\(150\) 0 0
\(151\) 56.1302 0.371723 0.185862 0.982576i \(-0.440492\pi\)
0.185862 + 0.982576i \(0.440492\pi\)
\(152\) 0 0
\(153\) 1.38275 7.01145i 0.00903756 0.0458265i
\(154\) 0 0
\(155\) 118.752i 0.766140i
\(156\) 0 0
\(157\) −274.266 −1.74692 −0.873460 0.486896i \(-0.838129\pi\)
−0.873460 + 0.486896i \(0.838129\pi\)
\(158\) 0 0
\(159\) 110.579 + 10.7998i 0.695466 + 0.0679232i
\(160\) 0 0
\(161\) 66.6172i 0.413771i
\(162\) 0 0
\(163\) 260.316 1.59703 0.798516 0.601974i \(-0.205619\pi\)
0.798516 + 0.601974i \(0.205619\pi\)
\(164\) 0 0
\(165\) −11.6520 + 119.305i −0.0706184 + 0.723061i
\(166\) 0 0
\(167\) 179.949i 1.07754i 0.842453 + 0.538769i \(0.181111\pi\)
−0.842453 + 0.538769i \(0.818889\pi\)
\(168\) 0 0
\(169\) −47.7635 −0.282624
\(170\) 0 0
\(171\) −234.745 46.2948i −1.37278 0.270730i
\(172\) 0 0
\(173\) 111.265i 0.643148i −0.946884 0.321574i \(-0.895788\pi\)
0.946884 0.321574i \(-0.104212\pi\)
\(174\) 0 0
\(175\) −22.3134 −0.127505
\(176\) 0 0
\(177\) −182.412 17.8154i −1.03057 0.100652i
\(178\) 0 0
\(179\) 77.8475i 0.434902i −0.976071 0.217451i \(-0.930226\pi\)
0.976071 0.217451i \(-0.0697743\pi\)
\(180\) 0 0
\(181\) −238.852 −1.31963 −0.659813 0.751430i \(-0.729364\pi\)
−0.659813 + 0.751430i \(0.729364\pi\)
\(182\) 0 0
\(183\) 28.5279 292.097i 0.155890 1.59616i
\(184\) 0 0
\(185\) 115.731i 0.625573i
\(186\) 0 0
\(187\) 14.1894 0.0758793
\(188\) 0 0
\(189\) −34.6941 + 115.389i −0.183567 + 0.610526i
\(190\) 0 0
\(191\) 177.248i 0.928002i 0.885835 + 0.464001i \(0.153587\pi\)
−0.885835 + 0.464001i \(0.846413\pi\)
\(192\) 0 0
\(193\) 284.254 1.47282 0.736409 0.676536i \(-0.236520\pi\)
0.736409 + 0.676536i \(0.236520\pi\)
\(194\) 0 0
\(195\) 73.5125 + 7.17966i 0.376987 + 0.0368188i
\(196\) 0 0
\(197\) 244.341i 1.24031i −0.784479 0.620156i \(-0.787069\pi\)
0.784479 0.620156i \(-0.212931\pi\)
\(198\) 0 0
\(199\) 74.0122 0.371921 0.185960 0.982557i \(-0.440460\pi\)
0.185960 + 0.982557i \(0.440460\pi\)
\(200\) 0 0
\(201\) 0.882239 9.03324i 0.00438925 0.0449415i
\(202\) 0 0
\(203\) 24.9260i 0.122788i
\(204\) 0 0
\(205\) 151.658 0.739796
\(206\) 0 0
\(207\) 25.9946 131.810i 0.125578 0.636763i
\(208\) 0 0
\(209\) 475.066i 2.27304i
\(210\) 0 0
\(211\) −31.0682 −0.147243 −0.0736214 0.997286i \(-0.523456\pi\)
−0.0736214 + 0.997286i \(0.523456\pi\)
\(212\) 0 0
\(213\) −170.425 16.6447i −0.800119 0.0781443i
\(214\) 0 0
\(215\) 91.2859i 0.424586i
\(216\) 0 0
\(217\) 237.001 1.09217
\(218\) 0 0
\(219\) −9.17668 + 93.9600i −0.0419026 + 0.429041i
\(220\) 0 0
\(221\) 8.74314i 0.0395617i
\(222\) 0 0
\(223\) 100.432 0.450366 0.225183 0.974316i \(-0.427702\pi\)
0.225183 + 0.974316i \(0.427702\pi\)
\(224\) 0 0
\(225\) 44.1496 + 8.70687i 0.196221 + 0.0386972i
\(226\) 0 0
\(227\) 349.117i 1.53796i −0.639273 0.768980i \(-0.720764\pi\)
0.639273 0.768980i \(-0.279236\pi\)
\(228\) 0 0
\(229\) −165.007 −0.720555 −0.360278 0.932845i \(-0.617318\pi\)
−0.360278 + 0.932845i \(0.617318\pi\)
\(230\) 0 0
\(231\) −238.105 23.2548i −1.03076 0.100670i
\(232\) 0 0
\(233\) 124.800i 0.535620i 0.963472 + 0.267810i \(0.0863000\pi\)
−0.963472 + 0.267810i \(0.913700\pi\)
\(234\) 0 0
\(235\) 27.6116 0.117496
\(236\) 0 0
\(237\) −0.630033 + 6.45091i −0.00265837 + 0.0272190i
\(238\) 0 0
\(239\) 61.8321i 0.258712i −0.991598 0.129356i \(-0.958709\pi\)
0.991598 0.129356i \(-0.0412910\pi\)
\(240\) 0 0
\(241\) 2.25555 0.00935913 0.00467956 0.999989i \(-0.498510\pi\)
0.00467956 + 0.999989i \(0.498510\pi\)
\(242\) 0 0
\(243\) 113.672 214.773i 0.467787 0.883841i
\(244\) 0 0
\(245\) 65.0350i 0.265449i
\(246\) 0 0
\(247\) −292.723 −1.18511
\(248\) 0 0
\(249\) −39.0274 3.81164i −0.156736 0.0153078i
\(250\) 0 0
\(251\) 108.993i 0.434234i 0.976146 + 0.217117i \(0.0696654\pi\)
−0.976146 + 0.217117i \(0.930335\pi\)
\(252\) 0 0
\(253\) 266.750 1.05435
\(254\) 0 0
\(255\) 0.517771 5.30146i 0.00203048 0.0207900i
\(256\) 0 0
\(257\) 31.4664i 0.122437i 0.998124 + 0.0612187i \(0.0194987\pi\)
−0.998124 + 0.0612187i \(0.980501\pi\)
\(258\) 0 0
\(259\) 230.972 0.891785
\(260\) 0 0
\(261\) 9.72636 49.3191i 0.0372657 0.188962i
\(262\) 0 0
\(263\) 235.190i 0.894260i 0.894469 + 0.447130i \(0.147554\pi\)
−0.894469 + 0.447130i \(0.852446\pi\)
\(264\) 0 0
\(265\) 82.8129 0.312502
\(266\) 0 0
\(267\) −518.609 50.6504i −1.94236 0.189702i
\(268\) 0 0
\(269\) 221.066i 0.821808i 0.911679 + 0.410904i \(0.134787\pi\)
−0.911679 + 0.410904i \(0.865213\pi\)
\(270\) 0 0
\(271\) 268.830 0.991991 0.495995 0.868325i \(-0.334803\pi\)
0.495995 + 0.868325i \(0.334803\pi\)
\(272\) 0 0
\(273\) −14.3290 + 146.714i −0.0524870 + 0.537414i
\(274\) 0 0
\(275\) 89.3479i 0.324901i
\(276\) 0 0
\(277\) 144.697 0.522370 0.261185 0.965289i \(-0.415887\pi\)
0.261185 + 0.965289i \(0.415887\pi\)
\(278\) 0 0
\(279\) −468.934 92.4798i −1.68077 0.331469i
\(280\) 0 0
\(281\) 189.426i 0.674112i 0.941485 + 0.337056i \(0.109431\pi\)
−0.941485 + 0.337056i \(0.890569\pi\)
\(282\) 0 0
\(283\) −420.621 −1.48629 −0.743146 0.669129i \(-0.766667\pi\)
−0.743146 + 0.669129i \(0.766667\pi\)
\(284\) 0 0
\(285\) −177.494 17.3351i −0.622788 0.0608251i
\(286\) 0 0
\(287\) 302.675i 1.05462i
\(288\) 0 0
\(289\) 288.369 0.997818
\(290\) 0 0
\(291\) −26.7226 + 273.612i −0.0918302 + 0.940249i
\(292\) 0 0
\(293\) 283.828i 0.968696i −0.874875 0.484348i \(-0.839057\pi\)
0.874875 0.484348i \(-0.160943\pi\)
\(294\) 0 0
\(295\) −136.609 −0.463080
\(296\) 0 0
\(297\) 462.045 + 138.923i 1.55571 + 0.467754i
\(298\) 0 0
\(299\) 164.364i 0.549713i
\(300\) 0 0
\(301\) −182.186 −0.605268
\(302\) 0 0
\(303\) 347.406 + 33.9297i 1.14656 + 0.111979i
\(304\) 0 0
\(305\) 218.752i 0.717220i
\(306\) 0 0
\(307\) 167.979 0.547162 0.273581 0.961849i \(-0.411792\pi\)
0.273581 + 0.961849i \(0.411792\pi\)
\(308\) 0 0
\(309\) −53.0938 + 543.628i −0.171825 + 1.75931i
\(310\) 0 0
\(311\) 192.970i 0.620482i 0.950658 + 0.310241i \(0.100410\pi\)
−0.950658 + 0.310241i \(0.899590\pi\)
\(312\) 0 0
\(313\) 161.056 0.514555 0.257278 0.966338i \(-0.417175\pi\)
0.257278 + 0.966338i \(0.417175\pi\)
\(314\) 0 0
\(315\) −17.3769 + 88.1125i −0.0551648 + 0.279722i
\(316\) 0 0
\(317\) 514.761i 1.62385i 0.583761 + 0.811926i \(0.301581\pi\)
−0.583761 + 0.811926i \(0.698419\pi\)
\(318\) 0 0
\(319\) 99.8096 0.312883
\(320\) 0 0
\(321\) 307.024 + 29.9858i 0.956462 + 0.0934136i
\(322\) 0 0
\(323\) 21.1101i 0.0653564i
\(324\) 0 0
\(325\) 55.0537 0.169396
\(326\) 0 0
\(327\) 21.9949 225.206i 0.0672627 0.688702i
\(328\) 0 0
\(329\) 55.1064i 0.167497i
\(330\) 0 0
\(331\) 63.7466 0.192588 0.0962939 0.995353i \(-0.469301\pi\)
0.0962939 + 0.995353i \(0.469301\pi\)
\(332\) 0 0
\(333\) −457.006 90.1274i −1.37239 0.270653i
\(334\) 0 0
\(335\) 6.76502i 0.0201941i
\(336\) 0 0
\(337\) −64.2444 −0.190636 −0.0953181 0.995447i \(-0.530387\pi\)
−0.0953181 + 0.995447i \(0.530387\pi\)
\(338\) 0 0
\(339\) 423.754 + 41.3863i 1.25001 + 0.122083i
\(340\) 0 0
\(341\) 949.006i 2.78301i
\(342\) 0 0
\(343\) −348.466 −1.01594
\(344\) 0 0
\(345\) 9.73371 99.6634i 0.0282136 0.288879i
\(346\) 0 0
\(347\) 66.1416i 0.190610i 0.995448 + 0.0953049i \(0.0303826\pi\)
−0.995448 + 0.0953049i \(0.969617\pi\)
\(348\) 0 0
\(349\) −188.752 −0.540837 −0.270419 0.962743i \(-0.587162\pi\)
−0.270419 + 0.962743i \(0.587162\pi\)
\(350\) 0 0
\(351\) 85.6006 284.700i 0.243876 0.811110i
\(352\) 0 0
\(353\) 435.927i 1.23492i 0.786602 + 0.617461i \(0.211839\pi\)
−0.786602 + 0.617461i \(0.788161\pi\)
\(354\) 0 0
\(355\) −127.632 −0.359527
\(356\) 0 0
\(357\) 10.5805 + 1.03335i 0.0296372 + 0.00289454i
\(358\) 0 0
\(359\) 188.255i 0.524386i 0.965015 + 0.262193i \(0.0844457\pi\)
−0.965015 + 0.262193i \(0.915554\pi\)
\(360\) 0 0
\(361\) 345.773 0.957820
\(362\) 0 0
\(363\) −57.8326 + 592.148i −0.159318 + 1.63126i
\(364\) 0 0
\(365\) 70.3668i 0.192786i
\(366\) 0 0
\(367\) 276.868 0.754409 0.377205 0.926130i \(-0.376885\pi\)
0.377205 + 0.926130i \(0.376885\pi\)
\(368\) 0 0
\(369\) 118.106 598.877i 0.320071 1.62297i
\(370\) 0 0
\(371\) 165.275i 0.445486i
\(372\) 0 0
\(373\) −510.098 −1.36756 −0.683778 0.729691i \(-0.739664\pi\)
−0.683778 + 0.729691i \(0.739664\pi\)
\(374\) 0 0
\(375\) 33.3822 + 3.26030i 0.0890192 + 0.00869413i
\(376\) 0 0
\(377\) 61.4999i 0.163130i
\(378\) 0 0
\(379\) −298.461 −0.787497 −0.393748 0.919218i \(-0.628822\pi\)
−0.393748 + 0.919218i \(0.628822\pi\)
\(380\) 0 0
\(381\) 32.9285 337.155i 0.0864266 0.884922i
\(382\) 0 0
\(383\) 500.548i 1.30691i −0.756963 0.653457i \(-0.773318\pi\)
0.756963 0.653457i \(-0.226682\pi\)
\(384\) 0 0
\(385\) −178.318 −0.463163
\(386\) 0 0
\(387\) 360.476 + 71.0904i 0.931462 + 0.183696i
\(388\) 0 0
\(389\) 465.726i 1.19724i 0.801033 + 0.598620i \(0.204284\pi\)
−0.801033 + 0.598620i \(0.795716\pi\)
\(390\) 0 0
\(391\) −11.8534 −0.0303155
\(392\) 0 0
\(393\) −320.175 31.2701i −0.814694 0.0795678i
\(394\) 0 0
\(395\) 4.83110i 0.0122306i
\(396\) 0 0
\(397\) −344.998 −0.869013 −0.434507 0.900669i \(-0.643077\pi\)
−0.434507 + 0.900669i \(0.643077\pi\)
\(398\) 0 0
\(399\) 34.5969 354.238i 0.0867091 0.887815i
\(400\) 0 0
\(401\) 428.755i 1.06922i −0.845100 0.534608i \(-0.820459\pi\)
0.845100 0.534608i \(-0.179541\pi\)
\(402\) 0 0
\(403\) −584.752 −1.45100
\(404\) 0 0
\(405\) 68.7645 167.560i 0.169789 0.413729i
\(406\) 0 0
\(407\) 924.866i 2.27240i
\(408\) 0 0
\(409\) −349.445 −0.854389 −0.427194 0.904160i \(-0.640498\pi\)
−0.427194 + 0.904160i \(0.640498\pi\)
\(410\) 0 0
\(411\) 202.268 + 19.7547i 0.492136 + 0.0480648i
\(412\) 0 0
\(413\) 272.639i 0.660143i
\(414\) 0 0
\(415\) −29.2277 −0.0704281
\(416\) 0 0
\(417\) −41.1765 + 421.606i −0.0987447 + 1.01105i
\(418\) 0 0
\(419\) 225.745i 0.538770i −0.963033 0.269385i \(-0.913180\pi\)
0.963033 0.269385i \(-0.0868205\pi\)
\(420\) 0 0
\(421\) −138.931 −0.330003 −0.165002 0.986293i \(-0.552763\pi\)
−0.165002 + 0.986293i \(0.552763\pi\)
\(422\) 0 0
\(423\) 21.5030 109.034i 0.0508345 0.257765i
\(424\) 0 0
\(425\) 3.97027i 0.00934182i
\(426\) 0 0
\(427\) 436.579 1.02243
\(428\) 0 0
\(429\) 587.477 + 57.3764i 1.36941 + 0.133745i
\(430\) 0 0
\(431\) 289.802i 0.672394i 0.941792 + 0.336197i \(0.109141\pi\)
−0.941792 + 0.336197i \(0.890859\pi\)
\(432\) 0 0
\(433\) 53.8425 0.124348 0.0621738 0.998065i \(-0.480197\pi\)
0.0621738 + 0.998065i \(0.480197\pi\)
\(434\) 0 0
\(435\) 3.64205 37.2909i 0.00837252 0.0857262i
\(436\) 0 0
\(437\) 396.854i 0.908133i
\(438\) 0 0
\(439\) 333.179 0.758949 0.379474 0.925202i \(-0.376105\pi\)
0.379474 + 0.925202i \(0.376105\pi\)
\(440\) 0 0
\(441\) 256.814 + 50.6471i 0.582345 + 0.114846i
\(442\) 0 0
\(443\) 652.015i 1.47182i −0.677081 0.735909i \(-0.736755\pi\)
0.677081 0.735909i \(-0.263245\pi\)
\(444\) 0 0
\(445\) −388.388 −0.872782
\(446\) 0 0
\(447\) 164.467 + 16.0628i 0.367935 + 0.0359346i
\(448\) 0 0
\(449\) 115.054i 0.256245i −0.991758 0.128122i \(-0.959105\pi\)
0.991758 0.128122i \(-0.0408950\pi\)
\(450\) 0 0
\(451\) 1211.98 2.68731
\(452\) 0 0
\(453\) 16.3681 167.593i 0.0361327 0.369963i
\(454\) 0 0
\(455\) 109.875i 0.241482i
\(456\) 0 0
\(457\) −138.318 −0.302666 −0.151333 0.988483i \(-0.548357\pi\)
−0.151333 + 0.988483i \(0.548357\pi\)
\(458\) 0 0
\(459\) −20.5315 6.17321i −0.0447310 0.0134493i
\(460\) 0 0
\(461\) 300.475i 0.651789i 0.945406 + 0.325894i \(0.105665\pi\)
−0.945406 + 0.325894i \(0.894335\pi\)
\(462\) 0 0
\(463\) −91.5721 −0.197780 −0.0988899 0.995098i \(-0.531529\pi\)
−0.0988899 + 0.995098i \(0.531529\pi\)
\(464\) 0 0
\(465\) −354.568 34.6292i −0.762512 0.0744714i
\(466\) 0 0
\(467\) 308.136i 0.659821i −0.944012 0.329910i \(-0.892981\pi\)
0.944012 0.329910i \(-0.107019\pi\)
\(468\) 0 0
\(469\) 13.5014 0.0287877
\(470\) 0 0
\(471\) −79.9788 + 818.903i −0.169806 + 1.73865i
\(472\) 0 0
\(473\) 729.513i 1.54231i
\(474\) 0 0
\(475\) −132.926 −0.279844
\(476\) 0 0
\(477\) 64.4919 327.017i 0.135203 0.685570i
\(478\) 0 0
\(479\) 218.332i 0.455808i 0.973684 + 0.227904i \(0.0731873\pi\)
−0.973684 + 0.227904i \(0.926813\pi\)
\(480\) 0 0
\(481\) −569.877 −1.18478
\(482\) 0 0
\(483\) 198.905 + 19.4262i 0.411812 + 0.0402200i
\(484\) 0 0
\(485\) 204.909i 0.422493i
\(486\) 0 0
\(487\) −538.368 −1.10548 −0.552739 0.833354i \(-0.686417\pi\)
−0.552739 + 0.833354i \(0.686417\pi\)
\(488\) 0 0
\(489\) 75.9108 777.250i 0.155237 1.58947i
\(490\) 0 0
\(491\) 418.223i 0.851777i −0.904776 0.425889i \(-0.859962\pi\)
0.904776 0.425889i \(-0.140038\pi\)
\(492\) 0 0
\(493\) −4.43515 −0.00899625
\(494\) 0 0
\(495\) 352.823 + 69.5811i 0.712773 + 0.140568i
\(496\) 0 0
\(497\) 254.724i 0.512523i
\(498\) 0 0
\(499\) −732.199 −1.46733 −0.733667 0.679510i \(-0.762193\pi\)
−0.733667 + 0.679510i \(0.762193\pi\)
\(500\) 0 0
\(501\) 537.291 + 52.4749i 1.07244 + 0.104740i
\(502\) 0 0
\(503\) 338.339i 0.672641i 0.941748 + 0.336321i \(0.109183\pi\)
−0.941748 + 0.336321i \(0.890817\pi\)
\(504\) 0 0
\(505\) 260.173 0.515195
\(506\) 0 0
\(507\) −13.9283 + 142.612i −0.0274720 + 0.281286i
\(508\) 0 0
\(509\) 864.760i 1.69894i 0.527637 + 0.849470i \(0.323078\pi\)
−0.527637 + 0.849470i \(0.676922\pi\)
\(510\) 0 0
\(511\) −140.436 −0.274826
\(512\) 0 0
\(513\) −206.681 + 687.401i −0.402887 + 1.33996i
\(514\) 0 0
\(515\) 407.124i 0.790532i
\(516\) 0 0
\(517\) 220.659 0.426806
\(518\) 0 0
\(519\) −332.213 32.4459i −0.640103 0.0625162i
\(520\) 0 0
\(521\) 294.647i 0.565541i 0.959188 + 0.282770i \(0.0912534\pi\)
−0.959188 + 0.282770i \(0.908747\pi\)
\(522\) 0 0
\(523\) −613.850 −1.17371 −0.586855 0.809692i \(-0.699634\pi\)
−0.586855 + 0.809692i \(0.699634\pi\)
\(524\) 0 0
\(525\) −6.50680 + 66.6231i −0.0123939 + 0.126901i
\(526\) 0 0
\(527\) 42.1702i 0.0800193i
\(528\) 0 0
\(529\) 306.166 0.578763
\(530\) 0 0
\(531\) −106.386 + 539.448i −0.200351 + 1.01591i
\(532\) 0 0
\(533\) 746.788i 1.40110i
\(534\) 0 0
\(535\) 229.931 0.429778
\(536\) 0 0
\(537\) −232.437 22.7011i −0.432843 0.0422740i
\(538\) 0 0
\(539\) 519.728i 0.964245i
\(540\) 0 0
\(541\) 188.436 0.348311 0.174156 0.984718i \(-0.444280\pi\)
0.174156 + 0.984718i \(0.444280\pi\)
\(542\) 0 0
\(543\) −69.6517 + 713.163i −0.128272 + 1.31338i
\(544\) 0 0
\(545\) 168.657i 0.309462i
\(546\) 0 0
\(547\) 637.744 1.16589 0.582947 0.812510i \(-0.301899\pi\)
0.582947 + 0.812510i \(0.301899\pi\)
\(548\) 0 0
\(549\) −863.822 170.357i −1.57345 0.310304i
\(550\) 0 0
\(551\) 148.490i 0.269492i
\(552\) 0 0
\(553\) −9.64176 −0.0174354
\(554\) 0 0
\(555\) −345.549 33.7483i −0.622611 0.0608078i
\(556\) 0 0
\(557\) 77.2307i 0.138655i 0.997594 + 0.0693274i \(0.0220853\pi\)
−0.997594 + 0.0693274i \(0.977915\pi\)
\(558\) 0 0
\(559\) 449.506 0.804125
\(560\) 0 0
\(561\) 4.13778 42.3667i 0.00737572 0.0755200i
\(562\) 0 0
\(563\) 257.584i 0.457521i 0.973483 + 0.228760i \(0.0734672\pi\)
−0.973483 + 0.228760i \(0.926533\pi\)
\(564\) 0 0
\(565\) 317.351 0.561682
\(566\) 0 0
\(567\) 334.412 + 137.238i 0.589791 + 0.242042i
\(568\) 0 0
\(569\) 307.483i 0.540392i 0.962805 + 0.270196i \(0.0870886\pi\)
−0.962805 + 0.270196i \(0.912911\pi\)
\(570\) 0 0
\(571\) −384.100 −0.672679 −0.336340 0.941741i \(-0.609189\pi\)
−0.336340 + 0.941741i \(0.609189\pi\)
\(572\) 0 0
\(573\) 529.227 + 51.6874i 0.923608 + 0.0902049i
\(574\) 0 0
\(575\) 74.6382i 0.129805i
\(576\) 0 0
\(577\) −235.337 −0.407863 −0.203932 0.978985i \(-0.565372\pi\)
−0.203932 + 0.978985i \(0.565372\pi\)
\(578\) 0 0
\(579\) 82.8913 848.724i 0.143163 1.46584i
\(580\) 0 0
\(581\) 58.3317i 0.100399i
\(582\) 0 0
\(583\) 661.801 1.13516
\(584\) 0 0
\(585\) 42.8740 217.400i 0.0732889 0.371623i
\(586\) 0 0
\(587\) 230.275i 0.392292i −0.980575 0.196146i \(-0.937157\pi\)
0.980575 0.196146i \(-0.0628426\pi\)
\(588\) 0 0
\(589\) 1411.87 2.39706
\(590\) 0 0
\(591\) −729.553 71.2524i −1.23444 0.120562i
\(592\) 0 0
\(593\) 1042.09i 1.75731i −0.477455 0.878656i \(-0.658441\pi\)
0.477455 0.878656i \(-0.341559\pi\)
\(594\) 0 0
\(595\) 7.92375 0.0133172
\(596\) 0 0
\(597\) 21.5827 220.985i 0.0361519 0.370160i
\(598\) 0 0
\(599\) 136.181i 0.227348i −0.993518 0.113674i \(-0.963738\pi\)
0.993518 0.113674i \(-0.0362619\pi\)
\(600\) 0 0
\(601\) 136.625 0.227329 0.113665 0.993519i \(-0.463741\pi\)
0.113665 + 0.993519i \(0.463741\pi\)
\(602\) 0 0
\(603\) −26.7141 5.26837i −0.0443020 0.00873693i
\(604\) 0 0
\(605\) 443.461i 0.732993i
\(606\) 0 0
\(607\) −426.666 −0.702910 −0.351455 0.936205i \(-0.614313\pi\)
−0.351455 + 0.936205i \(0.614313\pi\)
\(608\) 0 0
\(609\) 74.4240 + 7.26868i 0.122207 + 0.0119354i
\(610\) 0 0
\(611\) 135.964i 0.222527i
\(612\) 0 0
\(613\) 665.317 1.08535 0.542673 0.839944i \(-0.317412\pi\)
0.542673 + 0.839944i \(0.317412\pi\)
\(614\) 0 0
\(615\) 44.2250 452.820i 0.0719106 0.736292i
\(616\) 0 0
\(617\) 826.628i 1.33975i 0.742473 + 0.669877i \(0.233653\pi\)
−0.742473 + 0.669877i \(0.766347\pi\)
\(618\) 0 0
\(619\) 19.8176 0.0320155 0.0160078 0.999872i \(-0.494904\pi\)
0.0160078 + 0.999872i \(0.494904\pi\)
\(620\) 0 0
\(621\) −385.977 116.052i −0.621541 0.186879i
\(622\) 0 0
\(623\) 775.133i 1.24419i
\(624\) 0 0
\(625\) 25.0000 0.0400000
\(626\) 0 0
\(627\) −1418.45 138.534i −2.26228 0.220948i
\(628\) 0 0
\(629\) 41.0975i 0.0653378i
\(630\) 0 0
\(631\) −728.156 −1.15397 −0.576986 0.816754i \(-0.695771\pi\)
−0.576986 + 0.816754i \(0.695771\pi\)
\(632\) 0 0
\(633\) −9.05981 + 92.7633i −0.0143125 + 0.146546i
\(634\) 0 0
\(635\) 252.496i 0.397632i
\(636\) 0 0
\(637\) 320.242 0.502735
\(638\) 0 0
\(639\) −99.3955 + 504.001i −0.155548 + 0.788734i
\(640\) 0 0
\(641\) 438.969i 0.684819i 0.939551 + 0.342410i \(0.111243\pi\)
−0.939551 + 0.342410i \(0.888757\pi\)
\(642\) 0 0
\(643\) 483.535 0.751998 0.375999 0.926620i \(-0.377300\pi\)
0.375999 + 0.926620i \(0.377300\pi\)
\(644\) 0 0
\(645\) 272.561 + 26.6199i 0.422575 + 0.0412711i
\(646\) 0 0
\(647\) 575.687i 0.889780i 0.895585 + 0.444890i \(0.146757\pi\)
−0.895585 + 0.444890i \(0.853243\pi\)
\(648\) 0 0
\(649\) −1091.71 −1.68214
\(650\) 0 0
\(651\) 69.1119 707.636i 0.106163 1.08700i
\(652\) 0 0
\(653\) 407.885i 0.624633i −0.949978 0.312317i \(-0.898895\pi\)
0.949978 0.312317i \(-0.101105\pi\)
\(654\) 0 0
\(655\) −239.780 −0.366076
\(656\) 0 0
\(657\) 277.869 + 54.7993i 0.422936 + 0.0834084i
\(658\) 0 0
\(659\) 187.060i 0.283854i −0.989877 0.141927i \(-0.954670\pi\)
0.989877 0.141927i \(-0.0453298\pi\)
\(660\) 0 0
\(661\) 483.965 0.732171 0.366085 0.930581i \(-0.380698\pi\)
0.366085 + 0.930581i \(0.380698\pi\)
\(662\) 0 0
\(663\) −26.1052 2.54959i −0.0393744 0.00384553i
\(664\) 0 0
\(665\) 265.290i 0.398932i
\(666\) 0 0
\(667\) −83.3775 −0.125004
\(668\) 0 0
\(669\) 29.2869 299.868i 0.0437771 0.448233i
\(670\) 0 0
\(671\) 1748.16i 2.60531i
\(672\) 0 0
\(673\) 480.449 0.713891 0.356945 0.934125i \(-0.383818\pi\)
0.356945 + 0.934125i \(0.383818\pi\)
\(674\) 0 0
\(675\) 38.8714 129.283i 0.0575873 0.191530i
\(676\) 0 0
\(677\) 1245.12i 1.83918i −0.392881 0.919589i \(-0.628522\pi\)
0.392881 0.919589i \(-0.371478\pi\)
\(678\) 0 0
\(679\) −408.951 −0.602284
\(680\) 0 0
\(681\) −1042.39 101.806i −1.53068 0.149495i
\(682\) 0 0
\(683\) 118.409i 0.173366i −0.996236 0.0866832i \(-0.972373\pi\)
0.996236 0.0866832i \(-0.0276268\pi\)
\(684\) 0 0
\(685\) 151.479 0.221137
\(686\) 0 0
\(687\) −48.1177 + 492.677i −0.0700404 + 0.717143i
\(688\) 0 0
\(689\) 407.784i 0.591848i
\(690\) 0 0
\(691\) −481.257 −0.696465 −0.348232 0.937408i \(-0.613218\pi\)
−0.348232 + 0.937408i \(0.613218\pi\)
\(692\) 0 0
\(693\) −138.868 + 704.152i −0.200387 + 1.01609i
\(694\) 0 0
\(695\) 315.742i 0.454305i
\(696\) 0 0
\(697\) −53.8556 −0.0772678
\(698\) 0 0
\(699\) 372.626 + 36.3928i 0.533084 + 0.0520641i
\(700\) 0 0
\(701\) 644.879i 0.919941i −0.887934 0.459971i \(-0.847860\pi\)
0.887934 0.459971i \(-0.152140\pi\)
\(702\) 0 0
\(703\) 1375.96 1.95726
\(704\) 0 0
\(705\) 8.05182 82.4425i 0.0114210 0.116940i
\(706\) 0 0
\(707\) 519.246i 0.734436i
\(708\) 0 0
\(709\) −534.801 −0.754303 −0.377151 0.926152i \(-0.623096\pi\)
−0.377151 + 0.926152i \(0.623096\pi\)
\(710\) 0 0
\(711\) 19.0774 + 3.76230i 0.0268317 + 0.00529156i
\(712\) 0 0
\(713\) 792.767i 1.11188i
\(714\) 0 0
\(715\) 439.963 0.615332
\(716\) 0 0
\(717\) −184.618 18.0309i −0.257487 0.0251476i
\(718\) 0 0
\(719\) 891.507i 1.23993i 0.784631 + 0.619963i \(0.212852\pi\)
−0.784631 + 0.619963i \(0.787148\pi\)
\(720\) 0 0
\(721\) −812.526 −1.12694
\(722\) 0 0
\(723\) 0.657741 6.73461i 0.000909739 0.00931481i
\(724\) 0 0
\(725\) 27.9272i 0.0385203i
\(726\) 0 0
\(727\) −720.024 −0.990405 −0.495202 0.868778i \(-0.664906\pi\)
−0.495202 + 0.868778i \(0.664906\pi\)
\(728\) 0 0
\(729\) −608.121 402.032i −0.834185 0.551484i
\(730\) 0 0
\(731\) 32.4167i 0.0443458i
\(732\) 0 0
\(733\) 953.335 1.30059 0.650296 0.759681i \(-0.274645\pi\)
0.650296 + 0.759681i \(0.274645\pi\)
\(734\) 0 0
\(735\) 194.181 + 18.9649i 0.264192 + 0.0258025i
\(736\) 0 0
\(737\) 54.0627i 0.0733552i
\(738\) 0 0
\(739\) 615.723 0.833185 0.416592 0.909093i \(-0.363224\pi\)
0.416592 + 0.909093i \(0.363224\pi\)
\(740\) 0 0
\(741\) −85.3609 + 874.010i −0.115197 + 1.17950i
\(742\) 0 0
\(743\) 377.743i 0.508403i −0.967151 0.254201i \(-0.918187\pi\)
0.967151 0.254201i \(-0.0818126\pi\)
\(744\) 0 0
\(745\) 123.170 0.165328
\(746\) 0 0
\(747\) −22.7615 + 115.416i −0.0304706 + 0.154506i
\(748\) 0 0
\(749\) 458.890i 0.612670i
\(750\) 0 0
\(751\) 735.578 0.979465 0.489733 0.871873i \(-0.337094\pi\)
0.489733 + 0.871873i \(0.337094\pi\)
\(752\) 0 0
\(753\) 325.430 + 31.7834i 0.432178 + 0.0422090i
\(754\) 0 0
\(755\) 125.511i 0.166240i
\(756\) 0 0
\(757\) 921.601 1.21744 0.608719 0.793386i \(-0.291684\pi\)
0.608719 + 0.793386i \(0.291684\pi\)
\(758\) 0 0
\(759\) 77.7871 796.462i 0.102486 1.04936i
\(760\) 0 0
\(761\) 240.158i 0.315582i −0.987473 0.157791i \(-0.949563\pi\)
0.987473 0.157791i \(-0.0504372\pi\)
\(762\) 0 0
\(763\) 336.601 0.441154
\(764\) 0 0
\(765\) −15.6781 3.09192i −0.0204942 0.00404172i
\(766\) 0 0
\(767\) 672.682i 0.877029i
\(768\) 0 0
\(769\) −4.79672 −0.00623760 −0.00311880 0.999995i \(-0.500993\pi\)
−0.00311880 + 0.999995i \(0.500993\pi\)
\(770\) 0 0
\(771\) 93.9522 + 9.17592i 0.121858 + 0.0119013i
\(772\) 0 0
\(773\) 140.044i 0.181170i −0.995889 0.0905850i \(-0.971126\pi\)
0.995889 0.0905850i \(-0.0288737\pi\)
\(774\) 0 0
\(775\) −265.537 −0.342628
\(776\) 0 0
\(777\) 67.3539 689.636i 0.0866845 0.887562i
\(778\) 0 0
\(779\) 1803.10i 2.31464i
\(780\) 0 0
\(781\) −1019.97 −1.30598
\(782\) 0 0
\(783\) −144.420 43.4228i −0.184445 0.0554570i
\(784\) 0 0
\(785\) 613.278i 0.781246i
\(786\) 0 0
\(787\) 649.685 0.825520 0.412760 0.910840i \(-0.364565\pi\)
0.412760 + 0.910840i \(0.364565\pi\)
\(788\) 0 0
\(789\) 702.230 + 68.5838i 0.890025 + 0.0869250i
\(790\) 0 0
\(791\) 633.358i 0.800706i
\(792\) 0 0
\(793\) −1077.17 −1.35835
\(794\) 0 0
\(795\) 24.1491 247.262i 0.0303762 0.311022i
\(796\) 0 0
\(797\) 547.802i 0.687329i −0.939092 0.343665i \(-0.888332\pi\)
0.939092 0.343665i \(-0.111668\pi\)