Properties

Label 624.4.bv.c.49.1
Level $624$
Weight $4$
Character 624.49
Analytic conductor $36.817$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 624 = 2^{4} \cdot 3 \cdot 13 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 624.bv (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(36.8171918436\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\sqrt{-3}, \sqrt{-17})\)
Defining polynomial: \( x^{4} - 17x^{2} + 289 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 39)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 49.1
Root \(3.57071 - 2.06155i\) of defining polynomial
Character \(\chi\) \(=\) 624.49
Dual form 624.4.bv.c.433.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.50000 - 2.59808i) q^{3} -3.05006i q^{5} +(5.78786 + 3.34162i) q^{7} +(-4.50000 + 7.79423i) q^{9} +O(q^{10})\) \(q+(-1.50000 - 2.59808i) q^{3} -3.05006i q^{5} +(5.78786 + 3.34162i) q^{7} +(-4.50000 + 7.79423i) q^{9} +(27.9293 - 16.1250i) q^{11} +(-22.1364 - 41.3156i) q^{13} +(-7.92429 + 4.57509i) q^{15} +(-14.4293 + 24.9923i) q^{17} +(-87.6364 - 50.5969i) q^{19} -20.0497i q^{21} +(59.4950 + 103.048i) q^{23} +115.697 q^{25} +27.0000 q^{27} +(-80.0557 - 138.661i) q^{29} +38.0705i q^{31} +(-83.7879 - 48.3749i) q^{33} +(10.1921 - 17.6533i) q^{35} +(283.682 - 163.784i) q^{37} +(-74.1364 + 119.486i) q^{39} +(48.5707 - 28.0423i) q^{41} +(-63.9393 + 110.746i) q^{43} +(23.7729 + 13.7253i) q^{45} -517.983i q^{47} +(-149.167 - 258.365i) q^{49} +86.5757 q^{51} -695.546 q^{53} +(-49.1821 - 85.1860i) q^{55} +303.581i q^{57} +(-568.566 - 328.262i) q^{59} +(-350.652 + 607.347i) q^{61} +(-52.0907 + 30.0746i) q^{63} +(-126.015 + 67.5174i) q^{65} +(49.5150 - 28.5875i) q^{67} +(178.485 - 309.145i) q^{69} +(267.798 + 154.613i) q^{71} +389.711i q^{73} +(-173.546 - 300.590i) q^{75} +215.534 q^{77} -901.820 q^{79} +(-40.5000 - 70.1481i) q^{81} -687.095i q^{83} +(76.2279 + 44.0102i) q^{85} +(-240.167 + 415.982i) q^{87} +(-927.113 + 535.269i) q^{89} +(9.93858 - 313.100i) q^{91} +(98.9100 - 57.1057i) q^{93} +(-154.324 + 267.296i) q^{95} +(-1519.43 - 877.242i) q^{97} +290.250i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 6 q^{3} + 66 q^{7} - 18 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - 6 q^{3} + 66 q^{7} - 18 q^{9} + 126 q^{11} + 40 q^{13} + 54 q^{15} - 72 q^{17} - 222 q^{19} + 138 q^{23} + 120 q^{25} + 108 q^{27} - 6 q^{29} - 378 q^{33} - 402 q^{35} + 492 q^{37} - 168 q^{39} + 180 q^{41} - 470 q^{43} - 162 q^{45} + 346 q^{49} + 432 q^{51} - 2268 q^{53} + 446 q^{55} - 2160 q^{59} - 160 q^{61} - 594 q^{63} - 804 q^{65} + 498 q^{67} + 414 q^{69} + 1314 q^{71} - 180 q^{75} + 2976 q^{77} - 8 q^{79} - 162 q^{81} - 852 q^{85} - 18 q^{87} - 252 q^{89} + 1668 q^{91} - 1404 q^{93} + 54 q^{95} - 336 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/624\mathbb{Z}\right)^\times\).

\(n\) \(79\) \(145\) \(209\) \(469\)
\(\chi(n)\) \(1\) \(e\left(\frac{5}{6}\right)\) \(1\) \(1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −1.50000 2.59808i −0.288675 0.500000i
\(4\) 0 0
\(5\) 3.05006i 0.272806i −0.990653 0.136403i \(-0.956446\pi\)
0.990653 0.136403i \(-0.0435541\pi\)
\(6\) 0 0
\(7\) 5.78786 + 3.34162i 0.312515 + 0.180431i 0.648051 0.761597i \(-0.275584\pi\)
−0.335536 + 0.942027i \(0.608918\pi\)
\(8\) 0 0
\(9\) −4.50000 + 7.79423i −0.166667 + 0.288675i
\(10\) 0 0
\(11\) 27.9293 16.1250i 0.765545 0.441988i −0.0657380 0.997837i \(-0.520940\pi\)
0.831283 + 0.555849i \(0.187607\pi\)
\(12\) 0 0
\(13\) −22.1364 41.3156i −0.472272 0.881453i
\(14\) 0 0
\(15\) −7.92429 + 4.57509i −0.136403 + 0.0787522i
\(16\) 0 0
\(17\) −14.4293 + 24.9923i −0.205860 + 0.356560i −0.950406 0.311011i \(-0.899332\pi\)
0.744547 + 0.667571i \(0.232666\pi\)
\(18\) 0 0
\(19\) −87.6364 50.5969i −1.05817 0.610933i −0.133242 0.991083i \(-0.542539\pi\)
−0.924925 + 0.380150i \(0.875872\pi\)
\(20\) 0 0
\(21\) 20.0497i 0.208343i
\(22\) 0 0
\(23\) 59.4950 + 103.048i 0.539372 + 0.934220i 0.998938 + 0.0460765i \(0.0146718\pi\)
−0.459566 + 0.888144i \(0.651995\pi\)
\(24\) 0 0
\(25\) 115.697 0.925577
\(26\) 0 0
\(27\) 27.0000 0.192450
\(28\) 0 0
\(29\) −80.0557 138.661i −0.512620 0.887883i −0.999893 0.0146339i \(-0.995342\pi\)
0.487273 0.873250i \(-0.337992\pi\)
\(30\) 0 0
\(31\) 38.0705i 0.220570i 0.993900 + 0.110285i \(0.0351763\pi\)
−0.993900 + 0.110285i \(0.964824\pi\)
\(32\) 0 0
\(33\) −83.7879 48.3749i −0.441988 0.255182i
\(34\) 0 0
\(35\) 10.1921 17.6533i 0.0492225 0.0852558i
\(36\) 0 0
\(37\) 283.682 163.784i 1.26046 0.727727i 0.287297 0.957841i \(-0.407243\pi\)
0.973164 + 0.230114i \(0.0739099\pi\)
\(38\) 0 0
\(39\) −74.1364 + 119.486i −0.304393 + 0.490590i
\(40\) 0 0
\(41\) 48.5707 28.0423i 0.185011 0.106816i −0.404634 0.914479i \(-0.632601\pi\)
0.589645 + 0.807662i \(0.299268\pi\)
\(42\) 0 0
\(43\) −63.9393 + 110.746i −0.226759 + 0.392759i −0.956846 0.290596i \(-0.906146\pi\)
0.730087 + 0.683355i \(0.239480\pi\)
\(44\) 0 0
\(45\) 23.7729 + 13.7253i 0.0787522 + 0.0454676i
\(46\) 0 0
\(47\) 517.983i 1.60757i −0.594923 0.803783i \(-0.702817\pi\)
0.594923 0.803783i \(-0.297183\pi\)
\(48\) 0 0
\(49\) −149.167 258.365i −0.434890 0.753251i
\(50\) 0 0
\(51\) 86.5757 0.237706
\(52\) 0 0
\(53\) −695.546 −1.80265 −0.901326 0.433141i \(-0.857405\pi\)
−0.901326 + 0.433141i \(0.857405\pi\)
\(54\) 0 0
\(55\) −49.1821 85.1860i −0.120577 0.208845i
\(56\) 0 0
\(57\) 303.581i 0.705445i
\(58\) 0 0
\(59\) −568.566 328.262i −1.25459 0.724339i −0.282574 0.959245i \(-0.591188\pi\)
−0.972018 + 0.234906i \(0.924522\pi\)
\(60\) 0 0
\(61\) −350.652 + 607.347i −0.736007 + 1.27480i 0.218274 + 0.975888i \(0.429957\pi\)
−0.954280 + 0.298913i \(0.903376\pi\)
\(62\) 0 0
\(63\) −52.0907 + 30.0746i −0.104172 + 0.0601435i
\(64\) 0 0
\(65\) −126.015 + 67.5174i −0.240465 + 0.128839i
\(66\) 0 0
\(67\) 49.5150 28.5875i 0.0902869 0.0521271i −0.454177 0.890912i \(-0.650067\pi\)
0.544464 + 0.838784i \(0.316733\pi\)
\(68\) 0 0
\(69\) 178.485 309.145i 0.311407 0.539372i
\(70\) 0 0
\(71\) 267.798 + 154.613i 0.447630 + 0.258440i 0.706829 0.707385i \(-0.250125\pi\)
−0.259199 + 0.965824i \(0.583458\pi\)
\(72\) 0 0
\(73\) 389.711i 0.624826i 0.949946 + 0.312413i \(0.101137\pi\)
−0.949946 + 0.312413i \(0.898863\pi\)
\(74\) 0 0
\(75\) −173.546 300.590i −0.267191 0.462789i
\(76\) 0 0
\(77\) 215.534 0.318992
\(78\) 0 0
\(79\) −901.820 −1.28434 −0.642169 0.766563i \(-0.721965\pi\)
−0.642169 + 0.766563i \(0.721965\pi\)
\(80\) 0 0
\(81\) −40.5000 70.1481i −0.0555556 0.0962250i
\(82\) 0 0
\(83\) 687.095i 0.908657i −0.890834 0.454328i \(-0.849879\pi\)
0.890834 0.454328i \(-0.150121\pi\)
\(84\) 0 0
\(85\) 76.2279 + 44.0102i 0.0972714 + 0.0561597i
\(86\) 0 0
\(87\) −240.167 + 415.982i −0.295961 + 0.512620i
\(88\) 0 0
\(89\) −927.113 + 535.269i −1.10420 + 0.637510i −0.937321 0.348467i \(-0.886702\pi\)
−0.166879 + 0.985977i \(0.553369\pi\)
\(90\) 0 0
\(91\) 9.93858 313.100i 0.0114489 0.360679i
\(92\) 0 0
\(93\) 98.9100 57.1057i 0.110285 0.0636730i
\(94\) 0 0
\(95\) −154.324 + 267.296i −0.166666 + 0.288674i
\(96\) 0 0
\(97\) −1519.43 877.242i −1.59046 0.918251i −0.993228 0.116182i \(-0.962935\pi\)
−0.597230 0.802070i \(-0.703732\pi\)
\(98\) 0 0
\(99\) 290.250i 0.294658i
\(100\) 0 0
\(101\) −320.420 554.984i −0.315673 0.546762i 0.663907 0.747815i \(-0.268897\pi\)
−0.979580 + 0.201053i \(0.935564\pi\)
\(102\) 0 0
\(103\) −693.153 −0.663091 −0.331546 0.943439i \(-0.607570\pi\)
−0.331546 + 0.943439i \(0.607570\pi\)
\(104\) 0 0
\(105\) −61.1528 −0.0568372
\(106\) 0 0
\(107\) −202.838 351.325i −0.183262 0.317420i 0.759727 0.650242i \(-0.225332\pi\)
−0.942990 + 0.332822i \(0.891999\pi\)
\(108\) 0 0
\(109\) 479.516i 0.421370i −0.977554 0.210685i \(-0.932431\pi\)
0.977554 0.210685i \(-0.0675694\pi\)
\(110\) 0 0
\(111\) −851.046 491.352i −0.727727 0.420154i
\(112\) 0 0
\(113\) 773.602 1339.92i 0.644021 1.11548i −0.340506 0.940242i \(-0.610598\pi\)
0.984527 0.175235i \(-0.0560684\pi\)
\(114\) 0 0
\(115\) 314.304 181.463i 0.254861 0.147144i
\(116\) 0 0
\(117\) 421.637 + 13.3838i 0.333166 + 0.0105755i
\(118\) 0 0
\(119\) −167.029 + 96.4344i −0.128668 + 0.0742868i
\(120\) 0 0
\(121\) −145.470 + 251.961i −0.109294 + 0.189302i
\(122\) 0 0
\(123\) −145.712 84.1269i −0.106816 0.0616705i
\(124\) 0 0
\(125\) 734.140i 0.525308i
\(126\) 0 0
\(127\) 1247.58 + 2160.87i 0.871690 + 1.50981i 0.860248 + 0.509876i \(0.170309\pi\)
0.0114416 + 0.999935i \(0.496358\pi\)
\(128\) 0 0
\(129\) 383.636 0.261839
\(130\) 0 0
\(131\) −43.7571 −0.0291838 −0.0145919 0.999894i \(-0.504645\pi\)
−0.0145919 + 0.999894i \(0.504645\pi\)
\(132\) 0 0
\(133\) −338.151 585.695i −0.220462 0.381851i
\(134\) 0 0
\(135\) 82.3516i 0.0525015i
\(136\) 0 0
\(137\) −178.569 103.097i −0.111359 0.0642932i 0.443286 0.896380i \(-0.353813\pi\)
−0.554645 + 0.832087i \(0.687146\pi\)
\(138\) 0 0
\(139\) −50.0000 + 86.6025i −0.0305104 + 0.0528456i −0.880877 0.473344i \(-0.843047\pi\)
0.850367 + 0.526190i \(0.176380\pi\)
\(140\) 0 0
\(141\) −1345.76 + 776.974i −0.803783 + 0.464064i
\(142\) 0 0
\(143\) −1284.47 796.966i −0.751137 0.466053i
\(144\) 0 0
\(145\) −422.923 + 244.175i −0.242220 + 0.139846i
\(146\) 0 0
\(147\) −447.501 + 775.095i −0.251084 + 0.434890i
\(148\) 0 0
\(149\) −329.480 190.225i −0.181155 0.104590i 0.406680 0.913571i \(-0.366686\pi\)
−0.587835 + 0.808981i \(0.700020\pi\)
\(150\) 0 0
\(151\) 1517.45i 0.817805i −0.912578 0.408902i \(-0.865912\pi\)
0.912578 0.408902i \(-0.134088\pi\)
\(152\) 0 0
\(153\) −129.864 224.930i −0.0686199 0.118853i
\(154\) 0 0
\(155\) 116.117 0.0601726
\(156\) 0 0
\(157\) 1450.16 0.737166 0.368583 0.929595i \(-0.379843\pi\)
0.368583 + 0.929595i \(0.379843\pi\)
\(158\) 0 0
\(159\) 1043.32 + 1807.08i 0.520381 + 0.901326i
\(160\) 0 0
\(161\) 795.239i 0.389277i
\(162\) 0 0
\(163\) −2028.54 1171.18i −0.974772 0.562785i −0.0740844 0.997252i \(-0.523603\pi\)
−0.900688 + 0.434467i \(0.856937\pi\)
\(164\) 0 0
\(165\) −147.546 + 255.558i −0.0696150 + 0.120577i
\(166\) 0 0
\(167\) −34.7043 + 20.0365i −0.0160808 + 0.00928428i −0.508019 0.861346i \(-0.669622\pi\)
0.491938 + 0.870630i \(0.336289\pi\)
\(168\) 0 0
\(169\) −1216.96 + 1829.16i −0.553918 + 0.832571i
\(170\) 0 0
\(171\) 788.728 455.372i 0.352722 0.203644i
\(172\) 0 0
\(173\) 954.770 1653.71i 0.419594 0.726759i −0.576304 0.817235i \(-0.695506\pi\)
0.995899 + 0.0904765i \(0.0288390\pi\)
\(174\) 0 0
\(175\) 669.639 + 386.616i 0.289257 + 0.167002i
\(176\) 0 0
\(177\) 1969.57i 0.836395i
\(178\) 0 0
\(179\) 254.979 + 441.637i 0.106470 + 0.184411i 0.914338 0.404953i \(-0.132712\pi\)
−0.807868 + 0.589363i \(0.799379\pi\)
\(180\) 0 0
\(181\) 2136.88 0.877531 0.438766 0.898602i \(-0.355416\pi\)
0.438766 + 0.898602i \(0.355416\pi\)
\(182\) 0 0
\(183\) 2103.91 0.849867
\(184\) 0 0
\(185\) −499.551 865.247i −0.198528 0.343861i
\(186\) 0 0
\(187\) 930.688i 0.363950i
\(188\) 0 0
\(189\) 156.272 + 90.2238i 0.0601435 + 0.0347239i
\(190\) 0 0
\(191\) 2028.87 3514.11i 0.768607 1.33127i −0.169711 0.985494i \(-0.554283\pi\)
0.938318 0.345773i \(-0.112383\pi\)
\(192\) 0 0
\(193\) −756.381 + 436.697i −0.282101 + 0.162871i −0.634374 0.773026i \(-0.718742\pi\)
0.352273 + 0.935897i \(0.385409\pi\)
\(194\) 0 0
\(195\) 364.438 + 226.120i 0.133836 + 0.0830401i
\(196\) 0 0
\(197\) 3591.62 2073.62i 1.29895 0.749947i 0.318724 0.947848i \(-0.396746\pi\)
0.980222 + 0.197901i \(0.0634124\pi\)
\(198\) 0 0
\(199\) 1202.03 2081.98i 0.428189 0.741646i −0.568523 0.822667i \(-0.692485\pi\)
0.996712 + 0.0810216i \(0.0258183\pi\)
\(200\) 0 0
\(201\) −148.545 85.7625i −0.0521271 0.0300956i
\(202\) 0 0
\(203\) 1070.06i 0.369969i
\(204\) 0 0
\(205\) −85.5307 148.144i −0.0291401 0.0504722i
\(206\) 0 0
\(207\) −1070.91 −0.359582
\(208\) 0 0
\(209\) −3263.50 −1.08010
\(210\) 0 0
\(211\) 1934.43 + 3350.53i 0.631144 + 1.09317i 0.987318 + 0.158754i \(0.0507478\pi\)
−0.356174 + 0.934420i \(0.615919\pi\)
\(212\) 0 0
\(213\) 927.679i 0.298420i
\(214\) 0 0
\(215\) 337.782 + 195.019i 0.107147 + 0.0618612i
\(216\) 0 0
\(217\) −127.217 + 220.346i −0.0397975 + 0.0689313i
\(218\) 0 0
\(219\) 1012.50 584.567i 0.312413 0.180372i
\(220\) 0 0
\(221\) 1351.98 + 42.9153i 0.411512 + 0.0130624i
\(222\) 0 0
\(223\) −2436.61 + 1406.78i −0.731692 + 0.422443i −0.819041 0.573735i \(-0.805494\pi\)
0.0873487 + 0.996178i \(0.472161\pi\)
\(224\) 0 0
\(225\) −520.637 + 901.770i −0.154263 + 0.267191i
\(226\) 0 0
\(227\) −3913.02 2259.19i −1.14413 0.660561i −0.196677 0.980468i \(-0.563015\pi\)
−0.947449 + 0.319907i \(0.896348\pi\)
\(228\) 0 0
\(229\) 1305.27i 0.376658i 0.982106 + 0.188329i \(0.0603070\pi\)
−0.982106 + 0.188329i \(0.939693\pi\)
\(230\) 0 0
\(231\) −323.301 559.975i −0.0920852 0.159496i
\(232\) 0 0
\(233\) 3360.55 0.944879 0.472440 0.881363i \(-0.343373\pi\)
0.472440 + 0.881363i \(0.343373\pi\)
\(234\) 0 0
\(235\) −1579.88 −0.438553
\(236\) 0 0
\(237\) 1352.73 + 2343.00i 0.370756 + 0.642169i
\(238\) 0 0
\(239\) 4737.17i 1.28210i 0.767499 + 0.641050i \(0.221501\pi\)
−0.767499 + 0.641050i \(0.778499\pi\)
\(240\) 0 0
\(241\) 4144.17 + 2392.64i 1.10767 + 0.639516i 0.938226 0.346023i \(-0.112468\pi\)
0.169448 + 0.985539i \(0.445801\pi\)
\(242\) 0 0
\(243\) −121.500 + 210.444i −0.0320750 + 0.0555556i
\(244\) 0 0
\(245\) −788.029 + 454.969i −0.205491 + 0.118640i
\(246\) 0 0
\(247\) −150.484 + 4740.79i −0.0387655 + 1.22125i
\(248\) 0 0
\(249\) −1785.13 + 1030.64i −0.454328 + 0.262307i
\(250\) 0 0
\(251\) 1636.93 2835.25i 0.411642 0.712985i −0.583428 0.812165i \(-0.698289\pi\)
0.995069 + 0.0991805i \(0.0316221\pi\)
\(252\) 0 0
\(253\) 3323.31 + 1918.71i 0.825828 + 0.476792i
\(254\) 0 0
\(255\) 264.061i 0.0648476i
\(256\) 0 0
\(257\) −3272.91 5668.84i −0.794390 1.37592i −0.923226 0.384258i \(-0.874457\pi\)
0.128835 0.991666i \(-0.458876\pi\)
\(258\) 0 0
\(259\) 2189.22 0.525217
\(260\) 0 0
\(261\) 1441.00 0.341746
\(262\) 0 0
\(263\) 44.1007 + 76.3847i 0.0103398 + 0.0179091i 0.871149 0.491019i \(-0.163375\pi\)
−0.860809 + 0.508928i \(0.830042\pi\)
\(264\) 0 0
\(265\) 2121.46i 0.491773i
\(266\) 0 0
\(267\) 2781.34 + 1605.81i 0.637510 + 0.368067i
\(268\) 0 0
\(269\) 2263.80 3921.01i 0.513109 0.888730i −0.486776 0.873527i \(-0.661827\pi\)
0.999884 0.0152033i \(-0.00483956\pi\)
\(270\) 0 0
\(271\) 7206.91 4160.91i 1.61546 0.932684i 0.627380 0.778713i \(-0.284127\pi\)
0.988075 0.153971i \(-0.0492062\pi\)
\(272\) 0 0
\(273\) −828.366 + 443.829i −0.183645 + 0.0983948i
\(274\) 0 0
\(275\) 3231.34 1865.61i 0.708571 0.409094i
\(276\) 0 0
\(277\) −1440.65 + 2495.29i −0.312493 + 0.541254i −0.978901 0.204333i \(-0.934497\pi\)
0.666408 + 0.745587i \(0.267831\pi\)
\(278\) 0 0
\(279\) −296.730 171.317i −0.0636730 0.0367616i
\(280\) 0 0
\(281\) 2817.99i 0.598247i 0.954214 + 0.299123i \(0.0966942\pi\)
−0.954214 + 0.299123i \(0.903306\pi\)
\(282\) 0 0
\(283\) −132.301 229.152i −0.0277896 0.0481330i 0.851796 0.523873i \(-0.175514\pi\)
−0.879586 + 0.475740i \(0.842180\pi\)
\(284\) 0 0
\(285\) 925.941 0.192449
\(286\) 0 0
\(287\) 374.827 0.0770918
\(288\) 0 0
\(289\) 2040.09 + 3533.54i 0.415244 + 0.719223i
\(290\) 0 0
\(291\) 5263.45i 1.06031i
\(292\) 0 0
\(293\) 3717.43 + 2146.26i 0.741211 + 0.427938i 0.822509 0.568751i \(-0.192573\pi\)
−0.0812984 + 0.996690i \(0.525907\pi\)
\(294\) 0 0
\(295\) −1001.22 + 1734.16i −0.197604 + 0.342260i
\(296\) 0 0
\(297\) 754.091 435.374i 0.147329 0.0850606i
\(298\) 0 0
\(299\) 2940.50 4739.19i 0.568740 0.916638i
\(300\) 0 0
\(301\) −740.143 + 427.322i −0.141731 + 0.0818286i
\(302\) 0 0
\(303\) −961.260 + 1664.95i −0.182254 + 0.315673i
\(304\) 0 0
\(305\) 1852.45 + 1069.51i 0.347773 + 0.200787i
\(306\) 0 0
\(307\) 7026.26i 1.30622i 0.757263 + 0.653110i \(0.226536\pi\)
−0.757263 + 0.653110i \(0.773464\pi\)
\(308\) 0 0
\(309\) 1039.73 + 1800.86i 0.191418 + 0.331546i
\(310\) 0 0
\(311\) −1133.21 −0.206618 −0.103309 0.994649i \(-0.532943\pi\)
−0.103309 + 0.994649i \(0.532943\pi\)
\(312\) 0 0
\(313\) −5285.95 −0.954566 −0.477283 0.878750i \(-0.658378\pi\)
−0.477283 + 0.878750i \(0.658378\pi\)
\(314\) 0 0
\(315\) 91.7293 + 158.880i 0.0164075 + 0.0284186i
\(316\) 0 0
\(317\) 4782.16i 0.847296i −0.905827 0.423648i \(-0.860749\pi\)
0.905827 0.423648i \(-0.139251\pi\)
\(318\) 0 0
\(319\) −4471.80 2581.79i −0.784867 0.453143i
\(320\) 0 0
\(321\) −608.514 + 1053.98i −0.105807 + 0.183262i
\(322\) 0 0
\(323\) 2529.06 1460.15i 0.435668 0.251533i
\(324\) 0 0
\(325\) −2561.12 4780.10i −0.437124 0.815852i
\(326\) 0 0
\(327\) −1245.82 + 719.274i −0.210685 + 0.121639i
\(328\) 0 0
\(329\) 1730.90 2998.01i 0.290054 0.502388i
\(330\) 0 0
\(331\) 7508.43 + 4334.99i 1.24683 + 0.719857i 0.970476 0.241199i \(-0.0775407\pi\)
0.276353 + 0.961056i \(0.410874\pi\)
\(332\) 0 0
\(333\) 2948.11i 0.485152i
\(334\) 0 0
\(335\) −87.1936 151.024i −0.0142206 0.0246308i
\(336\) 0 0
\(337\) −8526.59 −1.37826 −0.689129 0.724639i \(-0.742007\pi\)
−0.689129 + 0.724639i \(0.742007\pi\)
\(338\) 0 0
\(339\) −4641.61 −0.743651
\(340\) 0 0
\(341\) 613.886 + 1063.28i 0.0974891 + 0.168856i
\(342\) 0 0
\(343\) 4286.19i 0.674731i
\(344\) 0 0
\(345\) −942.911 544.390i −0.147144 0.0849535i
\(346\) 0 0
\(347\) −6290.74 + 10895.9i −0.973213 + 1.68565i −0.287501 + 0.957780i \(0.592825\pi\)
−0.685711 + 0.727874i \(0.740509\pi\)
\(348\) 0 0
\(349\) 7760.61 4480.59i 1.19030 0.687222i 0.231928 0.972733i \(-0.425497\pi\)
0.958375 + 0.285511i \(0.0921633\pi\)
\(350\) 0 0
\(351\) −597.684 1115.52i −0.0908889 0.169636i
\(352\) 0 0
\(353\) −4640.16 + 2679.00i −0.699634 + 0.403934i −0.807211 0.590263i \(-0.799024\pi\)
0.107577 + 0.994197i \(0.465691\pi\)
\(354\) 0 0
\(355\) 471.579 816.799i 0.0705037 0.122116i
\(356\) 0 0
\(357\) 501.088 + 289.303i 0.0742868 + 0.0428895i
\(358\) 0 0
\(359\) 2705.40i 0.397731i −0.980027 0.198866i \(-0.936274\pi\)
0.980027 0.198866i \(-0.0637257\pi\)
\(360\) 0 0
\(361\) 1690.60 + 2928.20i 0.246478 + 0.426913i
\(362\) 0 0
\(363\) 872.820 0.126202
\(364\) 0 0
\(365\) 1188.64 0.170456
\(366\) 0 0
\(367\) 5236.88 + 9070.54i 0.744858 + 1.29013i 0.950261 + 0.311455i \(0.100816\pi\)
−0.205403 + 0.978678i \(0.565850\pi\)
\(368\) 0 0
\(369\) 504.762i 0.0712110i
\(370\) 0 0
\(371\) −4025.72 2324.25i −0.563356 0.325254i
\(372\) 0 0
\(373\) 6381.51 11053.1i 0.885850 1.53434i 0.0411127 0.999155i \(-0.486910\pi\)
0.844737 0.535182i \(-0.179757\pi\)
\(374\) 0 0
\(375\) −1907.35 + 1101.21i −0.262654 + 0.151643i
\(376\) 0 0
\(377\) −3956.70 + 6377.00i −0.540531 + 0.871173i
\(378\) 0 0
\(379\) 2007.47 1159.01i 0.272076 0.157083i −0.357755 0.933816i \(-0.616458\pi\)
0.629831 + 0.776733i \(0.283124\pi\)
\(380\) 0 0
\(381\) 3742.73 6482.60i 0.503270 0.871690i
\(382\) 0 0
\(383\) 1717.63 + 991.672i 0.229156 + 0.132303i 0.610183 0.792261i \(-0.291096\pi\)
−0.381027 + 0.924564i \(0.624429\pi\)
\(384\) 0 0
\(385\) 657.392i 0.0870229i
\(386\) 0 0
\(387\) −575.454 996.715i −0.0755864 0.130920i
\(388\) 0 0
\(389\) 3244.51 0.422887 0.211444 0.977390i \(-0.432184\pi\)
0.211444 + 0.977390i \(0.432184\pi\)
\(390\) 0 0
\(391\) −3433.88 −0.444140
\(392\) 0 0
\(393\) 65.6357 + 113.684i 0.00842464 + 0.0145919i
\(394\) 0 0
\(395\) 2750.60i 0.350374i
\(396\) 0 0
\(397\) 3256.02 + 1879.86i 0.411624 + 0.237651i 0.691487 0.722389i \(-0.256956\pi\)
−0.279863 + 0.960040i \(0.590289\pi\)
\(398\) 0 0
\(399\) −1014.45 + 1757.09i −0.127284 + 0.220462i
\(400\) 0 0
\(401\) 1729.93 998.773i 0.215432 0.124380i −0.388401 0.921490i \(-0.626973\pi\)
0.603833 + 0.797110i \(0.293639\pi\)
\(402\) 0 0
\(403\) 1572.90 842.744i 0.194422 0.104169i
\(404\) 0 0
\(405\) −213.956 + 123.527i −0.0262507 + 0.0151559i
\(406\) 0 0
\(407\) 5282.03 9148.74i 0.643293 1.11422i
\(408\) 0 0
\(409\) 4499.20 + 2597.62i 0.543940 + 0.314044i 0.746674 0.665190i \(-0.231650\pi\)
−0.202735 + 0.979234i \(0.564983\pi\)
\(410\) 0 0
\(411\) 618.582i 0.0742394i
\(412\) 0 0
\(413\) −2193.85 3799.86i −0.261386 0.452734i
\(414\) 0 0
\(415\) −2095.68 −0.247887
\(416\) 0 0
\(417\) 300.000 0.0352304
\(418\) 0 0
\(419\) −3411.05 5908.12i −0.397711 0.688855i 0.595732 0.803183i \(-0.296862\pi\)
−0.993443 + 0.114328i \(0.963529\pi\)
\(420\) 0 0
\(421\) 7537.70i 0.872601i 0.899801 + 0.436300i \(0.143712\pi\)
−0.899801 + 0.436300i \(0.856288\pi\)
\(422\) 0 0
\(423\) 4037.28 + 2330.92i 0.464064 + 0.267928i
\(424\) 0 0
\(425\) −1669.43 + 2891.53i −0.190539 + 0.330023i
\(426\) 0 0
\(427\) −4059.05 + 2343.49i −0.460026 + 0.265596i
\(428\) 0 0
\(429\) −143.876 + 4532.59i −0.0161920 + 0.510107i
\(430\) 0 0
\(431\) 11608.4 6702.10i 1.29735 0.749023i 0.317401 0.948291i \(-0.397190\pi\)
0.979945 + 0.199268i \(0.0638565\pi\)
\(432\) 0 0
\(433\) −8857.97 + 15342.5i −0.983110 + 1.70280i −0.333061 + 0.942905i \(0.608081\pi\)
−0.650050 + 0.759892i \(0.725252\pi\)
\(434\) 0 0
\(435\) 1268.77 + 732.524i 0.139846 + 0.0807398i
\(436\) 0 0
\(437\) 12041.1i 1.31808i
\(438\) 0 0
\(439\) −3581.73 6203.75i −0.389401 0.674462i 0.602968 0.797765i \(-0.293985\pi\)
−0.992369 + 0.123303i \(0.960651\pi\)
\(440\) 0 0
\(441\) 2685.01 0.289926
\(442\) 0 0
\(443\) 10169.2 1.09064 0.545321 0.838227i \(-0.316408\pi\)
0.545321 + 0.838227i \(0.316408\pi\)
\(444\) 0 0
\(445\) 1632.60 + 2827.75i 0.173916 + 0.301232i
\(446\) 0 0
\(447\) 1141.35i 0.120770i
\(448\) 0 0
\(449\) −14845.8 8571.24i −1.56040 0.900895i −0.997217 0.0745603i \(-0.976245\pi\)
−0.563179 0.826335i \(-0.690422\pi\)
\(450\) 0 0
\(451\) 904.364 1566.40i 0.0944231 0.163546i
\(452\) 0 0
\(453\) −3942.46 + 2276.18i −0.408902 + 0.236080i
\(454\) 0 0
\(455\) −954.974 30.3133i −0.0983954 0.00312331i
\(456\) 0 0
\(457\) 12203.3 7045.57i 1.24912 0.721177i 0.278183 0.960528i \(-0.410268\pi\)
0.970933 + 0.239351i \(0.0769346\pi\)
\(458\) 0 0
\(459\) −389.591 + 674.791i −0.0396177 + 0.0686199i
\(460\) 0 0
\(461\) 2530.72 + 1461.11i 0.255678 + 0.147616i 0.622361 0.782730i \(-0.286174\pi\)
−0.366684 + 0.930346i \(0.619507\pi\)
\(462\) 0 0
\(463\) 2072.61i 0.208040i −0.994575 0.104020i \(-0.966829\pi\)
0.994575 0.104020i \(-0.0331706\pi\)
\(464\) 0 0
\(465\) −174.176 301.681i −0.0173703 0.0300863i
\(466\) 0 0
\(467\) −2664.19 −0.263992 −0.131996 0.991250i \(-0.542139\pi\)
−0.131996 + 0.991250i \(0.542139\pi\)
\(468\) 0 0
\(469\) 382.114 0.0376213
\(470\) 0 0
\(471\) −2175.23 3767.61i −0.212801 0.368583i
\(472\) 0 0
\(473\) 4124.08i 0.400899i
\(474\) 0 0
\(475\) −10139.3 5853.92i −0.979415 0.565466i
\(476\) 0 0
\(477\) 3129.96 5421.24i 0.300442 0.520381i
\(478\) 0 0
\(479\) −4521.26 + 2610.35i −0.431277 + 0.248998i −0.699890 0.714250i \(-0.746768\pi\)
0.268614 + 0.963248i \(0.413434\pi\)
\(480\) 0 0
\(481\) −13046.5 8094.91i −1.23674 0.767351i
\(482\) 0 0
\(483\) 2066.09 1192.86i 0.194639 0.112375i
\(484\) 0 0
\(485\) −2675.64 + 4634.34i −0.250504 + 0.433886i
\(486\) 0 0
\(487\) −10586.8 6112.30i −0.985081 0.568737i −0.0812808 0.996691i \(-0.525901\pi\)
−0.903800 + 0.427954i \(0.859234\pi\)
\(488\) 0 0
\(489\) 7027.08i 0.649848i
\(490\) 0 0
\(491\) −9826.61 17020.2i −0.903195 1.56438i −0.823323 0.567574i \(-0.807882\pi\)
−0.0798720 0.996805i \(-0.525451\pi\)
\(492\) 0 0
\(493\) 4620.59 0.422111
\(494\) 0 0
\(495\) 885.279 0.0803845
\(496\) 0 0
\(497\) 1033.32 + 1789.76i 0.0932608 + 0.161532i
\(498\) 0 0
\(499\) 11713.6i 1.05084i 0.850842 + 0.525422i \(0.176093\pi\)
−0.850842 + 0.525422i \(0.823907\pi\)
\(500\) 0 0
\(501\) 104.113 + 60.1096i 0.00928428 + 0.00536028i
\(502\) 0 0
\(503\) 6501.67 11261.2i 0.576332 0.998236i −0.419563 0.907726i \(-0.637817\pi\)
0.995896 0.0905104i \(-0.0288498\pi\)
\(504\) 0 0
\(505\) −1692.73 + 977.300i −0.149160 + 0.0861174i
\(506\) 0 0
\(507\) 6577.73 + 418.008i 0.576188 + 0.0366162i
\(508\) 0 0
\(509\) −4614.99 + 2664.47i −0.401878 + 0.232024i −0.687294 0.726379i \(-0.741202\pi\)
0.285416 + 0.958404i \(0.407868\pi\)
\(510\) 0 0
\(511\) −1302.27 + 2255.59i −0.112738 + 0.195267i
\(512\) 0 0
\(513\) −2366.18 1366.12i −0.203644 0.117574i
\(514\) 0 0
\(515\) 2114.16i 0.180895i
\(516\) 0 0
\(517\) −8352.47 14466.9i −0.710524 1.23066i
\(518\) 0 0
\(519\) −5728.62 −0.484506
\(520\) 0 0
\(521\) −11700.3 −0.983876 −0.491938 0.870630i \(-0.663711\pi\)
−0.491938 + 0.870630i \(0.663711\pi\)
\(522\) 0 0
\(523\) −2267.52 3927.46i −0.189583 0.328367i 0.755528 0.655116i \(-0.227380\pi\)
−0.945111 + 0.326749i \(0.894047\pi\)
\(524\) 0 0
\(525\) 2319.70i 0.192838i
\(526\) 0 0
\(527\) −951.467 549.330i −0.0786462 0.0454064i
\(528\) 0 0
\(529\) −995.810 + 1724.79i −0.0818451 + 0.141760i
\(530\) 0 0
\(531\) 5117.09 2954.35i 0.418197 0.241446i
\(532\) 0 0
\(533\) −2233.77 1385.97i −0.181529 0.112632i
\(534\) 0 0
\(535\) −1071.56 + 618.667i −0.0865939 + 0.0499950i
\(536\) 0 0
\(537\) 764.938 1324.91i 0.0614702 0.106470i
\(538\) 0 0
\(539\) −8332.26 4810.63i −0.665855 0.384432i
\(540\) 0 0
\(541\) 5184.89i 0.412044i 0.978547 + 0.206022i \(0.0660519\pi\)
−0.978547 + 0.206022i \(0.933948\pi\)
\(542\) 0 0
\(543\) −3205.32 5551.78i −0.253321 0.438766i
\(544\) 0 0
\(545\) −1462.55 −0.114952
\(546\) 0 0
\(547\) −5609.12 −0.438443 −0.219222 0.975675i \(-0.570352\pi\)
−0.219222 + 0.975675i \(0.570352\pi\)
\(548\) 0 0
\(549\) −3155.87 5466.13i −0.245336 0.424934i
\(550\) 0 0
\(551\) 16202.3i 1.25271i
\(552\) 0 0
\(553\) −5219.61 3013.54i −0.401375 0.231734i
\(554\) 0 0
\(555\) −1498.65 + 2595.74i −0.114620 + 0.198528i
\(556\) 0 0
\(557\) 17450.9 10075.3i 1.32750 0.766432i 0.342586 0.939486i \(-0.388697\pi\)
0.984912 + 0.173055i \(0.0553637\pi\)
\(558\) 0 0
\(559\) 5990.93 + 190.167i 0.453290 + 0.0143886i
\(560\) 0 0
\(561\) 2418.00 1396.03i 0.181975 0.105063i
\(562\) 0 0
\(563\) −8146.10 + 14109.5i −0.609800 + 1.05620i 0.381474 + 0.924380i \(0.375417\pi\)
−0.991273 + 0.131824i \(0.957917\pi\)
\(564\) 0 0
\(565\) −4086.83 2359.53i −0.304308 0.175692i
\(566\) 0 0
\(567\) 541.343i 0.0400957i
\(568\) 0 0
\(569\) 5230.27 + 9059.09i 0.385350 + 0.667446i 0.991818 0.127662i \(-0.0407474\pi\)
−0.606468 + 0.795108i \(0.707414\pi\)
\(570\) 0 0
\(571\) 2225.96 0.163141 0.0815705 0.996668i \(-0.474006\pi\)
0.0815705 + 0.996668i \(0.474006\pi\)
\(572\) 0 0
\(573\) −12173.2 −0.887511
\(574\) 0 0
\(575\) 6883.40 + 11922.4i 0.499231 + 0.864693i
\(576\) 0 0
\(577\) 4686.23i 0.338112i 0.985606 + 0.169056i \(0.0540718\pi\)
−0.985606 + 0.169056i \(0.945928\pi\)
\(578\) 0 0
\(579\) 2269.14 + 1310.09i 0.162871 + 0.0940337i
\(580\) 0 0
\(581\) 2296.01 3976.81i 0.163949 0.283969i
\(582\) 0 0
\(583\) −19426.1 + 11215.7i −1.38001 + 0.796750i
\(584\) 0 0
\(585\) 40.8214 1286.02i 0.00288505 0.0908894i
\(586\) 0 0
\(587\) −10470.7 + 6045.28i −0.736241 + 0.425069i −0.820701 0.571358i \(-0.806417\pi\)
0.0844601 + 0.996427i \(0.473083\pi\)
\(588\) 0 0
\(589\) 1926.25 3336.36i 0.134753 0.233400i
\(590\) 0 0
\(591\) −10774.9 6220.87i −0.749947 0.432982i
\(592\) 0 0
\(593\) 6135.97i 0.424914i −0.977170 0.212457i \(-0.931853\pi\)
0.977170 0.212457i \(-0.0681466\pi\)
\(594\) 0 0
\(595\) 294.131 + 509.449i 0.0202658 + 0.0351015i
\(596\) 0 0
\(597\) −7212.18 −0.494431
\(598\) 0 0
\(599\) 6198.80 0.422831 0.211416 0.977396i \(-0.432193\pi\)
0.211416 + 0.977396i \(0.432193\pi\)
\(600\) 0 0
\(601\) −9172.69 15887.6i −0.622565 1.07831i −0.989006 0.147873i \(-0.952757\pi\)
0.366441 0.930441i \(-0.380576\pi\)
\(602\) 0 0
\(603\) 514.575i 0.0347514i
\(604\) 0 0
\(605\) 768.497 + 443.692i 0.0516427 + 0.0298159i
\(606\) 0 0
\(607\) 5194.06 8996.38i 0.347315 0.601568i −0.638456 0.769658i \(-0.720427\pi\)
0.985772 + 0.168090i \(0.0537600\pi\)
\(608\) 0 0
\(609\) −2780.11 + 1605.10i −0.184985 + 0.106801i
\(610\) 0 0
\(611\) −21400.8 + 11466.3i −1.41699 + 0.759209i
\(612\) 0 0
\(613\) −696.701 + 402.240i −0.0459045 + 0.0265030i −0.522777 0.852470i \(-0.675104\pi\)
0.476872 + 0.878973i \(0.341770\pi\)
\(614\) 0 0
\(615\) −256.592 + 444.431i −0.0168241 + 0.0291401i
\(616\) 0 0
\(617\) −13179.4 7609.13i −0.859940 0.496486i 0.00405239 0.999992i \(-0.498710\pi\)
−0.863992 + 0.503505i \(0.832043\pi\)
\(618\) 0 0
\(619\) 11462.5i 0.744291i −0.928174 0.372145i \(-0.878622\pi\)
0.928174 0.372145i \(-0.121378\pi\)
\(620\) 0 0
\(621\) 1606.36 + 2782.31i 0.103802 + 0.179791i
\(622\) 0 0
\(623\) −7154.66 −0.460105
\(624\) 0 0
\(625\) 12223.0 0.782270
\(626\) 0 0
\(627\) 4895.25 + 8478.81i 0.311798 + 0.540050i
\(628\) 0 0
\(629\) 9453.14i 0.599239i
\(630\) 0 0
\(631\) 3869.99 + 2234.34i 0.244155 + 0.140963i 0.617085 0.786896i \(-0.288313\pi\)
−0.372930 + 0.927860i \(0.621647\pi\)
\(632\) 0 0
\(633\) 5803.28 10051.6i 0.364391 0.631144i
\(634\) 0 0
\(635\) 6590.77 3805.18i 0.411885 0.237802i
\(636\) 0 0
\(637\) −7372.48 + 11882.2i −0.458569 + 0.739074i
\(638\) 0 0
\(639\) −2410.18 + 1391.52i −0.149210 + 0.0861465i
\(640\) 0 0
\(641\) 3071.18 5319.44i 0.189242 0.327777i −0.755756 0.654854i \(-0.772730\pi\)
0.944998 + 0.327077i \(0.106064\pi\)
\(642\) 0 0
\(643\) 17959.8 + 10369.1i 1.10150 + 0.635951i 0.936615 0.350361i \(-0.113941\pi\)
0.164886 + 0.986313i \(0.447274\pi\)
\(644\) 0 0
\(645\) 1170.11i 0.0714312i
\(646\) 0 0
\(647\) −426.379 738.509i −0.0259083 0.0448745i 0.852781 0.522269i \(-0.174914\pi\)
−0.878689 + 0.477395i \(0.841581\pi\)
\(648\) 0 0
\(649\) −21172.8 −1.28060
\(650\) 0 0
\(651\) 763.303 0.0459542
\(652\) 0 0
\(653\) 3672.88 + 6361.61i 0.220108 + 0.381239i 0.954841 0.297118i \(-0.0960256\pi\)
−0.734732 + 0.678357i \(0.762692\pi\)
\(654\) 0 0
\(655\) 133.462i 0.00796151i
\(656\) 0 0
\(657\) −3037.50 1753.70i −0.180372 0.104138i
\(658\) 0 0
\(659\) 6270.33 10860.5i 0.370648 0.641982i −0.619017 0.785378i \(-0.712469\pi\)
0.989665 + 0.143396i \(0.0458022\pi\)
\(660\) 0 0
\(661\) 1942.45 1121.48i 0.114301 0.0659915i −0.441760 0.897133i \(-0.645646\pi\)
0.556060 + 0.831142i \(0.312312\pi\)
\(662\) 0 0
\(663\) −1916.48 3576.93i −0.112262 0.209527i
\(664\) 0 0
\(665\) −1786.41 + 1031.38i −0.104171 + 0.0601433i
\(666\) 0 0
\(667\) 9525.83 16499.2i 0.552986 0.957800i
\(668\) 0 0
\(669\) 7309.83 + 4220.33i 0.422443 + 0.243897i
\(670\) 0 0
\(671\) 22617.0i 1.30122i
\(672\) 0 0
\(673\) −2388.23 4136.53i −0.136790 0.236927i 0.789490 0.613763i \(-0.210345\pi\)
−0.926280 + 0.376837i \(0.877012\pi\)
\(674\) 0 0
\(675\) 3123.82 0.178127
\(676\) 0 0
\(677\) −7933.57 −0.450387 −0.225193 0.974314i \(-0.572301\pi\)
−0.225193 + 0.974314i \(0.572301\pi\)
\(678\) 0 0
\(679\) −5862.82 10154.7i −0.331361 0.573935i
\(680\) 0 0
\(681\) 13555.1i 0.762750i
\(682\) 0 0
\(683\) −20415.5 11786.9i −1.14374 0.660340i −0.196388 0.980526i \(-0.562921\pi\)
−0.947355 + 0.320186i \(0.896255\pi\)
\(684\) 0 0
\(685\) −314.452 + 544.647i −0.0175396 + 0.0303794i
\(686\) 0 0
\(687\) 3391.19 1957.90i 0.188329 0.108732i
\(688\) 0 0
\(689\) 15396.9 + 28736.9i 0.851343 + 1.58895i
\(690\) 0 0
\(691\) 10863.2 6271.89i 0.598056 0.345288i −0.170221 0.985406i \(-0.554448\pi\)
0.768276 + 0.640118i \(0.221115\pi\)
\(692\) 0 0
\(693\) −969.904 + 1679.92i −0.0531654 + 0.0920852i
\(694\) 0 0
\(695\) 264.143 + 152.503i 0.0144166 + 0.00832340i
\(696\) 0 0
\(697\) 1618.52i 0.0879568i
\(698\) 0 0
\(699\) −5040.82 8730.96i −0.272763 0.472440i
\(700\) 0 0
\(701\) 581.786 0.0313463 0.0156731 0.999877i \(-0.495011\pi\)
0.0156731 + 0.999877i \(0.495011\pi\)
\(702\) 0 0
\(703\) −33147.9 −1.77837
\(704\) 0 0
\(705\) 2369.82 + 4104.64i 0.126599 + 0.219276i
\(706\) 0 0
\(707\) 4282.89i 0.227828i
\(708\) 0 0
\(709\) −17963.1 10371.0i −0.951507 0.549353i −0.0579583 0.998319i \(-0.518459\pi\)
−0.893549 + 0.448966i \(0.851792\pi\)
\(710\) 0 0
\(711\) 4058.19 7028.99i 0.214056 0.370756i
\(712\) 0 0
\(713\) −3923.10 + 2265.00i −0.206061 + 0.118969i
\(714\) 0 0
\(715\) −2430.79 + 3917.70i −0.127142 + 0.204914i
\(716\) 0 0
\(717\) 12307.5 7105.75i 0.641050 0.370110i
\(718\) 0 0
\(719\) −12675.1 + 21953.9i −0.657443 + 1.13872i 0.323832 + 0.946114i \(0.395029\pi\)
−0.981275 + 0.192610i \(0.938305\pi\)
\(720\) 0 0
\(721\) −4011.87 2316.25i −0.207226 0.119642i
\(722\) 0 0
\(723\) 14355.8i 0.738449i
\(724\) 0 0
\(725\) −9262.22 16042.6i −0.474469 0.821805i
\(726\) 0 0
\(727\) 33428.2 1.70534 0.852672 0.522447i \(-0.174981\pi\)
0.852672 + 0.522447i \(0.174981\pi\)
\(728\) 0 0
\(729\) 729.000 0.0370370
\(730\) 0 0
\(731\) −1845.20 3195.97i −0.0933612 0.161706i
\(732\) 0 0
\(733\) 3842.67i 0.193632i −0.995302 0.0968160i \(-0.969134\pi\)
0.995302 0.0968160i \(-0.0308658\pi\)
\(734\) 0 0
\(735\) 2364.09 + 1364.91i 0.118640 + 0.0684970i
\(736\) 0 0
\(737\) 921.946 1596.86i 0.0460791 0.0798114i
\(738\) 0 0
\(739\) 25140.4 14514.8i 1.25143 0.722511i 0.280034 0.959990i \(-0.409654\pi\)
0.971393 + 0.237479i \(0.0763211\pi\)
\(740\) 0 0
\(741\) 12542.7 6720.21i 0.621816 0.333162i
\(742\) 0 0
\(743\) 30308.0 17498.3i 1.49649 0.864000i 0.496500 0.868037i \(-0.334618\pi\)
0.999992 + 0.00403656i \(0.00128488\pi\)
\(744\) 0 0
\(745\) −580.199 + 1004.93i −0.0285327 + 0.0494200i
\(746\) 0 0
\(747\) 5355.38 + 3091.93i 0.262307 + 0.151443i
\(748\) 0 0
\(749\) 2711.23i 0.132265i
\(750\) 0 0
\(751\) −5227.06 9053.52i −0.253979 0.439904i 0.710639 0.703557i \(-0.248406\pi\)
−0.964618 + 0.263653i \(0.915073\pi\)
\(752\) 0 0
\(753\) −9821.58 −0.475323
\(754\) 0 0
\(755\) −4628.32 −0.223102
\(756\) 0 0
\(757\) 14065.2 + 24361.6i 0.675308 + 1.16967i 0.976379 + 0.216065i \(0.0693225\pi\)
−0.301071 + 0.953602i \(0.597344\pi\)
\(758\) 0 0
\(759\) 11512.3i 0.550552i
\(760\) 0 0
\(761\) 18261.9 + 10543.5i 0.869899 + 0.502236i 0.867315 0.497761i \(-0.165844\pi\)
0.00258400 + 0.999997i \(0.499177\pi\)
\(762\) 0 0
\(763\) 1602.36 2775.37i 0.0760280 0.131684i
\(764\) 0 0
\(765\) −686.051 + 396.092i −0.0324238 + 0.0187199i
\(766\) 0 0
\(767\) −976.309 + 30757.2i −0.0459615 + 1.44795i
\(768\) 0 0
\(769\) 16911.7 9763.96i 0.793044 0.457864i −0.0479893 0.998848i \(-0.515281\pi\)
0.841033 + 0.540984i \(0.181948\pi\)
\(770\) 0 0
\(771\) −9818.72 + 17006.5i −0.458641 + 0.794390i
\(772\) 0 0
\(773\) 25419.6 + 14676.0i 1.18277 + 0.682870i 0.956653 0.291231i \(-0.0940648\pi\)
0.226113 + 0.974101i \(0.427398\pi\)
\(774\) 0 0
\(775\) 4404.64i 0.204154i
\(776\) 0 0
\(777\) −3283.82 5687.75i −0.151617 0.262609i
\(778\) 0 0
\(779\) −5675.42 −0.261031
\(780\) 0 0
\(781\) 9972.54 0.456908
\(782\) 0 0
\(783\) −2161.50 3743.84i −0.0986537 0.170873i
\(784\) 0 0
\(785\) 4423.06i 0.201103i
\(786\) 0 0
\(787\) −3865.18 2231.56i −0.175068 0.101076i 0.409905 0.912128i \(-0.365562\pi\)
−0.584974 + 0.811052i \(0.698895\pi\)
\(788\) 0 0
\(789\) 132.302 229.154i 0.00596968