Properties

Label 117.4.q.b.82.1
Level $117$
Weight $4$
Character 117.82
Analytic conductor $6.903$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 117 = 3^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 117.q (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.90322347067\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Defining polynomial: \( x^{2} - x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 39)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 82.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 117.82
Dual form 117.4.q.b.10.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-4.00000 - 6.92820i) q^{4} +5.19615i q^{5} +(9.00000 - 5.19615i) q^{7} +O(q^{10})\) \(q+(-4.00000 - 6.92820i) q^{4} +5.19615i q^{5} +(9.00000 - 5.19615i) q^{7} +(-45.0000 - 25.9808i) q^{11} +(-32.5000 - 33.7750i) q^{13} +(-32.0000 + 55.4256i) q^{16} +(-58.5000 - 101.325i) q^{17} +(-21.0000 + 12.1244i) q^{19} +(36.0000 - 20.7846i) q^{20} +(9.00000 - 15.5885i) q^{23} +98.0000 q^{25} +(-72.0000 - 41.5692i) q^{28} +(-49.5000 + 85.7365i) q^{29} -193.990i q^{31} +(27.0000 + 46.7654i) q^{35} +(97.5000 + 56.2917i) q^{37} +(31.5000 + 18.1865i) q^{41} +(41.0000 + 71.0141i) q^{43} +415.692i q^{44} -72.7461i q^{47} +(-117.500 + 203.516i) q^{49} +(-104.000 + 360.267i) q^{52} +261.000 q^{53} +(135.000 - 233.827i) q^{55} +(684.000 - 394.908i) q^{59} +(359.500 + 622.672i) q^{61} +512.000 q^{64} +(175.500 - 168.875i) q^{65} +(-609.000 - 351.606i) q^{67} +(-468.000 + 810.600i) q^{68} +(405.000 - 233.827i) q^{71} -684.160i q^{73} +(168.000 + 96.9948i) q^{76} -540.000 q^{77} -440.000 q^{79} +(-288.000 - 166.277i) q^{80} +1195.12i q^{83} +(526.500 - 303.975i) q^{85} +(-1314.00 - 758.638i) q^{89} +(-468.000 - 135.100i) q^{91} -144.000 q^{92} +(-63.0000 - 109.119i) q^{95} +(-1002.00 + 578.505i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - 8 q^{4} + 18 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 2 q - 8 q^{4} + 18 q^{7} - 90 q^{11} - 65 q^{13} - 64 q^{16} - 117 q^{17} - 42 q^{19} + 72 q^{20} + 18 q^{23} + 196 q^{25} - 144 q^{28} - 99 q^{29} + 54 q^{35} + 195 q^{37} + 63 q^{41} + 82 q^{43} - 235 q^{49} - 208 q^{52} + 522 q^{53} + 270 q^{55} + 1368 q^{59} + 719 q^{61} + 1024 q^{64} + 351 q^{65} - 1218 q^{67} - 936 q^{68} + 810 q^{71} + 336 q^{76} - 1080 q^{77} - 880 q^{79} - 576 q^{80} + 1053 q^{85} - 2628 q^{89} - 936 q^{91} - 288 q^{92} - 126 q^{95} - 2004 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/117\mathbb{Z}\right)^\times\).

\(n\) \(28\) \(92\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\) \(1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(3\) 0 0
\(4\) −4.00000 6.92820i −0.500000 0.866025i
\(5\) 5.19615i 0.464758i 0.972625 + 0.232379i \(0.0746510\pi\)
−0.972625 + 0.232379i \(0.925349\pi\)
\(6\) 0 0
\(7\) 9.00000 5.19615i 0.485954 0.280566i −0.236940 0.971524i \(-0.576145\pi\)
0.722895 + 0.690958i \(0.242811\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −45.0000 25.9808i −1.23346 0.712136i −0.265707 0.964054i \(-0.585605\pi\)
−0.967749 + 0.251918i \(0.918939\pi\)
\(12\) 0 0
\(13\) −32.5000 33.7750i −0.693375 0.720577i
\(14\) 0 0
\(15\) 0 0
\(16\) −32.0000 + 55.4256i −0.500000 + 0.866025i
\(17\) −58.5000 101.325i −0.834608 1.44558i −0.894349 0.447369i \(-0.852361\pi\)
0.0597414 0.998214i \(-0.480972\pi\)
\(18\) 0 0
\(19\) −21.0000 + 12.1244i −0.253565 + 0.146396i −0.621395 0.783497i \(-0.713434\pi\)
0.367831 + 0.929893i \(0.380101\pi\)
\(20\) 36.0000 20.7846i 0.402492 0.232379i
\(21\) 0 0
\(22\) 0 0
\(23\) 9.00000 15.5885i 0.0815926 0.141323i −0.822342 0.568994i \(-0.807333\pi\)
0.903934 + 0.427672i \(0.140666\pi\)
\(24\) 0 0
\(25\) 98.0000 0.784000
\(26\) 0 0
\(27\) 0 0
\(28\) −72.0000 41.5692i −0.485954 0.280566i
\(29\) −49.5000 + 85.7365i −0.316963 + 0.548996i −0.979853 0.199721i \(-0.935996\pi\)
0.662890 + 0.748717i \(0.269330\pi\)
\(30\) 0 0
\(31\) 193.990i 1.12392i −0.827164 0.561961i \(-0.810047\pi\)
0.827164 0.561961i \(-0.189953\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 27.0000 + 46.7654i 0.130395 + 0.225851i
\(36\) 0 0
\(37\) 97.5000 + 56.2917i 0.433214 + 0.250116i 0.700715 0.713442i \(-0.252865\pi\)
−0.267501 + 0.963558i \(0.586198\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 31.5000 + 18.1865i 0.119987 + 0.0692746i 0.558792 0.829308i \(-0.311265\pi\)
−0.438805 + 0.898582i \(0.644598\pi\)
\(42\) 0 0
\(43\) 41.0000 + 71.0141i 0.145406 + 0.251850i 0.929524 0.368761i \(-0.120218\pi\)
−0.784119 + 0.620611i \(0.786885\pi\)
\(44\) 415.692i 1.42427i
\(45\) 0 0
\(46\) 0 0
\(47\) 72.7461i 0.225768i −0.993608 0.112884i \(-0.963991\pi\)
0.993608 0.112884i \(-0.0360089\pi\)
\(48\) 0 0
\(49\) −117.500 + 203.516i −0.342566 + 0.593341i
\(50\) 0 0
\(51\) 0 0
\(52\) −104.000 + 360.267i −0.277350 + 0.960769i
\(53\) 261.000 0.676436 0.338218 0.941068i \(-0.390176\pi\)
0.338218 + 0.941068i \(0.390176\pi\)
\(54\) 0 0
\(55\) 135.000 233.827i 0.330971 0.573258i
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 684.000 394.908i 1.50931 0.871400i 0.509368 0.860549i \(-0.329879\pi\)
0.999941 0.0108508i \(-0.00345397\pi\)
\(60\) 0 0
\(61\) 359.500 + 622.672i 0.754578 + 1.30697i 0.945584 + 0.325379i \(0.105492\pi\)
−0.191006 + 0.981589i \(0.561175\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 512.000 1.00000
\(65\) 175.500 168.875i 0.334894 0.322252i
\(66\) 0 0
\(67\) −609.000 351.606i −1.11047 0.641128i −0.171516 0.985181i \(-0.554866\pi\)
−0.938950 + 0.344054i \(0.888200\pi\)
\(68\) −468.000 + 810.600i −0.834608 + 1.44558i
\(69\) 0 0
\(70\) 0 0
\(71\) 405.000 233.827i 0.676967 0.390847i −0.121744 0.992561i \(-0.538849\pi\)
0.798711 + 0.601714i \(0.205515\pi\)
\(72\) 0 0
\(73\) 684.160i 1.09692i −0.836178 0.548458i \(-0.815215\pi\)
0.836178 0.548458i \(-0.184785\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 168.000 + 96.9948i 0.253565 + 0.146396i
\(77\) −540.000 −0.799204
\(78\) 0 0
\(79\) −440.000 −0.626631 −0.313316 0.949649i \(-0.601440\pi\)
−0.313316 + 0.949649i \(0.601440\pi\)
\(80\) −288.000 166.277i −0.402492 0.232379i
\(81\) 0 0
\(82\) 0 0
\(83\) 1195.12i 1.58049i 0.612789 + 0.790247i \(0.290048\pi\)
−0.612789 + 0.790247i \(0.709952\pi\)
\(84\) 0 0
\(85\) 526.500 303.975i 0.671846 0.387891i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −1314.00 758.638i −1.56499 0.903545i −0.996740 0.0806862i \(-0.974289\pi\)
−0.568246 0.822859i \(-0.692378\pi\)
\(90\) 0 0
\(91\) −468.000 135.100i −0.539118 0.155630i
\(92\) −144.000 −0.163185
\(93\) 0 0
\(94\) 0 0
\(95\) −63.0000 109.119i −0.0680386 0.117846i
\(96\) 0 0
\(97\) −1002.00 + 578.505i −1.04884 + 0.605549i −0.922325 0.386415i \(-0.873713\pi\)
−0.126517 + 0.991964i \(0.540380\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) −392.000 678.964i −0.392000 0.678964i
\(101\) 787.500 1363.99i 0.775833 1.34378i −0.158491 0.987360i \(-0.550663\pi\)
0.934325 0.356423i \(-0.116004\pi\)
\(102\) 0 0
\(103\) 794.000 0.759565 0.379782 0.925076i \(-0.375999\pi\)
0.379782 + 0.925076i \(0.375999\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 225.000 389.711i 0.203286 0.352101i −0.746299 0.665610i \(-0.768171\pi\)
0.949585 + 0.313509i \(0.101505\pi\)
\(108\) 0 0
\(109\) 595.825i 0.523576i −0.965125 0.261788i \(-0.915688\pi\)
0.965125 0.261788i \(-0.0843120\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 665.108i 0.561132i
\(113\) −850.500 1473.11i −0.708038 1.22636i −0.965584 0.260092i \(-0.916247\pi\)
0.257546 0.966266i \(-0.417086\pi\)
\(114\) 0 0
\(115\) 81.0000 + 46.7654i 0.0656808 + 0.0379208i
\(116\) 792.000 0.633925
\(117\) 0 0
\(118\) 0 0
\(119\) −1053.00 607.950i −0.811163 0.468325i
\(120\) 0 0
\(121\) 684.500 + 1185.59i 0.514275 + 0.890750i
\(122\) 0 0
\(123\) 0 0
\(124\) −1344.00 + 775.959i −0.973345 + 0.561961i
\(125\) 1158.74i 0.829128i
\(126\) 0 0
\(127\) 832.000 1441.07i 0.581323 1.00688i −0.414000 0.910277i \(-0.635868\pi\)
0.995323 0.0966044i \(-0.0307982\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 1476.00 0.984418 0.492209 0.870477i \(-0.336190\pi\)
0.492209 + 0.870477i \(0.336190\pi\)
\(132\) 0 0
\(133\) −126.000 + 218.238i −0.0821473 + 0.142283i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −877.500 + 506.625i −0.547225 + 0.315941i −0.748002 0.663696i \(-0.768987\pi\)
0.200777 + 0.979637i \(0.435653\pi\)
\(138\) 0 0
\(139\) −562.000 973.413i −0.342937 0.593984i 0.642040 0.766671i \(-0.278088\pi\)
−0.984977 + 0.172687i \(0.944755\pi\)
\(140\) 216.000 374.123i 0.130395 0.225851i
\(141\) 0 0
\(142\) 0 0
\(143\) 585.000 + 2364.25i 0.342099 + 1.38258i
\(144\) 0 0
\(145\) −445.500 257.210i −0.255150 0.147311i
\(146\) 0 0
\(147\) 0 0
\(148\) 900.666i 0.500232i
\(149\) −2830.50 + 1634.19i −1.55627 + 0.898510i −0.558657 + 0.829399i \(0.688683\pi\)
−0.997609 + 0.0691115i \(0.977984\pi\)
\(150\) 0 0
\(151\) 1638.52i 0.883052i 0.897248 + 0.441526i \(0.145563\pi\)
−0.897248 + 0.441526i \(0.854437\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 1008.00 0.522352
\(156\) 0 0
\(157\) 1259.00 0.639995 0.319997 0.947418i \(-0.396318\pi\)
0.319997 + 0.947418i \(0.396318\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 187.061i 0.0915684i
\(162\) 0 0
\(163\) 2556.00 1475.71i 1.22823 0.709118i 0.261570 0.965185i \(-0.415760\pi\)
0.966659 + 0.256066i \(0.0824264\pi\)
\(164\) 290.985i 0.138549i
\(165\) 0 0
\(166\) 0 0
\(167\) 2718.00 + 1569.24i 1.25943 + 0.727133i 0.972964 0.230956i \(-0.0741855\pi\)
0.286468 + 0.958090i \(0.407519\pi\)
\(168\) 0 0
\(169\) −84.5000 + 2195.37i −0.0384615 + 0.999260i
\(170\) 0 0
\(171\) 0 0
\(172\) 328.000 568.113i 0.145406 0.251850i
\(173\) 2133.00 + 3694.46i 0.937393 + 1.62361i 0.770310 + 0.637669i \(0.220101\pi\)
0.167083 + 0.985943i \(0.446565\pi\)
\(174\) 0 0
\(175\) 882.000 509.223i 0.380988 0.219964i
\(176\) 2880.00 1662.77i 1.23346 0.712136i
\(177\) 0 0
\(178\) 0 0
\(179\) 1503.00 2603.27i 0.627595 1.08703i −0.360438 0.932783i \(-0.617373\pi\)
0.988033 0.154243i \(-0.0492939\pi\)
\(180\) 0 0
\(181\) −1873.00 −0.769166 −0.384583 0.923090i \(-0.625655\pi\)
−0.384583 + 0.923090i \(0.625655\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −292.500 + 506.625i −0.116243 + 0.201339i
\(186\) 0 0
\(187\) 6079.50i 2.37742i
\(188\) −504.000 + 290.985i −0.195521 + 0.112884i
\(189\) 0 0
\(190\) 0 0
\(191\) −1368.00 2369.45i −0.518246 0.897629i −0.999775 0.0211985i \(-0.993252\pi\)
0.481529 0.876430i \(-0.340082\pi\)
\(192\) 0 0
\(193\) −2254.50 1301.64i −0.840842 0.485460i 0.0167085 0.999860i \(-0.494681\pi\)
−0.857550 + 0.514400i \(0.828015\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 1880.00 0.685131
\(197\) −3222.00 1860.22i −1.16527 0.672768i −0.212708 0.977116i \(-0.568228\pi\)
−0.952561 + 0.304347i \(0.901562\pi\)
\(198\) 0 0
\(199\) −599.000 1037.50i −0.213377 0.369579i 0.739392 0.673275i \(-0.235113\pi\)
−0.952769 + 0.303695i \(0.901780\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 1028.84i 0.355716i
\(204\) 0 0
\(205\) −94.5000 + 163.679i −0.0321959 + 0.0557650i
\(206\) 0 0
\(207\) 0 0
\(208\) 2912.00 720.533i 0.970725 0.240192i
\(209\) 1260.00 0.417014
\(210\) 0 0
\(211\) −1196.00 + 2071.53i −0.390218 + 0.675878i −0.992478 0.122422i \(-0.960934\pi\)
0.602260 + 0.798300i \(0.294267\pi\)
\(212\) −1044.00 1808.26i −0.338218 0.585811i
\(213\) 0 0
\(214\) 0 0
\(215\) −369.000 + 213.042i −0.117049 + 0.0675784i
\(216\) 0 0
\(217\) −1008.00 1745.91i −0.315334 0.546175i
\(218\) 0 0
\(219\) 0 0
\(220\) −2160.00 −0.661942
\(221\) −1521.00 + 5268.90i −0.462957 + 1.60373i
\(222\) 0 0
\(223\) −1764.00 1018.45i −0.529714 0.305830i 0.211186 0.977446i \(-0.432267\pi\)
−0.740900 + 0.671615i \(0.765601\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −1863.00 + 1075.60i −0.544721 + 0.314495i −0.746990 0.664835i \(-0.768502\pi\)
0.202269 + 0.979330i \(0.435168\pi\)
\(228\) 0 0
\(229\) 3471.03i 1.00162i −0.865556 0.500812i \(-0.833035\pi\)
0.865556 0.500812i \(-0.166965\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 1854.00 0.521286 0.260643 0.965435i \(-0.416065\pi\)
0.260643 + 0.965435i \(0.416065\pi\)
\(234\) 0 0
\(235\) 378.000 0.104928
\(236\) −5472.00 3159.26i −1.50931 0.871400i
\(237\) 0 0
\(238\) 0 0
\(239\) 4458.30i 1.20662i −0.797505 0.603312i \(-0.793847\pi\)
0.797505 0.603312i \(-0.206153\pi\)
\(240\) 0 0
\(241\) −361.500 + 208.712i −0.0966235 + 0.0557856i −0.547533 0.836784i \(-0.684433\pi\)
0.450910 + 0.892570i \(0.351100\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 2876.00 4981.38i 0.754578 1.30697i
\(245\) −1057.50 610.548i −0.275760 0.159210i
\(246\) 0 0
\(247\) 1092.00 + 315.233i 0.281305 + 0.0812057i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 2052.00 + 3554.17i 0.516020 + 0.893773i 0.999827 + 0.0185985i \(0.00592043\pi\)
−0.483807 + 0.875175i \(0.660746\pi\)
\(252\) 0 0
\(253\) −810.000 + 467.654i −0.201282 + 0.116210i
\(254\) 0 0
\(255\) 0 0
\(256\) −2048.00 3547.24i −0.500000 0.866025i
\(257\) 994.500 1722.52i 0.241382 0.418086i −0.719726 0.694258i \(-0.755733\pi\)
0.961108 + 0.276172i \(0.0890660\pi\)
\(258\) 0 0
\(259\) 1170.00 0.280696
\(260\) −1872.00 540.400i −0.446525 0.128901i
\(261\) 0 0
\(262\) 0 0
\(263\) 369.000 639.127i 0.0865153 0.149849i −0.819521 0.573050i \(-0.805760\pi\)
0.906036 + 0.423201i \(0.139094\pi\)
\(264\) 0 0
\(265\) 1356.20i 0.314379i
\(266\) 0 0
\(267\) 0 0
\(268\) 5625.70i 1.28226i
\(269\) −1053.00 1823.85i −0.238671 0.413391i 0.721662 0.692246i \(-0.243378\pi\)
−0.960333 + 0.278855i \(0.910045\pi\)
\(270\) 0 0
\(271\) 594.000 + 342.946i 0.133147 + 0.0768727i 0.565094 0.825026i \(-0.308840\pi\)
−0.431947 + 0.901899i \(0.642173\pi\)
\(272\) 7488.00 1.66922
\(273\) 0 0
\(274\) 0 0
\(275\) −4410.00 2546.11i −0.967029 0.558315i
\(276\) 0 0
\(277\) −1832.50 3173.98i −0.397488 0.688470i 0.595927 0.803039i \(-0.296785\pi\)
−0.993415 + 0.114569i \(0.963451\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 1719.93i 0.365132i −0.983194 0.182566i \(-0.941560\pi\)
0.983194 0.182566i \(-0.0584404\pi\)
\(282\) 0 0
\(283\) 913.000 1581.36i 0.191775 0.332163i −0.754064 0.656801i \(-0.771909\pi\)
0.945838 + 0.324638i \(0.105242\pi\)
\(284\) −3240.00 1870.61i −0.676967 0.390847i
\(285\) 0 0
\(286\) 0 0
\(287\) 378.000 0.0777444
\(288\) 0 0
\(289\) −4388.00 + 7600.24i −0.893141 + 1.54696i
\(290\) 0 0
\(291\) 0 0
\(292\) −4740.00 + 2736.64i −0.949957 + 0.548458i
\(293\) 436.500 252.013i 0.0870328 0.0502484i −0.455852 0.890056i \(-0.650665\pi\)
0.542885 + 0.839807i \(0.317332\pi\)
\(294\) 0 0
\(295\) 2052.00 + 3554.17i 0.404990 + 0.701463i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −819.000 + 202.650i −0.158408 + 0.0391958i
\(300\) 0 0
\(301\) 738.000 + 426.084i 0.141321 + 0.0815917i
\(302\) 0 0
\(303\) 0 0
\(304\) 1551.92i 0.292791i
\(305\) −3235.50 + 1868.02i −0.607424 + 0.350696i
\(306\) 0 0
\(307\) 1950.29i 0.362570i −0.983431 0.181285i \(-0.941974\pi\)
0.983431 0.181285i \(-0.0580256\pi\)
\(308\) 2160.00 + 3741.23i 0.399602 + 0.692131i
\(309\) 0 0
\(310\) 0 0
\(311\) 3798.00 0.692491 0.346246 0.938144i \(-0.387456\pi\)
0.346246 + 0.938144i \(0.387456\pi\)
\(312\) 0 0
\(313\) 1378.00 0.248847 0.124424 0.992229i \(-0.460292\pi\)
0.124424 + 0.992229i \(0.460292\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 1760.00 + 3048.41i 0.313316 + 0.542679i
\(317\) 7103.14i 1.25852i 0.777193 + 0.629262i \(0.216643\pi\)
−0.777193 + 0.629262i \(0.783357\pi\)
\(318\) 0 0
\(319\) 4455.00 2572.10i 0.781919 0.451441i
\(320\) 2660.43i 0.464758i
\(321\) 0 0
\(322\) 0 0
\(323\) 2457.00 + 1418.55i 0.423254 + 0.244366i
\(324\) 0 0
\(325\) −3185.00 3309.95i −0.543606 0.564932i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −378.000 654.715i −0.0633429 0.109713i
\(330\) 0 0
\(331\) 8724.00 5036.80i 1.44868 0.836398i 0.450281 0.892887i \(-0.351324\pi\)
0.998403 + 0.0564889i \(0.0179906\pi\)
\(332\) 8280.00 4780.46i 1.36875 0.790247i
\(333\) 0 0
\(334\) 0 0
\(335\) 1827.00 3164.46i 0.297969 0.516098i
\(336\) 0 0
\(337\) 9001.00 1.45494 0.727471 0.686138i \(-0.240695\pi\)
0.727471 + 0.686138i \(0.240695\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) −4212.00 2431.80i −0.671846 0.387891i
\(341\) −5040.00 + 8729.54i −0.800385 + 1.38631i
\(342\) 0 0
\(343\) 6006.75i 0.945581i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 1647.00 + 2852.69i 0.254800 + 0.441327i 0.964841 0.262834i \(-0.0846570\pi\)
−0.710041 + 0.704160i \(0.751324\pi\)
\(348\) 0 0
\(349\) −9132.00 5272.36i −1.40064 0.808662i −0.406185 0.913791i \(-0.633141\pi\)
−0.994459 + 0.105129i \(0.966475\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 2146.50 + 1239.28i 0.323645 + 0.186856i 0.653016 0.757344i \(-0.273503\pi\)
−0.329371 + 0.944201i \(0.606837\pi\)
\(354\) 0 0
\(355\) 1215.00 + 2104.44i 0.181649 + 0.314626i
\(356\) 12138.2i 1.80709i
\(357\) 0 0
\(358\) 0 0
\(359\) 5414.39i 0.795991i −0.917387 0.397995i \(-0.869706\pi\)
0.917387 0.397995i \(-0.130294\pi\)
\(360\) 0 0
\(361\) −3135.50 + 5430.85i −0.457137 + 0.791784i
\(362\) 0 0
\(363\) 0 0
\(364\) 936.000 + 3782.80i 0.134779 + 0.544705i
\(365\) 3555.00 0.509801
\(366\) 0 0
\(367\) 4973.00 8613.49i 0.707326 1.22512i −0.258520 0.966006i \(-0.583235\pi\)
0.965846 0.259118i \(-0.0834318\pi\)
\(368\) 576.000 + 997.661i 0.0815926 + 0.141323i
\(369\) 0 0
\(370\) 0 0
\(371\) 2349.00 1356.20i 0.328717 0.189785i
\(372\) 0 0
\(373\) 3650.50 + 6322.85i 0.506745 + 0.877707i 0.999970 + 0.00780555i \(0.00248461\pi\)
−0.493225 + 0.869902i \(0.664182\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 4504.50 1114.57i 0.615368 0.152264i
\(378\) 0 0
\(379\) −2964.00 1711.27i −0.401716 0.231931i 0.285508 0.958376i \(-0.407838\pi\)
−0.687224 + 0.726445i \(0.741171\pi\)
\(380\) −504.000 + 872.954i −0.0680386 + 0.117846i
\(381\) 0 0
\(382\) 0 0
\(383\) 5004.00 2889.06i 0.667604 0.385442i −0.127564 0.991830i \(-0.540716\pi\)
0.795168 + 0.606389i \(0.207382\pi\)
\(384\) 0 0
\(385\) 2805.92i 0.371436i
\(386\) 0 0
\(387\) 0 0
\(388\) 8016.00 + 4628.04i 1.04884 + 0.605549i
\(389\) −9153.00 −1.19300 −0.596498 0.802614i \(-0.703442\pi\)
−0.596498 + 0.802614i \(0.703442\pi\)
\(390\) 0 0
\(391\) −2106.00 −0.272391
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 2286.31i 0.291232i
\(396\) 0 0
\(397\) 1752.00 1011.52i 0.221487 0.127876i −0.385152 0.922853i \(-0.625851\pi\)
0.606639 + 0.794978i \(0.292518\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) −3136.00 + 5431.71i −0.392000 + 0.678964i
\(401\) −7195.50 4154.32i −0.896075 0.517349i −0.0201504 0.999797i \(-0.506414\pi\)
−0.875925 + 0.482448i \(0.839748\pi\)
\(402\) 0 0
\(403\) −6552.00 + 6304.66i −0.809872 + 0.779300i
\(404\) −12600.0 −1.55167
\(405\) 0 0
\(406\) 0 0
\(407\) −2925.00 5066.25i −0.356233 0.617014i
\(408\) 0 0
\(409\) −9022.50 + 5209.14i −1.09079 + 0.629769i −0.933787 0.357829i \(-0.883517\pi\)
−0.157005 + 0.987598i \(0.550184\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) −3176.00 5500.99i −0.379782 0.657802i
\(413\) 4104.00 7108.34i 0.488970 0.846921i
\(414\) 0 0
\(415\) −6210.00 −0.734547
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 2088.00 3616.52i 0.243450 0.421667i −0.718245 0.695790i \(-0.755054\pi\)
0.961695 + 0.274123i \(0.0883875\pi\)
\(420\) 0 0
\(421\) 14471.3i 1.67527i −0.546233 0.837633i \(-0.683939\pi\)
0.546233 0.837633i \(-0.316061\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −5733.00 9929.85i −0.654333 1.13334i
\(426\) 0 0
\(427\) 6471.00 + 3736.03i 0.733381 + 0.423418i
\(428\) −3600.00 −0.406571
\(429\) 0 0
\(430\) 0 0
\(431\) 5697.00 + 3289.16i 0.636693 + 0.367595i 0.783340 0.621594i \(-0.213515\pi\)
−0.146646 + 0.989189i \(0.546848\pi\)
\(432\) 0 0
\(433\) 3302.50 + 5720.10i 0.366531 + 0.634851i 0.989021 0.147778i \(-0.0472120\pi\)
−0.622489 + 0.782628i \(0.713879\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) −4128.00 + 2383.30i −0.453430 + 0.261788i
\(437\) 436.477i 0.0477792i
\(438\) 0 0
\(439\) 4271.00 7397.59i 0.464336 0.804254i −0.534835 0.844957i \(-0.679626\pi\)
0.999171 + 0.0407023i \(0.0129595\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 14328.0 1.53667 0.768334 0.640049i \(-0.221086\pi\)
0.768334 + 0.640049i \(0.221086\pi\)
\(444\) 0 0
\(445\) 3942.00 6827.74i 0.419930 0.727340i
\(446\) 0 0
\(447\) 0 0
\(448\) 4608.00 2660.43i 0.485954 0.280566i
\(449\) −2610.00 + 1506.88i −0.274329 + 0.158384i −0.630853 0.775902i \(-0.717295\pi\)
0.356525 + 0.934286i \(0.383962\pi\)
\(450\) 0 0
\(451\) −945.000 1636.79i −0.0986659 0.170894i
\(452\) −6804.00 + 11784.9i −0.708038 + 1.22636i
\(453\) 0 0
\(454\) 0 0
\(455\) 702.000 2431.80i 0.0723303 0.250559i
\(456\) 0 0
\(457\) −2500.50 1443.66i −0.255948 0.147772i 0.366536 0.930404i \(-0.380543\pi\)
−0.622485 + 0.782632i \(0.713877\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 748.246i 0.0758416i
\(461\) −3118.50 + 1800.47i −0.315061 + 0.181900i −0.649189 0.760627i \(-0.724892\pi\)
0.334128 + 0.942528i \(0.391558\pi\)
\(462\) 0 0
\(463\) 2677.75i 0.268781i −0.990928 0.134391i \(-0.957092\pi\)
0.990928 0.134391i \(-0.0429077\pi\)
\(464\) −3168.00 5487.14i −0.316963 0.548996i
\(465\) 0 0
\(466\) 0 0
\(467\) −13878.0 −1.37515 −0.687577 0.726111i \(-0.741326\pi\)
−0.687577 + 0.726111i \(0.741326\pi\)
\(468\) 0 0
\(469\) −7308.00 −0.719514
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 4260.84i 0.414194i
\(474\) 0 0
\(475\) −2058.00 + 1188.19i −0.198795 + 0.114774i
\(476\) 9727.20i 0.936650i
\(477\) 0 0
\(478\) 0 0
\(479\) −954.000 550.792i −0.0910008 0.0525393i 0.453809 0.891099i \(-0.350065\pi\)
−0.544810 + 0.838560i \(0.683398\pi\)
\(480\) 0 0
\(481\) −1267.50 5122.54i −0.120152 0.485588i
\(482\) 0 0
\(483\) 0 0
\(484\) 5476.00 9484.71i 0.514275 0.890750i
\(485\) −3006.00 5206.54i −0.281434 0.487458i
\(486\) 0 0
\(487\) −14829.0 + 8561.53i −1.37981 + 0.796632i −0.992136 0.125166i \(-0.960054\pi\)
−0.387671 + 0.921798i \(0.626720\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 225.000 389.711i 0.0206805 0.0358196i −0.855500 0.517803i \(-0.826750\pi\)
0.876180 + 0.481983i \(0.160083\pi\)
\(492\) 0 0
\(493\) 11583.0 1.05816
\(494\) 0 0
\(495\) 0 0
\(496\) 10752.0 + 6207.67i 0.973345 + 0.561961i
\(497\) 2430.00 4208.88i 0.219317 0.379868i
\(498\) 0 0
\(499\) 13219.0i 1.18590i −0.805239 0.592950i \(-0.797963\pi\)
0.805239 0.592950i \(-0.202037\pi\)
\(500\) 8028.00 4634.97i 0.718046 0.414564i
\(501\) 0 0
\(502\) 0 0
\(503\) 2673.00 + 4629.77i 0.236945 + 0.410400i 0.959836 0.280561i \(-0.0905206\pi\)
−0.722891 + 0.690962i \(0.757187\pi\)
\(504\) 0 0
\(505\) 7087.50 + 4091.97i 0.624534 + 0.360575i
\(506\) 0 0
\(507\) 0 0
\(508\) −13312.0 −1.16265
\(509\) 5080.50 + 2933.23i 0.442415 + 0.255428i 0.704621 0.709583i \(-0.251117\pi\)
−0.262207 + 0.965012i \(0.584450\pi\)
\(510\) 0 0
\(511\) −3555.00 6157.44i −0.307757 0.533051i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 4125.75i 0.353014i
\(516\) 0 0
\(517\) −1890.00 + 3273.58i −0.160778 + 0.278475i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 9657.00 0.812055 0.406028 0.913861i \(-0.366914\pi\)
0.406028 + 0.913861i \(0.366914\pi\)
\(522\) 0 0
\(523\) −10813.0 + 18728.7i −0.904053 + 1.56586i −0.0818685 + 0.996643i \(0.526089\pi\)
−0.822184 + 0.569222i \(0.807245\pi\)
\(524\) −5904.00 10226.0i −0.492209 0.852531i
\(525\) 0 0
\(526\) 0 0
\(527\) −19656.0 + 11348.4i −1.62472 + 0.938034i
\(528\) 0 0
\(529\) 5921.50 + 10256.3i 0.486685 + 0.842964i
\(530\) 0 0
\(531\) 0 0
\(532\) 2016.00 0.164295
\(533\) −409.500 1654.97i −0.0332785 0.134493i
\(534\) 0 0
\(535\) 2025.00 + 1169.13i 0.163642 + 0.0944787i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 10575.0 6105.48i 0.845079 0.487906i
\(540\) 0 0
\(541\) 5371.09i 0.426841i 0.976960 + 0.213421i \(0.0684605\pi\)
−0.976960 + 0.213421i \(0.931540\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 3096.00 0.243336
\(546\) 0 0
\(547\) 16946.0 1.32460 0.662302 0.749237i \(-0.269579\pi\)
0.662302 + 0.749237i \(0.269579\pi\)
\(548\) 7020.00 + 4053.00i 0.547225 + 0.315941i
\(549\) 0 0
\(550\) 0 0
\(551\) 2400.62i 0.185608i
\(552\) 0 0
\(553\) −3960.00 + 2286.31i −0.304514 + 0.175811i
\(554\) 0 0
\(555\) 0 0
\(556\) −4496.00 + 7787.30i −0.342937 + 0.593984i
\(557\) −3343.50 1930.37i −0.254342 0.146845i 0.367409 0.930060i \(-0.380245\pi\)
−0.621751 + 0.783215i \(0.713578\pi\)
\(558\) 0 0
\(559\) 1066.00 3692.73i 0.0806565 0.279402i
\(560\) −3456.00 −0.260790
\(561\) 0 0
\(562\) 0 0
\(563\) 10836.0 + 18768.5i 0.811160 + 1.40497i 0.912053 + 0.410073i \(0.134497\pi\)
−0.100893 + 0.994897i \(0.532170\pi\)
\(564\) 0 0
\(565\) 7654.50 4419.33i 0.569960 0.329066i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −693.000 + 1200.31i −0.0510581 + 0.0884353i −0.890425 0.455130i \(-0.849593\pi\)
0.839367 + 0.543565i \(0.182926\pi\)
\(570\) 0 0
\(571\) 1162.00 0.0851632 0.0425816 0.999093i \(-0.486442\pi\)
0.0425816 + 0.999093i \(0.486442\pi\)
\(572\) 14040.0 13510.0i 1.02630 0.987555i
\(573\) 0 0
\(574\) 0 0
\(575\) 882.000 1527.67i 0.0639686 0.110797i
\(576\) 0 0
\(577\) 8045.38i 0.580474i 0.956955 + 0.290237i \(0.0937341\pi\)
−0.956955 + 0.290237i \(0.906266\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 4115.35i 0.294622i
\(581\) 6210.00 + 10756.0i 0.443432 + 0.768047i
\(582\) 0 0
\(583\) −11745.0 6780.98i −0.834354 0.481714i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 23922.0 + 13811.4i 1.68206 + 0.971135i 0.960293 + 0.278995i \(0.0900013\pi\)
0.721763 + 0.692140i \(0.243332\pi\)
\(588\) 0 0
\(589\) 2352.00 + 4073.78i 0.164537 + 0.284987i
\(590\) 0 0
\(591\) 0 0
\(592\) −6240.00 + 3602.67i −0.433214 + 0.250116i
\(593\) 275.396i 0.0190711i −0.999955 0.00953555i \(-0.996965\pi\)
0.999955 0.00953555i \(-0.00303531\pi\)
\(594\) 0 0
\(595\) 3159.00 5471.55i 0.217658 0.376994i
\(596\) 22644.0 + 13073.5i 1.55627 + 0.898510i
\(597\) 0 0
\(598\) 0 0
\(599\) −22356.0 −1.52494 −0.762472 0.647021i \(-0.776014\pi\)
−0.762472 + 0.647021i \(0.776014\pi\)
\(600\) 0 0
\(601\) 9041.50 15660.3i 0.613661 1.06289i −0.376956 0.926231i \(-0.623029\pi\)
0.990618 0.136662i \(-0.0436373\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 11352.0 6554.08i 0.764746 0.441526i
\(605\) −6160.50 + 3556.77i −0.413983 + 0.239013i
\(606\) 0 0
\(607\) −2740.00 4745.82i −0.183218 0.317342i 0.759757 0.650207i \(-0.225318\pi\)
−0.942975 + 0.332865i \(0.891985\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −2457.00 + 2364.25i −0.162683 + 0.156542i
\(612\) 0 0
\(613\) 15361.5 + 8868.97i 1.01215 + 0.584362i 0.911819 0.410592i \(-0.134678\pi\)
0.100326 + 0.994955i \(0.468011\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −8545.50 + 4933.75i −0.557583 + 0.321921i −0.752175 0.658963i \(-0.770995\pi\)
0.194592 + 0.980884i \(0.437662\pi\)
\(618\) 0 0
\(619\) 4115.35i 0.267221i −0.991034 0.133611i \(-0.957343\pi\)
0.991034 0.133611i \(-0.0426572\pi\)
\(620\) −4032.00 6983.63i −0.261176 0.452370i
\(621\) 0 0
\(622\) 0 0
\(623\) −15768.0 −1.01402
\(624\) 0 0
\(625\) 6229.00 0.398656
\(626\) 0 0
\(627\) 0 0
\(628\) −5036.00 8722.61i −0.319997 0.554252i
\(629\) 13172.2i 0.834995i
\(630\) 0 0
\(631\) −10968.0 + 6332.38i −0.691964 + 0.399506i −0.804347 0.594159i \(-0.797485\pi\)
0.112383 + 0.993665i \(0.464151\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 7488.00 + 4323.20i 0.467956 + 0.270175i
\(636\) 0 0
\(637\) 10692.5 2645.71i 0.665074 0.164563i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −1894.50 3281.37i −0.116737 0.202194i 0.801736 0.597678i \(-0.203910\pi\)
−0.918473 + 0.395484i \(0.870577\pi\)
\(642\) 0 0
\(643\) 14646.0 8455.87i 0.898261 0.518611i 0.0216255 0.999766i \(-0.493116\pi\)
0.876636 + 0.481155i \(0.159783\pi\)
\(644\) −1296.00 + 748.246i −0.0793006 + 0.0457842i
\(645\) 0 0
\(646\) 0 0
\(647\) −13896.0 + 24068.6i −0.844371 + 1.46249i 0.0417951 + 0.999126i \(0.486692\pi\)
−0.886166 + 0.463368i \(0.846641\pi\)
\(648\) 0 0
\(649\) −41040.0 −2.48222
\(650\) 0 0
\(651\) 0 0
\(652\) −20448.0 11805.7i −1.22823 0.709118i
\(653\) −297.000 + 514.419i −0.0177986 + 0.0308281i −0.874788 0.484507i \(-0.838999\pi\)
0.856989 + 0.515335i \(0.172332\pi\)
\(654\) 0 0
\(655\) 7669.52i 0.457516i
\(656\) −2016.00 + 1163.94i −0.119987 + 0.0692746i
\(657\) 0 0
\(658\) 0 0
\(659\) 8874.00 + 15370.2i 0.524555 + 0.908556i 0.999591 + 0.0285901i \(0.00910174\pi\)
−0.475036 + 0.879966i \(0.657565\pi\)
\(660\) 0 0
\(661\) 13675.5 + 7895.55i 0.804713 + 0.464601i 0.845117 0.534582i \(-0.179531\pi\)
−0.0404035 + 0.999183i \(0.512864\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −1134.00 654.715i −0.0661273 0.0381786i
\(666\) 0 0
\(667\) 891.000 + 1543.26i 0.0517236 + 0.0895879i
\(668\) 25107.8i 1.45427i
\(669\) 0 0
\(670\) 0 0
\(671\) 37360.3i 2.14945i
\(672\) 0 0
\(673\) −10466.5 + 18128.5i −0.599486 + 1.03834i 0.393411 + 0.919363i \(0.371295\pi\)
−0.992897 + 0.118977i \(0.962038\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 15548.0 8196.06i 0.884615 0.466321i
\(677\) −3402.00 −0.193131 −0.0965653 0.995327i \(-0.530786\pi\)
−0.0965653 + 0.995327i \(0.530786\pi\)
\(678\) 0 0
\(679\) −6012.00 + 10413.1i −0.339793 + 0.588539i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −21636.0 + 12491.6i −1.21212 + 0.699818i −0.963221 0.268711i \(-0.913402\pi\)
−0.248900 + 0.968529i \(0.580069\pi\)
\(684\) 0 0
\(685\) −2632.50 4559.62i −0.146836 0.254327i
\(686\) 0 0
\(687\) 0 0
\(688\) −5248.00 −0.290811
\(689\) −8482.50 8815.27i −0.469024 0.487424i
\(690\) 0 0
\(691\) 12009.0 + 6933.40i 0.661134 + 0.381706i 0.792709 0.609600i \(-0.208670\pi\)
−0.131575 + 0.991306i \(0.542003\pi\)
\(692\) 17064.0 29555.7i 0.937393 1.62361i
\(693\) 0 0
\(694\) 0 0
\(695\) 5058.00 2920.24i 0.276059 0.159383i
\(696\) 0 0
\(697\) 4255.65i 0.231269i
\(698\) 0 0
\(699\) 0 0
\(700\) −7056.00 4073.78i −0.380988 0.219964i
\(701\) 21906.0 1.18028 0.590141 0.807300i \(-0.299072\pi\)
0.590141 + 0.807300i \(0.299072\pi\)
\(702\) 0 0
\(703\) −2730.00 −0.146464
\(704\) −23040.0 13302.2i −1.23346 0.712136i
\(705\) 0 0
\(706\) 0 0
\(707\) 16367.9i 0.870690i
\(708\) 0 0
\(709\) −11308.5 + 6528.97i −0.599012 + 0.345840i −0.768653 0.639666i \(-0.779073\pi\)
0.169641 + 0.985506i \(0.445739\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −3024.00 1745.91i −0.158835 0.0917037i
\(714\) 0 0
\(715\) −12285.0 + 3039.75i −0.642564 + 0.158993i
\(716\) −24048.0 −1.25519
\(717\) 0 0
\(718\) 0 0
\(719\) −7110.00 12314.9i −0.368788 0.638759i 0.620589 0.784136i \(-0.286894\pi\)
−0.989376 + 0.145377i \(0.953560\pi\)
\(720\) 0 0
\(721\) 7146.00 4125.75i 0.369114 0.213108i
\(722\) 0 0
\(723\) 0 0
\(724\) 7492.00 + 12976.5i 0.384583 + 0.666117i
\(725\) −4851.00 + 8402.18i −0.248499 + 0.430413i
\(726\) 0 0
\(727\) −5282.00 −0.269462 −0.134731 0.990882i \(-0.543017\pi\)
−0.134731 + 0.990882i \(0.543017\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 4797.00 8308.65i 0.242713 0.420392i
\(732\) 0 0
\(733\) 11419.4i 0.575424i −0.957717 0.287712i \(-0.907105\pi\)
0.957717 0.287712i \(-0.0928945\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 18270.0 + 31644.6i 0.913140 + 1.58160i
\(738\) 0 0
\(739\) −17784.0 10267.6i −0.885244 0.511096i −0.0128599 0.999917i \(-0.504094\pi\)
−0.872384 + 0.488822i \(0.837427\pi\)
\(740\) 4680.00 0.232487
\(741\) 0 0
\(742\) 0 0
\(743\) 18036.0 + 10413.1i 0.890547 + 0.514158i 0.874121 0.485707i \(-0.161438\pi\)
0.0164258 + 0.999865i \(0.494771\pi\)
\(744\) 0 0
\(745\) −8491.50 14707.7i −0.417590 0.723287i
\(746\) 0 0
\(747\) 0 0
\(748\) 42120.0 24318.0i 2.05890 1.18871i
\(749\) 4676.54i 0.228140i
\(750\) 0 0
\(751\) 2417.00 4186.37i 0.117440 0.203412i −0.801312 0.598246i \(-0.795864\pi\)
0.918753 + 0.394834i \(0.129198\pi\)
\(752\) 4032.00 + 2327.88i 0.195521 + 0.112884i
\(753\) 0 0
\(754\) 0 0
\(755\) −8514.00 −0.410406
\(756\) 0 0
\(757\) −4523.00 + 7834.07i −0.217161 + 0.376135i −0.953939 0.300001i \(-0.903013\pi\)
0.736778 + 0.676135i \(0.236346\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 10422.0 6017.14i 0.496448 0.286625i −0.230797 0.973002i \(-0.574133\pi\)
0.727246 + 0.686377i \(0.240800\pi\)
\(762\) 0 0
\(763\) −3096.00 5362.43i −0.146897 0.254434i
\(764\) −10944.0 + 18955.6i −0.518246 + 0.897629i
\(765\) 0 0
\(766\) 0 0
\(767\) −35568.0 10267.6i −1.67443 0.483366i
\(768\) 0 0
\(769\) 32514.0 + 18772.0i 1.52469 + 0.880279i 0.999572 + 0.0292479i \(0.00931121\pi\)
0.525115 + 0.851031i \(0.324022\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 20826.2i 0.970920i
\(773\) 13608.0 7856.58i 0.633177 0.365565i −0.148804 0.988867i \(-0.547543\pi\)
0.781981 + 0.623302i \(0.214209\pi\)
\(774\) 0 0
\(775\) 19011.0i 0.881155i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −882.000 −0.0405660
\(780\) 0 0
\(781\) −24300.0 −1.11334
\(782\) 0 0
\(783\) 0 0
\(784\) −7520.00 13025.0i −0.342566 0.593341i
\(785\) 6541.96i 0.297443i
\(786\) 0 0
\(787\) −3252.00 + 1877.54i −0.147295 + 0.0850409i −0.571836 0.820368i \(-0.693769\pi\)
0.424541 + 0.905409i \(0.360435\pi\)
\(788\) 29763.6i 1.34554i
\(789\) 0 0
\(790\) 0 0
\(791\) −15309.0 8838.66i −0.688148 0.397303i
\(792\) 0 0