Properties

Label 336.4.bc.d.257.4
Level $336$
Weight $4$
Character 336.257
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 257.4
Root \(-0.232749 + 2.99096i\) of defining polynomial
Character \(\chi\) \(=\) 336.257
Dual form 336.4.bc.d.17.4

$q$-expansion

\(f(q)\) \(=\) \(q+(2.24112 - 4.68800i) q^{3} +(-5.80193 + 10.0492i) q^{5} +(18.4018 + 2.09174i) q^{7} +(-16.9548 - 21.0128i) q^{9} +O(q^{10})\) \(q+(2.24112 - 4.68800i) q^{3} +(-5.80193 + 10.0492i) q^{5} +(18.4018 + 2.09174i) q^{7} +(-16.9548 - 21.0128i) q^{9} +(-15.5157 + 8.95800i) q^{11} +62.4185i q^{13} +(34.1081 + 49.7211i) q^{15} +(10.7082 + 18.5472i) q^{17} +(-9.50747 - 5.48914i) q^{19} +(51.0467 - 81.5796i) q^{21} +(59.8367 + 34.5467i) q^{23} +(-4.82490 - 8.35697i) q^{25} +(-136.506 + 32.3918i) q^{27} +265.583i q^{29} +(-8.85795 + 5.11414i) q^{31} +(7.22254 + 92.8136i) q^{33} +(-127.786 + 172.788i) q^{35} +(-20.8257 + 36.0712i) q^{37} +(292.618 + 139.887i) q^{39} -31.0035 q^{41} +224.550 q^{43} +(309.533 - 48.4678i) q^{45} +(81.8595 - 141.785i) q^{47} +(334.249 + 76.9836i) q^{49} +(110.948 - 8.63368i) q^{51} +(456.586 - 263.610i) q^{53} -207.895i q^{55} +(-47.0405 + 32.2692i) q^{57} +(205.978 + 356.765i) q^{59} +(223.807 + 129.215i) q^{61} +(-268.044 - 422.137i) q^{63} +(-627.258 - 362.148i) q^{65} +(161.737 + 280.137i) q^{67} +(296.056 - 203.091i) q^{69} +45.4199i q^{71} +(-486.879 + 281.100i) q^{73} +(-49.9907 + 3.89016i) q^{75} +(-304.254 + 132.388i) q^{77} +(144.610 - 250.473i) q^{79} +(-154.073 + 712.532i) q^{81} -448.767 q^{83} -248.513 q^{85} +(1245.05 + 595.204i) q^{87} +(-280.814 + 486.384i) q^{89} +(-130.563 + 1148.61i) q^{91} +(4.12336 + 52.9875i) q^{93} +(110.323 - 63.6953i) q^{95} -214.364i q^{97} +(451.297 + 174.147i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q + 3 q^{3} + 56 q^{7} - 3 q^{9}+O(q^{10}) \) 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 \(\left(\mathbb{Z}/336\mathbb{Z}\right)^\times\).

\(n\) \(85\) \(113\) \(127\) \(241\)
\(\chi(n)\) \(1\) \(-1\) \(1\) \(e\left(\frac{5}{6}\right)\)

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
\(3\) 2.24112 4.68800i 0.431304 0.902207i
\(4\) 0 0
\(5\) −5.80193 + 10.0492i −0.518941 + 0.898832i 0.480817 + 0.876821i \(0.340340\pi\)
−0.999758 + 0.0220109i \(0.992993\pi\)
\(6\) 0 0
\(7\) 18.4018 + 2.09174i 0.993601 + 0.112944i
\(8\) 0 0
\(9\) −16.9548 21.0128i −0.627954 0.778251i
\(10\) 0 0
\(11\) −15.5157 + 8.95800i −0.425287 + 0.245540i −0.697337 0.716743i \(-0.745632\pi\)
0.272050 + 0.962283i \(0.412299\pi\)
\(12\) 0 0
\(13\) 62.4185i 1.33167i 0.746097 + 0.665837i \(0.231925\pi\)
−0.746097 + 0.665837i \(0.768075\pi\)
\(14\) 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 \(-0.117847\pi\)
−0.779474 + 0.626435i \(0.784513\pi\)
\(18\) 0 0
\(19\) −9.50747 5.48914i −0.114798 0.0662787i 0.441502 0.897261i \(-0.354446\pi\)
−0.556300 + 0.830982i \(0.687779\pi\)
\(20\) 0 0
\(21\) 51.0467 81.5796i 0.530443 0.847721i
\(22\) 0 0
\(23\) 59.8367 + 34.5467i 0.542470 + 0.313195i 0.746079 0.665857i \(-0.231934\pi\)
−0.203609 + 0.979052i \(0.565267\pi\)
\(24\) 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 −0.525441 0.850830i \(-0.676100\pi\)
0.474120 + 0.880460i \(0.342766\pi\)
\(32\) 0 0
\(33\) 7.22254 + 92.8136i 0.0380995 + 0.489599i
\(34\) 0 0
\(35\) −127.786 + 172.788i −0.617138 + 0.834470i
\(36\) 0 0
\(37\) −20.8257 + 36.0712i −0.0925331 + 0.160272i −0.908576 0.417719i \(-0.862830\pi\)
0.816043 + 0.577991i \(0.196163\pi\)
\(38\) 0 0
\(39\) 292.618 + 139.887i 1.20145 + 0.574356i
\(40\) 0 0
\(41\) −31.0035 −0.118096 −0.0590480 0.998255i \(-0.518807\pi\)
−0.0590480 + 0.998255i \(0.518807\pi\)
\(42\) 0 0
\(43\) 224.550 0.796363 0.398181 0.917307i \(-0.369641\pi\)
0.398181 + 0.917307i \(0.369641\pi\)
\(44\) 0 0
\(45\) 309.533 48.4678i 1.02539 0.160559i
\(46\) 0 0
\(47\) 81.8595 141.785i 0.254052 0.440031i −0.710586 0.703611i \(-0.751570\pi\)
0.964638 + 0.263580i \(0.0849033\pi\)
\(48\) 0 0
\(49\) 334.249 + 76.9836i 0.974487 + 0.224442i
\(50\) 0 0
\(51\) 110.948 8.63368i 0.304623 0.0237050i
\(52\) 0 0
\(53\) 456.586 263.610i 1.18334 0.683200i 0.226553 0.973999i \(-0.427254\pi\)
0.956784 + 0.290799i \(0.0939211\pi\)
\(54\) 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 \(-0.0164811\pi\)
−0.544150 + 0.838988i \(0.683148\pi\)
\(60\) 0 0
\(61\) 223.807 + 129.215i 0.469764 + 0.271218i 0.716141 0.697956i \(-0.245907\pi\)
−0.246377 + 0.969174i \(0.579240\pi\)
\(62\) 0 0
\(63\) −268.044 422.137i −0.536037 0.844194i
\(64\) 0 0
\(65\) −627.258 362.148i −1.19695 0.691060i
\(66\) 0 0
\(67\) 161.737 + 280.137i 0.294915 + 0.510808i 0.974965 0.222357i \(-0.0713752\pi\)
−0.680050 + 0.733166i \(0.738042\pi\)
\(68\) 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 −0.836648 0.547741i \(-0.815488\pi\)
0.0560334 + 0.998429i \(0.482155\pi\)
\(74\) 0 0
\(75\) −49.9907 + 3.89016i −0.0769657 + 0.00598929i
\(76\) 0 0
\(77\) −304.254 + 132.388i −0.450298 + 0.195935i
\(78\) 0 0
\(79\) 144.610 250.473i 0.205949 0.356714i −0.744486 0.667638i \(-0.767305\pi\)
0.950435 + 0.310925i \(0.100639\pi\)
\(80\) 0 0
\(81\) −154.073 + 712.532i −0.211348 + 0.977411i
\(82\) 0 0
\(83\) −448.767 −0.593477 −0.296738 0.954959i \(-0.595899\pi\)
−0.296738 + 0.954959i \(0.595899\pi\)
\(84\) 0 0
\(85\) −248.513 −0.317118
\(86\) 0 0
\(87\) 1245.05 + 595.204i 1.53430 + 0.733478i
\(88\) 0 0
\(89\) −280.814 + 486.384i −0.334452 + 0.579288i −0.983379 0.181562i \(-0.941885\pi\)
0.648927 + 0.760850i \(0.275218\pi\)
\(90\) 0 0
\(91\) −130.563 + 1148.61i −0.150404 + 1.32315i
\(92\) 0 0
\(93\) 4.12336 + 52.9875i 0.00459756 + 0.0590811i
\(94\) 0 0
\(95\) 110.323 63.6953i 0.119147 0.0687895i
\(96\) 0 0
\(97\) 214.364i 0.224385i −0.993686 0.112192i \(-0.964213\pi\)
0.993686 0.112192i \(-0.0357873\pi\)
\(98\) 0 0
\(99\) 451.297 + 174.147i 0.458152 + 0.176793i
\(100\) 0 0
\(101\) 858.845 + 1487.56i 0.846122 + 1.46553i 0.884644 + 0.466268i \(0.154402\pi\)
−0.0385219 + 0.999258i \(0.512265\pi\)
\(102\) 0 0
\(103\) −1002.61 578.855i −0.959123 0.553750i −0.0632200 0.998000i \(-0.520137\pi\)
−0.895903 + 0.444250i \(0.853470\pi\)
\(104\) 0 0
\(105\) 523.644 + 986.300i 0.486690 + 0.916696i
\(106\) 0 0
\(107\) −1054.64 608.897i −0.952859 0.550134i −0.0588912 0.998264i \(-0.518757\pi\)
−0.893968 + 0.448131i \(0.852090\pi\)
\(108\) 0 0
\(109\) −649.132 1124.33i −0.570418 0.987992i −0.996523 0.0833189i \(-0.973448\pi\)
0.426105 0.904674i \(-0.359885\pi\)
\(110\) 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
\(117\) 1311.58 1058.29i 1.03638 0.836230i
\(118\) 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
\(123\) −69.4827 + 145.345i −0.0509353 + 0.106547i
\(124\) 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
\(129\) 503.244 1052.69i 0.343474 0.718484i
\(130\) 0 0
\(131\) 801.637 1388.48i 0.534651 0.926043i −0.464529 0.885558i \(-0.653776\pi\)
0.999180 0.0404852i \(-0.0128904\pi\)
\(132\) 0 0
\(133\) −163.472 120.897i −0.106578 0.0788203i
\(134\) 0 0
\(135\) 466.484 1559.71i 0.297396 0.994361i
\(136\) 0 0
\(137\) 2007.90 1159.26i 1.25216 0.722938i 0.280626 0.959817i \(-0.409458\pi\)
0.971539 + 0.236879i \(0.0761246\pi\)
\(138\) 0 0
\(139\) 1841.57i 1.12374i 0.827225 + 0.561871i \(0.189918\pi\)
−0.827225 + 0.561871i \(0.810082\pi\)
\(140\) 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
\(147\) 1109.99 1394.43i 0.622793 0.782386i
\(148\) 0 0
\(149\) −1126.68 650.488i −0.619470 0.357651i 0.157193 0.987568i \(-0.449756\pi\)
−0.776663 + 0.629917i \(0.783089\pi\)
\(150\) 0 0
\(151\) −1308.24 2265.94i −0.705055 1.22119i −0.966672 0.256020i \(-0.917589\pi\)
0.261616 0.965172i \(-0.415745\pi\)
\(152\) 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 −0.691515 0.722362i \(-0.743056\pi\)
0.279826 + 0.960051i \(0.409723\pi\)
\(158\) 0 0
\(159\) −212.540 2731.26i −0.106010 1.36228i
\(160\) 0 0
\(161\) 1028.84 + 760.883i 0.503625 + 0.372460i
\(162\) 0 0
\(163\) −259.079 + 448.738i −0.124495 + 0.215631i −0.921535 0.388295i \(-0.873064\pi\)
0.797041 + 0.603926i \(0.206398\pi\)
\(164\) 0 0
\(165\) −974.612 465.918i −0.459839 0.219828i
\(166\) 0 0
\(167\) 3767.97 1.74595 0.872977 0.487761i \(-0.162186\pi\)
0.872977 + 0.487761i \(0.162186\pi\)
\(168\) 0 0
\(169\) −1699.06 −0.773356
\(170\) 0 0
\(171\) 45.8548 + 292.845i 0.0205064 + 0.130962i
\(172\) 0 0
\(173\) 1196.53 2072.45i 0.525841 0.910783i −0.473706 0.880683i \(-0.657084\pi\)
0.999547 0.0301000i \(-0.00958257\pi\)
\(174\) 0 0
\(175\) −71.3059 163.875i −0.0308013 0.0707875i
\(176\) 0 0
\(177\) 2134.14 166.074i 0.906280 0.0705246i
\(178\) 0 0
\(179\) −554.381 + 320.072i −0.231488 + 0.133650i −0.611258 0.791431i \(-0.709336\pi\)
0.379770 + 0.925081i \(0.376003\pi\)
\(180\) 0 0
\(181\) 4204.05i 1.72643i 0.504833 + 0.863217i \(0.331554\pi\)
−0.504833 + 0.863217i \(0.668446\pi\)
\(182\) 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
\(189\) −2579.70 + 310.531i −0.992833 + 0.119512i
\(190\) 0 0
\(191\) 1261.85 + 728.530i 0.478033 + 0.275993i 0.719597 0.694392i \(-0.244327\pi\)
−0.241563 + 0.970385i \(0.577660\pi\)
\(192\) 0 0
\(193\) −914.633 1584.19i −0.341123 0.590842i 0.643519 0.765430i \(-0.277474\pi\)
−0.984642 + 0.174588i \(0.944141\pi\)
\(194\) 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 −0.168253 0.985744i \(-0.553812\pi\)
0.769553 + 0.638583i \(0.220479\pi\)
\(200\) 0 0
\(201\) 1675.76 130.403i 0.588053 0.0457609i
\(202\) 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
\(207\) −288.594 1843.06i −0.0969017 0.618850i
\(208\) 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
\(213\) 212.929 + 101.792i 0.0684960 + 0.0327448i
\(214\) 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
\(219\) 226.642 + 2912.47i 0.0699316 + 0.898659i
\(220\) 0 0
\(221\) −1157.68 + 668.390i −0.352372 + 0.203442i
\(222\) 0 0
\(223\) 2143.28i 0.643608i −0.946806 0.321804i \(-0.895711\pi\)
0.946806 0.321804i \(-0.104289\pi\)
\(224\) 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 \(-0.289226\pi\)
−0.990415 + 0.138123i \(0.955893\pi\)
\(228\) 0 0
\(229\) 91.0827 + 52.5866i 0.0262835 + 0.0151748i 0.513084 0.858338i \(-0.328503\pi\)
−0.486801 + 0.873513i \(0.661836\pi\)
\(230\) 0 0
\(231\) −61.2350 + 1723.04i −0.0174414 + 0.490770i
\(232\) 0 0
\(233\) 2273.94 + 1312.86i 0.639360 + 0.369135i 0.784368 0.620296i \(-0.212987\pi\)
−0.145008 + 0.989431i \(0.546321\pi\)
\(234\) 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 0.142891 0.989738i \(-0.454360\pi\)
0.928584 + 0.371122i \(0.121027\pi\)
\(242\) 0 0
\(243\) 2995.06 + 2319.17i 0.790671 + 0.612241i
\(244\) 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
\(249\) −1005.74 + 2103.82i −0.255969 + 0.535439i
\(250\) 0 0
\(251\) −5967.85 −1.50075 −0.750373 0.661015i \(-0.770126\pi\)
−0.750373 + 0.661015i \(0.770126\pi\)
\(252\) 0 0
\(253\) −1237.88 −0.307607
\(254\) 0 0
\(255\) −556.948 + 1165.03i −0.136774 + 0.286106i
\(256\) 0 0
\(257\) −2819.70 + 4883.86i −0.684389 + 1.18540i 0.289239 + 0.957257i \(0.406598\pi\)
−0.973628 + 0.228140i \(0.926736\pi\)
\(258\) 0 0
\(259\) −458.681 + 620.211i −0.110043 + 0.148796i
\(260\) 0 0
\(261\) 5580.64 4502.90i 1.32350 1.06790i
\(262\) 0 0
\(263\) 3018.63 1742.81i 0.707745 0.408617i −0.102480 0.994735i \(-0.532678\pi\)
0.810226 + 0.586118i \(0.199345\pi\)
\(264\) 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 \(-0.308165\pi\)
−0.996876 + 0.0789869i \(0.974831\pi\)
\(270\) 0 0
\(271\) 6458.49 + 3728.81i 1.44769 + 0.835827i 0.998344 0.0575288i \(-0.0183221\pi\)
0.449351 + 0.893356i \(0.351655\pi\)
\(272\) 0 0
\(273\) 5092.07 + 3186.25i 1.12889 + 0.706377i
\(274\) 0 0
\(275\) 149.723 + 86.4428i 0.0328315 + 0.0189553i
\(276\) 0 0
\(277\) 1707.75 + 2957.90i 0.370428 + 0.641600i 0.989631 0.143631i \(-0.0458777\pi\)
−0.619203 + 0.785231i \(0.712544\pi\)
\(278\) 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 0.0927647 0.995688i \(-0.470430\pi\)
0.908674 + 0.417507i \(0.137096\pi\)
\(284\) 0 0
\(285\) −51.3554 659.946i −0.0106738 0.137164i
\(286\) 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
\(291\) −1004.94 480.415i −0.202442 0.0967781i
\(292\) 0 0
\(293\) 4101.08 0.817705 0.408853 0.912600i \(-0.365929\pi\)
0.408853 + 0.912600i \(0.365929\pi\)
\(294\) 0 0
\(295\) −4780.29 −0.943455
\(296\) 0 0
\(297\) 1827.82 1725.40i 0.357106 0.337097i
\(298\) 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
\(303\) 8898.48 692.459i 1.68714 0.131290i
\(304\) 0 0
\(305\) −2597.03 + 1499.40i −0.487560 + 0.281493i
\(306\) 0 0
\(307\) 8281.42i 1.53956i 0.638308 + 0.769781i \(0.279635\pi\)
−0.638308 + 0.769781i \(0.720365\pi\)
\(308\) 0 0
\(309\) −4960.63 + 3402.94i −0.913270 + 0.626493i
\(310\) 0 0
\(311\) 3435.52 + 5950.50i 0.626401 + 1.08496i 0.988268 + 0.152728i \(0.0488059\pi\)
−0.361868 + 0.932230i \(0.617861\pi\)
\(312\) 0 0
\(313\) −2922.40 1687.25i −0.527743 0.304693i 0.212354 0.977193i \(-0.431887\pi\)
−0.740097 + 0.672500i \(0.765220\pi\)
\(314\) 0 0
\(315\) 5797.33 244.428i 1.03696 0.0437205i
\(316\) 0 0
\(317\) 2052.28 + 1184.88i 0.363620 + 0.209936i 0.670667 0.741758i \(-0.266008\pi\)
−0.307048 + 0.951694i \(0.599341\pi\)
\(318\) 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
\(327\) −6725.64 + 523.374i −1.13740 + 0.0885096i
\(328\) 0 0
\(329\) 1802.94 2437.86i 0.302125 0.408521i
\(330\) 0 0
\(331\) 1901.80 3294.02i 0.315808 0.546996i −0.663801 0.747910i \(-0.731058\pi\)
0.979609 + 0.200913i \(0.0643910\pi\)
\(332\) 0 0
\(333\) 1111.05 173.972i 0.182838 0.0286295i
\(334\) 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
\(339\) −6740.69 3222.42i −1.07995 0.516276i
\(340\) 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
\(345\) 323.213 + 4153.46i 0.0504383 + 0.648159i
\(346\) 0 0
\(347\) 4137.14 2388.58i 0.640039 0.369527i −0.144590 0.989492i \(-0.546186\pi\)
0.784630 + 0.619965i \(0.212853\pi\)
\(348\) 0 0
\(349\) 7358.26i 1.12859i 0.825573 + 0.564296i \(0.190852\pi\)
−0.825573 + 0.564296i \(0.809148\pi\)
\(350\) 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 \(-0.0864982\pi\)
−0.714102 + 0.700041i \(0.753165\pi\)
\(354\) 0 0
\(355\) −456.436 263.524i −0.0682398 0.0393982i
\(356\) 0 0
\(357\) 2059.69 + 73.1991i 0.305351 + 0.0108518i
\(358\) 0 0
\(359\) 359.154 + 207.358i 0.0528006 + 0.0304845i 0.526168 0.850381i \(-0.323628\pi\)
−0.473367 + 0.880865i \(0.656962\pi\)
\(360\) 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 −0.495304 0.868720i \(-0.664943\pi\)
0.504681 + 0.863306i \(0.331610\pi\)
\(368\) 0 0
\(369\) 525.657 + 651.470i 0.0741588 + 0.0919083i
\(370\) 0 0
\(371\) 8953.38 3895.82i 1.25293 0.545178i
\(372\) 0 0
\(373\) 6150.49 10653.0i 0.853781 1.47879i −0.0239900 0.999712i \(-0.507637\pi\)
0.877771 0.479080i \(-0.159030\pi\)
\(374\) 0 0
\(375\) −2999.76 + 6274.93i −0.413085 + 0.864096i
\(376\) 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
\(381\) −6020.38 + 12593.5i −0.809536 + 1.69340i
\(382\) 0 0
\(383\) −2555.45 + 4426.17i −0.340933 + 0.590513i −0.984606 0.174787i \(-0.944076\pi\)
0.643673 + 0.765300i \(0.277410\pi\)
\(384\) 0 0
\(385\) 434.863 3825.63i 0.0575654 0.506421i
\(386\) 0 0
\(387\) −3807.19 4718.42i −0.500079 0.619770i
\(388\) 0 0
\(389\) 6339.84 3660.31i 0.826331 0.477083i −0.0262636 0.999655i \(-0.508361\pi\)
0.852595 + 0.522572i \(0.175028\pi\)
\(390\) 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 0.893158 0.449744i \(-0.148485\pi\)
0.0570893 + 0.998369i \(0.481818\pi\)
\(398\) 0 0
\(399\) −933.127 + 495.414i −0.117080 + 0.0621597i
\(400\) 0 0
\(401\) 8447.68 + 4877.27i 1.05201 + 0.607379i 0.923212 0.384291i \(-0.125554\pi\)
0.128800 + 0.991671i \(0.458887\pi\)
\(402\) 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 −0.311958 0.950096i \(-0.600985\pi\)
0.666828 + 0.745211i \(0.267651\pi\)
\(410\) 0 0
\(411\) −934.676 12011.1i −0.112176 1.44152i
\(412\) 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
\(417\) 8633.30 + 4127.19i 1.01385 + 0.484675i
\(418\) 0 0
\(419\) −12777.4 −1.48977 −0.744887 0.667191i \(-0.767496\pi\)
−0.744887 + 0.667191i \(0.767496\pi\)
\(420\) 0 0
\(421\) 11005.4 1.27404 0.637020 0.770848i \(-0.280167\pi\)
0.637020 + 0.770848i \(0.280167\pi\)
\(422\) 0 0
\(423\) −4367.20 + 683.831i −0.501987 + 0.0786029i
\(424\) 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
\(429\) −5793.28 + 450.820i −0.651987 + 0.0507361i
\(430\) 0 0
\(431\) −3279.13 + 1893.21i −0.366474 + 0.211584i −0.671917 0.740627i \(-0.734529\pi\)
0.305443 + 0.952210i \(0.401195\pi\)
\(432\) 0 0
\(433\) 3191.67i 0.354230i −0.984190 0.177115i \(-0.943323\pi\)
0.984190 0.177115i \(-0.0566765\pi\)
\(434\) 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 0.647972 0.761664i \(-0.275617\pi\)
−0.335635 + 0.941992i \(0.608951\pi\)
\(440\) 0 0
\(441\) −4049.47 8328.74i −0.437261 0.899335i
\(442\) 0 0
\(443\) 9266.95 + 5350.27i 0.993873 + 0.573813i 0.906430 0.422356i \(-0.138797\pi\)
0.0874435 + 0.996169i \(0.472130\pi\)
\(444\) 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
\(453\) −13554.7 + 1054.79i −1.40586 + 0.109401i
\(454\) 0 0
\(455\) −10785.1 7976.22i −1.11124 0.821826i
\(456\) 0 0
\(457\) −4584.83 + 7941.15i −0.469298 + 0.812848i −0.999384 0.0350961i \(-0.988826\pi\)
0.530086 + 0.847944i \(0.322160\pi\)
\(458\) 0 0
\(459\) −2062.51 2184.93i −0.209737 0.222187i
\(460\) 0 0
\(461\) −1289.80 −0.130308 −0.0651542 0.997875i \(-0.520754\pi\)
−0.0651542 + 0.997875i \(0.520754\pi\)
\(462\) 0 0
\(463\) −6976.52 −0.700273 −0.350137 0.936699i \(-0.613865\pi\)
−0.350137 + 0.936699i \(0.613865\pi\)
\(464\) 0 0
\(465\) −556.408 265.993i −0.0554899 0.0265272i
\(466\) 0 0
\(467\) 3931.83 6810.13i 0.389600 0.674808i −0.602795 0.797896i \(-0.705946\pi\)
0.992396 + 0.123088i \(0.0392798\pi\)
\(468\) 0 0
\(469\) 2390.27 + 5493.32i 0.235336 + 0.540849i
\(470\) 0 0
\(471\) 376.996 + 4844.61i 0.0368813 + 0.473944i
\(472\) 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 \(-0.223046\pi\)
−0.940574 + 0.339588i \(0.889712\pi\)
\(480\) 0 0
\(481\) −2251.51 1299.91i −0.213430 0.123224i
\(482\) 0 0
\(483\) 5872.77 3117.96i 0.553251 0.293731i
\(484\) 0 0
\(485\) 2154.19 + 1243.72i 0.201684 + 0.116442i
\(486\) 0 0
\(487\) −526.359 911.681i −0.0489766 0.0848300i 0.840498 0.541815i \(-0.182263\pi\)
−0.889474 + 0.456985i \(0.848929\pi\)
\(488\) 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
\(495\) −4368.45 + 3524.81i −0.396661 + 0.320057i
\(496\) 0 0
\(497\) −95.0069 + 835.807i −0.00857474 + 0.0754347i
\(498\) 0 0
\(499\) 9385.74 16256.6i 0.842011 1.45840i −0.0461818 0.998933i \(-0.514705\pi\)
0.888192 0.459472i \(-0.151961\pi\)
\(500\) 0 0
\(501\) 8444.48 17664.3i 0.753037 1.57521i
\(502\) 0 0
\(503\) 16095.2 1.42674 0.713370 0.700788i \(-0.247168\pi\)
0.713370 + 0.700788i \(0.247168\pi\)
\(504\) 0 0
\(505\) −19931.9 −1.75635
\(506\) 0 0
\(507\) −3807.81 + 7965.21i −0.333552 + 0.697727i
\(508\) 0 0
\(509\) 1575.31 2728.52i 0.137180 0.237603i −0.789248 0.614074i \(-0.789529\pi\)
0.926428 + 0.376472i \(0.122863\pi\)
\(510\) 0 0
\(511\) −9547.42 + 4154.30i −0.826522 + 0.359639i
\(512\) 0 0
\(513\) 1475.63 + 441.335i 0.126999 + 0.0379832i
\(514\) 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 \(-0.233802\pi\)
−0.951510 + 0.307618i \(0.900468\pi\)
\(522\) 0 0
\(523\) −11977.0 6914.92i −1.00137 0.578142i −0.0927181 0.995692i \(-0.529556\pi\)
−0.908654 + 0.417550i \(0.862889\pi\)
\(524\) 0 0
\(525\) −928.053 32.9820i −0.0771496 0.00274181i
\(526\) 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
\(537\) 258.064 + 3316.26i 0.0207379 + 0.266494i
\(538\) 0 0
\(539\) −5875.73 + 1799.75i −0.469547 + 0.143823i
\(540\) 0 0
\(541\) −2658.97 + 4605.48i −0.211309 + 0.365998i −0.952124 0.305711i \(-0.901106\pi\)
0.740815 + 0.671709i \(0.234439\pi\)
\(542\) 0 0
\(543\) 19708.6 + 9421.79i 1.55760 + 0.744618i
\(544\) 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
\(549\) −1079.43 6893.63i −0.0839142 0.535907i
\(550\) 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
\(555\) −2503.82 + 194.842i −0.191498 + 0.0149019i
\(556\) 0 0
\(557\) −125.920 + 72.6999i −0.00957881 + 0.00553033i −0.504782 0.863247i \(-0.668427\pi\)
0.495203 + 0.868777i \(0.335094\pi\)
\(558\) 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 \(-0.213493\pi\)
−0.929962 + 0.367657i \(0.880160\pi\)
\(564\) 0 0
\(565\) 14449.4 + 8342.36i 1.07591 + 0.621178i
\(566\) 0 0
\(567\) −4325.65 + 12789.6i −0.320388 + 0.947286i
\(568\) 0 0
\(569\) −7404.97 4275.26i −0.545576 0.314988i 0.201760 0.979435i \(-0.435334\pi\)
−0.747336 + 0.664447i \(0.768667\pi\)
\(570\) 0 0
\(571\) −11956.8 20709.8i −0.876318 1.51783i −0.855352 0.518047i \(-0.826659\pi\)
−0.0209659 0.999780i \(-0.506674\pi\)
\(572\) 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 −0.0312386 0.999512i \(-0.509945\pi\)
0.849983 + 0.526809i \(0.176612\pi\)
\(578\) 0 0
\(579\) −9476.49 + 737.439i −0.680189 + 0.0529307i
\(580\) 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
\(585\) 3025.28 + 19320.6i 0.213812 + 1.36548i
\(586\) 0 0
\(587\) −18034.7 −1.26809 −0.634047 0.773294i \(-0.718608\pi\)
−0.634047 + 0.773294i \(0.718608\pi\)
\(588\) 0 0
\(589\) 112.289 0.00785532
\(590\) 0 0
\(591\) 3099.56 + 1481.76i 0.215734 + 0.103133i
\(592\) 0 0
\(593\) 11358.1 19672.8i 0.786547 1.36234i −0.141524 0.989935i \(-0.545200\pi\)
0.928071 0.372404i \(-0.121466\pi\)
\(594\) 0 0
\(595\) −4573.08 519.826i −0.315089 0.0358165i
\(596\) 0 0
\(597\) −785.759 10097.4i −0.0538677 0.692229i
\(598\) 0 0
\(599\) −11720.4 + 6766.78i −0.799471 + 0.461575i −0.843286 0.537465i \(-0.819382\pi\)
0.0438153 + 0.999040i \(0.486049\pi\)
\(600\) 0 0
\(601\) 3667.98i 0.248952i 0.992223 + 0.124476i \(0.0397250\pi\)
−0.992223 + 0.124476i \(0.960275\pi\)
\(602\) 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 0.713833 0.700316i \(-0.246958\pi\)
−0.249575 + 0.968355i \(0.580291\pi\)
\(608\) 0 0
\(609\) 21666.2 + 13557.1i 1.44164 + 0.902074i
\(610\) 0 0
\(611\) 8849.99 + 5109.54i 0.585977 + 0.338314i
\(612\) 0 0
\(613\) −4698.26 8137.63i −0.309561 0.536176i 0.668705 0.743528i \(-0.266849\pi\)
−0.978266 + 0.207352i \(0.933515\pi\)
\(614\) 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 −0.289010 0.957326i \(-0.593326\pi\)
0.684563 + 0.728953i \(0.259993\pi\)
\(620\) 0 0
\(621\) −9287.07 2777.60i −0.600124 0.179487i
\(622\) 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
\(627\) 440.799 922.069i 0.0280763 0.0587303i
\(628\) 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
\(633\) −7489.74 + 15667.1i −0.470285 + 0.983747i
\(634\) 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
\(639\) 954.399 770.084i 0.0590852 0.0476746i
\(640\) 0 0
\(641\) −8593.58 + 4961.51i −0.529526 + 0.305722i −0.740823 0.671700i \(-0.765564\pi\)
0.211297 + 0.977422i \(0.432231\pi\)
\(642\) 0 0
\(643\) 294.191i 0.0180432i 0.999959 + 0.00902160i \(0.00287170\pi\)
−0.999959 + 0.00902160i \(0.997128\pi\)
\(644\) 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 \(-0.0913179\pi\)
−0.724620 + 0.689149i \(0.757985\pi\)
\(648\) 0 0
\(649\) −6391.80 3690.30i −0.386595 0.223201i
\(650\) 0 0
\(651\) −34.9592 + 983.688i −0.00210470 + 0.0592224i
\(652\) 0 0
\(653\) −9846.89 5685.11i −0.590105 0.340697i 0.175034 0.984562i \(-0.443996\pi\)
−0.765139 + 0.643865i \(0.777330\pi\)
\(654\) 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 0.588219 0.808702i \(-0.299829\pi\)
0.994466 0.105062i \(-0.0335041\pi\)
\(662\) 0 0
\(663\) 538.901 + 6925.17i 0.0315674 + 0.405658i
\(664\) 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
\(669\) −10047.7 4803.34i −0.580667 0.277590i
\(670\) 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
\(675\) 929.322 + 984.486i 0.0529920 + 0.0561376i
\(676\) 0 0
\(677\) −12478.3 + 21613.0i −0.708389 + 1.22697i 0.257066 + 0.966394i \(0.417244\pi\)
−0.965455 + 0.260571i \(0.916089\pi\)
\(678\) 0 0
\(679\) 448.394 3944.67i 0.0253428 0.222949i
\(680\) 0 0
\(681\) −13309.2 + 1035.69i −0.748914 + 0.0582788i
\(682\) 0 0
\(683\) −9706.83 + 5604.24i −0.543809 + 0.313968i −0.746621 0.665249i \(-0.768325\pi\)
0.202812 + 0.979218i \(0.434992\pi\)
\(684\) 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 0.737542 0.675301i \(-0.235986\pi\)
−0.216057 + 0.976381i \(0.569320\pi\)
\(692\) 0 0
\(693\) 7940.39 + 4148.61i 0.435253 + 0.227407i
\(694\) 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
\(705\) 9841.76 765.863i 0.525762 0.0409136i
\(706\) 0 0
\(707\) 12692.7 + 29170.3i 0.675186 + 1.55171i
\(708\) 0 0
\(709\) −10472.7 + 18139.3i −0.554741 + 0.960840i 0.443183 + 0.896431i \(0.353849\pi\)
−0.997924 + 0.0644082i \(0.979484\pi\)
\(710\) 0 0
\(711\) −7714.96 + 1208.04i −0.406939 + 0.0637200i
\(712\) 0 0
\(713\) −706.707 −0.0371197
\(714\) 0 0
\(715\) 12976.5 0.678731
\(716\) 0 0
\(717\) −28507.1 13627.9i −1.48482 0.709825i
\(718\) 0 0
\(719\) −4150.10 + 7188.19i −0.215261 + 0.372843i −0.953353 0.301857i \(-0.902394\pi\)
0.738092 + 0.674700i \(0.235727\pi\)
\(720\) 0 0
\(721\) −17238.9 12749.1i −0.890443 0.658533i
\(722\) 0 0
\(723\) −1866.06 23979.9i −0.0959884 1.23350i
\(724\) 0 0
\(725\) 2219.47 1281.41i 0.113695 0.0656420i
\(726\) 0 0
\(727\) 20951.5i 1.06884i 0.845218 + 0.534421i \(0.179470\pi\)
−0.845218 + 0.534421i \(0.820530\pi\)
\(728\) 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 0.618019 0.786163i \(-0.287935\pi\)
−0.371827 + 0.928302i \(0.621269\pi\)
\(734\) 0 0
\(735\) 7572.89 + 19245.0i 0.380041 + 0.965799i
\(736\) 0 0
\(737\) −5018.93 2897.68i −0.250848 0.144827i
\(738\) 0 0
\(739\) −5691.08 9857.24i −0.283288 0.490669i 0.688905 0.724852i \(-0.258092\pi\)
−0.972193 + 0.234183i \(0.924758\pi\)
\(740\) 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
\(747\) 7608.73 + 9429.84i 0.372676 + 0.461874i
\(748\) 0 0
\(749\) −18133.6 13410.8i −0.884628 0.654233i
\(750\) 0 0
\(751\) −4780.43 + 8279.95i −0.232277 + 0.402316i −0.958478 0.285167i \(-0.907951\pi\)
0.726200 + 0.687483i \(0.241284\pi\)
\(752\) 0 0
\(753\) −13374.7 + 27977.3i −0.647278 + 1.35398i
\(754\) 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
\(759\) −2774.23 + 5803.17i −0.132672 + 0.277525i
\(760\) 0 0
\(761\) 11215.0 19424.9i 0.534221 0.925298i −0.464980 0.885321i \(-0.653938\pi\)
0.999201 0.0399765i \(-0.0127283\pi\)
\(762\) 0 0
\(763\) −9593.35 22047.4i −0.455180 1.04610i
\(764\) 0 0
\(765\) 4213.48 + 5221.95i 0.199136 + 0.246797i
\(766\) 0 0
\(767\) −22268.7 + 12856.8i −1.04834 + 0.605259i
\(768\) 0 0
\(769\) 26887.4i 1.26084i −0.776254 0.630420i \(-0.782883\pi\)
0.776254 0.630420i \(-0.217117\pi\)
\(770\) 0 0
\(771\) 16576.3 + 24164.1i 0.774293 + 1.12873i
\(772\) 0 0
\(773\) 11104.6 + 19233.7i 0.516693 + 0.894938i 0.999812 + 0.0193838i \(0.00617045\pi\)
−0.483119 + 0.875555i \(0.660496\pi\)
\(774\) 0 0
\(775\) 85.4774 + 49.3504i 0.00396185 + 0.00228738i
\(776\) 0 0
\(777\) 1879.59 + 3540.27i 0.0867824 + 0.163457i
\(778\) 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 −0.0510919 0.998694i \(-0.516270\pi\)
0.839348 + 0.543594i \(0.182937\pi\)
\(788\) 0 0
\(789\) −1405.17 18057.2i −0.0634035