Properties

Label 117.4.b.d.64.2
Level $117$
Weight $4$
Character 117.64
Analytic conductor $6.903$
Analytic rank $0$
Dimension $4$
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.b (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.90322347067\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: 4.0.5054412.1
Defining polynomial: \( x^{4} + 29x^{2} + 48 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: no (minimal twist has level 39)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 64.2
Root \(-1.32750i\) of defining polynomial
Character \(\chi\) \(=\) 117.64
Dual form 117.4.b.d.64.3

$q$-expansion

\(f(q)\) \(=\) \(q-1.32750i q^{2} +6.23774 q^{4} -15.4241i q^{5} +7.96501i q^{7} -18.9006i q^{8} +O(q^{10})\) \(q-1.32750i q^{2} +6.23774 q^{4} -15.4241i q^{5} +7.96501i q^{7} -18.9006i q^{8} -20.4755 q^{10} +12.7691i q^{11} +(7.47548 - 46.2722i) q^{13} +10.5736 q^{14} +24.8113 q^{16} -54.0000 q^{17} -84.5794i q^{19} -96.2113i q^{20} +16.9510 q^{22} +122.853 q^{23} -112.902 q^{25} +(-61.4264 - 9.92371i) q^{26} +49.6837i q^{28} -140.853 q^{29} -116.439i q^{31} -184.142i q^{32} +71.6851i q^{34} +122.853 q^{35} +433.898i q^{37} -112.279 q^{38} -291.525 q^{40} +205.823i q^{41} +418.853 q^{43} +79.6501i q^{44} -163.087i q^{46} +485.861i q^{47} +279.559 q^{49} +149.877i q^{50} +(46.6301 - 288.634i) q^{52} +674.559 q^{53} +196.951 q^{55} +150.544 q^{56} +186.982i q^{58} +186.226i q^{59} -671.902 q^{61} -154.574 q^{62} -45.9584 q^{64} +(-713.706 - 115.302i) q^{65} +14.0364i q^{67} -336.838 q^{68} -163.087i q^{70} +346.789i q^{71} +832.900i q^{73} +576.000 q^{74} -527.584i q^{76} -101.706 q^{77} -335.608 q^{79} -382.691i q^{80} +273.230 q^{82} -568.797i q^{83} +832.900i q^{85} -556.028i q^{86} +241.343 q^{88} -236.671i q^{89} +(368.559 + 59.5423i) q^{91} +766.324 q^{92} +644.981 q^{94} -1304.56 q^{95} -1278.94i q^{97} -371.115i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 26 q^{4}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - 26 q^{4} + 20 q^{10} - 72 q^{13} + 348 q^{14} + 354 q^{16} - 216 q^{17} - 136 q^{22} - 120 q^{23} - 44 q^{25} + 60 q^{26} + 48 q^{29} - 120 q^{35} + 468 q^{38} - 1268 q^{40} + 1064 q^{43} - 716 q^{49} + 1766 q^{52} + 864 q^{53} + 584 q^{55} - 3372 q^{56} - 2280 q^{61} - 924 q^{62} - 1050 q^{64} - 1632 q^{65} + 1404 q^{68} + 2304 q^{74} + 816 q^{77} + 288 q^{79} - 28 q^{82} + 2392 q^{88} - 360 q^{91} + 8568 q^{92} + 6656 q^{94} - 3384 q^{95}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(28\) \(92\)
\(\chi(n)\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.32750i 0.469343i −0.972075 0.234671i \(-0.924599\pi\)
0.972075 0.234671i \(-0.0754014\pi\)
\(3\) 0 0
\(4\) 6.23774 0.779717
\(5\) 15.4241i 1.37957i −0.724014 0.689785i \(-0.757705\pi\)
0.724014 0.689785i \(-0.242295\pi\)
\(6\) 0 0
\(7\) 7.96501i 0.430070i 0.976606 + 0.215035i \(0.0689866\pi\)
−0.976606 + 0.215035i \(0.931013\pi\)
\(8\) 18.9006i 0.835297i
\(9\) 0 0
\(10\) −20.4755 −0.647491
\(11\) 12.7691i 0.350002i 0.984568 + 0.175001i \(0.0559928\pi\)
−0.984568 + 0.175001i \(0.944007\pi\)
\(12\) 0 0
\(13\) 7.47548 46.2722i 0.159487 0.987200i
\(14\) 10.5736 0.201850
\(15\) 0 0
\(16\) 24.8113 0.387677
\(17\) −54.0000 −0.770407 −0.385204 0.922832i \(-0.625869\pi\)
−0.385204 + 0.922832i \(0.625869\pi\)
\(18\) 0 0
\(19\) 84.5794i 1.02126i −0.859802 0.510628i \(-0.829413\pi\)
0.859802 0.510628i \(-0.170587\pi\)
\(20\) 96.2113i 1.07568i
\(21\) 0 0
\(22\) 16.9510 0.164271
\(23\) 122.853 1.11376 0.556882 0.830591i \(-0.311997\pi\)
0.556882 + 0.830591i \(0.311997\pi\)
\(24\) 0 0
\(25\) −112.902 −0.903215
\(26\) −61.4264 9.92371i −0.463335 0.0748538i
\(27\) 0 0
\(28\) 49.6837i 0.335333i
\(29\) −140.853 −0.901921 −0.450961 0.892544i \(-0.648919\pi\)
−0.450961 + 0.892544i \(0.648919\pi\)
\(30\) 0 0
\(31\) 116.439i 0.674617i −0.941394 0.337309i \(-0.890483\pi\)
0.941394 0.337309i \(-0.109517\pi\)
\(32\) 184.142i 1.01725i
\(33\) 0 0
\(34\) 71.6851i 0.361585i
\(35\) 122.853 0.593312
\(36\) 0 0
\(37\) 433.898i 1.92790i 0.266081 + 0.963951i \(0.414271\pi\)
−0.266081 + 0.963951i \(0.585729\pi\)
\(38\) −112.279 −0.479319
\(39\) 0 0
\(40\) −291.525 −1.15235
\(41\) 205.823i 0.784003i 0.919965 + 0.392002i \(0.128217\pi\)
−0.919965 + 0.392002i \(0.871783\pi\)
\(42\) 0 0
\(43\) 418.853 1.48545 0.742726 0.669595i \(-0.233532\pi\)
0.742726 + 0.669595i \(0.233532\pi\)
\(44\) 79.6501i 0.272902i
\(45\) 0 0
\(46\) 163.087i 0.522737i
\(47\) 485.861i 1.50787i 0.656947 + 0.753937i \(0.271848\pi\)
−0.656947 + 0.753937i \(0.728152\pi\)
\(48\) 0 0
\(49\) 279.559 0.815040
\(50\) 149.877i 0.423918i
\(51\) 0 0
\(52\) 46.6301 288.634i 0.124354 0.769737i
\(53\) 674.559 1.74826 0.874130 0.485693i \(-0.161433\pi\)
0.874130 + 0.485693i \(0.161433\pi\)
\(54\) 0 0
\(55\) 196.951 0.482852
\(56\) 150.544 0.359236
\(57\) 0 0
\(58\) 186.982i 0.423310i
\(59\) 186.226i 0.410925i 0.978665 + 0.205462i \(0.0658698\pi\)
−0.978665 + 0.205462i \(0.934130\pi\)
\(60\) 0 0
\(61\) −671.902 −1.41030 −0.705149 0.709059i \(-0.749120\pi\)
−0.705149 + 0.709059i \(0.749120\pi\)
\(62\) −154.574 −0.316627
\(63\) 0 0
\(64\) −45.9584 −0.0897626
\(65\) −713.706 115.302i −1.36191 0.220023i
\(66\) 0 0
\(67\) 14.0364i 0.0255944i 0.999918 + 0.0127972i \(0.00407358\pi\)
−0.999918 + 0.0127972i \(0.995926\pi\)
\(68\) −336.838 −0.600700
\(69\) 0 0
\(70\) 163.087i 0.278467i
\(71\) 346.789i 0.579665i 0.957077 + 0.289833i \(0.0935996\pi\)
−0.957077 + 0.289833i \(0.906400\pi\)
\(72\) 0 0
\(73\) 832.900i 1.33539i 0.744435 + 0.667695i \(0.232719\pi\)
−0.744435 + 0.667695i \(0.767281\pi\)
\(74\) 576.000 0.904846
\(75\) 0 0
\(76\) 527.584i 0.796290i
\(77\) −101.706 −0.150525
\(78\) 0 0
\(79\) −335.608 −0.477960 −0.238980 0.971025i \(-0.576813\pi\)
−0.238980 + 0.971025i \(0.576813\pi\)
\(80\) 382.691i 0.534827i
\(81\) 0 0
\(82\) 273.230 0.367966
\(83\) 568.797i 0.752212i −0.926577 0.376106i \(-0.877263\pi\)
0.926577 0.376106i \(-0.122737\pi\)
\(84\) 0 0
\(85\) 832.900i 1.06283i
\(86\) 556.028i 0.697186i
\(87\) 0 0
\(88\) 241.343 0.292355
\(89\) 236.671i 0.281877i −0.990018 0.140939i \(-0.954988\pi\)
0.990018 0.140939i \(-0.0450120\pi\)
\(90\) 0 0
\(91\) 368.559 + 59.5423i 0.424565 + 0.0685904i
\(92\) 766.324 0.868422
\(93\) 0 0
\(94\) 644.981 0.707710
\(95\) −1304.56 −1.40889
\(96\) 0 0
\(97\) 1278.94i 1.33873i −0.742934 0.669365i \(-0.766566\pi\)
0.742934 0.669365i \(-0.233434\pi\)
\(98\) 371.115i 0.382533i
\(99\) 0 0
\(100\) −704.253 −0.704253
\(101\) 632.264 0.622898 0.311449 0.950263i \(-0.399186\pi\)
0.311449 + 0.950263i \(0.399186\pi\)
\(102\) 0 0
\(103\) −1506.26 −1.44094 −0.720469 0.693487i \(-0.756073\pi\)
−0.720469 + 0.693487i \(0.756073\pi\)
\(104\) −874.574 141.291i −0.824606 0.133219i
\(105\) 0 0
\(106\) 895.478i 0.820533i
\(107\) 1268.56 1.14613 0.573066 0.819509i \(-0.305754\pi\)
0.573066 + 0.819509i \(0.305754\pi\)
\(108\) 0 0
\(109\) 347.425i 0.305296i 0.988281 + 0.152648i \(0.0487801\pi\)
−0.988281 + 0.152648i \(0.951220\pi\)
\(110\) 261.453i 0.226623i
\(111\) 0 0
\(112\) 197.622i 0.166728i
\(113\) −659.706 −0.549203 −0.274601 0.961558i \(-0.588546\pi\)
−0.274601 + 0.961558i \(0.588546\pi\)
\(114\) 0 0
\(115\) 1894.89i 1.53652i
\(116\) −878.603 −0.703244
\(117\) 0 0
\(118\) 247.215 0.192865
\(119\) 430.111i 0.331329i
\(120\) 0 0
\(121\) 1167.95 0.877499
\(122\) 891.951i 0.661913i
\(123\) 0 0
\(124\) 726.319i 0.526011i
\(125\) 186.602i 0.133521i
\(126\) 0 0
\(127\) −275.019 −0.192157 −0.0960787 0.995374i \(-0.530630\pi\)
−0.0960787 + 0.995374i \(0.530630\pi\)
\(128\) 1412.13i 0.975121i
\(129\) 0 0
\(130\) −153.064 + 947.446i −0.103266 + 0.639204i
\(131\) 1183.97 0.789648 0.394824 0.918757i \(-0.370805\pi\)
0.394824 + 0.918757i \(0.370805\pi\)
\(132\) 0 0
\(133\) 673.676 0.439211
\(134\) 18.6334 0.0120125
\(135\) 0 0
\(136\) 1020.63i 0.643519i
\(137\) 2557.36i 1.59482i 0.603438 + 0.797410i \(0.293797\pi\)
−0.603438 + 0.797410i \(0.706203\pi\)
\(138\) 0 0
\(139\) 545.736 0.333012 0.166506 0.986040i \(-0.446751\pi\)
0.166506 + 0.986040i \(0.446751\pi\)
\(140\) 766.324 0.462616
\(141\) 0 0
\(142\) 460.362 0.272062
\(143\) 590.853 + 95.4549i 0.345522 + 0.0558205i
\(144\) 0 0
\(145\) 2172.52i 1.24426i
\(146\) 1105.68 0.626756
\(147\) 0 0
\(148\) 2706.54i 1.50322i
\(149\) 1376.78i 0.756981i −0.925605 0.378491i \(-0.876443\pi\)
0.925605 0.378491i \(-0.123557\pi\)
\(150\) 0 0
\(151\) 2733.47i 1.47316i −0.676352 0.736579i \(-0.736440\pi\)
0.676352 0.736579i \(-0.263560\pi\)
\(152\) −1598.60 −0.853052
\(153\) 0 0
\(154\) 135.015i 0.0706479i
\(155\) −1795.97 −0.930683
\(156\) 0 0
\(157\) 1029.97 0.523570 0.261785 0.965126i \(-0.415689\pi\)
0.261785 + 0.965126i \(0.415689\pi\)
\(158\) 445.520i 0.224327i
\(159\) 0 0
\(160\) −2840.22 −1.40337
\(161\) 978.524i 0.478997i
\(162\) 0 0
\(163\) 2882.91i 1.38532i 0.721264 + 0.692660i \(0.243561\pi\)
−0.721264 + 0.692660i \(0.756439\pi\)
\(164\) 1283.87i 0.611301i
\(165\) 0 0
\(166\) −755.079 −0.353045
\(167\) 1153.90i 0.534679i 0.963602 + 0.267340i \(0.0861446\pi\)
−0.963602 + 0.267340i \(0.913855\pi\)
\(168\) 0 0
\(169\) −2085.23 691.814i −0.949128 0.314890i
\(170\) 1105.68 0.498832
\(171\) 0 0
\(172\) 2612.69 1.15823
\(173\) −1688.85 −0.742203 −0.371101 0.928592i \(-0.621020\pi\)
−0.371101 + 0.928592i \(0.621020\pi\)
\(174\) 0 0
\(175\) 899.265i 0.388446i
\(176\) 316.817i 0.135687i
\(177\) 0 0
\(178\) −314.181 −0.132297
\(179\) −942.793 −0.393674 −0.196837 0.980436i \(-0.563067\pi\)
−0.196837 + 0.980436i \(0.563067\pi\)
\(180\) 0 0
\(181\) −482.030 −0.197950 −0.0989751 0.995090i \(-0.531556\pi\)
−0.0989751 + 0.995090i \(0.531556\pi\)
\(182\) 79.0425 489.262i 0.0321924 0.199267i
\(183\) 0 0
\(184\) 2322.00i 0.930325i
\(185\) 6692.47 2.65968
\(186\) 0 0
\(187\) 689.530i 0.269644i
\(188\) 3030.67i 1.17572i
\(189\) 0 0
\(190\) 1731.80i 0.661254i
\(191\) −4223.32 −1.59994 −0.799971 0.600039i \(-0.795152\pi\)
−0.799971 + 0.600039i \(0.795152\pi\)
\(192\) 0 0
\(193\) 229.092i 0.0854424i 0.999087 + 0.0427212i \(0.0136027\pi\)
−0.999087 + 0.0427212i \(0.986397\pi\)
\(194\) −1697.80 −0.628323
\(195\) 0 0
\(196\) 1743.81 0.635501
\(197\) 228.335i 0.0825798i 0.999147 + 0.0412899i \(0.0131467\pi\)
−0.999147 + 0.0412899i \(0.986853\pi\)
\(198\) 0 0
\(199\) −2939.02 −1.04694 −0.523471 0.852043i \(-0.675363\pi\)
−0.523471 + 0.852043i \(0.675363\pi\)
\(200\) 2133.92i 0.754453i
\(201\) 0 0
\(202\) 839.332i 0.292352i
\(203\) 1121.89i 0.387889i
\(204\) 0 0
\(205\) 3174.63 1.08159
\(206\) 1999.57i 0.676294i
\(207\) 0 0
\(208\) 185.476 1148.07i 0.0618292 0.382714i
\(209\) 1080.00 0.357441
\(210\) 0 0
\(211\) −1607.02 −0.524321 −0.262161 0.965024i \(-0.584435\pi\)
−0.262161 + 0.965024i \(0.584435\pi\)
\(212\) 4207.72 1.36315
\(213\) 0 0
\(214\) 1684.01i 0.537929i
\(215\) 6460.42i 2.04929i
\(216\) 0 0
\(217\) 927.441 0.290133
\(218\) 461.207 0.143288
\(219\) 0 0
\(220\) 1228.53 0.376488
\(221\) −403.676 + 2498.70i −0.122870 + 0.760546i
\(222\) 0 0
\(223\) 130.867i 0.0392981i 0.999807 + 0.0196490i \(0.00625488\pi\)
−0.999807 + 0.0196490i \(0.993745\pi\)
\(224\) 1466.69 0.437489
\(225\) 0 0
\(226\) 875.761i 0.257764i
\(227\) 4325.19i 1.26464i −0.774708 0.632319i \(-0.782103\pi\)
0.774708 0.632319i \(-0.217897\pi\)
\(228\) 0 0
\(229\) 2621.57i 0.756499i 0.925704 + 0.378250i \(0.123474\pi\)
−0.925704 + 0.378250i \(0.876526\pi\)
\(230\) −2515.47 −0.721153
\(231\) 0 0
\(232\) 2662.21i 0.753373i
\(233\) −4643.12 −1.30550 −0.652748 0.757575i \(-0.726384\pi\)
−0.652748 + 0.757575i \(0.726384\pi\)
\(234\) 0 0
\(235\) 7493.95 2.08022
\(236\) 1161.63i 0.320405i
\(237\) 0 0
\(238\) −570.972 −0.155507
\(239\) 6696.69i 1.81244i −0.422809 0.906219i \(-0.638956\pi\)
0.422809 0.906219i \(-0.361044\pi\)
\(240\) 0 0
\(241\) 2301.47i 0.615148i −0.951524 0.307574i \(-0.900483\pi\)
0.951524 0.307574i \(-0.0995171\pi\)
\(242\) 1550.46i 0.411848i
\(243\) 0 0
\(244\) −4191.15 −1.09963
\(245\) 4311.93i 1.12440i
\(246\) 0 0
\(247\) −3913.68 632.272i −1.00818 0.162876i
\(248\) −2200.78 −0.563506
\(249\) 0 0
\(250\) −247.714 −0.0626673
\(251\) 828.000 0.208219 0.104109 0.994566i \(-0.466801\pi\)
0.104109 + 0.994566i \(0.466801\pi\)
\(252\) 0 0
\(253\) 1568.72i 0.389820i
\(254\) 365.088i 0.0901877i
\(255\) 0 0
\(256\) −2242.27 −0.547429
\(257\) 884.763 0.214747 0.107374 0.994219i \(-0.465756\pi\)
0.107374 + 0.994219i \(0.465756\pi\)
\(258\) 0 0
\(259\) −3456.00 −0.829133
\(260\) −4451.91 719.226i −1.06191 0.171556i
\(261\) 0 0
\(262\) 1571.72i 0.370616i
\(263\) 8343.94 1.95631 0.978155 0.207878i \(-0.0666557\pi\)
0.978155 + 0.207878i \(0.0666557\pi\)
\(264\) 0 0
\(265\) 10404.4i 2.41185i
\(266\) 894.306i 0.206141i
\(267\) 0 0
\(268\) 87.5556i 0.0199564i
\(269\) −2762.56 −0.626157 −0.313078 0.949727i \(-0.601360\pi\)
−0.313078 + 0.949727i \(0.601360\pi\)
\(270\) 0 0
\(271\) 3116.54i 0.698585i 0.937014 + 0.349293i \(0.113578\pi\)
−0.937014 + 0.349293i \(0.886422\pi\)
\(272\) −1339.81 −0.298669
\(273\) 0 0
\(274\) 3394.91 0.748517
\(275\) 1441.65i 0.316127i
\(276\) 0 0
\(277\) 502.060 0.108902 0.0544510 0.998516i \(-0.482659\pi\)
0.0544510 + 0.998516i \(0.482659\pi\)
\(278\) 724.465i 0.156297i
\(279\) 0 0
\(280\) 2322.00i 0.495592i
\(281\) 6607.56i 1.40275i 0.712791 + 0.701377i \(0.247431\pi\)
−0.712791 + 0.701377i \(0.752569\pi\)
\(282\) 0 0
\(283\) 4368.98 0.917699 0.458850 0.888514i \(-0.348262\pi\)
0.458850 + 0.888514i \(0.348262\pi\)
\(284\) 2163.18i 0.451975i
\(285\) 0 0
\(286\) 126.717 784.358i 0.0261990 0.162168i
\(287\) −1639.38 −0.337176
\(288\) 0 0
\(289\) −1997.00 −0.406473
\(290\) 2884.03 0.583986
\(291\) 0 0
\(292\) 5195.41i 1.04123i
\(293\) 5348.12i 1.06635i 0.846005 + 0.533175i \(0.179001\pi\)
−0.846005 + 0.533175i \(0.820999\pi\)
\(294\) 0 0
\(295\) 2872.36 0.566900
\(296\) 8200.94 1.61037
\(297\) 0 0
\(298\) −1827.68 −0.355284
\(299\) 918.384 5684.67i 0.177630 1.09951i
\(300\) 0 0
\(301\) 3336.17i 0.638849i
\(302\) −3628.69 −0.691416
\(303\) 0 0
\(304\) 2098.53i 0.395917i
\(305\) 10363.5i 1.94561i
\(306\) 0 0
\(307\) 4502.46i 0.837032i −0.908210 0.418516i \(-0.862550\pi\)
0.908210 0.418516i \(-0.137450\pi\)
\(308\) −634.414 −0.117367
\(309\) 0 0
\(310\) 2384.15i 0.436809i
\(311\) −7447.20 −1.35785 −0.678926 0.734207i \(-0.737554\pi\)
−0.678926 + 0.734207i \(0.737554\pi\)
\(312\) 0 0
\(313\) −6508.93 −1.17542 −0.587710 0.809072i \(-0.699970\pi\)
−0.587710 + 0.809072i \(0.699970\pi\)
\(314\) 1367.29i 0.245734i
\(315\) 0 0
\(316\) −2093.43 −0.372673
\(317\) 2465.57i 0.436846i 0.975854 + 0.218423i \(0.0700913\pi\)
−0.975854 + 0.218423i \(0.929909\pi\)
\(318\) 0 0
\(319\) 1798.56i 0.315674i
\(320\) 708.866i 0.123834i
\(321\) 0 0
\(322\) 1298.99 0.224814
\(323\) 4567.29i 0.786782i
\(324\) 0 0
\(325\) −843.996 + 5224.22i −0.144051 + 0.891654i
\(326\) 3827.07 0.650190
\(327\) 0 0
\(328\) 3890.18 0.654876
\(329\) −3869.89 −0.648491
\(330\) 0 0
\(331\) 4114.84i 0.683300i 0.939827 + 0.341650i \(0.110986\pi\)
−0.939827 + 0.341650i \(0.889014\pi\)
\(332\) 3548.01i 0.586513i
\(333\) 0 0
\(334\) 1531.80 0.250948
\(335\) 216.499 0.0353092
\(336\) 0 0
\(337\) −4798.05 −0.775568 −0.387784 0.921750i \(-0.626759\pi\)
−0.387784 + 0.921750i \(0.626759\pi\)
\(338\) −918.384 + 2768.15i −0.147791 + 0.445466i
\(339\) 0 0
\(340\) 5195.41i 0.828708i
\(341\) 1486.82 0.236117
\(342\) 0 0
\(343\) 4958.69i 0.780594i
\(344\) 7916.58i 1.24079i
\(345\) 0 0
\(346\) 2241.96i 0.348348i
\(347\) 3314.76 0.512812 0.256406 0.966569i \(-0.417462\pi\)
0.256406 + 0.966569i \(0.417462\pi\)
\(348\) 0 0
\(349\) 371.740i 0.0570166i −0.999594 0.0285083i \(-0.990924\pi\)
0.999594 0.0285083i \(-0.00907570\pi\)
\(350\) −1193.78 −0.182314
\(351\) 0 0
\(352\) 2351.32 0.356039
\(353\) 7539.10i 1.13673i 0.822776 + 0.568365i \(0.192424\pi\)
−0.822776 + 0.568365i \(0.807576\pi\)
\(354\) 0 0
\(355\) 5348.89 0.799689
\(356\) 1476.29i 0.219785i
\(357\) 0 0
\(358\) 1251.56i 0.184768i
\(359\) 12741.5i 1.87317i −0.350437 0.936586i \(-0.613967\pi\)
0.350437 0.936586i \(-0.386033\pi\)
\(360\) 0 0
\(361\) −294.676 −0.0429619
\(362\) 639.896i 0.0929065i
\(363\) 0 0
\(364\) 2298.97 + 371.409i 0.331041 + 0.0534811i
\(365\) 12846.7 1.84227
\(366\) 0 0
\(367\) 7187.26 1.02227 0.511134 0.859501i \(-0.329226\pi\)
0.511134 + 0.859501i \(0.329226\pi\)
\(368\) 3048.14 0.431781
\(369\) 0 0
\(370\) 8884.26i 1.24830i
\(371\) 5372.87i 0.751874i
\(372\) 0 0
\(373\) −2087.99 −0.289845 −0.144922 0.989443i \(-0.546293\pi\)
−0.144922 + 0.989443i \(0.546293\pi\)
\(374\) −915.352 −0.126555
\(375\) 0 0
\(376\) 9183.07 1.25952
\(377\) −1052.94 + 6517.57i −0.143844 + 0.890377i
\(378\) 0 0
\(379\) 3982.08i 0.539699i −0.962902 0.269850i \(-0.913026\pi\)
0.962902 0.269850i \(-0.0869740\pi\)
\(380\) −8137.50 −1.09854
\(381\) 0 0
\(382\) 5606.47i 0.750921i
\(383\) 8638.43i 1.15249i 0.817278 + 0.576244i \(0.195482\pi\)
−0.817278 + 0.576244i \(0.804518\pi\)
\(384\) 0 0
\(385\) 1568.72i 0.207660i
\(386\) 304.120 0.0401018
\(387\) 0 0
\(388\) 7977.70i 1.04383i
\(389\) −1275.74 −0.166279 −0.0831393 0.996538i \(-0.526495\pi\)
−0.0831393 + 0.996538i \(0.526495\pi\)
\(390\) 0 0
\(391\) −6634.06 −0.858053
\(392\) 5283.83i 0.680801i
\(393\) 0 0
\(394\) 303.115 0.0387582
\(395\) 5176.44i 0.659379i
\(396\) 0 0
\(397\) 4622.65i 0.584394i −0.956358 0.292197i \(-0.905614\pi\)
0.956358 0.292197i \(-0.0943862\pi\)
\(398\) 3901.55i 0.491375i
\(399\) 0 0
\(400\) −2801.24 −0.350155
\(401\) 138.075i 0.0171949i 0.999963 + 0.00859743i \(0.00273668\pi\)
−0.999963 + 0.00859743i \(0.997263\pi\)
\(402\) 0 0
\(403\) −5387.91 870.441i −0.665982 0.107592i
\(404\) 3943.90 0.485684
\(405\) 0 0
\(406\) −1489.32 −0.182053
\(407\) −5540.47 −0.674769
\(408\) 0 0
\(409\) 1204.64i 0.145637i 0.997345 + 0.0728186i \(0.0231994\pi\)
−0.997345 + 0.0728186i \(0.976801\pi\)
\(410\) 4214.32i 0.507635i
\(411\) 0 0
\(412\) −9395.68 −1.12352
\(413\) −1483.29 −0.176726
\(414\) 0 0
\(415\) −8773.16 −1.03773
\(416\) −8520.66 1376.55i −1.00423 0.162238i
\(417\) 0 0
\(418\) 1433.70i 0.167762i
\(419\) −5199.85 −0.606275 −0.303138 0.952947i \(-0.598034\pi\)
−0.303138 + 0.952947i \(0.598034\pi\)
\(420\) 0 0
\(421\) 14136.5i 1.63651i 0.574854 + 0.818256i \(0.305059\pi\)
−0.574854 + 0.818256i \(0.694941\pi\)
\(422\) 2133.32i 0.246086i
\(423\) 0 0
\(424\) 12749.6i 1.46032i
\(425\) 6096.70 0.695844
\(426\) 0 0
\(427\) 5351.71i 0.606527i
\(428\) 7912.94 0.893660
\(429\) 0 0
\(430\) −8576.21 −0.961818
\(431\) 2279.83i 0.254793i −0.991852 0.127396i \(-0.959338\pi\)
0.991852 0.127396i \(-0.0406620\pi\)
\(432\) 0 0
\(433\) 13298.7 1.47597 0.737984 0.674819i \(-0.235778\pi\)
0.737984 + 0.674819i \(0.235778\pi\)
\(434\) 1231.18i 0.136172i
\(435\) 0 0
\(436\) 2167.14i 0.238045i
\(437\) 10390.8i 1.13744i
\(438\) 0 0
\(439\) 10452.3 1.13635 0.568177 0.822907i \(-0.307649\pi\)
0.568177 + 0.822907i \(0.307649\pi\)
\(440\) 3722.50i 0.403325i
\(441\) 0 0
\(442\) 3317.03 + 535.880i 0.356957 + 0.0576679i
\(443\) −5363.50 −0.575232 −0.287616 0.957746i \(-0.592863\pi\)
−0.287616 + 0.957746i \(0.592863\pi\)
\(444\) 0 0
\(445\) −3650.43 −0.388870
\(446\) 173.726 0.0184443
\(447\) 0 0
\(448\) 366.059i 0.0386042i
\(449\) 9681.73i 1.01762i −0.860880 0.508808i \(-0.830086\pi\)
0.860880 0.508808i \(-0.169914\pi\)
\(450\) 0 0
\(451\) −2628.17 −0.274402
\(452\) −4115.07 −0.428223
\(453\) 0 0
\(454\) −5741.69 −0.593548
\(455\) 918.384 5684.67i 0.0946253 0.585718i
\(456\) 0 0
\(457\) 3537.94i 0.362139i 0.983470 + 0.181070i \(0.0579560\pi\)
−0.983470 + 0.181070i \(0.942044\pi\)
\(458\) 3480.14 0.355057
\(459\) 0 0
\(460\) 11819.8i 1.19805i
\(461\) 15074.9i 1.52302i −0.648156 0.761508i \(-0.724459\pi\)
0.648156 0.761508i \(-0.275541\pi\)
\(462\) 0 0
\(463\) 11070.0i 1.11116i −0.831463 0.555580i \(-0.812496\pi\)
0.831463 0.555580i \(-0.187504\pi\)
\(464\) −3494.74 −0.349654
\(465\) 0 0
\(466\) 6163.75i 0.612725i
\(467\) 13252.8 1.31320 0.656600 0.754239i \(-0.271994\pi\)
0.656600 + 0.754239i \(0.271994\pi\)
\(468\) 0 0
\(469\) −111.800 −0.0110074
\(470\) 9948.23i 0.976335i
\(471\) 0 0
\(472\) 3519.79 0.343244
\(473\) 5348.36i 0.519911i
\(474\) 0 0
\(475\) 9549.18i 0.922413i
\(476\) 2682.92i 0.258343i
\(477\) 0 0
\(478\) −8889.86 −0.850654
\(479\) 12241.4i 1.16769i −0.811866 0.583843i \(-0.801548\pi\)
0.811866 0.583843i \(-0.198452\pi\)
\(480\) 0 0
\(481\) 20077.4 + 3243.59i 1.90322 + 0.307474i
\(482\) −3055.20 −0.288715
\(483\) 0 0
\(484\) 7285.37 0.684201
\(485\) −19726.5 −1.84687
\(486\) 0 0
\(487\) 13413.3i 1.24808i 0.781392 + 0.624041i \(0.214510\pi\)
−0.781392 + 0.624041i \(0.785490\pi\)
\(488\) 12699.4i 1.17802i
\(489\) 0 0
\(490\) −5724.10 −0.527731
\(491\) −737.885 −0.0678214 −0.0339107 0.999425i \(-0.510796\pi\)
−0.0339107 + 0.999425i \(0.510796\pi\)
\(492\) 0 0
\(493\) 7606.06 0.694847
\(494\) −839.342 + 5195.41i −0.0764449 + 0.473183i
\(495\) 0 0
\(496\) 2889.01i 0.261533i
\(497\) −2762.17 −0.249297
\(498\) 0 0
\(499\) 1865.65i 0.167370i −0.996492 0.0836852i \(-0.973331\pi\)
0.996492 0.0836852i \(-0.0266690\pi\)
\(500\) 1163.97i 0.104109i
\(501\) 0 0
\(502\) 1099.17i 0.0977259i
\(503\) 16632.0 1.47432 0.737161 0.675717i \(-0.236166\pi\)
0.737161 + 0.675717i \(0.236166\pi\)
\(504\) 0 0
\(505\) 9752.09i 0.859331i
\(506\) 2082.47 0.182959
\(507\) 0 0
\(508\) −1715.50 −0.149829
\(509\) 4128.91i 0.359549i 0.983708 + 0.179775i \(0.0575368\pi\)
−0.983708 + 0.179775i \(0.942463\pi\)
\(510\) 0 0
\(511\) −6634.06 −0.574312
\(512\) 8320.40i 0.718190i
\(513\) 0 0
\(514\) 1174.52i 0.100790i
\(515\) 23232.7i 1.98788i
\(516\) 0 0
\(517\) −6203.99 −0.527758
\(518\) 4587.85i 0.389147i
\(519\) 0 0
\(520\) −2179.29 + 13489.5i −0.183785 + 1.13760i
\(521\) 988.234 0.0831005 0.0415502 0.999136i \(-0.486770\pi\)
0.0415502 + 0.999136i \(0.486770\pi\)
\(522\) 0 0
\(523\) −9441.62 −0.789394 −0.394697 0.918811i \(-0.629150\pi\)
−0.394697 + 0.918811i \(0.629150\pi\)
\(524\) 7385.30 0.615703
\(525\) 0 0
\(526\) 11076.6i 0.918180i
\(527\) 6287.73i 0.519730i
\(528\) 0 0
\(529\) 2925.83 0.240472
\(530\) −13811.9 −1.13198
\(531\) 0 0
\(532\) 4202.21 0.342461
\(533\) 9523.88 + 1538.62i 0.773968 + 0.125038i
\(534\) 0 0
\(535\) 19566.3i 1.58117i
\(536\) 265.297 0.0213789
\(537\) 0 0
\(538\) 3667.30i 0.293882i
\(539\) 3569.70i 0.285265i
\(540\) 0 0
\(541\) 14001.5i 1.11270i 0.830948 + 0.556351i \(0.187799\pi\)
−0.830948 + 0.556351i \(0.812201\pi\)
\(542\) 4137.22 0.327876
\(543\) 0 0
\(544\) 9943.67i 0.783697i
\(545\) 5358.70 0.421177
\(546\) 0 0
\(547\) −4244.85 −0.331804 −0.165902 0.986142i \(-0.553053\pi\)
−0.165902 + 0.986142i \(0.553053\pi\)
\(548\) 15952.2i 1.24351i
\(549\) 0 0
\(550\) −1913.80 −0.148372
\(551\) 11913.3i 0.921092i
\(552\) 0 0
\(553\) 2673.12i 0.205556i
\(554\) 666.485i 0.0511124i
\(555\) 0 0
\(556\) 3404.16 0.259655
\(557\) 11732.2i 0.892473i 0.894915 + 0.446236i \(0.147236\pi\)
−0.894915 + 0.446236i \(0.852764\pi\)
\(558\) 0 0
\(559\) 3131.13 19381.2i 0.236910 1.46644i
\(560\) 3048.14 0.230013
\(561\) 0 0
\(562\) 8771.54 0.658372
\(563\) −9941.80 −0.744222 −0.372111 0.928188i \(-0.621366\pi\)
−0.372111 + 0.928188i \(0.621366\pi\)
\(564\) 0 0
\(565\) 10175.3i 0.757664i
\(566\) 5799.83i 0.430716i
\(567\) 0 0
\(568\) 6554.52 0.484193
\(569\) 3690.77 0.271925 0.135962 0.990714i \(-0.456587\pi\)
0.135962 + 0.990714i \(0.456587\pi\)
\(570\) 0 0
\(571\) 5685.09 0.416661 0.208331 0.978058i \(-0.433197\pi\)
0.208331 + 0.978058i \(0.433197\pi\)
\(572\) 3685.59 + 595.423i 0.269409 + 0.0435242i
\(573\) 0 0
\(574\) 2176.28i 0.158251i
\(575\) −13870.3 −1.00597
\(576\) 0 0
\(577\) 7746.50i 0.558910i −0.960159 0.279455i \(-0.909846\pi\)
0.960159 0.279455i \(-0.0901537\pi\)
\(578\) 2651.02i 0.190775i
\(579\) 0 0
\(580\) 13551.6i 0.970175i
\(581\) 4530.47 0.323504
\(582\) 0 0
\(583\) 8613.48i 0.611894i
\(584\) 15742.3 1.11545
\(585\) 0 0
\(586\) 7099.64 0.500484
\(587\) 2766.54i 0.194527i −0.995259 0.0972635i \(-0.968991\pi\)
0.995259 0.0972635i \(-0.0310089\pi\)
\(588\) 0 0
\(589\) −9848.38 −0.688957
\(590\) 3813.07i 0.266070i
\(591\) 0 0
\(592\) 10765.6i 0.747402i
\(593\) 1440.79i 0.0997743i 0.998755 + 0.0498871i \(0.0158862\pi\)
−0.998755 + 0.0498871i \(0.984114\pi\)
\(594\) 0 0
\(595\) −6634.06 −0.457092
\(596\) 8587.99i 0.590231i
\(597\) 0 0
\(598\) −7546.41 1219.16i −0.516047 0.0833696i
\(599\) −23837.5 −1.62600 −0.813001 0.582263i \(-0.802168\pi\)
−0.813001 + 0.582263i \(0.802168\pi\)
\(600\) 0 0
\(601\) −6694.23 −0.454348 −0.227174 0.973854i \(-0.572949\pi\)
−0.227174 + 0.973854i \(0.572949\pi\)
\(602\) 4428.77 0.299839
\(603\) 0 0
\(604\) 17050.7i 1.14865i
\(605\) 18014.6i 1.21057i
\(606\) 0 0
\(607\) 3330.50 0.222703 0.111352 0.993781i \(-0.464482\pi\)
0.111352 + 0.993781i \(0.464482\pi\)
\(608\) −15574.6 −1.03887
\(609\) 0 0
\(610\) 13757.5 0.913156
\(611\) 22481.8 + 3632.04i 1.48857 + 0.240486i
\(612\) 0 0
\(613\) 13490.3i 0.888857i 0.895814 + 0.444428i \(0.146593\pi\)
−0.895814 + 0.444428i \(0.853407\pi\)
\(614\) −5977.02 −0.392855
\(615\) 0 0
\(616\) 1922.30i 0.125733i
\(617\) 7470.76i 0.487458i 0.969843 + 0.243729i \(0.0783707\pi\)
−0.969843 + 0.243729i \(0.921629\pi\)
\(618\) 0 0
\(619\) 24806.9i 1.61078i 0.592746 + 0.805389i \(0.298044\pi\)
−0.592746 + 0.805389i \(0.701956\pi\)
\(620\) −11202.8 −0.725669
\(621\) 0 0
\(622\) 9886.17i 0.637298i
\(623\) 1885.09 0.121227
\(624\) 0 0
\(625\) −16990.9 −1.08742
\(626\) 8640.61i 0.551675i
\(627\) 0 0
\(628\) 6424.68 0.408237
\(629\) 23430.5i 1.48527i
\(630\) 0 0
\(631\) 314.333i 0.0198311i 0.999951 + 0.00991554i \(0.00315627\pi\)
−0.999951 + 0.00991554i \(0.996844\pi\)
\(632\) 6343.19i 0.399238i
\(633\) 0 0
\(634\) 3273.05 0.205031
\(635\) 4241.91i 0.265095i
\(636\) 0 0
\(637\) 2089.83 12935.8i 0.129988 0.804607i
\(638\) −2387.59 −0.148159
\(639\) 0 0
\(640\) −21780.7 −1.34525
\(641\) 5550.41 0.342009 0.171005 0.985270i \(-0.445299\pi\)
0.171005 + 0.985270i \(0.445299\pi\)
\(642\) 0 0
\(643\) 5479.48i 0.336065i −0.985781 0.168032i \(-0.946259\pi\)
0.985781 0.168032i \(-0.0537413\pi\)
\(644\) 6103.78i 0.373482i
\(645\) 0 0
\(646\) 6063.08 0.369271
\(647\) 4724.83 0.287098 0.143549 0.989643i \(-0.454149\pi\)
0.143549 + 0.989643i \(0.454149\pi\)
\(648\) 0 0
\(649\) −2377.93 −0.143824
\(650\) 6935.16 + 1120.41i 0.418491 + 0.0676091i
\(651\) 0 0
\(652\) 17982.9i 1.08016i
\(653\) −3463.91 −0.207585 −0.103793 0.994599i \(-0.533098\pi\)
−0.103793 + 0.994599i \(0.533098\pi\)
\(654\) 0 0
\(655\) 18261.6i 1.08938i
\(656\) 5106.73i 0.303940i
\(657\) 0 0
\(658\) 5137.28i 0.304365i
\(659\) 2606.35 0.154065 0.0770327 0.997029i \(-0.475455\pi\)
0.0770327 + 0.997029i \(0.475455\pi\)
\(660\) 0 0
\(661\) 22436.7i 1.32025i −0.751154 0.660127i \(-0.770502\pi\)
0.751154 0.660127i \(-0.229498\pi\)
\(662\) 5462.46 0.320702
\(663\) 0 0
\(664\) −10750.6 −0.628321
\(665\) 10390.8i 0.605923i
\(666\) 0 0
\(667\) −17304.2 −1.00453
\(668\) 7197.73i 0.416899i
\(669\) 0 0
\(670\) 287.403i 0.0165721i
\(671\) 8579.56i 0.493607i
\(672\) 0 0
\(673\) 633.970 0.0363117 0.0181558 0.999835i \(-0.494221\pi\)
0.0181558 + 0.999835i \(0.494221\pi\)
\(674\) 6369.42i 0.364007i
\(675\) 0 0
\(676\) −13007.1 4315.35i −0.740052 0.245525i
\(677\) −24457.4 −1.38844 −0.694221 0.719762i \(-0.744251\pi\)
−0.694221 + 0.719762i \(0.744251\pi\)
\(678\) 0 0
\(679\) 10186.8 0.575747
\(680\) 15742.3 0.887780
\(681\) 0 0
\(682\) 1973.76i 0.110820i
\(683\) 12367.6i 0.692875i 0.938073 + 0.346437i \(0.112609\pi\)
−0.938073 + 0.346437i \(0.887391\pi\)
\(684\) 0 0
\(685\) 39445.0 2.20017
\(686\) 6582.66 0.366366
\(687\) 0 0
\(688\) 10392.3 0.575875
\(689\) 5042.65 31213.3i 0.278824 1.72588i
\(690\) 0 0
\(691\) 1050.99i 0.0578605i −0.999581 0.0289302i \(-0.990790\pi\)
0.999581 0.0289302i \(-0.00921006\pi\)
\(692\) −10534.6 −0.578709
\(693\) 0 0
\(694\) 4400.35i 0.240685i
\(695\) 8417.46i 0.459414i
\(696\) 0 0
\(697\) 11114.4i 0.604002i
\(698\) −493.486 −0.0267603
\(699\) 0 0
\(700\) 5609.38i 0.302878i
\(701\) −24294.1 −1.30895 −0.654476 0.756083i \(-0.727111\pi\)
−0.654476 + 0.756083i \(0.727111\pi\)
\(702\) 0 0
\(703\) 36698.8 1.96888
\(704\) 586.846i 0.0314170i
\(705\) 0 0
\(706\) 10008.2 0.533516
\(707\) 5035.99i 0.267890i
\(708\) 0 0
\(709\) 27465.9i 1.45487i −0.686176 0.727436i \(-0.740712\pi\)
0.686176 0.727436i \(-0.259288\pi\)
\(710\) 7100.66i 0.375328i
\(711\) 0 0
\(712\) −4473.23 −0.235451
\(713\) 14304.9i 0.751365i
\(714\) 0 0
\(715\) 1472.30 9113.36i 0.0770084 0.476672i
\(716\) −5880.90 −0.306955
\(717\) 0 0
\(718\) −16914.3 −0.879160
\(719\) 36433.5 1.88976 0.944882 0.327411i \(-0.106176\pi\)
0.944882 + 0.327411i \(0.106176\pi\)
\(720\) 0 0
\(721\) 11997.4i 0.619704i
\(722\) 391.183i 0.0201639i
\(723\) 0 0
\(724\) −3006.78 −0.154345
\(725\) 15902.6 0.814629
\(726\) 0 0
\(727\) −551.608 −0.0281403 −0.0140701 0.999901i \(-0.504479\pi\)
−0.0140701 + 0.999901i \(0.504479\pi\)
\(728\) 1125.39 6965.99i 0.0572934 0.354638i
\(729\) 0 0
\(730\) 17054.0i 0.864654i
\(731\) −22618.1 −1.14440
\(732\) 0 0
\(733\) 20317.2i 1.02379i 0.859049 + 0.511893i \(0.171055\pi\)
−0.859049 + 0.511893i \(0.828945\pi\)
\(734\) 9541.10i 0.479794i
\(735\) 0 0
\(736\) 22622.4i 1.13298i
\(737\) −179.232 −0.00895807
\(738\) 0 0
\(739\) 29931.6i 1.48992i 0.667107 + 0.744962i \(0.267532\pi\)
−0.667107 + 0.744962i \(0.732468\pi\)
\(740\) 41745.9 2.07380
\(741\) 0 0
\(742\) 7132.49 0.352887
\(743\) 24376.4i 1.20361i −0.798643 0.601805i \(-0.794448\pi\)
0.798643 0.601805i \(-0.205552\pi\)
\(744\) 0 0
\(745\) −21235.5 −1.04431
\(746\) 2771.81i 0.136037i
\(747\) 0 0
\(748\) 4301.11i 0.210246i
\(749\) 10104.1i 0.492917i
\(750\) 0 0
\(751\) −22692.2 −1.10260 −0.551298 0.834308i \(-0.685867\pi\)
−0.551298 + 0.834308i \(0.685867\pi\)
\(752\) 12054.8i 0.584567i
\(753\) 0 0
\(754\) 8652.09 + 1397.78i 0.417892 + 0.0675123i
\(755\) −42161.3 −2.03232
\(756\) 0 0
\(757\) −33063.5 −1.58747 −0.793734 0.608265i \(-0.791866\pi\)
−0.793734 + 0.608265i \(0.791866\pi\)
\(758\) −5286.22 −0.253304
\(759\) 0 0
\(760\) 24657.0i 1.17685i
\(761\) 216.324i 0.0103045i −0.999987 0.00515226i \(-0.998360\pi\)
0.999987 0.00515226i \(-0.00164002\pi\)
\(762\) 0 0
\(763\) −2767.24 −0.131299
\(764\) −26344.0 −1.24750
\(765\) 0 0
\(766\) 11467.5 0.540912
\(767\) 8617.09 + 1392.13i 0.405665 + 0.0655369i
\(768\) 0 0
\(769\) 19214.4i 0.901025i 0.892770 + 0.450512i \(0.148759\pi\)
−0.892770 + 0.450512i \(0.851241\pi\)
\(770\) 2082.47 0.0974638
\(771\) 0 0
\(772\) 1429.01i 0.0666209i
\(773\) 33175.6i 1.54365i −0.635834 0.771826i \(-0.719344\pi\)
0.635834 0.771826i \(-0.280656\pi\)
\(774\) 0 0
\(775\) 13146.2i 0.609325i
\(776\) −24172.8 −1.11824
\(777\) 0 0
\(778\) 1693.54i 0.0780416i
\(779\) 17408.4 0.800667
\(780\) 0 0
\(781\) −4428.17 −0.202884
\(782\) 8806.72i 0.402721i
\(783\) 0 0
\(784\) 6936.21 0.315972
\(785\) 15886.3i 0.722302i
\(786\) 0 0
\(787\) 14887.9i 0.674330i 0.941446 + 0.337165i \(0.109468\pi\)
−0.941446 + 0.337165i \(0.890532\pi\)
\(788\) 1424.30i 0.0643889i
\(789\) 0 0
\(790\) 6871.73 0.309475
\(791\) 5254.56i 0.236196i
\(792\) 0 0
\(793\) −5022.79 + 31090.4i