Properties

Label 324.4.i.a.145.1
Level 324
Weight 4
Character 324.145
Analytic conductor 19.117
Analytic rank 0
Dimension 54
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) \(=\) \( 324 = 2^{2} \cdot 3^{4} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 324.i (of order \(9\), degree \(6\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(19.1166188419\)
Analytic rank: \(0\)
Dimension: \(54\)
Relative dimension: \(9\) over \(\Q(\zeta_{9})\)
Twist minimal: no (minimal twist has level 108)
Sato-Tate group: $\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label 145.1
Character \(\chi\) \(=\) 324.145
Dual form 324.4.i.a.181.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-3.27839 + 18.5927i) q^{5} +(4.82725 - 4.05055i) q^{7} +O(q^{10})\) \(q+(-3.27839 + 18.5927i) q^{5} +(4.82725 - 4.05055i) q^{7} +(2.23683 + 12.6857i) q^{11} +(47.4125 - 17.2567i) q^{13} +(-60.2331 + 104.327i) q^{17} +(24.7623 + 42.8896i) q^{19} +(-118.398 - 99.3476i) q^{23} +(-217.478 - 79.1554i) q^{25} +(112.034 + 40.7770i) q^{29} +(-211.590 - 177.545i) q^{31} +(59.4848 + 103.031i) q^{35} +(-174.234 + 301.781i) q^{37} +(-213.827 + 77.8266i) q^{41} +(-16.3018 - 92.4523i) q^{43} +(-46.5415 + 39.0530i) q^{47} +(-52.6659 + 298.683i) q^{49} +5.44580 q^{53} -243.194 q^{55} +(-76.8449 + 435.809i) q^{59} +(-77.8976 + 65.3638i) q^{61} +(165.412 + 938.098i) q^{65} +(-130.865 + 47.6308i) q^{67} +(253.364 - 438.839i) q^{71} +(-5.24944 - 9.09230i) q^{73} +(62.1817 + 52.1767i) q^{77} +(1142.37 + 415.787i) q^{79} +(-350.889 - 127.713i) q^{83} +(-1742.24 - 1461.92i) q^{85} +(-703.340 - 1218.22i) q^{89} +(158.973 - 275.349i) q^{91} +(-878.613 + 319.789i) q^{95} +(-132.037 - 748.818i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 54q - 12q^{5} + O(q^{10}) \) \( 54q - 12q^{5} + 87q^{11} - 204q^{17} - 96q^{23} - 216q^{25} - 318q^{29} - 54q^{31} - 6q^{35} - 867q^{41} - 513q^{43} + 1548q^{47} + 594q^{49} + 1068q^{53} + 1218q^{59} - 54q^{61} - 96q^{65} - 2997q^{67} + 120q^{71} - 216q^{73} - 3480q^{77} + 2808q^{79} - 4464q^{83} + 2160q^{85} - 4029q^{89} + 270q^{91} + 1650q^{95} - 3483q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/324\mathbb{Z}\right)^\times\).

\(n\) \(163\) \(245\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{9}\right)\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 0 0
\(4\) 0 0
\(5\) −3.27839 + 18.5927i −0.293228 + 1.66298i 0.381091 + 0.924538i \(0.375548\pi\)
−0.674319 + 0.738440i \(0.735563\pi\)
\(6\) 0 0
\(7\) 4.82725 4.05055i 0.260647 0.218709i −0.503094 0.864232i \(-0.667805\pi\)
0.763741 + 0.645523i \(0.223361\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 2.23683 + 12.6857i 0.0613118 + 0.347716i 0.999996 + 0.00293738i \(0.000934999\pi\)
−0.938684 + 0.344779i \(0.887954\pi\)
\(12\) 0 0
\(13\) 47.4125 17.2567i 1.01153 0.368166i 0.217508 0.976059i \(-0.430207\pi\)
0.794019 + 0.607893i \(0.207985\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −60.2331 + 104.327i −0.859333 + 1.48841i 0.0132328 + 0.999912i \(0.495788\pi\)
−0.872566 + 0.488496i \(0.837546\pi\)
\(18\) 0 0
\(19\) 24.7623 + 42.8896i 0.298993 + 0.517871i 0.975906 0.218192i \(-0.0700159\pi\)
−0.676913 + 0.736063i \(0.736683\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −118.398 99.3476i −1.07338 0.900670i −0.0780228 0.996952i \(-0.524861\pi\)
−0.995354 + 0.0962813i \(0.969305\pi\)
\(24\) 0 0
\(25\) −217.478 79.1554i −1.73982 0.633243i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 112.034 + 40.7770i 0.717386 + 0.261107i 0.674815 0.737986i \(-0.264223\pi\)
0.0425701 + 0.999093i \(0.486445\pi\)
\(30\) 0 0
\(31\) −211.590 177.545i −1.22589 1.02865i −0.998495 0.0548445i \(-0.982534\pi\)
−0.227398 0.973802i \(-0.573022\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 59.4848 + 103.031i 0.287279 + 0.497582i
\(36\) 0 0
\(37\) −174.234 + 301.781i −0.774157 + 1.34088i 0.161110 + 0.986937i \(0.448493\pi\)
−0.935267 + 0.353943i \(0.884841\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −213.827 + 77.8266i −0.814491 + 0.296451i −0.715478 0.698635i \(-0.753791\pi\)
−0.0990136 + 0.995086i \(0.531569\pi\)
\(42\) 0 0
\(43\) −16.3018 92.4523i −0.0578141 0.327880i 0.942159 0.335165i \(-0.108792\pi\)
−0.999973 + 0.00728516i \(0.997681\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −46.5415 + 39.0530i −0.144442 + 0.121201i −0.712146 0.702032i \(-0.752276\pi\)
0.567704 + 0.823233i \(0.307832\pi\)
\(48\) 0 0
\(49\) −52.6659 + 298.683i −0.153545 + 0.870796i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 5.44580 0.0141139 0.00705696 0.999975i \(-0.497754\pi\)
0.00705696 + 0.999975i \(0.497754\pi\)
\(54\) 0 0
\(55\) −243.194 −0.596223
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −76.8449 + 435.809i −0.169565 + 0.961653i 0.774666 + 0.632370i \(0.217918\pi\)
−0.944232 + 0.329282i \(0.893193\pi\)
\(60\) 0 0
\(61\) −77.8976 + 65.3638i −0.163504 + 0.137196i −0.720869 0.693071i \(-0.756257\pi\)
0.557365 + 0.830268i \(0.311813\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 165.412 + 938.098i 0.315644 + 1.79010i
\(66\) 0 0
\(67\) −130.865 + 47.6308i −0.238622 + 0.0868512i −0.458563 0.888662i \(-0.651636\pi\)
0.219941 + 0.975513i \(0.429413\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 253.364 438.839i 0.423503 0.733529i −0.572776 0.819712i \(-0.694133\pi\)
0.996279 + 0.0861825i \(0.0274668\pi\)
\(72\) 0 0
\(73\) −5.24944 9.09230i −0.00841645 0.0145777i 0.861787 0.507271i \(-0.169346\pi\)
−0.870203 + 0.492693i \(0.836012\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 62.1817 + 52.1767i 0.0920294 + 0.0772219i
\(78\) 0 0
\(79\) 1142.37 + 415.787i 1.62691 + 0.592148i 0.984682 0.174363i \(-0.0557865\pi\)
0.642232 + 0.766511i \(0.278009\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −350.889 127.713i −0.464036 0.168895i 0.0994126 0.995046i \(-0.468304\pi\)
−0.563449 + 0.826151i \(0.690526\pi\)
\(84\) 0 0
\(85\) −1742.24 1461.92i −2.22321 1.86549i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −703.340 1218.22i −0.837684 1.45091i −0.891827 0.452377i \(-0.850576\pi\)
0.0541431 0.998533i \(-0.482757\pi\)
\(90\) 0 0
\(91\) 158.973 275.349i 0.183131 0.317191i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −878.613 + 319.789i −0.948882 + 0.345365i
\(96\) 0 0
\(97\) −132.037 748.818i −0.138209 0.783824i −0.972571 0.232606i \(-0.925275\pi\)
0.834362 0.551217i \(-0.185837\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −605.089 + 507.730i −0.596125 + 0.500208i −0.890197 0.455575i \(-0.849434\pi\)
0.294072 + 0.955783i \(0.404989\pi\)
\(102\) 0 0
\(103\) −350.805 + 1989.51i −0.335590 + 1.90323i 0.0857336 + 0.996318i \(0.472677\pi\)
−0.421324 + 0.906910i \(0.638435\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 1574.24 1.42232 0.711159 0.703032i \(-0.248171\pi\)
0.711159 + 0.703032i \(0.248171\pi\)
\(108\) 0 0
\(109\) 574.546 0.504876 0.252438 0.967613i \(-0.418768\pi\)
0.252438 + 0.967613i \(0.418768\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 132.721 752.697i 0.110490 0.626618i −0.878395 0.477935i \(-0.841386\pi\)
0.988885 0.148683i \(-0.0475033\pi\)
\(114\) 0 0
\(115\) 2235.29 1875.63i 1.81254 1.52090i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 131.820 + 747.588i 0.101546 + 0.575893i
\(120\) 0 0
\(121\) 1094.81 398.477i 0.822545 0.299382i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 1004.72 1740.22i 0.718917 1.24520i
\(126\) 0 0
\(127\) 1253.56 + 2171.24i 0.875872 + 1.51706i 0.855830 + 0.517256i \(0.173047\pi\)
0.0200420 + 0.999799i \(0.493620\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −522.756 438.644i −0.348652 0.292554i 0.451597 0.892222i \(-0.350855\pi\)
−0.800248 + 0.599669i \(0.795299\pi\)
\(132\) 0 0
\(133\) 293.261 + 106.738i 0.191195 + 0.0695892i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 1648.98 + 600.181i 1.02834 + 0.374284i 0.800448 0.599402i \(-0.204595\pi\)
0.227890 + 0.973687i \(0.426817\pi\)
\(138\) 0 0
\(139\) −283.325 237.738i −0.172887 0.145070i 0.552238 0.833686i \(-0.313774\pi\)
−0.725126 + 0.688617i \(0.758218\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 324.967 + 562.859i 0.190036 + 0.329152i
\(144\) 0 0
\(145\) −1125.44 + 1949.33i −0.644573 + 1.11643i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −1051.01 + 382.536i −0.577866 + 0.210326i −0.614384 0.789007i \(-0.710596\pi\)
0.0365181 + 0.999333i \(0.488373\pi\)
\(150\) 0 0
\(151\) 185.477 + 1051.89i 0.0999594 + 0.566898i 0.993114 + 0.117149i \(0.0373755\pi\)
−0.893155 + 0.449749i \(0.851513\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 3994.71 3351.96i 2.07008 1.73701i
\(156\) 0 0
\(157\) 566.859 3214.81i 0.288154 1.63420i −0.405641 0.914033i \(-0.632952\pi\)
0.693795 0.720172i \(-0.255937\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) −973.949 −0.476757
\(162\) 0 0
\(163\) 1661.39 0.798343 0.399171 0.916876i \(-0.369298\pi\)
0.399171 + 0.916876i \(0.369298\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 291.364 1652.41i 0.135009 0.765671i −0.839845 0.542826i \(-0.817354\pi\)
0.974854 0.222845i \(-0.0715345\pi\)
\(168\) 0 0
\(169\) 267.147 224.163i 0.121596 0.102032i
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 452.070 + 2563.82i 0.198672 + 1.12672i 0.907092 + 0.420933i \(0.138297\pi\)
−0.708420 + 0.705792i \(0.750591\pi\)
\(174\) 0 0
\(175\) −1370.44 + 498.800i −0.591975 + 0.215461i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 1515.37 2624.70i 0.632761 1.09597i −0.354224 0.935161i \(-0.615255\pi\)
0.986985 0.160814i \(-0.0514118\pi\)
\(180\) 0 0
\(181\) 1367.06 + 2367.82i 0.561398 + 0.972369i 0.997375 + 0.0724114i \(0.0230694\pi\)
−0.435977 + 0.899958i \(0.643597\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −5039.71 4228.82i −2.00285 1.68059i
\(186\) 0 0
\(187\) −1458.19 530.737i −0.570231 0.207547i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −334.925 121.903i −0.126881 0.0461810i 0.277799 0.960639i \(-0.410395\pi\)
−0.404680 + 0.914458i \(0.632617\pi\)
\(192\) 0 0
\(193\) 463.595 + 389.003i 0.172903 + 0.145083i 0.725133 0.688609i \(-0.241778\pi\)
−0.552230 + 0.833692i \(0.686223\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −192.402 333.251i −0.0695843 0.120524i 0.829134 0.559050i \(-0.188834\pi\)
−0.898718 + 0.438526i \(0.855501\pi\)
\(198\) 0 0
\(199\) −785.524 + 1360.57i −0.279821 + 0.484663i −0.971340 0.237694i \(-0.923608\pi\)
0.691519 + 0.722358i \(0.256942\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 705.986 256.958i 0.244091 0.0888419i
\(204\) 0 0
\(205\) −745.996 4230.76i −0.254159 1.44141i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −488.695 + 410.064i −0.161740 + 0.135716i
\(210\) 0 0
\(211\) 483.481 2741.96i 0.157745 0.894617i −0.798488 0.602011i \(-0.794366\pi\)
0.956233 0.292606i \(-0.0945226\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 1772.38 0.562210
\(216\) 0 0
\(217\) −1740.55 −0.544500
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −1055.46 + 5985.81i −0.321258 + 1.82194i
\(222\) 0 0
\(223\) 1950.78 1636.90i 0.585801 0.491546i −0.301045 0.953610i \(-0.597335\pi\)
0.886846 + 0.462064i \(0.152891\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 933.533 + 5294.33i 0.272955 + 1.54800i 0.745384 + 0.666636i \(0.232266\pi\)
−0.472429 + 0.881369i \(0.656623\pi\)
\(228\) 0 0
\(229\) −4266.30 + 1552.81i −1.23111 + 0.448089i −0.873979 0.485964i \(-0.838469\pi\)
−0.357135 + 0.934053i \(0.616246\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −1383.43 + 2396.17i −0.388977 + 0.673727i −0.992312 0.123760i \(-0.960505\pi\)
0.603336 + 0.797487i \(0.293838\pi\)
\(234\) 0 0
\(235\) −573.517 993.361i −0.159201 0.275744i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 3482.56 + 2922.21i 0.942543 + 0.790888i 0.978026 0.208483i \(-0.0668525\pi\)
−0.0354828 + 0.999370i \(0.511297\pi\)
\(240\) 0 0
\(241\) 6957.69 + 2532.39i 1.85969 + 0.676870i 0.979234 + 0.202735i \(0.0649829\pi\)
0.880452 + 0.474135i \(0.157239\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −5380.65 1958.40i −1.40309 0.510683i
\(246\) 0 0
\(247\) 1914.18 + 1606.19i 0.493102 + 0.413762i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −390.307 676.032i −0.0981513 0.170003i 0.812768 0.582587i \(-0.197960\pi\)
−0.910919 + 0.412584i \(0.864626\pi\)
\(252\) 0 0
\(253\) 995.457 1724.18i 0.247367 0.428452i
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −4467.24 + 1625.94i −1.08427 + 0.394644i −0.821497 0.570213i \(-0.806861\pi\)
−0.262777 + 0.964857i \(0.584638\pi\)
\(258\) 0 0
\(259\) 381.310 + 2162.52i 0.0914805 + 0.518812i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −887.670 + 744.844i −0.208122 + 0.174635i −0.740890 0.671626i \(-0.765596\pi\)
0.532768 + 0.846261i \(0.321152\pi\)
\(264\) 0 0
\(265\) −17.8534 + 101.252i −0.00413860 + 0.0234711i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −247.976 −0.0562058 −0.0281029 0.999605i \(-0.508947\pi\)
−0.0281029 + 0.999605i \(0.508947\pi\)
\(270\) 0 0
\(271\) 1822.09 0.408427 0.204214 0.978926i \(-0.434536\pi\)
0.204214 + 0.978926i \(0.434536\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 517.680 2935.91i 0.113517 0.643789i
\(276\) 0 0
\(277\) −5726.87 + 4805.42i −1.24222 + 1.04234i −0.244871 + 0.969556i \(0.578746\pi\)
−0.997347 + 0.0727890i \(0.976810\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 994.844 + 5642.04i 0.211201 + 1.19778i 0.887379 + 0.461041i \(0.152524\pi\)
−0.676178 + 0.736738i \(0.736365\pi\)
\(282\) 0 0
\(283\) −7822.43 + 2847.13i −1.64309 + 0.598037i −0.987576 0.157144i \(-0.949771\pi\)
−0.655517 + 0.755181i \(0.727549\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −716.956 + 1241.80i −0.147458 + 0.255406i
\(288\) 0 0
\(289\) −4799.54 8313.05i −0.976907 1.69205i
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 5895.42 + 4946.85i 1.17547 + 0.986341i 0.999998 + 0.00185700i \(0.000591103\pi\)
0.175477 + 0.984484i \(0.443853\pi\)
\(294\) 0 0
\(295\) −7850.92 2857.50i −1.54949 0.563967i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −7327.95 2667.16i −1.41735 0.515872i
\(300\) 0 0
\(301\) −453.176 380.259i −0.0867794 0.0728166i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −959.909 1662.61i −0.180211 0.312134i
\(306\) 0 0
\(307\) −492.501 + 853.036i −0.0915586 + 0.158584i −0.908167 0.418608i \(-0.862518\pi\)
0.816609 + 0.577192i \(0.195852\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 4910.29 1787.20i 0.895295 0.325861i 0.146929 0.989147i \(-0.453061\pi\)
0.748366 + 0.663286i \(0.230839\pi\)
\(312\) 0 0
\(313\) 233.562 + 1324.60i 0.0421780 + 0.239203i 0.998607 0.0527613i \(-0.0168022\pi\)
−0.956429 + 0.291964i \(0.905691\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 6538.61 5486.55i 1.15850 0.972098i 0.158618 0.987340i \(-0.449296\pi\)
0.999884 + 0.0152416i \(0.00485174\pi\)
\(318\) 0 0
\(319\) −266.684 + 1512.44i −0.0468070 + 0.265456i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −5966.05 −1.02774
\(324\) 0 0
\(325\) −11677.1 −1.99301
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −66.4818 + 377.037i −0.0111406 + 0.0631816i
\(330\) 0 0
\(331\) 933.837 783.583i 0.155071 0.130120i −0.561951 0.827170i \(-0.689949\pi\)
0.717022 + 0.697051i \(0.245505\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −456.559 2589.27i −0.0744611 0.422290i
\(336\) 0 0
\(337\) −2735.67 + 995.702i −0.442200 + 0.160948i −0.553518 0.832837i \(-0.686715\pi\)
0.111318 + 0.993785i \(0.464493\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 1778.99 3081.30i 0.282515 0.489331i
\(342\) 0 0
\(343\) 2036.31 + 3526.99i 0.320555 + 0.555218i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −3.10433 2.60485i −0.000480258 0.000402984i 0.642547 0.766246i \(-0.277878\pi\)
−0.643028 + 0.765843i \(0.722322\pi\)
\(348\) 0 0
\(349\) −766.910 279.132i −0.117627 0.0428126i 0.282536 0.959257i \(-0.408824\pi\)
−0.400163 + 0.916444i \(0.631046\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −6770.69 2464.33i −1.02087 0.371567i −0.223273 0.974756i \(-0.571674\pi\)
−0.797598 + 0.603189i \(0.793896\pi\)
\(354\) 0 0
\(355\) 7328.56 + 6149.39i 1.09566 + 0.919368i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 4552.44 + 7885.06i 0.669272 + 1.15921i 0.978108 + 0.208098i \(0.0667273\pi\)
−0.308836 + 0.951115i \(0.599939\pi\)
\(360\) 0 0
\(361\) 2203.15 3815.97i 0.321206 0.556346i
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 186.260 67.7930i 0.0267104 0.00972178i
\(366\) 0 0
\(367\) 859.398 + 4873.89i 0.122235 + 0.693229i 0.982912 + 0.184077i \(0.0589296\pi\)
−0.860677 + 0.509152i \(0.829959\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 26.2883 22.0585i 0.00367875 0.00308684i
\(372\) 0 0
\(373\) 1220.42 6921.37i 0.169413 0.960791i −0.774983 0.631982i \(-0.782242\pi\)
0.944396 0.328809i \(-0.106647\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 6015.48 0.821786
\(378\) 0 0
\(379\) 12299.7 1.66700 0.833498 0.552523i \(-0.186335\pi\)
0.833498 + 0.552523i \(0.186335\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 187.769 1064.89i 0.0250510 0.142071i −0.969717 0.244231i \(-0.921464\pi\)
0.994768 + 0.102160i \(0.0325755\pi\)
\(384\) 0 0
\(385\) −1173.96 + 985.068i −0.155404 + 0.130399i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 1084.45 + 6150.21i 0.141346 + 0.801615i 0.970228 + 0.242192i \(0.0778662\pi\)
−0.828882 + 0.559423i \(0.811023\pi\)
\(390\) 0 0
\(391\) 17496.1 6368.05i 2.26295 0.823648i
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −11475.7 + 19876.5i −1.46179 + 2.53189i
\(396\) 0 0
\(397\) 674.465 + 1168.21i 0.0852655 + 0.147684i 0.905504 0.424337i \(-0.139493\pi\)
−0.820239 + 0.572021i \(0.806159\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −5214.03 4375.09i −0.649318 0.544842i 0.257546 0.966266i \(-0.417086\pi\)
−0.906864 + 0.421424i \(0.861530\pi\)
\(402\) 0 0
\(403\) −13095.8 4766.50i −1.61874 0.589172i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −4218.04 1535.24i −0.513711 0.186975i
\(408\) 0 0
\(409\) 5656.78 + 4746.60i 0.683887 + 0.573849i 0.917139 0.398567i \(-0.130492\pi\)
−0.233252 + 0.972416i \(0.574937\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 1394.32 + 2415.03i 0.166125 + 0.287738i
\(414\) 0 0
\(415\) 3524.87 6105.26i 0.416938 0.722157i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 7526.42 2739.39i 0.877541 0.319399i 0.136324 0.990664i \(-0.456471\pi\)
0.741217 + 0.671265i \(0.234249\pi\)
\(420\) 0 0
\(421\) 646.492 + 3666.44i 0.0748410 + 0.424445i 0.999090 + 0.0426540i \(0.0135813\pi\)
−0.924249 + 0.381791i \(0.875308\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 21357.4 17921.0i 2.43761 2.04540i
\(426\) 0 0
\(427\) −111.272 + 631.056i −0.0126109 + 0.0715197i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −12885.0 −1.44003 −0.720013 0.693961i \(-0.755864\pi\)
−0.720013 + 0.693961i \(0.755864\pi\)
\(432\) 0 0
\(433\) −3411.32 −0.378609 −0.189304 0.981918i \(-0.560623\pi\)
−0.189304 + 0.981918i \(0.560623\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 1329.17 7538.12i 0.145499 0.825165i
\(438\) 0 0
\(439\) −4680.52 + 3927.42i −0.508859 + 0.426983i −0.860727 0.509066i \(-0.829991\pi\)
0.351869 + 0.936049i \(0.385546\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −484.348 2746.88i −0.0519460 0.294600i 0.947756 0.318995i \(-0.103345\pi\)
−0.999702 + 0.0243946i \(0.992234\pi\)
\(444\) 0 0
\(445\) 24955.8 9083.16i 2.65846 0.967602i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −1297.43 + 2247.22i −0.136369 + 0.236198i −0.926120 0.377230i \(-0.876877\pi\)
0.789751 + 0.613428i \(0.210210\pi\)
\(450\) 0 0
\(451\) −1465.58 2538.46i −0.153019 0.265036i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 4598.30 + 3858.43i 0.473783 + 0.397551i
\(456\) 0 0
\(457\) 13770.5 + 5012.04i 1.40953 + 0.513027i 0.930992 0.365041i \(-0.118945\pi\)
0.478537 + 0.878067i \(0.341167\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −7857.56 2859.92i −0.793846 0.288936i −0.0869123 0.996216i \(-0.527700\pi\)
−0.706934 + 0.707280i \(0.749922\pi\)
\(462\) 0 0
\(463\) −6948.19 5830.23i −0.697430 0.585213i 0.223611 0.974678i \(-0.428215\pi\)
−0.921041 + 0.389465i \(0.872660\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −5164.61 8945.37i −0.511755 0.886386i −0.999907 0.0136276i \(-0.995662\pi\)
0.488152 0.872759i \(-0.337671\pi\)
\(468\) 0 0
\(469\) −438.786 + 760.000i −0.0432010 + 0.0748263i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 1136.36 413.600i 0.110465 0.0402058i
\(474\) 0 0
\(475\) −1990.31 11287.6i −0.192256 1.09034i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 12778.9 10722.7i 1.21896 1.02283i 0.220079 0.975482i \(-0.429368\pi\)
0.998879 0.0473453i \(-0.0150761\pi\)
\(480\) 0 0
\(481\) −3053.08 + 17314.9i −0.289415 + 1.64135i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 14355.4 1.34401
\(486\) 0 0
\(487\) −44.5903 −0.00414904 −0.00207452 0.999998i \(-0.500660\pi\)
−0.00207452 + 0.999998i \(0.500660\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 472.750 2681.10i 0.0434520 0.246428i −0.955343 0.295498i \(-0.904514\pi\)
0.998795 + 0.0490695i \(0.0156256\pi\)
\(492\) 0 0
\(493\) −11002.3 + 9232.01i −1.00511 + 0.843385i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −554.486 3144.65i −0.0500445 0.283816i
\(498\) 0 0
\(499\) 633.315 230.508i 0.0568158 0.0206792i −0.313456 0.949603i \(-0.601487\pi\)
0.370272 + 0.928924i \(0.379265\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 6369.04 11031.5i 0.564576 0.977874i −0.432513 0.901628i \(-0.642373\pi\)
0.997089 0.0762462i \(-0.0242935\pi\)
\(504\) 0 0
\(505\) −7456.34 12914.8i −0.657035 1.13802i
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 4229.88 + 3549.29i 0.368342 + 0.309076i 0.808105 0.589038i \(-0.200493\pi\)
−0.439763 + 0.898114i \(0.644938\pi\)
\(510\) 0 0
\(511\) −62.1692 22.6277i −0.00538200 0.00195889i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −35840.3 13044.8i −3.06662 1.11616i
\(516\) 0 0
\(517\) −599.519 503.056i −0.0509997 0.0427938i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −1158.06 2005.82i −0.0973811 0.168669i 0.813219 0.581958i \(-0.197713\pi\)
−0.910600 + 0.413289i \(0.864380\pi\)
\(522\) 0 0
\(523\) 5416.67 9381.95i 0.452876 0.784405i −0.545687 0.837989i \(-0.683731\pi\)
0.998563 + 0.0535841i \(0.0170645\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 31267.4 11380.4i 2.58450 0.940680i
\(528\) 0 0
\(529\) 2035.33 + 11543.0i 0.167283 + 0.948710i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −8795.03 + 7379.90i −0.714737 + 0.599736i
\(534\) 0 0
\(535\) −5160.98 + 29269.4i −0.417063 + 2.36528i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −3906.80 −0.312204
\(540\) 0 0
\(541\) 13970.7 1.11025 0.555127 0.831765i \(-0.312670\pi\)
0.555127 + 0.831765i \(0.312670\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −1883.58 + 10682.3i −0.148044 + 0.839598i
\(546\) 0 0
\(547\) 3549.94 2978.75i 0.277485 0.232838i −0.493414 0.869794i \(-0.664251\pi\)
0.770900 + 0.636956i \(0.219807\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 1025.31 + 5814.83i 0.0792735 + 0.449583i
\(552\) 0 0
\(553\) 7198.65 2620.10i 0.553559 0.201479i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 4026.97 6974.91i 0.306334 0.530586i −0.671223 0.741255i \(-0.734231\pi\)
0.977557 + 0.210669i \(0.0675642\pi\)
\(558\) 0 0
\(559\) −2368.33 4102.08i −0.179195 0.310374i
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 3552.22 + 2980.66i 0.265911 + 0.223126i 0.765988 0.642855i \(-0.222250\pi\)
−0.500076 + 0.865981i \(0.666695\pi\)
\(564\) 0 0
\(565\) 13559.5 + 4935.27i 1.00965 + 0.367483i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 17270.2 + 6285.84i 1.27241 + 0.463121i 0.887917 0.460005i \(-0.152152\pi\)
0.384498 + 0.923126i \(0.374374\pi\)
\(570\) 0 0
\(571\) −10862.7 9114.85i −0.796126 0.668029i 0.151127 0.988514i \(-0.451710\pi\)
−0.947254 + 0.320485i \(0.896154\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 17885.0 + 30977.7i 1.29714 + 2.24671i
\(576\) 0 0
\(577\) −1079.77 + 1870.21i −0.0779051 + 0.134936i −0.902346 0.431013i \(-0.858156\pi\)
0.824441 + 0.565948i \(0.191490\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −2211.14 + 804.788i −0.157889 + 0.0574668i
\(582\) 0 0
\(583\) 12.1813 + 69.0837i 0.000865350 + 0.00490764i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −4721.75 + 3962.02i −0.332006 + 0.278586i −0.793517 0.608548i \(-0.791752\pi\)
0.461510 + 0.887135i \(0.347308\pi\)
\(588\) 0 0
\(589\) 2375.38 13471.4i 0.166173 0.942413i
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −24524.4 −1.69831 −0.849155 0.528143i \(-0.822888\pi\)
−0.849155 + 0.528143i \(0.822888\pi\)
\(594\) 0 0
\(595\) −14331.8 −0.987474
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 512.331 2905.57i 0.0349470 0.198194i −0.962336 0.271864i \(-0.912360\pi\)
0.997283 + 0.0736696i \(0.0234710\pi\)
\(600\) 0 0
\(601\) 4584.26 3846.65i 0.311141 0.261078i −0.473822 0.880620i \(-0.657126\pi\)
0.784963 + 0.619542i \(0.212682\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 3819.55 + 21661.7i 0.256672 + 1.45566i
\(606\) 0 0
\(607\) −23151.1 + 8426.31i −1.54806 + 0.563448i −0.967962 0.251097i \(-0.919209\pi\)
−0.580100 + 0.814545i \(0.696986\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −1532.72 + 2654.75i −0.101485 + 0.175777i
\(612\) 0 0
\(613\) 4499.01 + 7792.52i 0.296433 + 0.513437i 0.975317 0.220808i \(-0.0708695\pi\)
−0.678884 + 0.734245i \(0.737536\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 9712.00 + 8149.34i 0.633696 + 0.531734i 0.902075 0.431579i \(-0.142043\pi\)
−0.268379 + 0.963313i \(0.586488\pi\)
\(618\) 0 0
\(619\) −15322.8 5577.06i −0.994954 0.362134i −0.207318 0.978274i \(-0.566473\pi\)
−0.787637 + 0.616140i \(0.788696\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −8329.66 3031.75i −0.535667 0.194967i
\(624\) 0 0
\(625\) 6900.30 + 5790.04i 0.441619 + 0.370563i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −20989.2 36354.4i −1.33052 2.30452i
\(630\) 0 0
\(631\) 7036.53 12187.6i 0.443930 0.768909i −0.554047 0.832485i \(-0.686917\pi\)
0.997977 + 0.0635763i \(0.0202506\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −44478.7 + 16188.9i −2.77966 + 1.01171i
\(636\) 0 0
\(637\) 2657.27 + 15070.1i 0.165282 + 0.937364i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 4012.91 3367.23i 0.247270 0.207485i −0.510725 0.859744i \(-0.670623\pi\)
0.757996 + 0.652259i \(0.226179\pi\)
\(642\) 0 0
\(643\) 354.032 2007.82i 0.0217133 0.123142i −0.972024 0.234880i \(-0.924530\pi\)
0.993738 + 0.111737i \(0.0356415\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 6881.39 0.418138 0.209069 0.977901i \(-0.432957\pi\)
0.209069 + 0.977901i \(0.432957\pi\)
\(648\) 0 0
\(649\) −5700.43 −0.344779
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −1091.47 + 6190.04i −0.0654097 + 0.370957i 0.934479 + 0.356019i \(0.115866\pi\)
−0.999888 + 0.0149379i \(0.995245\pi\)
\(654\) 0 0
\(655\) 9869.36 8281.37i 0.588745 0.494015i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −1916.11 10866.8i −0.113264 0.642354i −0.987595 0.157023i \(-0.949810\pi\)
0.874331 0.485331i \(-0.161301\pi\)
\(660\) 0 0
\(661\) 4442.15 1616.81i 0.261391 0.0951385i −0.208000 0.978129i \(-0.566696\pi\)
0.469391 + 0.882990i \(0.344473\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −2945.97 + 5102.56i −0.171789 + 0.297547i
\(666\) 0 0
\(667\) −9213.48 15958.2i −0.534854 0.926394i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −1003.43 841.977i −0.0577302 0.0484414i
\(672\) 0 0
\(673\) −19864.3 7230.00i −1.13776 0.414110i −0.296655 0.954985i \(-0.595871\pi\)
−0.841103 + 0.540875i \(0.818093\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −15927.8 5797.25i −0.904218 0.329108i −0.152276 0.988338i \(-0.548660\pi\)
−0.751942 + 0.659230i \(0.770883\pi\)
\(678\) 0 0
\(679\) −3670.50 3079.91i −0.207453 0.174074i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 11348.3 + 19655.9i 0.635771 + 1.10119i 0.986351 + 0.164655i \(0.0526512\pi\)
−0.350580 + 0.936533i \(0.614015\pi\)
\(684\) 0 0
\(685\) −16565.0 + 28691.4i −0.923964 + 1.60035i
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 258.199 93.9766i 0.0142766 0.00519626i
\(690\) 0 0
\(691\) −2443.78 13859.4i −0.134538 0.763004i −0.975180 0.221413i \(-0.928933\pi\)
0.840642 0.541591i \(-0.182178\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 5349.03 4488.37i 0.291943 0.244969i
\(696\) 0 0
\(697\) 4760.05 26995.6i 0.258680 1.46705i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 24229.9 1.30549 0.652747 0.757576i \(-0.273616\pi\)
0.652747 + 0.757576i \(0.273616\pi\)
\(702\) 0 0
\(703\) −17257.7 −0.925871
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −864.334 + 4901.88i −0.0459783 + 0.260756i
\(708\) 0 0
\(709\) −7698.64 + 6459.93i −0.407798 + 0.342183i −0.823498 0.567319i \(-0.807981\pi\)
0.415701 + 0.909501i \(0.363536\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 7413.13 + 42041.9i 0.389374 + 2.20825i
\(714\) 0 0
\(715\) −11530.4 + 4196.73i −0.603096 + 0.219509i
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −9663.42 + 16737.5i −0.501231 + 0.868157i 0.498768 + 0.866735i \(0.333786\pi\)
−0.999999 + 0.00142169i \(0.999547\pi\)
\(720\) 0 0
\(721\) 6365.19 + 11024.8i 0.328782 + 0.569468i
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −21137.1 17736.2i −1.08278 0.908559i
\(726\) 0 0
\(727\) −2721.32 990.481i −0.138828 0.0505294i 0.271671 0.962390i \(-0.412424\pi\)
−0.410500 + 0.911861i \(0.634646\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 10627.2 + 3867.97i 0.537701 + 0.195707i
\(732\) 0 0
\(733\) −11980.4 10052.8i −0.603692 0.506558i 0.288938 0.957348i \(-0.406698\pi\)
−0.892630 + 0.450790i \(0.851142\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −896.952 1553.57i −0.0448299 0.0776477i
\(738\) 0 0
\(739\) −11274.3 + 19527.6i −0.561205 + 0.972036i 0.436186 + 0.899856i \(0.356329\pi\)
−0.997392 + 0.0721798i \(0.977004\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −27399.7 + 9972.67i −1.35289 + 0.492412i −0.913849 0.406055i \(-0.866904\pi\)
−0.439042 + 0.898467i \(0.644682\pi\)
\(744\) 0 0
\(745\) −3666.75 20795.2i −0.180321 1.02265i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 7599.28 6376.55i 0.370723 0.311074i
\(750\) 0 0
\(751\) −812.925 + 4610.33i −0.0394994 + 0.224012i −0.998167 0.0605152i \(-0.980726\pi\)
0.958668 + 0.284528i \(0.0918367\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −20165.5 −0.972050
\(756\) 0 0
\(757\) 11943.5 0.573440 0.286720 0.958014i \(-0.407435\pi\)
0.286720 + 0.958014i \(0.407435\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 5096.74 28905.0i 0.242781 1.37688i −0.582808 0.812610i \(-0.698046\pi\)
0.825589 0.564271i \(-0.190843\pi\)
\(762\) 0 0
\(763\) 2773.48 2327.22i 0.131595 0.110421i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 3877.23 + 21988.9i 0.182528 + 1.03517i
\(768\) 0 0
\(769\) −5688.13 + 2070.31i −0.266735 + 0.0970836i −0.471925 0.881638i \(-0.656441\pi\)
0.205190 + 0.978722i \(0.434219\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −524.285 + 908.088i −0.0243948 + 0.0422531i −0.877965 0.478725i \(-0.841099\pi\)
0.853570 + 0.520978i \(0.174433\pi\)
\(774\) 0 0
\(775\) 31962.4 + 55360.5i 1.48145 + 2.56595i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −8632.81 7243.78i −0.397051 0.333165i
\(780\) 0 0
\(781\) 6133.71 + 2232.49i 0.281026 + 0.102285i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 57913.6 + 21078.8i 2.63315 + 0.958389i
\(786\) 0 0
\(787\) 6681.12 + 5606.12i 0.302613 + 0.253922i 0.781431 0.623992i \(-0.214490\pi\)
−0.478818 + 0.877914i \(0.658935\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −2408.16 4171.05i