Properties

Label 624.4.bv.c.433.2
Level $624$
Weight $4$
Character 624.433
Analytic conductor $36.817$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

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 433.2
Root \(3.57071 + 2.06155i\) of defining polynomial
Character \(\chi\) \(=\) 624.433
Dual form 624.4.bv.c.49.1

$q$-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 \(\left(\mathbb{Z}/624\mathbb{Z}\right)^\times\).

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

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 \(0.0435541\pi\)
−0.990653 + 0.136403i \(0.956446\pi\)
\(6\) 0 0
\(7\) 5.78786 3.34162i 0.312515 0.180431i −0.335536 0.942027i \(-0.608918\pi\)
0.648051 + 0.761597i \(0.275584\pi\)
\(8\) 0 0
\(9\) −4.50000 7.79423i −0.166667 0.288675i
\(10\) 0 0
\(11\) 27.9293 + 16.1250i 0.765545 + 0.441988i 0.831283 0.555849i \(-0.187607\pi\)
−0.0657380 + 0.997837i \(0.520940\pi\)
\(12\) 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 0.744547 0.667571i \(-0.232666\pi\)
−0.950406 + 0.311011i \(0.899332\pi\)
\(18\) 0 0
\(19\) −87.6364 + 50.5969i −1.05817 + 0.610933i −0.924925 0.380150i \(-0.875872\pi\)
−0.133242 + 0.991083i \(0.542539\pi\)
\(20\) 0 0
\(21\) 20.0497i 0.208343i
\(22\) 0 0
\(23\) 59.4950 103.048i 0.539372 0.934220i −0.459566 0.888144i \(-0.651995\pi\)
0.998938 0.0460765i \(-0.0146718\pi\)
\(24\) 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 0.487273 + 0.873250i \(0.337992\pi\)
−0.999893 + 0.0146339i \(0.995342\pi\)
\(30\) 0 0
\(31\) 38.0705i 0.220570i −0.993900 0.110285i \(-0.964824\pi\)
0.993900 0.110285i \(-0.0351763\pi\)
\(32\) 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 0.973164 0.230114i \(-0.0739099\pi\)
0.287297 + 0.957841i \(0.407243\pi\)
\(38\) 0 0
\(39\) −74.1364 119.486i −0.304393 0.490590i
\(40\) 0 0
\(41\) 48.5707 + 28.0423i 0.185011 + 0.106816i 0.589645 0.807662i \(-0.299268\pi\)
−0.404634 + 0.914479i \(0.632601\pi\)
\(42\) 0 0
\(43\) −63.9393 110.746i −0.226759 0.392759i 0.730087 0.683355i \(-0.239480\pi\)
−0.956846 + 0.290596i \(0.906146\pi\)
\(44\) 0 0
\(45\) 23.7729 13.7253i 0.0787522 0.0454676i
\(46\) 0 0
\(47\) 517.983i 1.60757i 0.594923 + 0.803783i \(0.297183\pi\)
−0.594923 + 0.803783i \(0.702817\pi\)
\(48\) 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 −0.972018 0.234906i \(-0.924522\pi\)
−0.282574 + 0.959245i \(0.591188\pi\)
\(60\) 0 0
\(61\) −350.652 607.347i −0.736007 1.27480i −0.954280 0.298913i \(-0.903376\pi\)
0.218274 0.975888i \(-0.429957\pi\)
\(62\) 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 0.544464 0.838784i \(-0.316733\pi\)
−0.454177 + 0.890912i \(0.650067\pi\)
\(68\) 0 0
\(69\) 178.485 + 309.145i 0.311407 + 0.539372i
\(70\) 0 0
\(71\) 267.798 154.613i 0.447630 0.258440i −0.259199 0.965824i \(-0.583458\pi\)
0.706829 + 0.707385i \(0.250125\pi\)
\(72\) 0 0
\(73\) 389.711i 0.624826i −0.949946 0.312413i \(-0.898863\pi\)
0.949946 0.312413i \(-0.101137\pi\)
\(74\) 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 \(0.150121\pi\)
−0.890834 + 0.454328i \(0.849879\pi\)
\(84\) 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 −0.166879 0.985977i \(-0.553369\pi\)
−0.937321 + 0.348467i \(0.886702\pi\)
\(90\) 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 −0.597230 + 0.802070i \(0.703732\pi\)
−0.993228 + 0.116182i \(0.962935\pi\)
\(98\) 0 0
\(99\) 290.250i 0.294658i
\(100\) 0 0
\(101\) −320.420 + 554.984i −0.315673 + 0.546762i −0.979580 0.201053i \(-0.935564\pi\)
0.663907 + 0.747815i \(0.268897\pi\)
\(102\) 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 −0.942990 0.332822i \(-0.891999\pi\)
0.759727 + 0.650242i \(0.225332\pi\)
\(108\) 0 0
\(109\) 479.516i 0.421370i 0.977554 + 0.210685i \(0.0675694\pi\)
−0.977554 + 0.210685i \(0.932431\pi\)
\(110\) 0 0
\(111\) −851.046 + 491.352i −0.727727 + 0.420154i
\(112\) 0 0
\(113\) 773.602 + 1339.92i 0.644021 + 1.11548i 0.984527 + 0.175235i \(0.0560684\pi\)
−0.340506 + 0.940242i \(0.610598\pi\)
\(114\) 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 0.0114416 0.999935i \(-0.496358\pi\)
0.860248 0.509876i \(-0.170309\pi\)
\(128\) 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 −0.554645 0.832087i \(-0.687146\pi\)
0.443286 + 0.896380i \(0.353813\pi\)
\(138\) 0 0
\(139\) −50.0000 86.6025i −0.0305104 0.0528456i 0.850367 0.526190i \(-0.176380\pi\)
−0.880877 + 0.473344i \(0.843047\pi\)
\(140\) 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 −0.587835 0.808981i \(-0.700020\pi\)
0.406680 + 0.913571i \(0.366686\pi\)
\(150\) 0 0
\(151\) 1517.45i 0.817805i 0.912578 + 0.408902i \(0.134088\pi\)
−0.912578 + 0.408902i \(0.865912\pi\)
\(152\) 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 −0.900688 0.434467i \(-0.856937\pi\)
−0.0740844 + 0.997252i \(0.523603\pi\)
\(164\) 0 0
\(165\) −147.546 255.558i −0.0696150 0.120577i
\(166\) 0 0
\(167\) −34.7043 20.0365i −0.0160808 0.00928428i 0.491938 0.870630i \(-0.336289\pi\)
−0.508019 + 0.861346i \(0.669622\pi\)
\(168\) 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 0.995899 0.0904765i \(-0.0288390\pi\)
−0.576304 + 0.817235i \(0.695506\pi\)
\(174\) 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 −0.807868 0.589363i \(-0.799379\pi\)
0.914338 + 0.404953i \(0.132712\pi\)
\(180\) 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 0.938318 + 0.345773i \(0.112383\pi\)
−0.169711 + 0.985494i \(0.554283\pi\)
\(192\) 0 0
\(193\) −756.381 436.697i −0.282101 0.162871i 0.352273 0.935897i \(-0.385409\pi\)
−0.634374 + 0.773026i \(0.718742\pi\)
\(194\) 0 0
\(195\) 364.438 226.120i 0.133836 0.0830401i
\(196\) 0 0
\(197\) 3591.62 + 2073.62i 1.29895 + 0.749947i 0.980222 0.197901i \(-0.0634124\pi\)
0.318724 + 0.947848i \(0.396746\pi\)
\(198\) 0 0
\(199\) 1202.03 + 2081.98i 0.428189 + 0.741646i 0.996712 0.0810216i \(-0.0258183\pi\)
−0.568523 + 0.822667i \(0.692485\pi\)
\(200\) 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 −0.356174 0.934420i \(-0.615919\pi\)
0.987318 0.158754i \(-0.0507478\pi\)
\(212\) 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 0.0873487 0.996178i \(-0.472161\pi\)
−0.819041 + 0.573735i \(0.805494\pi\)
\(224\) 0 0
\(225\) −520.637 901.770i −0.154263 0.267191i
\(226\) 0 0
\(227\) −3913.02 + 2259.19i −1.14413 + 0.660561i −0.947449 0.319907i \(-0.896348\pi\)
−0.196677 + 0.980468i \(0.563015\pi\)
\(228\) 0 0
\(229\) 1305.27i 0.376658i −0.982106 0.188329i \(-0.939693\pi\)
0.982106 0.188329i \(-0.0603070\pi\)
\(230\) 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 \(-0.778499\pi\)
0.767499 0.641050i \(-0.221501\pi\)
\(240\) 0 0
\(241\) 4144.17 2392.64i 1.10767 0.639516i 0.169448 0.985539i \(-0.445801\pi\)
0.938226 + 0.346023i \(0.112468\pi\)
\(242\) 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 0.995069 0.0991805i \(-0.0316221\pi\)
−0.583428 + 0.812165i \(0.698289\pi\)
\(252\) 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 0.128835 + 0.991666i \(0.458876\pi\)
−0.923226 + 0.384258i \(0.874457\pi\)
\(258\) 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 −0.860809 0.508928i \(-0.830042\pi\)
0.871149 + 0.491019i \(0.163375\pi\)
\(264\) 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 0.999884 + 0.0152033i \(0.00483956\pi\)
−0.486776 + 0.873527i \(0.661827\pi\)
\(270\) 0 0
\(271\) 7206.91 + 4160.91i 1.61546 + 0.932684i 0.988075 + 0.153971i \(0.0492062\pi\)
0.627380 + 0.778713i \(0.284127\pi\)
\(272\) 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 0.666408 0.745587i \(-0.267831\pi\)
−0.978901 + 0.204333i \(0.934497\pi\)
\(278\) 0 0
\(279\) −296.730 + 171.317i −0.0636730 + 0.0367616i
\(280\) 0 0
\(281\) 2817.99i 0.598247i −0.954214 0.299123i \(-0.903306\pi\)
0.954214 0.299123i \(-0.0966942\pi\)
\(282\) 0 0
\(283\) −132.301 + 229.152i −0.0277896 + 0.0481330i −0.879586 0.475740i \(-0.842180\pi\)
0.851796 + 0.523873i \(0.175514\pi\)
\(284\) 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 −0.0812984 0.996690i \(-0.525907\pi\)
0.822509 + 0.568751i \(0.192573\pi\)
\(294\) 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 \(-0.773464\pi\)
0.757263 0.653110i \(-0.226536\pi\)
\(308\) 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 \(0.139251\pi\)
−0.905827 + 0.423648i \(0.860749\pi\)
\(318\) 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 0.276353 0.961056i \(-0.410874\pi\)
0.970476 + 0.241199i \(0.0775407\pi\)
\(332\) 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 −0.685711 0.727874i \(-0.740509\pi\)
−0.287501 0.957780i \(-0.592825\pi\)
\(348\) 0 0
\(349\) 7760.61 + 4480.59i 1.19030 + 0.687222i 0.958375 0.285511i \(-0.0921633\pi\)
0.231928 + 0.972733i \(0.425497\pi\)
\(350\) 0 0
\(351\) −597.684 + 1115.52i −0.0908889 + 0.169636i
\(352\) 0 0
\(353\) −4640.16 2679.00i −0.699634 0.403934i 0.107577 0.994197i \(-0.465691\pi\)
−0.807211 + 0.590263i \(0.799024\pi\)
\(354\) 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 \(0.0637257\pi\)
−0.980027 + 0.198866i \(0.936274\pi\)
\(360\) 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 −0.205403 0.978678i \(-0.565850\pi\)
0.950261 0.311455i \(-0.100816\pi\)
\(368\) 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 0.844737 + 0.535182i \(0.179757\pi\)
0.0411127 + 0.999155i \(0.486910\pi\)
\(374\) 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 0.629831 0.776733i \(-0.283124\pi\)
−0.357755 + 0.933816i \(0.616458\pi\)
\(380\) 0 0
\(381\) 3742.73 + 6482.60i 0.503270 + 0.871690i
\(382\) 0 0
\(383\) 1717.63 991.672i 0.229156 0.132303i −0.381027 0.924564i \(-0.624429\pi\)
0.610183 + 0.792261i \(0.291096\pi\)
\(384\) 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 −0.279863 0.960040i \(-0.590289\pi\)
0.691487 + 0.722389i \(0.256956\pi\)
\(398\) 0 0
\(399\) −1014.45 1757.09i −0.127284 0.220462i
\(400\) 0 0
\(401\) 1729.93 + 998.773i 0.215432 + 0.124380i 0.603833 0.797110i \(-0.293639\pi\)
−0.388401 + 0.921490i \(0.626973\pi\)
\(402\) 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 −0.202735 0.979234i \(-0.564983\pi\)
0.746674 + 0.665190i \(0.231650\pi\)
\(410\) 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 −0.993443 0.114328i \(-0.963529\pi\)
0.595732 + 0.803183i \(0.296862\pi\)
\(420\) 0 0
\(421\) 7537.70i 0.872601i −0.899801 0.436300i \(-0.856288\pi\)
0.899801 0.436300i \(-0.143712\pi\)
\(422\) 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 0.979945 0.199268i \(-0.0638565\pi\)
0.317401 + 0.948291i \(0.397190\pi\)
\(432\) 0 0
\(433\) −8857.97 15342.5i −0.983110 1.70280i −0.650050 0.759892i \(-0.725252\pi\)
−0.333061 0.942905i \(-0.608081\pi\)
\(434\) 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 −0.992369 0.123303i \(-0.960651\pi\)
0.602968 + 0.797765i \(0.293985\pi\)
\(440\) 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 −0.563179 + 0.826335i \(0.690422\pi\)
−0.997217 + 0.0745603i \(0.976245\pi\)
\(450\) 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 0.970933 0.239351i \(-0.0769346\pi\)
0.278183 + 0.960528i \(0.410268\pi\)
\(458\) 0 0
\(459\) −389.591 674.791i −0.0396177 0.0686199i
\(460\) 0 0
\(461\) 2530.72 1461.11i 0.255678 0.147616i −0.366684 0.930346i \(-0.619507\pi\)
0.622361 + 0.782730i \(0.286174\pi\)
\(462\) 0 0
\(463\) 2072.61i 0.208040i 0.994575 + 0.104020i \(0.0331706\pi\)
−0.994575 + 0.104020i \(0.966829\pi\)
\(464\) 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 0.268614 0.963248i \(-0.413434\pi\)
−0.699890 + 0.714250i \(0.746768\pi\)
\(480\) 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 −0.903800 0.427954i \(-0.859234\pi\)
−0.0812808 + 0.996691i \(0.525901\pi\)
\(488\) 0 0
\(489\) 7027.08i 0.649848i
\(490\) 0 0
\(491\) −9826.61 + 17020.2i −0.903195 + 1.56438i −0.0798720 + 0.996805i \(0.525451\pi\)
−0.823323 + 0.567574i \(0.807882\pi\)
\(492\) 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 \(-0.823907\pi\)
0.850842 0.525422i \(-0.176093\pi\)
\(500\) 0 0
\(501\) 104.113 60.1096i 0.00928428 0.00536028i
\(502\) 0 0
\(503\) 6501.67 + 11261.2i 0.576332 + 0.998236i 0.995896 + 0.0905104i \(0.0288498\pi\)
−0.419563 + 0.907726i \(0.637817\pi\)
\(504\) 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 0.285416 0.958404i \(-0.407868\pi\)
−0.687294 + 0.726379i \(0.741202\pi\)
\(510\) 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 −0.945111 0.326749i \(-0.894047\pi\)
0.755528 + 0.655116i \(0.227380\pi\)
\(524\) 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 \(-0.933948\pi\)
0.978547 0.206022i \(-0.0660519\pi\)
\(542\) 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 0.984912 0.173055i \(-0.0553637\pi\)
0.342586 + 0.939486i \(0.388697\pi\)
\(558\) 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 −0.991273 0.131824i \(-0.957917\pi\)
0.381474 0.924380i \(-0.375417\pi\)
\(564\) 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 −0.606468 0.795108i \(-0.707414\pi\)
0.991818 + 0.127662i \(0.0407474\pi\)
\(570\) 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 \(-0.945928\pi\)
0.985606 0.169056i \(-0.0540718\pi\)
\(578\) 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 0.0844601 0.996427i \(-0.473083\pi\)
−0.820701 + 0.571358i \(0.806417\pi\)
\(588\) 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 \(0.0681466\pi\)
−0.977170 + 0.212457i \(0.931853\pi\)
\(594\) 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 0.366441 + 0.930441i \(0.380576\pi\)
−0.989006 + 0.147873i \(0.952757\pi\)
\(602\) 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 0.985772 0.168090i \(-0.0537600\pi\)
−0.638456 + 0.769658i \(0.720427\pi\)
\(608\) 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 0.476872 0.878973i \(-0.341770\pi\)
−0.522777 + 0.852470i \(0.675104\pi\)
\(614\) 0 0
\(615\) −256.592 444.431i −0.0168241 0.0291401i
\(616\) 0 0
\(617\) −13179.4 + 7609.13i −0.859940 + 0.496486i −0.863992 0.503505i \(-0.832043\pi\)
0.00405239 + 0.999992i \(0.498710\pi\)
\(618\) 0 0
\(619\) 11462.5i 0.744291i 0.928174 + 0.372145i \(0.121378\pi\)
−0.928174 + 0.372145i \(0.878622\pi\)
\(620\) 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 −0.372930 0.927860i \(-0.621647\pi\)
0.617085 + 0.786896i \(0.288313\pi\)
\(632\) 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 0.944998 0.327077i \(-0.106064\pi\)
−0.755756 + 0.654854i \(0.772730\pi\)
\(642\) 0 0
\(643\) 17959.8 10369.1i 1.10150 0.635951i 0.164886 0.986313i \(-0.447274\pi\)
0.936615 + 0.350361i \(0.113941\pi\)
\(644\) 0 0
\(645\) 1170.11i 0.0714312i
\(646\) 0 0
\(647\) −426.379 + 738.509i −0.0259083 + 0.0448745i −0.878689 0.477395i \(-0.841581\pi\)
0.852781 + 0.522269i \(0.174914\pi\)
\(648\) 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 −0.734732 0.678357i \(-0.762692\pi\)
0.954841 + 0.297118i \(0.0960256\pi\)
\(654\) 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 0.989665 0.143396i \(-0.0458022\pi\)
−0.619017 + 0.785378i \(0.712469\pi\)
\(660\) 0 0
\(661\) 1942.45 + 1121.48i 0.114301 + 0.0659915i 0.556060 0.831142i \(-0.312312\pi\)
−0.441760 + 0.897133i \(0.645646\pi\)
\(662\) 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 −0.926280 0.376837i \(-0.877012\pi\)
0.789490 + 0.613763i \(0.210345\pi\)
\(674\) 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 −0.947355 0.320186i \(-0.896255\pi\)
−0.196388 + 0.980526i \(0.562921\pi\)
\(684\) 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 0.768276 0.640118i \(-0.221115\pi\)
−0.170221 + 0.985406i \(0.554448\pi\)
\(692\) 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 −0.893549 0.448966i \(-0.851792\pi\)
−0.0579583 + 0.998319i \(0.518459\pi\)
\(710\) 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 −0.981275 0.192610i \(-0.938305\pi\)
0.323832 0.946114i \(-0.395029\pi\)
\(720\) 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 \(0.0308658\pi\)
−0.995302 + 0.0968160i \(0.969134\pi\)
\(734\) 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 0.971393 0.237479i \(-0.0763211\pi\)
0.280034 + 0.959990i \(0.409654\pi\)
\(740\) 0 0
\(741\) 12542.7 + 6720.21i 0.621816 + 0.333162i
\(742\) 0 0
\(743\) 30308.0 + 17498.3i 1.49649 + 0.864000i 0.999992 0.00403656i \(-0.00128488\pi\)
0.496500 + 0.868037i \(0.334618\pi\)
\(744\) 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 −0.964618 0.263653i \(-0.915073\pi\)
0.710639 + 0.703557i \(0.248406\pi\)
\(752\) 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 −0.301071 0.953602i \(-0.597344\pi\)
0.976379 0.216065i \(-0.0693225\pi\)
\(758\) 0 0
\(759\) 11512.3i 0.550552i
\(760\) 0 0
\(761\) 18261.9 10543.5i 0.869899 0.502236i 0.00258400 0.999997i \(-0.499177\pi\)
0.867315 + 0.497761i \(0.165844\pi\)
\(762\) 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 0.841033 0.540984i \(-0.181948\pi\)
−0.0479893 + 0.998848i \(0.515281\pi\)
\(770\) 0 0
\(771\) −9818.72 17006.5i −0.458641 0.794390i
\(772\) 0 0
\(773\) 25419.6 14676.0i 1.18277 0.682870i 0.226113 0.974101i \(-0.427398\pi\)
0.956653 + 0.291231i \(0.0940648\pi\)
\(774\) 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 −0.584974 0.811052i \(-0.698895\pi\)
0.409905 + 0.912128i \(0.365562\pi\)
\(788\) 0 0
\(789\) 132.302 + 229.154i 0.00596968