Properties

Label 324.4.i.a.145.2
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 145.2
Character \(\chi\) \(=\) 324.145
Dual form 324.4.i.a.181.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-2.26368 + 12.8380i) q^{5} +(-3.04053 + 2.55131i) q^{7} +O(q^{10})\) \(q+(-2.26368 + 12.8380i) q^{5} +(-3.04053 + 2.55131i) q^{7} +(1.56137 + 8.85499i) q^{11} +(-33.8700 + 12.3277i) q^{13} +(-0.988527 + 1.71218i) q^{17} +(-56.3039 - 97.5212i) q^{19} +(73.1185 + 61.3537i) q^{23} +(-42.2272 - 15.3695i) q^{25} +(-237.316 - 86.3761i) q^{29} +(-154.385 - 129.544i) q^{31} +(-25.8708 - 44.8096i) q^{35} +(112.630 - 195.081i) q^{37} +(-209.778 + 76.3529i) q^{41} +(-10.6717 - 60.5223i) q^{43} +(-140.866 + 118.201i) q^{47} +(-56.8257 + 322.274i) q^{49} -596.365 q^{53} -117.214 q^{55} +(-26.4036 + 149.742i) q^{59} +(-282.206 + 236.799i) q^{61} +(-81.5913 - 462.727i) q^{65} +(869.318 - 316.406i) q^{67} +(-384.966 + 666.780i) q^{71} +(-329.352 - 570.454i) q^{73} +(-27.3392 - 22.9403i) q^{77} +(-1099.10 - 400.040i) q^{79} +(189.025 + 68.7996i) q^{83} +(-19.7432 - 16.5665i) q^{85} +(246.987 + 427.794i) q^{89} +(71.5311 - 123.896i) q^{91} +(1379.43 - 502.070i) q^{95} +(-95.1067 - 539.377i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 54q - 12q^{5} + O(q^{10}) \) \( 54q - 12q^{5} + 87q^{11} - 204q^{17} - 96q^{23} - 216q^{25} - 318q^{29} - 54q^{31} - 6q^{35} - 867q^{41} - 513q^{43} + 1548q^{47} + 594q^{49} + 1068q^{53} + 1218q^{59} - 54q^{61} - 96q^{65} - 2997q^{67} + 120q^{71} - 216q^{73} - 3480q^{77} + 2808q^{79} - 4464q^{83} + 2160q^{85} - 4029q^{89} + 270q^{91} + 1650q^{95} - 3483q^{97} + O(q^{100}) \)

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
\(5\) −2.26368 + 12.8380i −0.202469 + 1.14826i 0.698903 + 0.715217i \(0.253672\pi\)
−0.901372 + 0.433045i \(0.857439\pi\)
\(6\) 0 0
\(7\) −3.04053 + 2.55131i −0.164173 + 0.137758i −0.721173 0.692755i \(-0.756397\pi\)
0.557000 + 0.830513i \(0.311952\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 1.56137 + 8.85499i 0.0427974 + 0.242716i 0.998700 0.0509665i \(-0.0162302\pi\)
−0.955903 + 0.293683i \(0.905119\pi\)
\(12\) 0 0
\(13\) −33.8700 + 12.3277i −0.722603 + 0.263006i −0.677031 0.735955i \(-0.736734\pi\)
−0.0455728 + 0.998961i \(0.514511\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −0.988527 + 1.71218i −0.0141031 + 0.0244273i −0.872991 0.487737i \(-0.837823\pi\)
0.858888 + 0.512164i \(0.171156\pi\)
\(18\) 0 0
\(19\) −56.3039 97.5212i −0.679842 1.17752i −0.975028 0.222081i \(-0.928715\pi\)
0.295186 0.955440i \(-0.404618\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 73.1185 + 61.3537i 0.662881 + 0.556223i 0.910949 0.412520i \(-0.135351\pi\)
−0.248068 + 0.968743i \(0.579796\pi\)
\(24\) 0 0
\(25\) −42.2272 15.3695i −0.337818 0.122956i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −237.316 86.3761i −1.51960 0.553091i −0.558555 0.829467i \(-0.688644\pi\)
−0.961049 + 0.276377i \(0.910866\pi\)
\(30\) 0 0
\(31\) −154.385 129.544i −0.894462 0.750543i 0.0746377 0.997211i \(-0.476220\pi\)
−0.969100 + 0.246668i \(0.920664\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −25.8708 44.8096i −0.124942 0.216406i
\(36\) 0 0
\(37\) 112.630 195.081i 0.500440 0.866788i −0.499560 0.866280i \(-0.666505\pi\)
1.00000 0.000508554i \(-0.000161878\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −209.778 + 76.3529i −0.799069 + 0.290837i −0.709101 0.705107i \(-0.750899\pi\)
−0.0899682 + 0.995945i \(0.528677\pi\)
\(42\) 0 0
\(43\) −10.6717 60.5223i −0.0378470 0.214641i 0.960019 0.279934i \(-0.0903127\pi\)
−0.997866 + 0.0652936i \(0.979202\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −140.866 + 118.201i −0.437180 + 0.366837i −0.834653 0.550776i \(-0.814332\pi\)
0.397473 + 0.917614i \(0.369887\pi\)
\(48\) 0 0
\(49\) −56.8257 + 322.274i −0.165672 + 0.939575i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −596.365 −1.54561 −0.772803 0.634647i \(-0.781146\pi\)
−0.772803 + 0.634647i \(0.781146\pi\)
\(54\) 0 0
\(55\) −117.214 −0.287367
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −26.4036 + 149.742i −0.0582620 + 0.330420i −0.999982 0.00597705i \(-0.998097\pi\)
0.941720 + 0.336397i \(0.109209\pi\)
\(60\) 0 0
\(61\) −282.206 + 236.799i −0.592340 + 0.497033i −0.888973 0.457959i \(-0.848581\pi\)
0.296633 + 0.954992i \(0.404136\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −81.5913 462.727i −0.155695 0.882988i
\(66\) 0 0
\(67\) 869.318 316.406i 1.58514 0.576942i 0.608823 0.793306i \(-0.291642\pi\)
0.976313 + 0.216364i \(0.0694197\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −384.966 + 666.780i −0.643479 + 1.11454i 0.341171 + 0.940001i \(0.389176\pi\)
−0.984651 + 0.174537i \(0.944157\pi\)
\(72\) 0 0
\(73\) −329.352 570.454i −0.528051 0.914611i −0.999465 0.0326994i \(-0.989590\pi\)
0.471414 0.881912i \(-0.343744\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −27.3392 22.9403i −0.0404623 0.0339519i
\(78\) 0 0
\(79\) −1099.10 400.040i −1.56530 0.569721i −0.593354 0.804941i \(-0.702197\pi\)
−0.971942 + 0.235220i \(0.924419\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 189.025 + 68.7996i 0.249979 + 0.0909849i 0.463971 0.885851i \(-0.346424\pi\)
−0.213992 + 0.976835i \(0.568647\pi\)
\(84\) 0 0
\(85\) −19.7432 16.5665i −0.0251935 0.0211399i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 246.987 + 427.794i 0.294164 + 0.509506i 0.974790 0.223124i \(-0.0716256\pi\)
−0.680626 + 0.732631i \(0.738292\pi\)
\(90\) 0 0
\(91\) 71.5311 123.896i 0.0824011 0.142723i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 1379.43 502.070i 1.48975 0.542224i
\(96\) 0 0
\(97\) −95.1067 539.377i −0.0995529 0.564592i −0.993257 0.115935i \(-0.963014\pi\)
0.893704 0.448657i \(-0.148098\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 1429.40 1199.41i 1.40822 1.18164i 0.450915 0.892567i \(-0.351098\pi\)
0.957307 0.289072i \(-0.0933467\pi\)
\(102\) 0 0
\(103\) −218.788 + 1240.81i −0.209299 + 1.18699i 0.681230 + 0.732069i \(0.261445\pi\)
−0.890530 + 0.454925i \(0.849666\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −440.582 −0.398062 −0.199031 0.979993i \(-0.563779\pi\)
−0.199031 + 0.979993i \(0.563779\pi\)
\(108\) 0 0
\(109\) 492.564 0.432836 0.216418 0.976301i \(-0.430563\pi\)
0.216418 + 0.976301i \(0.430563\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −17.6894 + 100.321i −0.0147263 + 0.0835171i −0.991285 0.131733i \(-0.957946\pi\)
0.976559 + 0.215251i \(0.0690568\pi\)
\(114\) 0 0
\(115\) −953.172 + 799.806i −0.772902 + 0.648542i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −1.36265 7.72797i −0.00104970 0.00595313i
\(120\) 0 0
\(121\) 1174.76 427.577i 0.882613 0.321245i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −521.849 + 903.869i −0.373405 + 0.646756i
\(126\) 0 0
\(127\) 409.633 + 709.506i 0.286213 + 0.495736i 0.972903 0.231215i \(-0.0742701\pi\)
−0.686689 + 0.726951i \(0.740937\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 1924.49 + 1614.84i 1.28354 + 1.07702i 0.992746 + 0.120233i \(0.0383642\pi\)
0.290795 + 0.956785i \(0.406080\pi\)
\(132\) 0 0
\(133\) 420.001 + 152.868i 0.273825 + 0.0996640i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −2588.91 942.285i −1.61449 0.587626i −0.632169 0.774831i \(-0.717835\pi\)
−0.982321 + 0.187204i \(0.940057\pi\)
\(138\) 0 0
\(139\) 2395.25 + 2009.85i 1.46160 + 1.22643i 0.923528 + 0.383531i \(0.125292\pi\)
0.538073 + 0.842898i \(0.319152\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −162.045 280.670i −0.0947614 0.164132i
\(144\) 0 0
\(145\) 1646.10 2851.13i 0.942766 1.63292i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 1326.33 482.746i 0.729245 0.265424i 0.0494000 0.998779i \(-0.484269\pi\)
0.679845 + 0.733355i \(0.262047\pi\)
\(150\) 0 0
\(151\) 597.674 + 3389.58i 0.322106 + 1.82675i 0.529278 + 0.848449i \(0.322463\pi\)
−0.207172 + 0.978305i \(0.566426\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 2012.56 1688.74i 1.04292 0.875115i
\(156\) 0 0
\(157\) −408.190 + 2314.96i −0.207497 + 1.17678i 0.685964 + 0.727636i \(0.259381\pi\)
−0.893461 + 0.449141i \(0.851730\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) −378.851 −0.185451
\(162\) 0 0
\(163\) 1291.76 0.620729 0.310364 0.950618i \(-0.399549\pi\)
0.310364 + 0.950618i \(0.399549\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −83.6793 + 474.569i −0.0387742 + 0.219900i −0.998038 0.0626128i \(-0.980057\pi\)
0.959264 + 0.282512i \(0.0911678\pi\)
\(168\) 0 0
\(169\) −687.795 + 577.129i −0.313061 + 0.262689i
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −313.847 1779.91i −0.137927 0.782222i −0.972777 0.231744i \(-0.925557\pi\)
0.834850 0.550478i \(-0.185554\pi\)
\(174\) 0 0
\(175\) 167.606 61.0034i 0.0723988 0.0263510i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 692.110 1198.77i 0.288998 0.500560i −0.684572 0.728945i \(-0.740011\pi\)
0.973571 + 0.228385i \(0.0733444\pi\)
\(180\) 0 0
\(181\) −1360.40 2356.28i −0.558660 0.967628i −0.997609 0.0691156i \(-0.977982\pi\)
0.438948 0.898512i \(-0.355351\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 2249.49 + 1887.54i 0.893975 + 0.750135i
\(186\) 0 0
\(187\) −16.7048 6.08004i −0.00653248 0.00237763i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −696.042 253.339i −0.263685 0.0959735i 0.206795 0.978384i \(-0.433697\pi\)
−0.470480 + 0.882411i \(0.655919\pi\)
\(192\) 0 0
\(193\) 140.297 + 117.723i 0.0523253 + 0.0439062i 0.668575 0.743644i \(-0.266904\pi\)
−0.616250 + 0.787551i \(0.711349\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −264.489 458.109i −0.0956552 0.165680i 0.814227 0.580547i \(-0.197161\pi\)
−0.909882 + 0.414867i \(0.863828\pi\)
\(198\) 0 0
\(199\) −129.667 + 224.589i −0.0461901 + 0.0800036i −0.888196 0.459465i \(-0.848041\pi\)
0.842006 + 0.539468i \(0.181375\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 941.940 342.838i 0.325671 0.118535i
\(204\) 0 0
\(205\) −505.346 2865.96i −0.172170 0.976426i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 775.638 650.837i 0.256708 0.215404i
\(210\) 0 0
\(211\) 260.176 1475.53i 0.0848875 0.481421i −0.912493 0.409092i \(-0.865846\pi\)
0.997381 0.0723293i \(-0.0230432\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 801.139 0.254127
\(216\) 0 0
\(217\) 799.920 0.250240
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 12.3742 70.1777i 0.00376643 0.0213605i
\(222\) 0 0
\(223\) −1309.46 + 1098.77i −0.393219 + 0.329950i −0.817866 0.575409i \(-0.804843\pi\)
0.424647 + 0.905359i \(0.360398\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 602.888 + 3419.15i 0.176278 + 0.999722i 0.936658 + 0.350244i \(0.113901\pi\)
−0.760380 + 0.649478i \(0.774987\pi\)
\(228\) 0 0
\(229\) −3281.93 + 1194.52i −0.947056 + 0.344700i −0.768949 0.639311i \(-0.779220\pi\)
−0.178108 + 0.984011i \(0.556998\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −2934.66 + 5082.98i −0.825133 + 1.42917i 0.0766840 + 0.997055i \(0.475567\pi\)
−0.901817 + 0.432117i \(0.857767\pi\)
\(234\) 0 0
\(235\) −1198.58 2076.00i −0.332710 0.576270i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −907.681 761.635i −0.245661 0.206134i 0.511640 0.859200i \(-0.329038\pi\)
−0.757301 + 0.653066i \(0.773483\pi\)
\(240\) 0 0
\(241\) −4055.91 1476.23i −1.08408 0.394574i −0.262658 0.964889i \(-0.584599\pi\)
−0.821426 + 0.570315i \(0.806821\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −4008.71 1459.05i −1.04533 0.380471i
\(246\) 0 0
\(247\) 3109.22 + 2608.95i 0.800951 + 0.672078i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 1097.56 + 1901.04i 0.276006 + 0.478057i 0.970389 0.241549i \(-0.0776556\pi\)
−0.694382 + 0.719606i \(0.744322\pi\)
\(252\) 0 0
\(253\) −429.121 + 743.259i −0.106635 + 0.184697i
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −2279.52 + 829.676i −0.553277 + 0.201376i −0.603502 0.797361i \(-0.706228\pi\)
0.0502247 + 0.998738i \(0.484006\pi\)
\(258\) 0 0
\(259\) 155.257 + 880.506i 0.0372479 + 0.211243i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 2454.03 2059.17i 0.575368 0.482791i −0.308054 0.951369i \(-0.599678\pi\)
0.883422 + 0.468577i \(0.155233\pi\)
\(264\) 0 0
\(265\) 1349.98 7656.11i 0.312938 1.77476i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −5960.11 −1.35091 −0.675454 0.737402i \(-0.736052\pi\)
−0.675454 + 0.737402i \(0.736052\pi\)
\(270\) 0 0
\(271\) −5019.58 −1.12516 −0.562579 0.826743i \(-0.690191\pi\)
−0.562579 + 0.826743i \(0.690191\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 70.1639 397.919i 0.0153856 0.0872561i
\(276\) 0 0
\(277\) 146.113 122.603i 0.0316934 0.0265939i −0.626803 0.779177i \(-0.715637\pi\)
0.658497 + 0.752584i \(0.271193\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 767.156 + 4350.76i 0.162864 + 0.923646i 0.951240 + 0.308452i \(0.0998111\pi\)
−0.788376 + 0.615194i \(0.789078\pi\)
\(282\) 0 0
\(283\) −1405.36 + 511.510i −0.295195 + 0.107442i −0.485372 0.874308i \(-0.661316\pi\)
0.190177 + 0.981750i \(0.439094\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 443.037 767.362i 0.0911207 0.157826i
\(288\) 0 0
\(289\) 2454.55 + 4251.40i 0.499602 + 0.865336i
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −3504.42 2940.56i −0.698739 0.586312i 0.222676 0.974893i \(-0.428521\pi\)
−0.921415 + 0.388581i \(0.872965\pi\)
\(294\) 0 0
\(295\) −1862.62 677.937i −0.367613 0.133800i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −3232.87 1176.67i −0.625290 0.227587i
\(300\) 0 0
\(301\) 186.859 + 156.793i 0.0357819 + 0.0300246i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −2401.19 4158.98i −0.450792 0.780795i
\(306\) 0 0
\(307\) −117.958 + 204.309i −0.0219290 + 0.0379822i −0.876782 0.480889i \(-0.840314\pi\)
0.854853 + 0.518871i \(0.173647\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −5819.65 + 2118.18i −1.06110 + 0.386209i −0.812841 0.582485i \(-0.802080\pi\)
−0.248258 + 0.968694i \(0.579858\pi\)
\(312\) 0 0
\(313\) −1715.58 9729.51i −0.309809 1.75701i −0.599959 0.800031i \(-0.704816\pi\)
0.290150 0.956981i \(-0.406295\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 4080.53 3423.97i 0.722982 0.606654i −0.205227 0.978714i \(-0.565793\pi\)
0.928208 + 0.372061i \(0.121349\pi\)
\(318\) 0 0
\(319\) 394.320 2236.30i 0.0692090 0.392504i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 222.632 0.0383516
\(324\) 0 0
\(325\) 1619.71 0.276446
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 126.742 718.787i 0.0212386 0.120450i
\(330\) 0 0
\(331\) 4838.20 4059.73i 0.803419 0.674148i −0.145609 0.989342i \(-0.546514\pi\)
0.949027 + 0.315194i \(0.102070\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 2094.15 + 11876.5i 0.341539 + 1.93696i
\(336\) 0 0
\(337\) −2402.61 + 874.479i −0.388364 + 0.141353i −0.528820 0.848734i \(-0.677365\pi\)
0.140456 + 0.990087i \(0.455143\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 906.060 1569.34i 0.143888 0.249222i
\(342\) 0 0
\(343\) −1330.15 2303.88i −0.209391 0.362677i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −8752.25 7344.01i −1.35402 1.13616i −0.977779 0.209637i \(-0.932772\pi\)
−0.376241 0.926522i \(-0.622784\pi\)
\(348\) 0 0
\(349\) 6887.34 + 2506.79i 1.05636 + 0.384485i 0.811061 0.584962i \(-0.198890\pi\)
0.245303 + 0.969447i \(0.421113\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −12232.6 4452.30i −1.84441 0.671309i −0.987883 0.155199i \(-0.950398\pi\)
−0.856522 0.516110i \(-0.827380\pi\)
\(354\) 0 0
\(355\) −7688.65 6451.55i −1.14950 0.964542i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 2710.16 + 4694.13i 0.398431 + 0.690102i 0.993533 0.113548i \(-0.0362216\pi\)
−0.595102 + 0.803650i \(0.702888\pi\)
\(360\) 0 0
\(361\) −2910.76 + 5041.58i −0.424370 + 0.735031i
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 8069.01 2936.88i 1.15713 0.421160i
\(366\) 0 0
\(367\) 2194.97 + 12448.3i 0.312198 + 1.77056i 0.587520 + 0.809209i \(0.300104\pi\)
−0.275323 + 0.961352i \(0.588785\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 1813.27 1521.51i 0.253747 0.212919i
\(372\) 0 0
\(373\) −658.319 + 3733.51i −0.0913847 + 0.518268i 0.904411 + 0.426663i \(0.140311\pi\)
−0.995795 + 0.0916052i \(0.970800\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 9102.71 1.24354
\(378\) 0 0
\(379\) −2493.23 −0.337912 −0.168956 0.985624i \(-0.554040\pi\)
−0.168956 + 0.985624i \(0.554040\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −1316.89 + 7468.43i −0.175691 + 0.996395i 0.761652 + 0.647987i \(0.224389\pi\)
−0.937343 + 0.348408i \(0.886722\pi\)
\(384\) 0 0
\(385\) 356.394 299.050i 0.0471780 0.0395870i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 1875.22 + 10634.9i 0.244415 + 1.38615i 0.821848 + 0.569707i \(0.192943\pi\)
−0.577433 + 0.816438i \(0.695945\pi\)
\(390\) 0 0
\(391\) −177.328 + 64.5421i −0.0229357 + 0.00834792i
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 7623.70 13204.6i 0.971114 1.68202i
\(396\) 0 0
\(397\) 3857.11 + 6680.72i 0.487615 + 0.844573i 0.999899 0.0142430i \(-0.00453383\pi\)
−0.512284 + 0.858816i \(0.671200\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 7720.76 + 6478.49i 0.961487 + 0.806783i 0.981194 0.193022i \(-0.0618290\pi\)
−0.0197074 + 0.999806i \(0.506273\pi\)
\(402\) 0 0
\(403\) 6825.99 + 2484.46i 0.843739 + 0.307096i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 1903.30 + 692.744i 0.231801 + 0.0843687i
\(408\) 0 0
\(409\) −4145.48 3478.47i −0.501175 0.420536i 0.356836 0.934167i \(-0.383856\pi\)
−0.858011 + 0.513631i \(0.828300\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −301.758 522.661i −0.0359529 0.0622723i
\(414\) 0 0
\(415\) −1311.14 + 2270.96i −0.155087 + 0.268619i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −11675.1 + 4249.40i −1.36126 + 0.495457i −0.916443 0.400166i \(-0.868953\pi\)
−0.444815 + 0.895623i \(0.646730\pi\)
\(420\) 0 0
\(421\) −428.725 2431.42i −0.0496313 0.281473i 0.949884 0.312602i \(-0.101201\pi\)
−0.999515 + 0.0311294i \(0.990090\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 68.0580 57.1074i 0.00776776 0.00651792i
\(426\) 0 0
\(427\) 253.909 1439.99i 0.0287764 0.163199i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 11653.1 1.30234 0.651172 0.758930i \(-0.274278\pi\)
0.651172 + 0.758930i \(0.274278\pi\)
\(432\) 0 0
\(433\) 5397.02 0.598994 0.299497 0.954097i \(-0.403181\pi\)
0.299497 + 0.954097i \(0.403181\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 1866.43 10585.0i 0.204310 1.15870i
\(438\) 0 0
\(439\) 7244.36 6078.74i 0.787595 0.660871i −0.157554 0.987510i \(-0.550361\pi\)
0.945149 + 0.326640i \(0.105916\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 2289.99 + 12987.2i 0.245600 + 1.39286i 0.819096 + 0.573656i \(0.194476\pi\)
−0.573496 + 0.819208i \(0.694413\pi\)
\(444\) 0 0
\(445\) −6051.10 + 2202.42i −0.644606 + 0.234617i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 3593.50 6224.12i 0.377701 0.654197i −0.613027 0.790062i \(-0.710048\pi\)
0.990727 + 0.135866i \(0.0433815\pi\)
\(450\) 0 0
\(451\) −1003.65 1738.37i −0.104789 0.181500i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 1428.64 + 1198.77i 0.147199 + 0.123515i
\(456\) 0 0
\(457\) 10349.3 + 3766.83i 1.05934 + 0.385568i 0.812180 0.583406i \(-0.198280\pi\)
0.247160 + 0.968975i \(0.420503\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 9343.16 + 3400.63i 0.943936 + 0.343565i 0.767719 0.640787i \(-0.221392\pi\)
0.176217 + 0.984351i \(0.443614\pi\)
\(462\) 0 0
\(463\) −5891.36 4943.44i −0.591349 0.496201i 0.297303 0.954783i \(-0.403913\pi\)
−0.888652 + 0.458582i \(0.848357\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −4935.93 8549.27i −0.489095 0.847137i 0.510826 0.859684i \(-0.329340\pi\)
−0.999921 + 0.0125465i \(0.996006\pi\)
\(468\) 0 0
\(469\) −1835.94 + 3179.94i −0.180759 + 0.313083i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 519.261 188.996i 0.0504771 0.0183722i
\(474\) 0 0
\(475\) 878.710 + 4983.41i 0.0848799 + 0.481378i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 9244.93 7757.42i 0.881861 0.739969i −0.0846996 0.996407i \(-0.526993\pi\)
0.966561 + 0.256437i \(0.0825486\pi\)
\(480\) 0 0
\(481\) −1409.89 + 7995.87i −0.133649 + 0.757963i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 7139.79 0.668456
\(486\) 0 0
\(487\) −6706.32 −0.624009 −0.312004 0.950081i \(-0.601000\pi\)
−0.312004 + 0.950081i \(0.601000\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 1760.17 9982.44i 0.161783 0.917517i −0.790536 0.612415i \(-0.790198\pi\)
0.952320 0.305102i \(-0.0986907\pi\)
\(492\) 0 0
\(493\) 382.485 320.943i 0.0349417 0.0293196i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −530.662 3009.53i −0.0478942 0.271622i
\(498\) 0 0
\(499\) 16918.8 6157.95i 1.51782 0.552441i 0.557216 0.830368i \(-0.311870\pi\)
0.960602 + 0.277927i \(0.0896474\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 4061.30 7034.37i 0.360009 0.623553i −0.627953 0.778251i \(-0.716107\pi\)
0.987962 + 0.154698i \(0.0494404\pi\)
\(504\) 0 0
\(505\) 12162.2 + 21065.6i 1.07171 + 1.85625i
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −6075.88 5098.27i −0.529094 0.443962i 0.338695 0.940896i \(-0.390015\pi\)
−0.867788 + 0.496934i \(0.834459\pi\)
\(510\) 0 0
\(511\) 2456.81 + 894.206i 0.212687 + 0.0774117i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −15434.2 5617.58i −1.32060 0.480660i
\(516\) 0 0
\(517\) −1266.61 1062.81i −0.107748 0.0904110i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 6585.42 + 11406.3i 0.553766 + 0.959151i 0.997998 + 0.0632397i \(0.0201433\pi\)
−0.444232 + 0.895912i \(0.646523\pi\)
\(522\) 0 0
\(523\) −2530.57 + 4383.08i −0.211576 + 0.366460i −0.952208 0.305451i \(-0.901193\pi\)
0.740632 + 0.671911i \(0.234526\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 374.416 136.276i 0.0309485 0.0112643i
\(528\) 0 0
\(529\) −530.742 3009.99i −0.0436214 0.247389i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 6163.92 5172.15i 0.500918 0.420320i
\(534\) 0 0
\(535\) 997.335 5656.17i 0.0805954 0.457079i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −2942.46 −0.235141
\(540\) 0 0
\(541\) 6681.41 0.530973 0.265486 0.964115i \(-0.414467\pi\)
0.265486 + 0.964115i \(0.414467\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −1115.01 + 6323.52i −0.0876360 + 0.497008i
\(546\) 0 0
\(547\) 5816.65 4880.75i 0.454665 0.381510i −0.386498 0.922290i \(-0.626315\pi\)
0.841164 + 0.540781i \(0.181871\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 4938.33 + 28006.7i 0.381815 + 2.16538i
\(552\) 0 0
\(553\) 4362.48 1587.81i 0.335463 0.122099i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −11184.2 + 19371.6i −0.850789 + 1.47361i 0.0297091 + 0.999559i \(0.490542\pi\)
−0.880498 + 0.474050i \(0.842791\pi\)
\(558\) 0 0
\(559\) 1107.55 + 1918.33i 0.0838002 + 0.145146i
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −19967.2 16754.5i −1.49470 1.25420i −0.888488 0.458900i \(-0.848244\pi\)
−0.606213 0.795303i \(-0.707312\pi\)
\(564\) 0 0
\(565\) −1247.88 454.190i −0.0929179 0.0338193i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −9061.94 3298.28i −0.667656 0.243007i −0.0141178 0.999900i \(-0.504494\pi\)
−0.653538 + 0.756893i \(0.726716\pi\)
\(570\) 0 0
\(571\) −515.270 432.363i −0.0377642 0.0316879i 0.623710 0.781656i \(-0.285625\pi\)
−0.661474 + 0.749968i \(0.730069\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −2144.62 3714.59i −0.155542 0.269407i
\(576\) 0 0
\(577\) −8963.79 + 15525.7i −0.646738 + 1.12018i 0.337160 + 0.941448i \(0.390534\pi\)
−0.983897 + 0.178735i \(0.942800\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −750.267 + 273.075i −0.0535737 + 0.0194992i
\(582\) 0 0
\(583\) −931.149 5280.81i −0.0661479 0.375144i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 5963.06 5003.60i 0.419287 0.351824i −0.408604 0.912712i \(-0.633984\pi\)
0.827892 + 0.560888i \(0.189540\pi\)
\(588\) 0 0
\(589\) −3940.84 + 22349.6i −0.275687 + 1.56350i
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −10084.0 −0.698313 −0.349156 0.937064i \(-0.613532\pi\)
−0.349156 + 0.937064i \(0.613532\pi\)
\(594\) 0 0
\(595\) 102.296 0.00704828
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 1532.38 8690.56i 0.104526 0.592799i −0.886882 0.461996i \(-0.847133\pi\)
0.991408 0.130803i \(-0.0417555\pi\)
\(600\) 0 0
\(601\) 4597.20 3857.51i 0.312019 0.261815i −0.473307 0.880898i \(-0.656940\pi\)
0.785326 + 0.619082i \(0.212495\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 2829.94 + 16049.4i 0.190171 + 1.07851i
\(606\) 0 0
\(607\) 8273.70 3011.38i 0.553244 0.201364i −0.0502433 0.998737i \(-0.516000\pi\)
0.603487 + 0.797373i \(0.293777\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 3314.00 5740.01i 0.219427 0.380059i
\(612\) 0 0
\(613\) −9300.79 16109.4i −0.612814 1.06143i −0.990764 0.135599i \(-0.956704\pi\)
0.377949 0.925826i \(-0.376629\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 13785.7 + 11567.6i 0.899502 + 0.754772i 0.970093 0.242734i \(-0.0780441\pi\)
−0.0705912 + 0.997505i \(0.522489\pi\)
\(618\) 0 0
\(619\) −13208.1 4807.34i −0.857636 0.312154i −0.124486 0.992221i \(-0.539728\pi\)
−0.733149 + 0.680068i \(0.761950\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −1842.41 670.581i −0.118482 0.0431240i
\(624\) 0 0
\(625\) −14725.5 12356.2i −0.942433 0.790795i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 222.676 + 385.686i 0.0141155 + 0.0244488i
\(630\) 0 0
\(631\) −215.873 + 373.904i −0.0136193 + 0.0235893i −0.872755 0.488159i \(-0.837669\pi\)
0.859135 + 0.511748i \(0.171002\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −10035.9 + 3652.76i −0.627184 + 0.228276i
\(636\) 0 0
\(637\) −2048.21 11616.0i −0.127399 0.722513i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 19141.2 16061.4i 1.17946 0.989683i 0.179476 0.983762i \(-0.442560\pi\)
0.999982 0.00592039i \(-0.00188453\pi\)
\(642\) 0 0
\(643\) 4953.92 28095.1i 0.303831 1.72311i −0.325124 0.945671i \(-0.605406\pi\)
0.628955 0.777441i \(-0.283483\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −3112.39 −0.189120 −0.0945601 0.995519i \(-0.530144\pi\)
−0.0945601 + 0.995519i \(0.530144\pi\)
\(648\) 0 0
\(649\) −1367.19 −0.0826919
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −3977.39 + 22556.9i −0.238357 + 1.35179i 0.597070 + 0.802189i \(0.296331\pi\)
−0.835427 + 0.549601i \(0.814780\pi\)
\(654\) 0 0
\(655\) −25087.7 + 21051.1i −1.49658 + 1.25578i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −2358.50 13375.7i −0.139415 0.790659i −0.971683 0.236287i \(-0.924069\pi\)
0.832269 0.554372i \(-0.187042\pi\)
\(660\) 0 0
\(661\) −18384.6 + 6691.43i −1.08181 + 0.393747i −0.820581 0.571530i \(-0.806350\pi\)
−0.261229 + 0.965277i \(0.584128\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −2913.25 + 5045.91i −0.169881 + 0.294243i
\(666\) 0 0
\(667\) −12052.7 20875.9i −0.699674 1.21187i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −2537.48 2129.20i −0.145989 0.122499i
\(672\) 0 0
\(673\) −17264.6 6283.82i −0.988861 0.359916i −0.203582 0.979058i \(-0.565258\pi\)
−0.785279 + 0.619142i \(0.787480\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −15478.3 5633.63i −0.878697 0.319820i −0.137013 0.990569i \(-0.543750\pi\)
−0.741684 + 0.670750i \(0.765973\pi\)
\(678\) 0 0
\(679\) 1665.29 + 1397.35i 0.0941209 + 0.0789768i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −6770.96 11727.7i −0.379332 0.657022i 0.611633 0.791141i \(-0.290513\pi\)
−0.990965 + 0.134119i \(0.957179\pi\)
\(684\) 0 0
\(685\) 17957.5 31103.2i 1.00163 1.73488i
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 20198.9 7351.79i 1.11686 0.406504i
\(690\) 0 0
\(691\) 159.678 + 905.576i 0.00879077 + 0.0498549i 0.988888 0.148665i \(-0.0474976\pi\)
−0.980097 + 0.198520i \(0.936387\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −31224.5 + 26200.5i −1.70419 + 1.42999i
\(696\) 0 0
\(697\) 76.6413 434.654i 0.00416499 0.0236208i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 12265.5 0.660857 0.330429 0.943831i \(-0.392807\pi\)
0.330429 + 0.943831i \(0.392807\pi\)
\(702\) 0 0
\(703\) −25366.1 −1.36088
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −1286.07 + 7293.68i −0.0684126 + 0.387987i
\(708\) 0 0
\(709\) 6415.08 5382.89i 0.339807 0.285132i −0.456875 0.889531i \(-0.651031\pi\)
0.796682 + 0.604399i \(0.206587\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −3340.37 18944.2i −0.175453 0.995041i
\(714\) 0 0
\(715\) 3970.05 1444.98i 0.207652 0.0755793i
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −3738.55 + 6475.35i −0.193914 + 0.335869i −0.946544 0.322575i \(-0.895452\pi\)
0.752630 + 0.658444i \(0.228785\pi\)
\(720\) 0 0
\(721\) −2500.45 4330.91i −0.129156 0.223705i
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 8693.66 + 7294.84i 0.445344 + 0.373688i
\(726\) 0 0
\(727\) 10590.1 + 3854.47i 0.540253 + 0.196636i 0.597710 0.801712i \(-0.296077\pi\)
−0.0574578 + 0.998348i \(0.518299\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 114.174 + 41.5560i 0.00577686 + 0.00210261i
\(732\) 0 0
\(733\) 13571.6 + 11387.9i 0.683871 + 0.573836i 0.917135 0.398578i \(-0.130496\pi\)
−0.233264 + 0.972414i \(0.574940\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 4159.10 + 7203.77i 0.207873 + 0.360047i
\(738\) 0 0
\(739\) 9518.62 16486.7i 0.473813 0.820669i −0.525737 0.850647i \(-0.676210\pi\)
0.999551 + 0.0299781i \(0.00954375\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −10852.2 + 3949.86i −0.535837 + 0.195029i −0.595743 0.803175i \(-0.703142\pi\)
0.0599057 + 0.998204i \(0.480920\pi\)
\(744\) 0 0
\(745\) 3195.08 + 18120.2i 0.157126 + 0.891105i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 1339.60 1124.06i 0.0653512 0.0548361i
\(750\) 0 0
\(751\) −2308.21 + 13090.5i −0.112154 + 0.636058i 0.875966 + 0.482374i \(0.160225\pi\)
−0.988120 + 0.153685i \(0.950886\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −44868.2 −2.16281
\(756\) 0 0
\(757\) 8467.78 0.406561 0.203280 0.979121i \(-0.434840\pi\)
0.203280 + 0.979121i \(0.434840\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 1320.32 7487.93i 0.0628932 0.356685i −0.937078 0.349119i \(-0.886481\pi\)
0.999971 0.00756534i \(-0.00240815\pi\)
\(762\) 0 0
\(763\) −1497.66 + 1256.68i −0.0710601 + 0.0596265i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −951.684 5397.27i −0.0448022 0.254086i
\(768\) 0 0
\(769\) −26939.6 + 9805.21i −1.26329 + 0.459799i −0.884870 0.465837i \(-0.845753\pi\)
−0.378416 + 0.925636i \(0.623531\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −14194.6 + 24585.8i −0.660473 + 1.14397i 0.320019 + 0.947411i \(0.396311\pi\)
−0.980492 + 0.196561i \(0.937023\pi\)
\(774\) 0 0
\(775\) 4528.22 + 7843.11i 0.209882 + 0.363526i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 19257.3 + 16158.8i 0.885707 + 0.743197i
\(780\) 0 0
\(781\) −6505.40 2367.77i −0.298056 0.108483i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −28795.3 10480.6i −1.30923 0.476523i
\(786\) 0 0
\(787\) 24754.7 + 20771.6i 1.12123 + 0.940824i 0.998666 0.0516363i \(-0.0164437\pi\)
0.122565 + 0.992461i \(0.460888\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) &mi