Properties

Label 117.4.q.b.10.1
Level $117$
Weight $4$
Character 117.10
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 10.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 117.10
Dual form 117.4.q.b.82.1

$q$-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 \(\left(\mathbb{Z}/117\mathbb{Z}\right)^\times\).

\(n\) \(28\) \(92\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(1\)

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 \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(3\) 0 0
\(4\) −4.00000 + 6.92820i −0.500000 + 0.866025i
\(5\) 5.19615i 0.464758i −0.972625 0.232379i \(-0.925349\pi\)
0.972625 0.232379i \(-0.0746510\pi\)
\(6\) 0 0
\(7\) 9.00000 + 5.19615i 0.485954 + 0.280566i 0.722895 0.690958i \(-0.242811\pi\)
−0.236940 + 0.971524i \(0.576145\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −45.0000 + 25.9808i −1.23346 + 0.712136i −0.967749 0.251918i \(-0.918939\pi\)
−0.265707 + 0.964054i \(0.585605\pi\)
\(12\) 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 0.0597414 + 0.998214i \(0.480972\pi\)
−0.894349 + 0.447369i \(0.852361\pi\)
\(18\) 0 0
\(19\) −21.0000 12.1244i −0.253565 0.146396i 0.367831 0.929893i \(-0.380101\pi\)
−0.621395 + 0.783497i \(0.713434\pi\)
\(20\) 36.0000 + 20.7846i 0.402492 + 0.232379i
\(21\) 0 0
\(22\) 0 0
\(23\) 9.00000 + 15.5885i 0.0815926 + 0.141323i 0.903934 0.427672i \(-0.140666\pi\)
−0.822342 + 0.568994i \(0.807333\pi\)
\(24\) 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 0.662890 0.748717i \(-0.269330\pi\)
−0.979853 + 0.199721i \(0.935996\pi\)
\(30\) 0 0
\(31\) 193.990i 1.12392i 0.827164 + 0.561961i \(0.189953\pi\)
−0.827164 + 0.561961i \(0.810047\pi\)
\(32\) 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 −0.267501 0.963558i \(-0.586198\pi\)
0.700715 + 0.713442i \(0.252865\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 31.5000 18.1865i 0.119987 0.0692746i −0.438805 0.898582i \(-0.644598\pi\)
0.558792 + 0.829308i \(0.311265\pi\)
\(42\) 0 0
\(43\) 41.0000 71.0141i 0.145406 0.251850i −0.784119 0.620611i \(-0.786885\pi\)
0.929524 + 0.368761i \(0.120218\pi\)
\(44\) 415.692i 1.42427i
\(45\) 0 0
\(46\) 0 0
\(47\) 72.7461i 0.225768i 0.993608 + 0.112884i \(0.0360089\pi\)
−0.993608 + 0.112884i \(0.963991\pi\)
\(48\) 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 0.999941 + 0.0108508i \(0.00345397\pi\)
0.509368 + 0.860549i \(0.329879\pi\)
\(60\) 0 0
\(61\) 359.500 622.672i 0.754578 1.30697i −0.191006 0.981589i \(-0.561175\pi\)
0.945584 0.325379i \(-0.105492\pi\)
\(62\) 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 −0.938950 0.344054i \(-0.888200\pi\)
−0.171516 + 0.985181i \(0.554866\pi\)
\(68\) −468.000 810.600i −0.834608 1.44558i
\(69\) 0 0
\(70\) 0 0
\(71\) 405.000 + 233.827i 0.676967 + 0.390847i 0.798711 0.601714i \(-0.205515\pi\)
−0.121744 + 0.992561i \(0.538849\pi\)
\(72\) 0 0
\(73\) 684.160i 1.09692i 0.836178 + 0.548458i \(0.184785\pi\)
−0.836178 + 0.548458i \(0.815215\pi\)
\(74\) 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 \(-0.709952\pi\)
0.612789 0.790247i \(-0.290048\pi\)
\(84\) 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 −0.568246 + 0.822859i \(0.692378\pi\)
−0.996740 + 0.0806862i \(0.974289\pi\)
\(90\) 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 −0.126517 0.991964i \(-0.540380\pi\)
−0.922325 + 0.386415i \(0.873713\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) −392.000 + 678.964i −0.392000 + 0.678964i
\(101\) 787.500 + 1363.99i 0.775833 + 1.34378i 0.934325 + 0.356423i \(0.116004\pi\)
−0.158491 + 0.987360i \(0.550663\pi\)
\(102\) 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 0.949585 0.313509i \(-0.101505\pi\)
−0.746299 + 0.665610i \(0.768171\pi\)
\(108\) 0 0
\(109\) 595.825i 0.523576i 0.965125 + 0.261788i \(0.0843120\pi\)
−0.965125 + 0.261788i \(0.915688\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 665.108i 0.561132i
\(113\) −850.500 + 1473.11i −0.708038 + 1.22636i 0.257546 + 0.966266i \(0.417086\pi\)
−0.965584 + 0.260092i \(0.916247\pi\)
\(114\) 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 0.995323 + 0.0966044i \(0.0307982\pi\)
−0.414000 + 0.910277i \(0.635868\pi\)
\(128\) 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 0.200777 0.979637i \(-0.435653\pi\)
−0.748002 + 0.663696i \(0.768987\pi\)
\(138\) 0 0
\(139\) −562.000 + 973.413i −0.342937 + 0.593984i −0.984977 0.172687i \(-0.944755\pi\)
0.642040 + 0.766671i \(0.278088\pi\)
\(140\) 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 −0.997609 0.0691115i \(-0.977984\pi\)
−0.558657 0.829399i \(-0.688683\pi\)
\(150\) 0 0
\(151\) 1638.52i 0.883052i −0.897248 0.441526i \(-0.854437\pi\)
0.897248 0.441526i \(-0.145563\pi\)
\(152\) 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 0.966659 0.256066i \(-0.0824264\pi\)
0.261570 + 0.965185i \(0.415760\pi\)
\(164\) 290.985i 0.138549i
\(165\) 0 0
\(166\) 0 0
\(167\) 2718.00 1569.24i 1.25943 0.727133i 0.286468 0.958090i \(-0.407519\pi\)
0.972964 + 0.230956i \(0.0741855\pi\)
\(168\) 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 0.167083 0.985943i \(-0.446565\pi\)
0.770310 0.637669i \(-0.220101\pi\)
\(174\) 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 0.988033 + 0.154243i \(0.0492939\pi\)
−0.360438 + 0.932783i \(0.617373\pi\)
\(180\) 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 0.481529 + 0.876430i \(0.340082\pi\)
−0.999775 + 0.0211985i \(0.993252\pi\)
\(192\) 0 0
\(193\) −2254.50 + 1301.64i −0.840842 + 0.485460i −0.857550 0.514400i \(-0.828015\pi\)
0.0167085 + 0.999860i \(0.494681\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 1880.00 0.685131
\(197\) −3222.00 + 1860.22i −1.16527 + 0.672768i −0.952561 0.304347i \(-0.901562\pi\)
−0.212708 + 0.977116i \(0.568228\pi\)
\(198\) 0 0
\(199\) −599.000 + 1037.50i −0.213377 + 0.369579i −0.952769 0.303695i \(-0.901780\pi\)
0.739392 + 0.673275i \(0.235113\pi\)
\(200\) 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 0.602260 0.798300i \(-0.294267\pi\)
−0.992478 + 0.122422i \(0.960934\pi\)
\(212\) −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 −0.740900 0.671615i \(-0.765601\pi\)
0.211186 + 0.977446i \(0.432267\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −1863.00 1075.60i −0.544721 0.314495i 0.202269 0.979330i \(-0.435168\pi\)
−0.746990 + 0.664835i \(0.768502\pi\)
\(228\) 0 0
\(229\) 3471.03i 1.00162i 0.865556 + 0.500812i \(0.166965\pi\)
−0.865556 + 0.500812i \(0.833035\pi\)
\(230\) 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 \(0.206153\pi\)
−0.797505 + 0.603312i \(0.793847\pi\)
\(240\) 0 0
\(241\) −361.500 208.712i −0.0966235 0.0557856i 0.450910 0.892570i \(-0.351100\pi\)
−0.547533 + 0.836784i \(0.684433\pi\)
\(242\) 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 −0.483807 0.875175i \(-0.660746\pi\)
0.999827 0.0185985i \(-0.00592043\pi\)
\(252\) 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 0.961108 0.276172i \(-0.0890660\pi\)
−0.719726 + 0.694258i \(0.755733\pi\)
\(258\) 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 0.906036 0.423201i \(-0.139094\pi\)
−0.819521 + 0.573050i \(0.805760\pi\)
\(264\) 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 −0.960333 0.278855i \(-0.910045\pi\)
0.721662 + 0.692246i \(0.243378\pi\)
\(270\) 0 0
\(271\) 594.000 342.946i 0.133147 0.0768727i −0.431947 0.901899i \(-0.642173\pi\)
0.565094 + 0.825026i \(0.308840\pi\)
\(272\) 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 −0.993415 0.114569i \(-0.963451\pi\)
0.595927 + 0.803039i \(0.296785\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 1719.93i 0.365132i 0.983194 + 0.182566i \(0.0584404\pi\)
−0.983194 + 0.182566i \(0.941560\pi\)
\(282\) 0 0
\(283\) 913.000 + 1581.36i 0.191775 + 0.332163i 0.945838 0.324638i \(-0.105242\pi\)
−0.754064 + 0.656801i \(0.771909\pi\)
\(284\) −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 0.542885 0.839807i \(-0.317332\pi\)
−0.455852 + 0.890056i \(0.650665\pi\)
\(294\) 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 \(0.0580256\pi\)
−0.983431 + 0.181285i \(0.941974\pi\)
\(308\) 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 \(-0.783357\pi\)
0.777193 0.629262i \(-0.216643\pi\)
\(318\) 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 0.998403 0.0564889i \(-0.0179906\pi\)
0.450281 + 0.892887i \(0.351324\pi\)
\(332\) 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 −0.710041 0.704160i \(-0.751324\pi\)
0.964841 + 0.262834i \(0.0846570\pi\)
\(348\) 0 0
\(349\) −9132.00 + 5272.36i −1.40064 + 0.808662i −0.994459 0.105129i \(-0.966475\pi\)
−0.406185 + 0.913791i \(0.633141\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 2146.50 1239.28i 0.323645 0.186856i −0.329371 0.944201i \(-0.606837\pi\)
0.653016 + 0.757344i \(0.273503\pi\)
\(354\) 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 \(0.130294\pi\)
−0.917387 + 0.397995i \(0.869706\pi\)
\(360\) 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 0.965846 + 0.259118i \(0.0834318\pi\)
−0.258520 + 0.966006i \(0.583235\pi\)
\(368\) 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 −0.493225 0.869902i \(-0.664182\pi\)
0.999970 0.00780555i \(-0.00248461\pi\)
\(374\) 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 −0.687224 0.726445i \(-0.741171\pi\)
0.285508 + 0.958376i \(0.407838\pi\)
\(380\) −504.000 872.954i −0.0680386 0.117846i
\(381\) 0 0
\(382\) 0 0
\(383\) 5004.00 + 2889.06i 0.667604 + 0.385442i 0.795168 0.606389i \(-0.207382\pi\)
−0.127564 + 0.991830i \(0.540716\pi\)
\(384\) 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 0.606639 0.794978i \(-0.292518\pi\)
−0.385152 + 0.922853i \(0.625851\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) −3136.00 5431.71i −0.392000 0.678964i
\(401\) −7195.50 + 4154.32i −0.896075 + 0.517349i −0.875925 0.482448i \(-0.839748\pi\)
−0.0201504 + 0.999797i \(0.506414\pi\)
\(402\) 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 −0.157005 0.987598i \(-0.550184\pi\)
−0.933787 + 0.357829i \(0.883517\pi\)
\(410\) 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 0.961695 0.274123i \(-0.0883875\pi\)
−0.718245 + 0.695790i \(0.755054\pi\)
\(420\) 0 0
\(421\) 14471.3i 1.67527i 0.546233 + 0.837633i \(0.316061\pi\)
−0.546233 + 0.837633i \(0.683939\pi\)
\(422\) 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 −0.146646 0.989189i \(-0.546848\pi\)
0.783340 + 0.621594i \(0.213515\pi\)
\(432\) 0 0
\(433\) 3302.50 5720.10i 0.366531 0.634851i −0.622489 0.782628i \(-0.713879\pi\)
0.989021 + 0.147778i \(0.0472120\pi\)
\(434\) 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 0.999171 0.0407023i \(-0.0129595\pi\)
−0.534835 + 0.844957i \(0.679626\pi\)
\(440\) 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 0.356525 0.934286i \(-0.383962\pi\)
−0.630853 + 0.775902i \(0.717295\pi\)
\(450\) 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 −0.622485 0.782632i \(-0.713877\pi\)
0.366536 + 0.930404i \(0.380543\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 748.246i 0.0758416i
\(461\) −3118.50 1800.47i −0.315061 0.181900i 0.334128 0.942528i \(-0.391558\pi\)
−0.649189 + 0.760627i \(0.724892\pi\)
\(462\) 0 0
\(463\) 2677.75i 0.268781i 0.990928 + 0.134391i \(0.0429077\pi\)
−0.990928 + 0.134391i \(0.957092\pi\)
\(464\) −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 −0.544810 0.838560i \(-0.683398\pi\)
0.453809 + 0.891099i \(0.350065\pi\)
\(480\) 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 −0.387671 0.921798i \(-0.626720\pi\)
−0.992136 + 0.125166i \(0.960054\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 225.000 + 389.711i 0.0206805 + 0.0358196i 0.876180 0.481983i \(-0.160083\pi\)
−0.855500 + 0.517803i \(0.826750\pi\)
\(492\) 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 \(0.202037\pi\)
−0.805239 + 0.592950i \(0.797963\pi\)
\(500\) 8028.00 + 4634.97i 0.718046 + 0.414564i
\(501\) 0 0
\(502\) 0 0
\(503\) 2673.00 4629.77i 0.236945 0.410400i −0.722891 0.690962i \(-0.757187\pi\)
0.959836 + 0.280561i \(0.0905206\pi\)
\(504\) 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 −0.262207 0.965012i \(-0.584450\pi\)
0.704621 + 0.709583i \(0.251117\pi\)
\(510\) 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 −0.822184 0.569222i \(-0.807245\pi\)
−0.0818685 0.996643i \(-0.526089\pi\)
\(524\) −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 \(-0.931540\pi\)
0.976960 0.213421i \(-0.0684605\pi\)
\(542\) 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 −0.621751 0.783215i \(-0.713578\pi\)
0.367409 + 0.930060i \(0.380245\pi\)
\(558\) 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 −0.100893 0.994897i \(-0.532170\pi\)
0.912053 0.410073i \(-0.134497\pi\)
\(564\) 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 0.839367 0.543565i \(-0.182926\pi\)
−0.890425 + 0.455130i \(0.849593\pi\)
\(570\) 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 \(-0.906266\pi\)
0.956955 0.290237i \(-0.0937341\pi\)
\(578\) 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 0.721763 0.692140i \(-0.243332\pi\)
0.960293 0.278995i \(-0.0900013\pi\)
\(588\) 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 \(0.00303531\pi\)
−0.999955 + 0.00953555i \(0.996965\pi\)
\(594\) 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 0.990618 + 0.136662i \(0.0436373\pi\)
−0.376956 + 0.926231i \(0.623029\pi\)
\(602\) 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 −0.942975 0.332865i \(-0.891985\pi\)
0.759757 + 0.650207i \(0.225318\pi\)
\(608\) 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 0.100326 0.994955i \(-0.468011\pi\)
0.911819 + 0.410592i \(0.134678\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −8545.50 4933.75i −0.557583 0.321921i 0.194592 0.980884i \(-0.437662\pi\)
−0.752175 + 0.658963i \(0.770995\pi\)
\(618\) 0 0
\(619\) 4115.35i 0.267221i 0.991034 + 0.133611i \(0.0426572\pi\)
−0.991034 + 0.133611i \(0.957343\pi\)
\(620\) −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 0.112383 0.993665i \(-0.464151\pi\)
−0.804347 + 0.594159i \(0.797485\pi\)
\(632\) 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 −0.918473 0.395484i \(-0.870577\pi\)
0.801736 + 0.597678i \(0.203910\pi\)
\(642\) 0 0
\(643\) 14646.0 + 8455.87i 0.898261 + 0.518611i 0.876636 0.481155i \(-0.159783\pi\)
0.0216255 + 0.999766i \(0.493116\pi\)
\(644\) −1296.00 748.246i −0.0793006 0.0457842i
\(645\) 0 0
\(646\) 0 0
\(647\) −13896.0 24068.6i −0.844371 1.46249i −0.886166 0.463368i \(-0.846641\pi\)
0.0417951 0.999126i \(-0.486692\pi\)
\(648\) 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 0.856989 0.515335i \(-0.172332\pi\)
−0.874788 + 0.484507i \(0.838999\pi\)
\(654\) 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 −0.475036 0.879966i \(-0.657565\pi\)
0.999591 0.0285901i \(-0.00910174\pi\)
\(660\) 0 0
\(661\) 13675.5 7895.55i 0.804713 0.464601i −0.0404035 0.999183i \(-0.512864\pi\)
0.845117 + 0.534582i \(0.179531\pi\)
\(662\) 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 −0.992897 0.118977i \(-0.962038\pi\)
0.393411 0.919363i \(-0.371295\pi\)
\(674\) 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 −0.248900 0.968529i \(-0.580069\pi\)
−0.963221 + 0.268711i \(0.913402\pi\)
\(684\) 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 −0.131575 0.991306i \(-0.542003\pi\)
0.792709 + 0.609600i \(0.208670\pi\)
\(692\) 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 0.169641 0.985506i \(-0.445739\pi\)
−0.768653 + 0.639666i \(0.779073\pi\)
\(710\) 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 −0.989376 0.145377i \(-0.953560\pi\)
0.620589 + 0.784136i \(0.286894\pi\)
\(720\) 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 \(0.0928945\pi\)
−0.957717 + 0.287712i \(0.907105\pi\)
\(734\) 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 −0.872384 0.488822i \(-0.837427\pi\)
−0.0128599 + 0.999917i \(0.504094\pi\)
\(740\) 4680.00 0.232487
\(741\) 0 0
\(742\) 0 0
\(743\) 18036.0 10413.1i 0.890547 0.514158i 0.0164258 0.999865i \(-0.494771\pi\)
0.874121 + 0.485707i \(0.161438\pi\)
\(744\) 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 0.918753 0.394834i \(-0.129198\pi\)
−0.801312 + 0.598246i \(0.795864\pi\)
\(752\) 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 0.736778 0.676135i \(-0.236346\pi\)
−0.953939 + 0.300001i \(0.903013\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 10422.0 + 6017.14i 0.496448 + 0.286625i 0.727246 0.686377i \(-0.240800\pi\)
−0.230797 + 0.973002i \(0.574133\pi\)
\(762\) 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 0.525115 0.851031i \(-0.324022\pi\)
0.999572 0.0292479i \(-0.00931121\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 20826.2i 0.970920i
\(773\) 13608.0 + 7856.58i 0.633177 + 0.365565i 0.781981 0.623302i \(-0.214209\pi\)
−0.148804 + 0.988867i \(0.547543\pi\)
\(774\) 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 0.424541 0.905409i \(-0.360435\pi\)
−0.571836 + 0.820368i \(0.693769\pi\)
\(788\) 29763.6i 1.34554i
\(789\) 0 0
\(790\) 0 0
\(791\) −15309.0 + 8838.66i −0.688148 + 0.397303i
\(792\) 0 0