Properties

Label 336.4.bc.d.17.6
Level $336$
Weight $4$
Character 336.17
Analytic conductor $19.825$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 336 = 2^{4} \cdot 3 \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 336.bc (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(19.8246417619\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
Defining polynomial: \( x^{12} - x^{11} - 29x^{9} + 6x^{8} - 49x^{7} + 1564x^{6} - 441x^{5} + 486x^{4} - 21141x^{3} - 59049x + 531441 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 2^{4}\cdot 3^{3} \)
Twist minimal: no (minimal twist has level 21)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 17.6
Root \(2.70662 - 1.29391i\) of defining polynomial
Character \(\chi\) \(=\) 336.17
Dual form 336.4.bc.d.257.6

$q$-expansion

\(f(q)\) \(=\) \(q+(5.18049 - 0.403134i) q^{3} +(5.80193 + 10.0492i) q^{5} +(18.4018 - 2.09174i) q^{7} +(26.6750 - 4.17686i) q^{9} +O(q^{10})\) \(q+(5.18049 - 0.403134i) q^{3} +(5.80193 + 10.0492i) q^{5} +(18.4018 - 2.09174i) q^{7} +(26.6750 - 4.17686i) q^{9} +(15.5157 + 8.95800i) q^{11} -62.4185i q^{13} +(34.1081 + 49.7211i) q^{15} +(-10.7082 + 18.5472i) q^{17} +(-9.50747 + 5.48914i) q^{19} +(94.4869 - 18.2546i) q^{21} +(-59.8367 + 34.5467i) q^{23} +(-4.82490 + 8.35697i) q^{25} +(136.506 - 32.3918i) q^{27} +265.583i q^{29} +(-8.85795 - 5.11414i) q^{31} +(83.9902 + 40.1519i) q^{33} +(127.786 + 172.788i) q^{35} +(-20.8257 - 36.0712i) q^{37} +(-25.1630 - 323.358i) q^{39} +31.0035 q^{41} +224.550 q^{43} +(196.741 + 243.829i) q^{45} +(-81.8595 - 141.785i) q^{47} +(334.249 - 76.9836i) q^{49} +(-47.9968 + 100.400i) q^{51} +(-456.586 - 263.610i) q^{53} +207.895i q^{55} +(-47.0405 + 32.2692i) q^{57} +(-205.978 + 356.765i) q^{59} +(223.807 - 129.215i) q^{61} +(482.129 - 132.659i) q^{63} +(627.258 - 362.148i) q^{65} +(161.737 - 280.137i) q^{67} +(-296.056 + 203.091i) q^{69} +45.4199i q^{71} +(-486.879 - 281.100i) q^{73} +(-21.6264 + 45.2383i) q^{75} +(304.254 + 132.388i) q^{77} +(144.610 + 250.473i) q^{79} +(694.108 - 222.835i) q^{81} +448.767 q^{83} -248.513 q^{85} +(107.066 + 1375.85i) q^{87} +(280.814 + 486.384i) q^{89} +(-130.563 - 1148.61i) q^{91} +(-47.9502 - 22.9228i) q^{93} +(-110.323 - 63.6953i) q^{95} +214.364i q^{97} +(451.297 + 174.147i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q + 3 q^{3} + 56 q^{7} - 3 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 12 q + 3 q^{3} + 56 q^{7} - 3 q^{9} - 6 q^{15} - 300 q^{19} + 357 q^{21} - 42 q^{25} + 930 q^{31} - 855 q^{33} + 764 q^{37} + 426 q^{39} + 1012 q^{43} + 2367 q^{45} - 336 q^{49} + 1341 q^{51} + 270 q^{57} + 2358 q^{61} - 1071 q^{63} - 792 q^{67} - 2904 q^{73} + 2418 q^{75} - 1674 q^{79} + 837 q^{81} + 348 q^{85} - 1638 q^{87} + 1218 q^{91} - 1479 q^{93} + 3354 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/336\mathbb{Z}\right)^\times\).

\(n\) \(85\) \(113\) \(127\) \(241\)
\(\chi(n)\) \(1\) \(-1\) \(1\) \(e\left(\frac{1}{6}\right)\)

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
\(3\) 5.18049 0.403134i 0.996986 0.0775831i
\(4\) 0 0
\(5\) 5.80193 + 10.0492i 0.518941 + 0.898832i 0.999758 + 0.0220109i \(0.00700684\pi\)
−0.480817 + 0.876821i \(0.659660\pi\)
\(6\) 0 0
\(7\) 18.4018 2.09174i 0.993601 0.112944i
\(8\) 0 0
\(9\) 26.6750 4.17686i 0.987962 0.154699i
\(10\) 0 0
\(11\) 15.5157 + 8.95800i 0.425287 + 0.245540i 0.697337 0.716743i \(-0.254368\pi\)
−0.272050 + 0.962283i \(0.587701\pi\)
\(12\) 0 0
\(13\) 62.4185i 1.33167i −0.746097 0.665837i \(-0.768075\pi\)
0.746097 0.665837i \(-0.231925\pi\)
\(14\) 0 0
\(15\) 34.1081 + 49.7211i 0.587111 + 0.855862i
\(16\) 0 0
\(17\) −10.7082 + 18.5472i −0.152772 + 0.264609i −0.932245 0.361826i \(-0.882153\pi\)
0.779474 + 0.626435i \(0.215487\pi\)
\(18\) 0 0
\(19\) −9.50747 + 5.48914i −0.114798 + 0.0662787i −0.556300 0.830982i \(-0.687779\pi\)
0.441502 + 0.897261i \(0.354446\pi\)
\(20\) 0 0
\(21\) 94.4869 18.2546i 0.981844 0.189690i
\(22\) 0 0
\(23\) −59.8367 + 34.5467i −0.542470 + 0.313195i −0.746079 0.665857i \(-0.768066\pi\)
0.203609 + 0.979052i \(0.434733\pi\)
\(24\) 0 0
\(25\) −4.82490 + 8.35697i −0.0385992 + 0.0668557i
\(26\) 0 0
\(27\) 136.506 32.3918i 0.972982 0.230881i
\(28\) 0 0
\(29\) 265.583i 1.70061i 0.526294 + 0.850303i \(0.323581\pi\)
−0.526294 + 0.850303i \(0.676419\pi\)
\(30\) 0 0
\(31\) −8.85795 5.11414i −0.0513205 0.0296299i 0.474120 0.880460i \(-0.342766\pi\)
−0.525441 + 0.850830i \(0.676100\pi\)
\(32\) 0 0
\(33\) 83.9902 + 40.1519i 0.443055 + 0.211805i
\(34\) 0 0
\(35\) 127.786 + 172.788i 0.617138 + 0.834470i
\(36\) 0 0
\(37\) −20.8257 36.0712i −0.0925331 0.160272i 0.816043 0.577991i \(-0.196163\pi\)
−0.908576 + 0.417719i \(0.862830\pi\)
\(38\) 0 0
\(39\) −25.1630 323.358i −0.103315 1.32766i
\(40\) 0 0
\(41\) 31.0035 0.118096 0.0590480 0.998255i \(-0.481193\pi\)
0.0590480 + 0.998255i \(0.481193\pi\)
\(42\) 0 0
\(43\) 224.550 0.796363 0.398181 0.917307i \(-0.369641\pi\)
0.398181 + 0.917307i \(0.369641\pi\)
\(44\) 0 0
\(45\) 196.741 + 243.829i 0.651742 + 0.807732i
\(46\) 0 0
\(47\) −81.8595 141.785i −0.254052 0.440031i 0.710586 0.703611i \(-0.248430\pi\)
−0.964638 + 0.263580i \(0.915097\pi\)
\(48\) 0 0
\(49\) 334.249 76.9836i 0.974487 0.224442i
\(50\) 0 0
\(51\) −47.9968 + 100.400i −0.131782 + 0.275664i
\(52\) 0 0
\(53\) −456.586 263.610i −1.18334 0.683200i −0.226553 0.973999i \(-0.572746\pi\)
−0.956784 + 0.290799i \(0.906079\pi\)
\(54\) 0 0
\(55\) 207.895i 0.509682i
\(56\) 0 0
\(57\) −47.0405 + 32.2692i −0.109310 + 0.0749853i
\(58\) 0 0
\(59\) −205.978 + 356.765i −0.454510 + 0.787234i −0.998660 0.0517537i \(-0.983519\pi\)
0.544150 + 0.838988i \(0.316852\pi\)
\(60\) 0 0
\(61\) 223.807 129.215i 0.469764 0.271218i −0.246377 0.969174i \(-0.579240\pi\)
0.716141 + 0.697956i \(0.245907\pi\)
\(62\) 0 0
\(63\) 482.129 132.659i 0.964168 0.265293i
\(64\) 0 0
\(65\) 627.258 362.148i 1.19695 0.691060i
\(66\) 0 0
\(67\) 161.737 280.137i 0.294915 0.510808i −0.680050 0.733166i \(-0.738042\pi\)
0.974965 + 0.222357i \(0.0713752\pi\)
\(68\) 0 0
\(69\) −296.056 + 203.091i −0.516536 + 0.354338i
\(70\) 0 0
\(71\) 45.4199i 0.0759205i 0.999279 + 0.0379603i \(0.0120860\pi\)
−0.999279 + 0.0379603i \(0.987914\pi\)
\(72\) 0 0
\(73\) −486.879 281.100i −0.780615 0.450688i 0.0560334 0.998429i \(-0.482155\pi\)
−0.836648 + 0.547741i \(0.815488\pi\)
\(74\) 0 0
\(75\) −21.6264 + 45.2383i −0.0332960 + 0.0696489i
\(76\) 0 0
\(77\) 304.254 + 132.388i 0.450298 + 0.195935i
\(78\) 0 0
\(79\) 144.610 + 250.473i 0.205949 + 0.356714i 0.950435 0.310925i \(-0.100639\pi\)
−0.744486 + 0.667638i \(0.767305\pi\)
\(80\) 0 0
\(81\) 694.108 222.835i 0.952137 0.305673i
\(82\) 0 0
\(83\) 448.767 0.593477 0.296738 0.954959i \(-0.404101\pi\)
0.296738 + 0.954959i \(0.404101\pi\)
\(84\) 0 0
\(85\) −248.513 −0.317118
\(86\) 0 0
\(87\) 107.066 + 1375.85i 0.131938 + 1.69548i
\(88\) 0 0
\(89\) 280.814 + 486.384i 0.334452 + 0.579288i 0.983379 0.181562i \(-0.0581155\pi\)
−0.648927 + 0.760850i \(0.724782\pi\)
\(90\) 0 0
\(91\) −130.563 1148.61i −0.150404 1.32315i
\(92\) 0 0
\(93\) −47.9502 22.9228i −0.0534645 0.0255590i
\(94\) 0 0
\(95\) −110.323 63.6953i −0.119147 0.0687895i
\(96\) 0 0
\(97\) 214.364i 0.224385i 0.993686 + 0.112192i \(0.0357873\pi\)
−0.993686 + 0.112192i \(0.964213\pi\)
\(98\) 0 0
\(99\) 451.297 + 174.147i 0.458152 + 0.176793i
\(100\) 0 0
\(101\) −858.845 + 1487.56i −0.846122 + 1.46553i 0.0385219 + 0.999258i \(0.487735\pi\)
−0.884644 + 0.466268i \(0.845598\pi\)
\(102\) 0 0
\(103\) −1002.61 + 578.855i −0.959123 + 0.553750i −0.895903 0.444250i \(-0.853470\pi\)
−0.0632200 + 0.998000i \(0.520137\pi\)
\(104\) 0 0
\(105\) 731.652 + 843.610i 0.680018 + 0.784075i
\(106\) 0 0
\(107\) 1054.64 608.897i 0.952859 0.550134i 0.0588912 0.998264i \(-0.481243\pi\)
0.893968 + 0.448131i \(0.147910\pi\)
\(108\) 0 0
\(109\) −649.132 + 1124.33i −0.570418 + 0.987992i 0.426105 + 0.904674i \(0.359885\pi\)
−0.996523 + 0.0833189i \(0.973448\pi\)
\(110\) 0 0
\(111\) −122.429 178.471i −0.104689 0.152610i
\(112\) 0 0
\(113\) 1437.86i 1.19701i −0.801118 0.598506i \(-0.795761\pi\)
0.801118 0.598506i \(-0.204239\pi\)
\(114\) 0 0
\(115\) −694.337 400.876i −0.563019 0.325059i
\(116\) 0 0
\(117\) −260.713 1665.01i −0.206008 1.31564i
\(118\) 0 0
\(119\) −158.254 + 363.699i −0.121908 + 0.280170i
\(120\) 0 0
\(121\) −505.009 874.701i −0.379420 0.657175i
\(122\) 0 0
\(123\) 160.613 12.4986i 0.117740 0.00916226i
\(124\) 0 0
\(125\) 1338.51 0.957759
\(126\) 0 0
\(127\) −2686.32 −1.87695 −0.938475 0.345347i \(-0.887761\pi\)
−0.938475 + 0.345347i \(0.887761\pi\)
\(128\) 0 0
\(129\) 1163.28 90.5238i 0.793962 0.0617843i
\(130\) 0 0
\(131\) −801.637 1388.48i −0.534651 0.926043i −0.999180 0.0404852i \(-0.987110\pi\)
0.464529 0.885558i \(-0.346224\pi\)
\(132\) 0 0
\(133\) −163.472 + 120.897i −0.106578 + 0.0788203i
\(134\) 0 0
\(135\) 1117.51 + 1183.84i 0.712444 + 0.754733i
\(136\) 0 0
\(137\) −2007.90 1159.26i −1.25216 0.722938i −0.280626 0.959817i \(-0.590542\pi\)
−0.971539 + 0.236879i \(0.923875\pi\)
\(138\) 0 0
\(139\) 1841.57i 1.12374i −0.827225 0.561871i \(-0.810082\pi\)
0.827225 0.561871i \(-0.189918\pi\)
\(140\) 0 0
\(141\) −481.230 701.514i −0.287425 0.418994i
\(142\) 0 0
\(143\) 559.144 968.466i 0.326979 0.566344i
\(144\) 0 0
\(145\) −2668.91 + 1540.90i −1.52856 + 0.882514i
\(146\) 0 0
\(147\) 1700.54 533.560i 0.954137 0.299369i
\(148\) 0 0
\(149\) 1126.68 650.488i 0.619470 0.357651i −0.157193 0.987568i \(-0.550244\pi\)
0.776663 + 0.629917i \(0.216911\pi\)
\(150\) 0 0
\(151\) −1308.24 + 2265.94i −0.705055 + 1.22119i 0.261616 + 0.965172i \(0.415745\pi\)
−0.966672 + 0.256020i \(0.917589\pi\)
\(152\) 0 0
\(153\) −208.172 + 539.472i −0.109998 + 0.285057i
\(154\) 0 0
\(155\) 118.688i 0.0615046i
\(156\) 0 0
\(157\) −809.876 467.582i −0.411689 0.237689i 0.279826 0.960051i \(-0.409723\pi\)
−0.691515 + 0.722362i \(0.743056\pi\)
\(158\) 0 0
\(159\) −2471.61 1181.56i −1.23278 0.589334i
\(160\) 0 0
\(161\) −1028.84 + 760.883i −0.503625 + 0.372460i
\(162\) 0 0
\(163\) −259.079 448.738i −0.124495 0.215631i 0.797041 0.603926i \(-0.206398\pi\)
−0.921535 + 0.388295i \(0.873064\pi\)
\(164\) 0 0
\(165\) 83.8094 + 1077.00i 0.0395428 + 0.508146i
\(166\) 0 0
\(167\) −3767.97 −1.74595 −0.872977 0.487761i \(-0.837814\pi\)
−0.872977 + 0.487761i \(0.837814\pi\)
\(168\) 0 0
\(169\) −1699.06 −0.773356
\(170\) 0 0
\(171\) −230.684 + 186.134i −0.103163 + 0.0832399i
\(172\) 0 0
\(173\) −1196.53 2072.45i −0.525841 0.910783i −0.999547 0.0301000i \(-0.990417\pi\)
0.473706 0.880683i \(-0.342916\pi\)
\(174\) 0 0
\(175\) −71.3059 + 163.875i −0.0308013 + 0.0707875i
\(176\) 0 0
\(177\) −923.244 + 1931.25i −0.392064 + 0.820124i
\(178\) 0 0
\(179\) 554.381 + 320.072i 0.231488 + 0.133650i 0.611258 0.791431i \(-0.290664\pi\)
−0.379770 + 0.925081i \(0.623997\pi\)
\(180\) 0 0
\(181\) 4204.05i 1.72643i −0.504833 0.863217i \(-0.668446\pi\)
0.504833 0.863217i \(-0.331554\pi\)
\(182\) 0 0
\(183\) 1107.34 759.623i 0.447306 0.306847i
\(184\) 0 0
\(185\) 241.659 418.565i 0.0960384 0.166343i
\(186\) 0 0
\(187\) −332.291 + 191.848i −0.129944 + 0.0750231i
\(188\) 0 0
\(189\) 2444.19 881.600i 0.940680 0.339296i
\(190\) 0 0
\(191\) −1261.85 + 728.530i −0.478033 + 0.275993i −0.719597 0.694392i \(-0.755673\pi\)
0.241563 + 0.970385i \(0.422340\pi\)
\(192\) 0 0
\(193\) −914.633 + 1584.19i −0.341123 + 0.590842i −0.984642 0.174588i \(-0.944141\pi\)
0.643519 + 0.765430i \(0.277474\pi\)
\(194\) 0 0
\(195\) 3103.51 2128.97i 1.13973 0.781840i
\(196\) 0 0
\(197\) 661.168i 0.239118i 0.992827 + 0.119559i \(0.0381481\pi\)
−0.992827 + 0.119559i \(0.961852\pi\)
\(198\) 0 0
\(199\) 1687.99 + 974.564i 0.601300 + 0.347161i 0.769553 0.638583i \(-0.220479\pi\)
−0.168253 + 0.985744i \(0.553812\pi\)
\(200\) 0 0
\(201\) 724.945 1516.45i 0.254396 0.532149i
\(202\) 0 0
\(203\) 555.532 + 4887.20i 0.192073 + 1.68972i
\(204\) 0 0
\(205\) 179.880 + 311.562i 0.0612849 + 0.106148i
\(206\) 0 0
\(207\) −1451.84 + 1171.46i −0.487489 + 0.393344i
\(208\) 0 0
\(209\) −196.687 −0.0650963
\(210\) 0 0
\(211\) −3341.96 −1.09038 −0.545189 0.838313i \(-0.683542\pi\)
−0.545189 + 0.838313i \(0.683542\pi\)
\(212\) 0 0
\(213\) 18.3103 + 235.298i 0.00589015 + 0.0756917i
\(214\) 0 0
\(215\) 1302.83 + 2256.56i 0.413265 + 0.715796i
\(216\) 0 0
\(217\) −173.699 75.5805i −0.0543386 0.0236440i
\(218\) 0 0
\(219\) −2635.59 1259.96i −0.813228 0.388767i
\(220\) 0 0
\(221\) 1157.68 + 668.390i 0.352372 + 0.203442i
\(222\) 0 0
\(223\) 2143.28i 0.643608i 0.946806 + 0.321804i \(0.104289\pi\)
−0.946806 + 0.321804i \(0.895711\pi\)
\(224\) 0 0
\(225\) −93.7981 + 243.075i −0.0277920 + 0.0720221i
\(226\) 0 0
\(227\) 1284.55 2224.91i 0.375589 0.650540i −0.614826 0.788663i \(-0.710774\pi\)
0.990415 + 0.138123i \(0.0441070\pi\)
\(228\) 0 0
\(229\) 91.0827 52.5866i 0.0262835 0.0151748i −0.486801 0.873513i \(-0.661836\pi\)
0.513084 + 0.858338i \(0.328503\pi\)
\(230\) 0 0
\(231\) 1629.56 + 563.180i 0.464142 + 0.160409i
\(232\) 0 0
\(233\) −2273.94 + 1312.86i −0.639360 + 0.369135i −0.784368 0.620296i \(-0.787013\pi\)
0.145008 + 0.989431i \(0.453679\pi\)
\(234\) 0 0
\(235\) 949.887 1645.25i 0.263676 0.456700i
\(236\) 0 0
\(237\) 850.127 + 1239.27i 0.233003 + 0.339660i
\(238\) 0 0
\(239\) 6080.85i 1.64576i −0.568212 0.822882i \(-0.692365\pi\)
0.568212 0.822882i \(-0.307635\pi\)
\(240\) 0 0
\(241\) 4008.74 + 2314.45i 1.07147 + 0.618616i 0.928584 0.371122i \(-0.121027\pi\)
0.142891 + 0.989738i \(0.454360\pi\)
\(242\) 0 0
\(243\) 3505.99 1434.21i 0.925552 0.378621i
\(244\) 0 0
\(245\) 2712.92 + 2912.30i 0.707437 + 0.759428i
\(246\) 0 0
\(247\) 342.624 + 593.442i 0.0882617 + 0.152874i
\(248\) 0 0
\(249\) 2324.83 180.913i 0.591688 0.0460438i
\(250\) 0 0
\(251\) 5967.85 1.50075 0.750373 0.661015i \(-0.229874\pi\)
0.750373 + 0.661015i \(0.229874\pi\)
\(252\) 0 0
\(253\) −1237.88 −0.307607
\(254\) 0 0
\(255\) −1287.42 + 100.184i −0.316162 + 0.0246030i
\(256\) 0 0
\(257\) 2819.70 + 4883.86i 0.684389 + 1.18540i 0.973628 + 0.228140i \(0.0732643\pi\)
−0.289239 + 0.957257i \(0.593402\pi\)
\(258\) 0 0
\(259\) −458.681 620.211i −0.110043 0.148796i
\(260\) 0 0
\(261\) 1109.30 + 7084.42i 0.263081 + 1.68013i
\(262\) 0 0
\(263\) −3018.63 1742.81i −0.707745 0.408617i 0.102480 0.994735i \(-0.467322\pi\)
−0.810226 + 0.586118i \(0.800655\pi\)
\(264\) 0 0
\(265\) 6117.79i 1.41816i
\(266\) 0 0
\(267\) 1650.83 + 2406.50i 0.378387 + 0.551594i
\(268\) 0 0
\(269\) 1897.28 3286.18i 0.430033 0.744839i −0.566842 0.823826i \(-0.691835\pi\)
0.996876 + 0.0789869i \(0.0251685\pi\)
\(270\) 0 0
\(271\) 6458.49 3728.81i 1.44769 0.835827i 0.449351 0.893356i \(-0.351655\pi\)
0.998344 + 0.0575288i \(0.0183221\pi\)
\(272\) 0 0
\(273\) −1139.43 5897.72i −0.252605 1.30750i
\(274\) 0 0
\(275\) −149.723 + 86.4428i −0.0328315 + 0.0189553i
\(276\) 0 0
\(277\) 1707.75 2957.90i 0.370428 0.641600i −0.619203 0.785231i \(-0.712544\pi\)
0.989631 + 0.143631i \(0.0458777\pi\)
\(278\) 0 0
\(279\) −257.646 99.4210i −0.0552863 0.0213340i
\(280\) 0 0
\(281\) 2762.14i 0.586390i −0.956053 0.293195i \(-0.905281\pi\)
0.956053 0.293195i \(-0.0947185\pi\)
\(282\) 0 0
\(283\) 4767.64 + 2752.60i 1.00144 + 0.578181i 0.908674 0.417507i \(-0.137096\pi\)
0.0927647 + 0.995688i \(0.470430\pi\)
\(284\) 0 0
\(285\) −597.208 285.498i −0.124125 0.0593383i
\(286\) 0 0
\(287\) 570.519 64.8515i 0.117340 0.0133382i
\(288\) 0 0
\(289\) 2227.17 + 3857.57i 0.453322 + 0.785176i
\(290\) 0 0
\(291\) 86.4172 + 1110.51i 0.0174085 + 0.223709i
\(292\) 0 0
\(293\) −4101.08 −0.817705 −0.408853 0.912600i \(-0.634071\pi\)
−0.408853 + 0.912600i \(0.634071\pi\)
\(294\) 0 0
\(295\) −4780.29 −0.943455
\(296\) 0 0
\(297\) 2408.15 + 720.235i 0.470488 + 0.140715i
\(298\) 0 0
\(299\) 2156.35 + 3734.91i 0.417074 + 0.722393i
\(300\) 0 0
\(301\) 4132.12 469.702i 0.791267 0.0899441i
\(302\) 0 0
\(303\) −3849.55 + 8052.54i −0.729871 + 1.52675i
\(304\) 0 0
\(305\) 2597.03 + 1499.40i 0.487560 + 0.281493i
\(306\) 0 0
\(307\) 8281.42i 1.53956i −0.638308 0.769781i \(-0.720365\pi\)
0.638308 0.769781i \(-0.279635\pi\)
\(308\) 0 0
\(309\) −4960.63 + 3402.94i −0.913270 + 0.626493i
\(310\) 0 0
\(311\) −3435.52 + 5950.50i −0.626401 + 1.08496i 0.361868 + 0.932230i \(0.382139\pi\)
−0.988268 + 0.152728i \(0.951194\pi\)
\(312\) 0 0
\(313\) −2922.40 + 1687.25i −0.527743 + 0.304693i −0.740097 0.672500i \(-0.765220\pi\)
0.212354 + 0.977193i \(0.431887\pi\)
\(314\) 0 0
\(315\) 4130.40 + 4075.36i 0.738800 + 0.728954i
\(316\) 0 0
\(317\) −2052.28 + 1184.88i −0.363620 + 0.209936i −0.670667 0.741758i \(-0.733992\pi\)
0.307048 + 0.951694i \(0.400659\pi\)
\(318\) 0 0
\(319\) −2379.09 + 4120.71i −0.417566 + 0.723246i
\(320\) 0 0
\(321\) 5218.09 3579.55i 0.907306 0.622401i
\(322\) 0 0
\(323\) 235.116i 0.0405021i
\(324\) 0 0
\(325\) 521.629 + 301.163i 0.0890300 + 0.0514015i
\(326\) 0 0
\(327\) −2909.57 + 6086.26i −0.492047 + 1.02927i
\(328\) 0 0
\(329\) −1802.94 2437.86i −0.302125 0.408521i
\(330\) 0 0
\(331\) 1901.80 + 3294.02i 0.315808 + 0.546996i 0.979609 0.200913i \(-0.0643910\pi\)
−0.663801 + 0.747910i \(0.731058\pi\)
\(332\) 0 0
\(333\) −706.189 875.212i −0.116213 0.144028i
\(334\) 0 0
\(335\) 3753.55 0.612175
\(336\) 0 0
\(337\) −592.955 −0.0958466 −0.0479233 0.998851i \(-0.515260\pi\)
−0.0479233 + 0.998851i \(0.515260\pi\)
\(338\) 0 0
\(339\) −579.649 7448.81i −0.0928679 1.19340i
\(340\) 0 0
\(341\) −91.6249 158.699i −0.0145506 0.0252024i
\(342\) 0 0
\(343\) 5989.74 2115.80i 0.942903 0.333068i
\(344\) 0 0
\(345\) −3758.61 1796.82i −0.586542 0.280399i
\(346\) 0 0
\(347\) −4137.14 2388.58i −0.640039 0.369527i 0.144590 0.989492i \(-0.453814\pi\)
−0.784630 + 0.619965i \(0.787147\pi\)
\(348\) 0 0
\(349\) 7358.26i 1.12859i −0.825573 0.564296i \(-0.809148\pi\)
0.825573 0.564296i \(-0.190852\pi\)
\(350\) 0 0
\(351\) −2021.84 8520.47i −0.307459 1.29569i
\(352\) 0 0
\(353\) −1652.78 + 2862.69i −0.249202 + 0.431631i −0.963305 0.268410i \(-0.913502\pi\)
0.714102 + 0.700041i \(0.246835\pi\)
\(354\) 0 0
\(355\) −456.436 + 263.524i −0.0682398 + 0.0393982i
\(356\) 0 0
\(357\) −673.213 + 1947.94i −0.0998046 + 0.288784i
\(358\) 0 0
\(359\) −359.154 + 207.358i −0.0528006 + 0.0304845i −0.526168 0.850381i \(-0.676372\pi\)
0.473367 + 0.880865i \(0.343038\pi\)
\(360\) 0 0
\(361\) −3369.24 + 5835.69i −0.491214 + 0.850808i
\(362\) 0 0
\(363\) −2968.81 4327.79i −0.429263 0.625758i
\(364\) 0 0
\(365\) 6523.69i 0.935522i
\(366\) 0 0
\(367\) 65.9242 + 38.0613i 0.00937661 + 0.00541359i 0.504681 0.863306i \(-0.331610\pi\)
−0.495304 + 0.868720i \(0.664943\pi\)
\(368\) 0 0
\(369\) 827.018 129.497i 0.116674 0.0182693i
\(370\) 0 0
\(371\) −8953.38 3895.82i −1.25293 0.545178i
\(372\) 0 0
\(373\) 6150.49 + 10653.0i 0.853781 + 1.47879i 0.877771 + 0.479080i \(0.159030\pi\)
−0.0239900 + 0.999712i \(0.507637\pi\)
\(374\) 0 0
\(375\) 6934.13 539.598i 0.954872 0.0743059i
\(376\) 0 0
\(377\) 16577.3 2.26465
\(378\) 0 0
\(379\) 1429.02 0.193678 0.0968389 0.995300i \(-0.469127\pi\)
0.0968389 + 0.995300i \(0.469127\pi\)
\(380\) 0 0
\(381\) −13916.5 + 1082.95i −1.87129 + 0.145620i
\(382\) 0 0
\(383\) 2555.45 + 4426.17i 0.340933 + 0.590513i 0.984606 0.174787i \(-0.0559237\pi\)
−0.643673 + 0.765300i \(0.722590\pi\)
\(384\) 0 0
\(385\) 434.863 + 3825.63i 0.0575654 + 0.506421i
\(386\) 0 0
\(387\) 5989.87 937.915i 0.786776 0.123196i
\(388\) 0 0
\(389\) −6339.84 3660.31i −0.826331 0.477083i 0.0262636 0.999655i \(-0.491639\pi\)
−0.852595 + 0.522572i \(0.824972\pi\)
\(390\) 0 0
\(391\) 1479.73i 0.191390i
\(392\) 0 0
\(393\) −4712.61 6869.82i −0.604885 0.881772i
\(394\) 0 0
\(395\) −1678.04 + 2906.45i −0.213750 + 0.370227i
\(396\) 0 0
\(397\) 7516.61 4339.72i 0.950247 0.548625i 0.0570893 0.998369i \(-0.481818\pi\)
0.893158 + 0.449744i \(0.148485\pi\)
\(398\) 0 0
\(399\) −798.129 + 692.207i −0.100141 + 0.0868514i
\(400\) 0 0
\(401\) −8447.68 + 4877.27i −1.05201 + 0.607379i −0.923212 0.384291i \(-0.874446\pi\)
−0.128800 + 0.991671i \(0.541113\pi\)
\(402\) 0 0
\(403\) −319.217 + 552.899i −0.0394573 + 0.0683421i
\(404\) 0 0
\(405\) 6266.49 + 5682.38i 0.768851 + 0.697185i
\(406\) 0 0
\(407\) 746.226i 0.0908822i
\(408\) 0 0
\(409\) 2935.32 + 1694.71i 0.354871 + 0.204885i 0.666828 0.745211i \(-0.267651\pi\)
−0.311958 + 0.950096i \(0.600985\pi\)
\(410\) 0 0
\(411\) −10869.3 5196.10i −1.30448 0.623612i
\(412\) 0 0
\(413\) −3044.10 + 6995.95i −0.362689 + 0.833531i
\(414\) 0 0
\(415\) 2603.72 + 4509.77i 0.307979 + 0.533436i
\(416\) 0 0
\(417\) −742.400 9540.25i −0.0871834 1.12036i
\(418\) 0 0
\(419\) 12777.4 1.48977 0.744887 0.667191i \(-0.232504\pi\)
0.744887 + 0.667191i \(0.232504\pi\)
\(420\) 0 0
\(421\) 11005.4 1.27404 0.637020 0.770848i \(-0.280167\pi\)
0.637020 + 0.770848i \(0.280167\pi\)
\(422\) 0 0
\(423\) −2775.81 3440.19i −0.319065 0.395432i
\(424\) 0 0
\(425\) −103.332 178.976i −0.0117937 0.0204273i
\(426\) 0 0
\(427\) 3848.17 2845.94i 0.436126 0.322540i
\(428\) 0 0
\(429\) 2506.22 5242.54i 0.282055 0.590005i
\(430\) 0 0
\(431\) 3279.13 + 1893.21i 0.366474 + 0.211584i 0.671917 0.740627i \(-0.265471\pi\)
−0.305443 + 0.952210i \(0.598805\pi\)
\(432\) 0 0
\(433\) 3191.67i 0.354230i 0.984190 + 0.177115i \(0.0566765\pi\)
−0.984190 + 0.177115i \(0.943323\pi\)
\(434\) 0 0
\(435\) −13205.1 + 9058.53i −1.45548 + 0.998444i
\(436\) 0 0
\(437\) 379.264 656.904i 0.0415163 0.0719084i
\(438\) 0 0
\(439\) 2872.90 1658.67i 0.312337 0.180328i −0.335635 0.941992i \(-0.608951\pi\)
0.647972 + 0.761664i \(0.275617\pi\)
\(440\) 0 0
\(441\) 8594.54 3449.65i 0.928035 0.372492i
\(442\) 0 0
\(443\) −9266.95 + 5350.27i −0.993873 + 0.573813i −0.906430 0.422356i \(-0.861203\pi\)
−0.0874435 + 0.996169i \(0.527870\pi\)
\(444\) 0 0
\(445\) −3258.53 + 5643.94i −0.347122 + 0.601232i
\(446\) 0 0
\(447\) 5574.51 3824.05i 0.589855 0.404634i
\(448\) 0 0
\(449\) 4017.92i 0.422310i −0.977453 0.211155i \(-0.932278\pi\)
0.977453 0.211155i \(-0.0677225\pi\)
\(450\) 0 0
\(451\) 481.042 + 277.729i 0.0502248 + 0.0289973i
\(452\) 0 0
\(453\) −5863.87 + 12266.1i −0.608186 + 1.27221i
\(454\) 0 0
\(455\) 10785.1 7976.22i 1.11124 0.821826i
\(456\) 0 0
\(457\) −4584.83 7941.15i −0.469298 0.812848i 0.530086 0.847944i \(-0.322160\pi\)
−0.999384 + 0.0350961i \(0.988826\pi\)
\(458\) 0 0
\(459\) −860.955 + 2878.65i −0.0875510 + 0.292732i
\(460\) 0 0
\(461\) 1289.80 0.130308 0.0651542 0.997875i \(-0.479246\pi\)
0.0651542 + 0.997875i \(0.479246\pi\)
\(462\) 0 0
\(463\) −6976.52 −0.700273 −0.350137 0.936699i \(-0.613865\pi\)
−0.350137 + 0.936699i \(0.613865\pi\)
\(464\) 0 0
\(465\) −47.8470 614.860i −0.00477172 0.0613192i
\(466\) 0 0
\(467\) −3931.83 6810.13i −0.389600 0.674808i 0.602795 0.797896i \(-0.294054\pi\)
−0.992396 + 0.123088i \(0.960720\pi\)
\(468\) 0 0
\(469\) 2390.27 5493.32i 0.235336 0.540849i
\(470\) 0 0
\(471\) −4384.05 2095.82i −0.428889 0.205032i
\(472\) 0 0
\(473\) 3484.06 + 2011.52i 0.338683 + 0.195539i
\(474\) 0 0
\(475\) 105.938i 0.0102332i
\(476\) 0 0
\(477\) −13280.5 5124.69i −1.27478 0.491915i
\(478\) 0 0
\(479\) 1847.13 3199.33i 0.176196 0.305180i −0.764379 0.644767i \(-0.776954\pi\)
0.940574 + 0.339588i \(0.110288\pi\)
\(480\) 0 0
\(481\) −2251.51 + 1299.91i −0.213430 + 0.123224i
\(482\) 0 0
\(483\) −5023.14 + 4356.51i −0.473211 + 0.410410i
\(484\) 0 0
\(485\) −2154.19 + 1243.72i −0.201684 + 0.116442i
\(486\) 0 0
\(487\) −526.359 + 911.681i −0.0489766 + 0.0848300i −0.889474 0.456985i \(-0.848929\pi\)
0.840498 + 0.541815i \(0.182263\pi\)
\(488\) 0 0
\(489\) −1523.06 2220.24i −0.140849 0.205322i
\(490\) 0 0
\(491\) 2378.40i 0.218607i −0.994008 0.109303i \(-0.965138\pi\)
0.994008 0.109303i \(-0.0348620\pi\)
\(492\) 0 0
\(493\) −4925.81 2843.92i −0.449995 0.259805i
\(494\) 0 0
\(495\) 868.348 + 5545.59i 0.0788471 + 0.503547i
\(496\) 0 0
\(497\) 95.0069 + 835.807i 0.00857474 + 0.0754347i
\(498\) 0 0
\(499\) 9385.74 + 16256.6i 0.842011 + 1.45840i 0.888192 + 0.459472i \(0.151961\pi\)
−0.0461818 + 0.998933i \(0.514705\pi\)
\(500\) 0 0
\(501\) −19519.9 + 1519.00i −1.74069 + 0.135457i
\(502\) 0 0
\(503\) −16095.2 −1.42674 −0.713370 0.700788i \(-0.752832\pi\)
−0.713370 + 0.700788i \(0.752832\pi\)
\(504\) 0 0
\(505\) −19931.9 −1.75635
\(506\) 0 0
\(507\) −8801.98 + 684.950i −0.771025 + 0.0599994i
\(508\) 0 0
\(509\) −1575.31 2728.52i −0.137180 0.237603i 0.789248 0.614074i \(-0.210471\pi\)
−0.926428 + 0.376472i \(0.877137\pi\)
\(510\) 0 0
\(511\) −9547.42 4154.30i −0.826522 0.359639i
\(512\) 0 0
\(513\) −1120.02 + 1057.26i −0.0963940 + 0.0909928i
\(514\) 0 0
\(515\) −11634.1 6716.95i −0.995456 0.574727i
\(516\) 0 0
\(517\) 2933.19i 0.249519i
\(518\) 0 0
\(519\) −7034.08 10253.9i −0.594917 0.867241i
\(520\) 0 0
\(521\) 2489.60 4312.12i 0.209350 0.362605i −0.742160 0.670223i \(-0.766198\pi\)
0.951510 + 0.307618i \(0.0995318\pi\)
\(522\) 0 0
\(523\) −11977.0 + 6914.92i −1.00137 + 0.578142i −0.908654 0.417550i \(-0.862889\pi\)
−0.0927181 + 0.995692i \(0.529556\pi\)
\(524\) 0 0
\(525\) −303.336 + 877.700i −0.0252165 + 0.0729638i
\(526\) 0 0
\(527\) 189.705 109.526i 0.0156806 0.00905322i
\(528\) 0 0
\(529\) −3696.55 + 6402.61i −0.303818 + 0.526228i
\(530\) 0 0
\(531\) −4004.31 + 10377.0i −0.327254 + 0.848069i
\(532\) 0 0
\(533\) 1935.19i 0.157265i
\(534\) 0 0
\(535\) 12237.9 + 7065.56i 0.988955 + 0.570973i
\(536\) 0 0
\(537\) 3001.00 + 1434.64i 0.241159 + 0.115287i
\(538\) 0 0
\(539\) 5875.73 + 1799.75i 0.469547 + 0.143823i
\(540\) 0 0
\(541\) −2658.97 4605.48i −0.211309 0.365998i 0.740815 0.671709i \(-0.234439\pi\)
−0.952124 + 0.305711i \(0.901106\pi\)
\(542\) 0 0
\(543\) −1694.79 21779.0i −0.133942 1.72123i
\(544\) 0 0
\(545\) −15064.9 −1.18405
\(546\) 0 0
\(547\) 9266.96 0.724363 0.362181 0.932108i \(-0.382032\pi\)
0.362181 + 0.932108i \(0.382032\pi\)
\(548\) 0 0
\(549\) 5430.34 4381.63i 0.422152 0.340625i
\(550\) 0 0
\(551\) −1457.82 2525.03i −0.112714 0.195226i
\(552\) 0 0
\(553\) 3185.01 + 4306.65i 0.244920 + 0.331171i
\(554\) 0 0
\(555\) 1083.17 2265.79i 0.0828435 0.173293i
\(556\) 0 0
\(557\) 125.920 + 72.6999i 0.00957881 + 0.00553033i 0.504782 0.863247i \(-0.331573\pi\)
−0.495203 + 0.868777i \(0.664906\pi\)
\(558\) 0 0
\(559\) 14016.1i 1.06050i
\(560\) 0 0
\(561\) −1644.09 + 1127.83i −0.123732 + 0.0848785i
\(562\) 0 0
\(563\) 1958.12 3391.56i 0.146581 0.253885i −0.783381 0.621542i \(-0.786507\pi\)
0.929962 + 0.367657i \(0.119840\pi\)
\(564\) 0 0
\(565\) 14449.4 8342.36i 1.07591 0.621178i
\(566\) 0 0
\(567\) 12306.7 5552.46i 0.911521 0.411254i
\(568\) 0 0
\(569\) 7404.97 4275.26i 0.545576 0.314988i −0.201760 0.979435i \(-0.564666\pi\)
0.747336 + 0.664447i \(0.231333\pi\)
\(570\) 0 0
\(571\) −11956.8 + 20709.8i −0.876318 + 1.51783i −0.0209659 + 0.999780i \(0.506674\pi\)
−0.855352 + 0.518047i \(0.826659\pi\)
\(572\) 0 0
\(573\) −6243.32 + 4282.84i −0.455180 + 0.312248i
\(574\) 0 0
\(575\) 666.737i 0.0483563i
\(576\) 0 0
\(577\) 11347.8 + 6551.66i 0.818745 + 0.472703i 0.849983 0.526809i \(-0.176612\pi\)
−0.0312386 + 0.999512i \(0.509945\pi\)
\(578\) 0 0
\(579\) −4099.61 + 8575.60i −0.294255 + 0.615527i
\(580\) 0 0
\(581\) 8258.10 938.706i 0.589679 0.0670294i
\(582\) 0 0
\(583\) −4722.83 8180.18i −0.335506 0.581113i
\(584\) 0 0
\(585\) 15219.5 12280.3i 1.07564 0.867908i
\(586\) 0 0
\(587\) 18034.7 1.26809 0.634047 0.773294i \(-0.281392\pi\)
0.634047 + 0.773294i \(0.281392\pi\)
\(588\) 0 0
\(589\) 112.289 0.00785532
\(590\) 0 0
\(591\) 266.539 + 3425.18i 0.0185515 + 0.238398i
\(592\) 0 0
\(593\) −11358.1 19672.8i −0.786547 1.36234i −0.928071 0.372404i \(-0.878534\pi\)
0.141524 0.989935i \(-0.454800\pi\)
\(594\) 0 0
\(595\) −4573.08 + 519.826i −0.315089 + 0.0358165i
\(596\) 0 0
\(597\) 9137.52 + 4368.23i 0.626422 + 0.299464i
\(598\) 0 0
\(599\) 11720.4 + 6766.78i 0.799471 + 0.461575i 0.843286 0.537465i \(-0.180618\pi\)
−0.0438153 + 0.999040i \(0.513951\pi\)
\(600\) 0 0
\(601\) 3667.98i 0.248952i −0.992223 0.124476i \(-0.960275\pi\)
0.992223 0.124476i \(-0.0397250\pi\)
\(602\) 0 0
\(603\) 3144.24 8148.20i 0.212344 0.550282i
\(604\) 0 0
\(605\) 5860.05 10149.9i 0.393794 0.682070i
\(606\) 0 0
\(607\) 6942.92 4008.50i 0.464258 0.268039i −0.249575 0.968355i \(-0.580291\pi\)
0.713833 + 0.700316i \(0.246958\pi\)
\(608\) 0 0
\(609\) 4848.12 + 25094.1i 0.322588 + 1.66973i
\(610\) 0 0
\(611\) −8849.99 + 5109.54i −0.585977 + 0.338314i
\(612\) 0 0
\(613\) −4698.26 + 8137.63i −0.309561 + 0.536176i −0.978266 0.207352i \(-0.933515\pi\)
0.668705 + 0.743528i \(0.266849\pi\)
\(614\) 0 0
\(615\) 1057.47 + 1541.53i 0.0693355 + 0.101074i
\(616\) 0 0
\(617\) 8906.76i 0.581155i 0.956851 + 0.290578i \(0.0938474\pi\)
−0.956851 + 0.290578i \(0.906153\pi\)
\(618\) 0 0
\(619\) 6091.73 + 3517.06i 0.395553 + 0.228373i 0.684563 0.728953i \(-0.259993\pi\)
−0.289010 + 0.957326i \(0.593326\pi\)
\(620\) 0 0
\(621\) −7049.01 + 6654.03i −0.455502 + 0.429979i
\(622\) 0 0
\(623\) 6184.86 + 8362.93i 0.397739 + 0.537807i
\(624\) 0 0
\(625\) 8369.05 + 14495.6i 0.535619 + 0.927720i
\(626\) 0 0
\(627\) −1018.93 + 79.2911i −0.0649000 + 0.00505037i
\(628\) 0 0
\(629\) 892.024 0.0565458
\(630\) 0 0
\(631\) 12628.6 0.796728 0.398364 0.917227i \(-0.369578\pi\)
0.398364 + 0.917227i \(0.369578\pi\)
\(632\) 0 0
\(633\) −17313.0 + 1347.26i −1.08709 + 0.0845950i
\(634\) 0 0
\(635\) −15585.9 26995.5i −0.974026 1.68706i
\(636\) 0 0
\(637\) −4805.19 20863.3i −0.298883 1.29770i
\(638\) 0 0
\(639\) 189.713 + 1211.58i 0.0117448 + 0.0750066i
\(640\) 0 0
\(641\) 8593.58 + 4961.51i 0.529526 + 0.305722i 0.740823 0.671700i \(-0.234436\pi\)
−0.211297 + 0.977422i \(0.567769\pi\)
\(642\) 0 0
\(643\) 294.191i 0.0180432i −0.999959 0.00902160i \(-0.997128\pi\)
0.999959 0.00902160i \(-0.00287170\pi\)
\(644\) 0 0
\(645\) 7658.97 + 11164.9i 0.467553 + 0.681576i
\(646\) 0 0
\(647\) −3859.39 + 6684.67i −0.234511 + 0.406184i −0.959130 0.282965i \(-0.908682\pi\)
0.724620 + 0.689149i \(0.242015\pi\)
\(648\) 0 0
\(649\) −6391.80 + 3690.30i −0.386595 + 0.223201i
\(650\) 0 0
\(651\) −930.316 321.520i −0.0560092 0.0193569i
\(652\) 0 0
\(653\) 9846.89 5685.11i 0.590105 0.340697i −0.175034 0.984562i \(-0.556004\pi\)
0.765139 + 0.643865i \(0.222670\pi\)
\(654\) 0 0
\(655\) 9302.09 16111.7i 0.554905 0.961123i
\(656\) 0 0
\(657\) −14161.6 5464.70i −0.840938 0.324503i
\(658\) 0 0
\(659\) 19795.1i 1.17012i 0.810990 + 0.585060i \(0.198929\pi\)
−0.810990 + 0.585060i \(0.801071\pi\)
\(660\) 0 0
\(661\) 26896.6 + 15528.7i 1.58268 + 0.913763i 0.994466 + 0.105062i \(0.0335041\pi\)
0.588219 + 0.808702i \(0.299829\pi\)
\(662\) 0 0
\(663\) 6266.83 + 2995.88i 0.367094 + 0.175491i
\(664\) 0 0
\(665\) −2163.38 941.337i −0.126154 0.0548924i
\(666\) 0 0
\(667\) −9175.03 15891.6i −0.532621 0.922527i
\(668\) 0 0
\(669\) 864.027 + 11103.2i 0.0499331 + 0.641668i
\(670\) 0 0
\(671\) 4630.04 0.266380
\(672\) 0 0
\(673\) 5340.26 0.305872 0.152936 0.988236i \(-0.451127\pi\)
0.152936 + 0.988236i \(0.451127\pi\)
\(674\) 0 0
\(675\) −387.928 + 1297.06i −0.0221205 + 0.0739612i
\(676\) 0 0
\(677\) 12478.3 + 21613.0i 0.708389 + 1.22697i 0.965455 + 0.260571i \(0.0839110\pi\)
−0.257066 + 0.966394i \(0.582756\pi\)
\(678\) 0 0
\(679\) 448.394 + 3944.67i 0.0253428 + 0.222949i
\(680\) 0 0
\(681\) 5757.68 12044.0i 0.323986 0.677718i
\(682\) 0 0
\(683\) 9706.83 + 5604.24i 0.543809 + 0.313968i 0.746621 0.665249i \(-0.231675\pi\)
−0.202812 + 0.979218i \(0.565008\pi\)
\(684\) 0 0
\(685\) 26903.9i 1.50065i
\(686\) 0 0
\(687\) 450.654 309.143i 0.0250269 0.0171682i
\(688\) 0 0
\(689\) −16454.1 + 28499.4i −0.909800 + 1.57582i
\(690\) 0 0
\(691\) 9472.37 5468.88i 0.521485 0.301079i −0.216057 0.976381i \(-0.569320\pi\)
0.737542 + 0.675301i \(0.235986\pi\)
\(692\) 0 0
\(693\) 8668.93 + 2260.62i 0.475188 + 0.123916i
\(694\) 0 0
\(695\) 18506.4 10684.7i 1.01006 0.583156i
\(696\) 0 0
\(697\) −331.992 + 575.027i −0.0180418 + 0.0312492i
\(698\) 0 0
\(699\) −11250.9 + 7717.97i −0.608795 + 0.417626i
\(700\) 0 0
\(701\) 27949.3i 1.50589i 0.658082 + 0.752947i \(0.271368\pi\)
−0.658082 + 0.752947i \(0.728632\pi\)
\(702\) 0 0
\(703\) 396.000 + 228.631i 0.0212453 + 0.0122660i
\(704\) 0 0
\(705\) 4257.62 8906.14i 0.227449 0.475780i
\(706\) 0 0
\(707\) −12692.7 + 29170.3i −0.675186 + 1.55171i
\(708\) 0 0
\(709\) −10472.7 18139.3i −0.554741 0.960840i −0.997924 0.0644082i \(-0.979484\pi\)
0.443183 0.896431i \(-0.353849\pi\)
\(710\) 0 0
\(711\) 4903.67 + 6077.33i 0.258653 + 0.320560i
\(712\) 0 0
\(713\) 706.707 0.0371197
\(714\) 0 0
\(715\) 12976.5 0.678731
\(716\) 0 0
\(717\) −2451.40 31501.8i −0.127684 1.64080i
\(718\) 0 0
\(719\) 4150.10 + 7188.19i 0.215261 + 0.372843i 0.953353 0.301857i \(-0.0976064\pi\)
−0.738092 + 0.674700i \(0.764273\pi\)
\(720\) 0 0
\(721\) −17238.9 + 12749.1i −0.890443 + 0.658533i
\(722\) 0 0
\(723\) 21700.3 + 10373.9i 1.11624 + 0.533623i
\(724\) 0 0
\(725\) −2219.47 1281.41i −0.113695 0.0656420i
\(726\) 0 0
\(727\) 20951.5i 1.06884i −0.845218 0.534421i \(-0.820530\pi\)
0.845218 0.534421i \(-0.179470\pi\)
\(728\) 0 0
\(729\) 17584.5 8843.31i 0.893388 0.449287i
\(730\) 0 0
\(731\) −2404.53 + 4164.77i −0.121662 + 0.210724i
\(732\) 0 0
\(733\) 4885.73 2820.78i 0.246192 0.142139i −0.371827 0.928302i \(-0.621269\pi\)
0.618019 + 0.786163i \(0.287935\pi\)
\(734\) 0 0
\(735\) 15228.3 + 13993.5i 0.764223 + 0.702254i
\(736\) 0 0
\(737\) 5018.93 2897.68i 0.250848 0.144827i
\(738\) 0 0
\(739\) −5691.08 + 9857.24i −0.283288 + 0.490669i −0.972193 0.234183i \(-0.924758\pi\)
0.688905 + 0.724852i \(0.258092\pi\)
\(740\) 0 0
\(741\) 2014.20 + 2936.20i 0.0998560 + 0.145565i
\(742\) 0 0
\(743\) 4665.46i 0.230362i 0.993345 + 0.115181i \(0.0367449\pi\)
−0.993345 + 0.115181i \(0.963255\pi\)
\(744\) 0 0
\(745\) 13073.8 + 7548.17i 0.642936 + 0.371200i
\(746\) 0 0
\(747\) 11970.8 1874.44i 0.586332 0.0918100i
\(748\) 0 0
\(749\) 18133.6 13410.8i 0.884628 0.654233i
\(750\) 0 0
\(751\) −4780.43 8279.95i −0.232277 0.402316i 0.726200 0.687483i \(-0.241284\pi\)
−0.958478 + 0.285167i \(0.907951\pi\)
\(752\) 0 0
\(753\) 30916.4 2405.84i 1.49622 0.116433i
\(754\) 0 0
\(755\) −30361.4 −1.46353
\(756\) 0 0
\(757\) 31574.1 1.51596 0.757979 0.652279i \(-0.226187\pi\)
0.757979 + 0.652279i \(0.226187\pi\)
\(758\) 0 0
\(759\) −6412.81 + 499.030i −0.306680 + 0.0238651i
\(760\) 0 0
\(761\) −11215.0 19424.9i −0.534221 0.925298i −0.999201 0.0399765i \(-0.987272\pi\)
0.464980 0.885321i \(-0.346062\pi\)
\(762\) 0 0
\(763\) −9593.35 + 22047.4i −0.455180 + 1.04610i
\(764\) 0 0
\(765\) −6629.08 + 1038.01i −0.313301 + 0.0490577i
\(766\) 0 0
\(767\) 22268.7 + 12856.8i 1.04834 + 0.605259i
\(768\) 0 0
\(769\) 26887.4i 1.26084i 0.776254 + 0.630420i \(0.217117\pi\)
−0.776254 + 0.630420i \(0.782883\pi\)
\(770\) 0 0
\(771\) 16576.3 + 24164.1i 0.774293 + 1.12873i
\(772\) 0 0
\(773\) −11104.6 + 19233.7i −0.516693 + 0.894938i 0.483119 + 0.875555i \(0.339504\pi\)
−0.999812 + 0.0193838i \(0.993830\pi\)
\(774\) 0 0
\(775\) 85.4774 49.3504i 0.00396185 0.00228738i
\(776\) 0 0
\(777\) −2626.22 3028.09i −0.121255 0.139810i
\(778\) 0 0
\(779\) −294.765 + 170.183i −0.0135572 + 0.00782725i
\(780\) 0 0
\(781\) −406.872 + 704.722i −0.0186415 + 0.0322880i
\(782\) 0 0
\(783\) 8602.71 + 36253.6i 0.392638 + 1.65466i
\(784\) 0 0
\(785\) 10851.5i 0.493385i
\(786\) 0 0
\(787\) 17403.2 + 10047.8i 0.788257 + 0.455100i 0.839348 0.543594i \(-0.182937\pi\)
−0.0510919 + 0.998694i \(0.516270\pi\)
\(788\) 0 0
\(789\) −16340.6 7811.69i −0.737314 0.352476i