Properties

Label 684.3.m.a.353.15
Level $684$
Weight $3$
Character 684.353
Analytic conductor $18.638$
Analytic rank $0$
Dimension $80$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 684 = 2^{2} \cdot 3^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 684.m (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(18.6376500822\)
Analytic rank: \(0\)
Dimension: \(80\)
Relative dimension: \(40\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 353.15
Character \(\chi\) \(=\) 684.353
Dual form 684.3.m.a.653.15

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.55115 + 2.56787i) q^{3} +5.60337i q^{5} +(-5.05578 + 8.75686i) q^{7} +(-4.18789 - 7.96628i) q^{9} +O(q^{10})\) \(q+(-1.55115 + 2.56787i) q^{3} +5.60337i q^{5} +(-5.05578 + 8.75686i) q^{7} +(-4.18789 - 7.96628i) q^{9} +(-4.84819 - 2.79910i) q^{11} +(-9.41378 + 16.3051i) q^{13} +(-14.3887 - 8.69164i) q^{15} +(1.70269 + 0.983049i) q^{17} +(-12.6901 - 14.1408i) q^{19} +(-14.6442 - 26.5657i) q^{21} +(14.6593 + 8.46356i) q^{23} -6.39771 q^{25} +(26.9524 + 1.60293i) q^{27} +12.2948i q^{29} +(3.88985 + 6.73742i) q^{31} +(14.7080 - 8.10768i) q^{33} +(-49.0679 - 28.3294i) q^{35} +47.4671 q^{37} +(-27.2673 - 49.4650i) q^{39} +36.8133i q^{41} +(-20.2784 - 35.1233i) q^{43} +(44.6380 - 23.4663i) q^{45} -1.53361i q^{47} +(-26.6218 - 46.1103i) q^{49} +(-5.16546 + 2.84743i) q^{51} +(15.7050 - 9.06730i) q^{53} +(15.6844 - 27.1662i) q^{55} +(55.9958 - 10.6521i) q^{57} -25.1714i q^{59} +63.5711 q^{61} +(90.9326 + 3.60298i) q^{63} +(-91.3637 - 52.7488i) q^{65} +(12.0682 - 20.9027i) q^{67} +(-44.4720 + 24.5150i) q^{69} +(-106.323 - 61.3856i) q^{71} +(-10.0030 + 17.3257i) q^{73} +(9.92379 - 16.4285i) q^{75} +(49.0227 - 28.3033i) q^{77} +(5.16465 + 8.94544i) q^{79} +(-45.9232 + 66.7238i) q^{81} +(-39.0802 - 22.5629i) q^{83} +(-5.50839 + 9.54080i) q^{85} +(-31.5714 - 19.0710i) q^{87} +(-141.530 + 81.7125i) q^{89} +(-95.1879 - 164.870i) q^{91} +(-23.3345 - 0.462105i) q^{93} +(79.2359 - 71.1073i) q^{95} +(-90.0648 - 155.997i) q^{97} +(-1.99477 + 50.3443i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 80 q - 2 q^{3} + q^{7} - 2 q^{9} + O(q^{10}) \) \( 80 q - 2 q^{3} + q^{7} - 2 q^{9} + 18 q^{11} - 5 q^{13} - 2 q^{15} - 9 q^{17} + 20 q^{19} - 30 q^{21} + 72 q^{23} - 400 q^{25} + 25 q^{27} - 8 q^{31} - 64 q^{33} + 22 q^{37} + 39 q^{39} - 44 q^{43} - 196 q^{45} - 267 q^{49} - 47 q^{51} - 36 q^{53} + 84 q^{57} - 14 q^{61} - 260 q^{63} - 144 q^{65} - 77 q^{67} + 44 q^{69} - 135 q^{71} + 43 q^{73} + 69 q^{75} + 216 q^{77} - 17 q^{79} - 254 q^{81} - 171 q^{83} - 244 q^{87} + 216 q^{89} + 122 q^{91} + 292 q^{93} - 288 q^{95} - 8 q^{97} + 172 q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/684\mathbb{Z}\right)^\times\).

\(n\) \(325\) \(343\) \(533\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(1\) \(e\left(\frac{1}{6}\right)\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −1.55115 + 2.56787i −0.517049 + 0.855956i
\(4\) 0 0
\(5\) 5.60337i 1.12067i 0.828265 + 0.560337i \(0.189328\pi\)
−0.828265 + 0.560337i \(0.810672\pi\)
\(6\) 0 0
\(7\) −5.05578 + 8.75686i −0.722254 + 1.25098i 0.237840 + 0.971304i \(0.423560\pi\)
−0.960094 + 0.279676i \(0.909773\pi\)
\(8\) 0 0
\(9\) −4.18789 7.96628i −0.465321 0.885142i
\(10\) 0 0
\(11\) −4.84819 2.79910i −0.440744 0.254464i 0.263169 0.964750i \(-0.415232\pi\)
−0.703913 + 0.710286i \(0.748566\pi\)
\(12\) 0 0
\(13\) −9.41378 + 16.3051i −0.724137 + 1.25424i 0.235192 + 0.971949i \(0.424428\pi\)
−0.959328 + 0.282292i \(0.908905\pi\)
\(14\) 0 0
\(15\) −14.3887 8.69164i −0.959247 0.579443i
\(16\) 0 0
\(17\) 1.70269 + 0.983049i 0.100158 + 0.0578264i 0.549242 0.835663i \(-0.314916\pi\)
−0.449084 + 0.893489i \(0.648250\pi\)
\(18\) 0 0
\(19\) −12.6901 14.1408i −0.667900 0.744251i
\(20\) 0 0
\(21\) −14.6442 26.5657i −0.697343 1.26504i
\(22\) 0 0
\(23\) 14.6593 + 8.46356i 0.637361 + 0.367981i 0.783597 0.621269i \(-0.213383\pi\)
−0.146236 + 0.989250i \(0.546716\pi\)
\(24\) 0 0
\(25\) −6.39771 −0.255909
\(26\) 0 0
\(27\) 26.9524 + 1.60293i 0.998236 + 0.0593677i
\(28\) 0 0
\(29\) 12.2948i 0.423958i 0.977274 + 0.211979i \(0.0679909\pi\)
−0.977274 + 0.211979i \(0.932009\pi\)
\(30\) 0 0
\(31\) 3.88985 + 6.73742i 0.125479 + 0.217336i 0.921920 0.387380i \(-0.126620\pi\)
−0.796441 + 0.604716i \(0.793287\pi\)
\(32\) 0 0
\(33\) 14.7080 8.10768i 0.445696 0.245687i
\(34\) 0 0
\(35\) −49.0679 28.3294i −1.40194 0.809411i
\(36\) 0 0
\(37\) 47.4671 1.28290 0.641448 0.767167i \(-0.278334\pi\)
0.641448 + 0.767167i \(0.278334\pi\)
\(38\) 0 0
\(39\) −27.2673 49.4650i −0.699161 1.26833i
\(40\) 0 0
\(41\) 36.8133i 0.897885i 0.893561 + 0.448942i \(0.148199\pi\)
−0.893561 + 0.448942i \(0.851801\pi\)
\(42\) 0 0
\(43\) −20.2784 35.1233i −0.471592 0.816821i 0.527880 0.849319i \(-0.322987\pi\)
−0.999472 + 0.0324982i \(0.989654\pi\)
\(44\) 0 0
\(45\) 44.6380 23.4663i 0.991955 0.521473i
\(46\) 0 0
\(47\) 1.53361i 0.0326299i −0.999867 0.0163150i \(-0.994807\pi\)
0.999867 0.0163150i \(-0.00519345\pi\)
\(48\) 0 0
\(49\) −26.6218 46.1103i −0.543302 0.941026i
\(50\) 0 0
\(51\) −5.16546 + 2.84743i −0.101284 + 0.0558320i
\(52\) 0 0
\(53\) 15.7050 9.06730i 0.296321 0.171081i −0.344468 0.938798i \(-0.611941\pi\)
0.640789 + 0.767717i \(0.278607\pi\)
\(54\) 0 0
\(55\) 15.6844 27.1662i 0.285171 0.493930i
\(56\) 0 0
\(57\) 55.9958 10.6521i 0.982383 0.186879i
\(58\) 0 0
\(59\) 25.1714i 0.426633i −0.976983 0.213317i \(-0.931573\pi\)
0.976983 0.213317i \(-0.0684266\pi\)
\(60\) 0 0
\(61\) 63.5711 1.04215 0.521074 0.853511i \(-0.325531\pi\)
0.521074 + 0.853511i \(0.325531\pi\)
\(62\) 0 0
\(63\) 90.9326 + 3.60298i 1.44338 + 0.0571901i
\(64\) 0 0
\(65\) −91.3637 52.7488i −1.40559 0.811520i
\(66\) 0 0
\(67\) 12.0682 20.9027i 0.180122 0.311980i −0.761800 0.647812i \(-0.775684\pi\)
0.941922 + 0.335832i \(0.109018\pi\)
\(68\) 0 0
\(69\) −44.4720 + 24.5150i −0.644522 + 0.355289i
\(70\) 0 0
\(71\) −106.323 61.3856i −1.49751 0.864586i −0.497511 0.867458i \(-0.665753\pi\)
−0.999996 + 0.00287158i \(0.999086\pi\)
\(72\) 0 0
\(73\) −10.0030 + 17.3257i −0.137028 + 0.237339i −0.926370 0.376614i \(-0.877088\pi\)
0.789343 + 0.613953i \(0.210422\pi\)
\(74\) 0 0
\(75\) 9.92379 16.4285i 0.132317 0.219046i
\(76\) 0 0
\(77\) 49.0227 28.3033i 0.636659 0.367575i
\(78\) 0 0
\(79\) 5.16465 + 8.94544i 0.0653753 + 0.113233i 0.896860 0.442314i \(-0.145842\pi\)
−0.831485 + 0.555547i \(0.812509\pi\)
\(80\) 0 0
\(81\) −45.9232 + 66.7238i −0.566953 + 0.823750i
\(82\) 0 0
\(83\) −39.0802 22.5629i −0.470845 0.271843i 0.245748 0.969334i \(-0.420966\pi\)
−0.716593 + 0.697491i \(0.754300\pi\)
\(84\) 0 0
\(85\) −5.50839 + 9.54080i −0.0648045 + 0.112245i
\(86\) 0 0
\(87\) −31.5714 19.0710i −0.362890 0.219207i
\(88\) 0 0
\(89\) −141.530 + 81.7125i −1.59023 + 0.918118i −0.596959 + 0.802272i \(0.703625\pi\)
−0.993267 + 0.115846i \(0.963042\pi\)
\(90\) 0 0
\(91\) −95.1879 164.870i −1.04602 1.81176i
\(92\) 0 0
\(93\) −23.3345 0.462105i −0.250909 0.00496887i
\(94\) 0 0
\(95\) 79.2359 71.1073i 0.834062 0.748498i
\(96\) 0 0
\(97\) −90.0648 155.997i −0.928503 1.60821i −0.785829 0.618444i \(-0.787763\pi\)
−0.142674 0.989770i \(-0.545570\pi\)
\(98\) 0 0
\(99\) −1.99477 + 50.3443i −0.0201492 + 0.508529i
\(100\) 0 0
\(101\) 148.940i 1.47466i 0.675534 + 0.737329i \(0.263913\pi\)
−0.675534 + 0.737329i \(0.736087\pi\)
\(102\) 0 0
\(103\) 4.85216 + 8.40418i 0.0471083 + 0.0815940i 0.888618 0.458648i \(-0.151666\pi\)
−0.841510 + 0.540242i \(0.818333\pi\)
\(104\) 0 0
\(105\) 148.858 82.0569i 1.41769 0.781494i
\(106\) 0 0
\(107\) 166.968i 1.56044i 0.625502 + 0.780222i \(0.284894\pi\)
−0.625502 + 0.780222i \(0.715106\pi\)
\(108\) 0 0
\(109\) 91.3345 158.196i 0.837931 1.45134i −0.0536900 0.998558i \(-0.517098\pi\)
0.891621 0.452782i \(-0.149568\pi\)
\(110\) 0 0
\(111\) −73.6285 + 121.889i −0.663320 + 1.09810i
\(112\) 0 0
\(113\) 143.535 82.8699i 1.27022 0.733362i 0.295191 0.955438i \(-0.404617\pi\)
0.975029 + 0.222076i \(0.0712834\pi\)
\(114\) 0 0
\(115\) −47.4244 + 82.1415i −0.412386 + 0.714274i
\(116\) 0 0
\(117\) 169.315 + 6.70869i 1.44714 + 0.0573392i
\(118\) 0 0
\(119\) −17.2169 + 9.94016i −0.144679 + 0.0835307i
\(120\) 0 0
\(121\) −44.8301 77.6479i −0.370496 0.641718i
\(122\) 0 0
\(123\) −94.5316 57.1028i −0.768550 0.464250i
\(124\) 0 0
\(125\) 104.235i 0.833883i
\(126\) 0 0
\(127\) −111.040 192.328i −0.874334 1.51439i −0.857471 0.514533i \(-0.827965\pi\)
−0.0168629 0.999858i \(-0.505368\pi\)
\(128\) 0 0
\(129\) 121.647 + 2.40903i 0.942998 + 0.0186746i
\(130\) 0 0
\(131\) 135.740i 1.03618i −0.855325 0.518092i \(-0.826643\pi\)
0.855325 0.518092i \(-0.173357\pi\)
\(132\) 0 0
\(133\) 187.987 39.6329i 1.41344 0.297992i
\(134\) 0 0
\(135\) −8.98180 + 151.024i −0.0665318 + 1.11870i
\(136\) 0 0
\(137\) 15.9506i 0.116428i 0.998304 + 0.0582138i \(0.0185405\pi\)
−0.998304 + 0.0582138i \(0.981459\pi\)
\(138\) 0 0
\(139\) −93.2674 + 161.544i −0.670988 + 1.16219i 0.306636 + 0.951827i \(0.400797\pi\)
−0.977624 + 0.210359i \(0.932537\pi\)
\(140\) 0 0
\(141\) 3.93810 + 2.37885i 0.0279298 + 0.0168713i
\(142\) 0 0
\(143\) 91.2795 52.7002i 0.638318 0.368533i
\(144\) 0 0
\(145\) −68.8922 −0.475119
\(146\) 0 0
\(147\) 159.699 + 3.16260i 1.08639 + 0.0215143i
\(148\) 0 0
\(149\) 152.829i 1.02570i 0.858479 + 0.512849i \(0.171410\pi\)
−0.858479 + 0.512849i \(0.828590\pi\)
\(150\) 0 0
\(151\) −95.9784 + 166.239i −0.635618 + 1.10092i 0.350765 + 0.936463i \(0.385921\pi\)
−0.986384 + 0.164460i \(0.947412\pi\)
\(152\) 0 0
\(153\) 0.700566 17.6810i 0.00457886 0.115562i
\(154\) 0 0
\(155\) −37.7523 + 21.7963i −0.243563 + 0.140621i
\(156\) 0 0
\(157\) 46.4968 0.296158 0.148079 0.988976i \(-0.452691\pi\)
0.148079 + 0.988976i \(0.452691\pi\)
\(158\) 0 0
\(159\) −1.07717 + 54.3932i −0.00677468 + 0.342095i
\(160\) 0 0
\(161\) −148.228 + 85.5797i −0.920674 + 0.531551i
\(162\) 0 0
\(163\) 48.7950 0.299356 0.149678 0.988735i \(-0.452176\pi\)
0.149678 + 0.988735i \(0.452176\pi\)
\(164\) 0 0
\(165\) 45.4303 + 82.4142i 0.275335 + 0.499480i
\(166\) 0 0
\(167\) 32.9129 + 19.0023i 0.197083 + 0.113786i 0.595294 0.803508i \(-0.297035\pi\)
−0.398211 + 0.917294i \(0.630369\pi\)
\(168\) 0 0
\(169\) −92.7383 160.628i −0.548748 0.950459i
\(170\) 0 0
\(171\) −59.5046 + 160.313i −0.347980 + 0.937502i
\(172\) 0 0
\(173\) −110.677 + 63.8991i −0.639749 + 0.369359i −0.784518 0.620106i \(-0.787089\pi\)
0.144769 + 0.989465i \(0.453756\pi\)
\(174\) 0 0
\(175\) 32.3454 56.0239i 0.184831 0.320137i
\(176\) 0 0
\(177\) 64.6368 + 39.0445i 0.365179 + 0.220590i
\(178\) 0 0
\(179\) 46.0254i 0.257125i 0.991701 + 0.128563i \(0.0410363\pi\)
−0.991701 + 0.128563i \(0.958964\pi\)
\(180\) 0 0
\(181\) 77.9537 + 135.020i 0.430683 + 0.745965i 0.996932 0.0782688i \(-0.0249392\pi\)
−0.566249 + 0.824234i \(0.691606\pi\)
\(182\) 0 0
\(183\) −98.6081 + 163.242i −0.538842 + 0.892033i
\(184\) 0 0
\(185\) 265.976i 1.43771i
\(186\) 0 0
\(187\) −5.50331 9.53201i −0.0294295 0.0509733i
\(188\) 0 0
\(189\) −150.302 + 227.914i −0.795248 + 1.20590i
\(190\) 0 0
\(191\) −95.8634 55.3467i −0.501902 0.289773i 0.227596 0.973756i \(-0.426913\pi\)
−0.729499 + 0.683982i \(0.760247\pi\)
\(192\) 0 0
\(193\) −111.059 −0.575438 −0.287719 0.957715i \(-0.592897\pi\)
−0.287719 + 0.957715i \(0.592897\pi\)
\(194\) 0 0
\(195\) 277.170 152.789i 1.42139 0.783531i
\(196\) 0 0
\(197\) 273.143i 1.38651i 0.720691 + 0.693257i \(0.243825\pi\)
−0.720691 + 0.693257i \(0.756175\pi\)
\(198\) 0 0
\(199\) −47.0505 81.4939i −0.236435 0.409517i 0.723254 0.690582i \(-0.242646\pi\)
−0.959689 + 0.281065i \(0.909312\pi\)
\(200\) 0 0
\(201\) 34.9558 + 63.4125i 0.173909 + 0.315485i
\(202\) 0 0
\(203\) −107.664 62.1597i −0.530364 0.306206i
\(204\) 0 0
\(205\) −206.278 −1.00624
\(206\) 0 0
\(207\) 6.03152 152.225i 0.0291378 0.735385i
\(208\) 0 0
\(209\) 21.9425 + 104.078i 0.104988 + 0.497981i
\(210\) 0 0
\(211\) 57.3158 0.271639 0.135820 0.990734i \(-0.456633\pi\)
0.135820 + 0.990734i \(0.456633\pi\)
\(212\) 0 0
\(213\) 322.553 177.805i 1.51433 0.834767i
\(214\) 0 0
\(215\) 196.809 113.628i 0.915389 0.528500i
\(216\) 0 0
\(217\) −78.6649 −0.362511
\(218\) 0 0
\(219\) −28.9740 52.5611i −0.132301 0.240005i
\(220\) 0 0
\(221\) −32.0575 + 18.5084i −0.145057 + 0.0837485i
\(222\) 0 0
\(223\) 4.88183 + 8.45557i 0.0218916 + 0.0379174i 0.876764 0.480921i \(-0.159698\pi\)
−0.854872 + 0.518839i \(0.826364\pi\)
\(224\) 0 0
\(225\) 26.7929 + 50.9660i 0.119080 + 0.226515i
\(226\) 0 0
\(227\) 70.3097 + 40.5933i 0.309735 + 0.178825i 0.646808 0.762653i \(-0.276104\pi\)
−0.337073 + 0.941478i \(0.609437\pi\)
\(228\) 0 0
\(229\) 91.3522 + 158.227i 0.398918 + 0.690946i 0.993593 0.113020i \(-0.0360525\pi\)
−0.594675 + 0.803966i \(0.702719\pi\)
\(230\) 0 0
\(231\) −3.36236 + 169.786i −0.0145557 + 0.735006i
\(232\) 0 0
\(233\) −143.327 82.7501i −0.615139 0.355151i 0.159835 0.987144i \(-0.448904\pi\)
−0.774974 + 0.631993i \(0.782237\pi\)
\(234\) 0 0
\(235\) 8.59336 0.0365675
\(236\) 0 0
\(237\) −30.9818 0.613548i −0.130725 0.00258881i
\(238\) 0 0
\(239\) −221.452 + 127.855i −0.926578 + 0.534960i −0.885728 0.464205i \(-0.846340\pi\)
−0.0408500 + 0.999165i \(0.513007\pi\)
\(240\) 0 0
\(241\) 254.134 1.05450 0.527250 0.849710i \(-0.323223\pi\)
0.527250 + 0.849710i \(0.323223\pi\)
\(242\) 0 0
\(243\) −100.104 221.423i −0.411951 0.911206i
\(244\) 0 0
\(245\) 258.373 149.172i 1.05458 0.608864i
\(246\) 0 0
\(247\) 350.029 73.7958i 1.41712 0.298768i
\(248\) 0 0
\(249\) 118.558 65.3542i 0.476135 0.262467i
\(250\) 0 0
\(251\) 49.7549 28.7260i 0.198227 0.114446i −0.397601 0.917558i \(-0.630157\pi\)
0.595828 + 0.803112i \(0.296824\pi\)
\(252\) 0 0
\(253\) −47.3807 82.0658i −0.187276 0.324371i
\(254\) 0 0
\(255\) −15.9552 28.9440i −0.0625694 0.113506i
\(256\) 0 0
\(257\) 390.962 + 225.722i 1.52125 + 0.878296i 0.999685 + 0.0250864i \(0.00798609\pi\)
0.521568 + 0.853210i \(0.325347\pi\)
\(258\) 0 0
\(259\) −239.983 + 415.663i −0.926577 + 1.60488i
\(260\) 0 0
\(261\) 97.9437 51.4892i 0.375263 0.197277i
\(262\) 0 0
\(263\) −372.041 + 214.798i −1.41460 + 0.816722i −0.995818 0.0913629i \(-0.970878\pi\)
−0.418786 + 0.908085i \(0.637544\pi\)
\(264\) 0 0
\(265\) 50.8074 + 88.0010i 0.191726 + 0.332079i
\(266\) 0 0
\(267\) 9.70724 490.179i 0.0363567 1.83588i
\(268\) 0 0
\(269\) −100.097 57.7912i −0.372109 0.214837i 0.302270 0.953222i \(-0.402255\pi\)
−0.674380 + 0.738385i \(0.735589\pi\)
\(270\) 0 0
\(271\) 100.230 173.603i 0.369851 0.640601i −0.619691 0.784846i \(-0.712742\pi\)
0.989542 + 0.144245i \(0.0460754\pi\)
\(272\) 0 0
\(273\) 571.016 + 11.3081i 2.09163 + 0.0414216i
\(274\) 0 0
\(275\) 31.0173 + 17.9079i 0.112790 + 0.0651195i
\(276\) 0 0
\(277\) −58.9086 + 102.033i −0.212666 + 0.368349i −0.952548 0.304388i \(-0.901548\pi\)
0.739882 + 0.672737i \(0.234881\pi\)
\(278\) 0 0
\(279\) 37.3819 59.2032i 0.133985 0.212198i
\(280\) 0 0
\(281\) 364.079i 1.29566i 0.761787 + 0.647828i \(0.224322\pi\)
−0.761787 + 0.647828i \(0.775678\pi\)
\(282\) 0 0
\(283\) −238.948 −0.844340 −0.422170 0.906517i \(-0.638731\pi\)
−0.422170 + 0.906517i \(0.638731\pi\)
\(284\) 0 0
\(285\) 59.6875 + 313.765i 0.209430 + 1.10093i
\(286\) 0 0
\(287\) −322.369 186.120i −1.12324 0.648501i
\(288\) 0 0
\(289\) −142.567 246.934i −0.493312 0.854442i
\(290\) 0 0
\(291\) 540.283 + 10.6995i 1.85664 + 0.0367680i
\(292\) 0 0
\(293\) 196.017 113.171i 0.669000 0.386248i −0.126697 0.991941i \(-0.540438\pi\)
0.795698 + 0.605694i \(0.207104\pi\)
\(294\) 0 0
\(295\) 141.044 0.478117
\(296\) 0 0
\(297\) −126.183 83.2138i −0.424860 0.280181i
\(298\) 0 0
\(299\) −275.999 + 159.348i −0.923073 + 0.532937i
\(300\) 0 0
\(301\) 410.093 1.36244
\(302\) 0 0
\(303\) −382.459 231.028i −1.26224 0.762470i
\(304\) 0 0
\(305\) 356.212i 1.16791i
\(306\) 0 0
\(307\) −37.7716 + 65.4224i −0.123035 + 0.213102i −0.920963 0.389650i \(-0.872596\pi\)
0.797928 + 0.602752i \(0.205929\pi\)
\(308\) 0 0
\(309\) −29.1072 0.576424i −0.0941981 0.00186545i
\(310\) 0 0
\(311\) −271.982 + 157.029i −0.874539 + 0.504915i −0.868854 0.495068i \(-0.835143\pi\)
−0.00568514 + 0.999984i \(0.501810\pi\)
\(312\) 0 0
\(313\) −474.866 −1.51714 −0.758571 0.651590i \(-0.774102\pi\)
−0.758571 + 0.651590i \(0.774102\pi\)
\(314\) 0 0
\(315\) −20.1888 + 509.529i −0.0640915 + 1.61755i
\(316\) 0 0
\(317\) 525.671i 1.65827i −0.559049 0.829135i \(-0.688834\pi\)
0.559049 0.829135i \(-0.311166\pi\)
\(318\) 0 0
\(319\) 34.4144 59.6074i 0.107882 0.186857i
\(320\) 0 0
\(321\) −428.751 258.991i −1.33567 0.806826i
\(322\) 0 0
\(323\) −7.70625 36.5524i −0.0238584 0.113165i
\(324\) 0 0
\(325\) 60.2266 104.316i 0.185313 0.320971i
\(326\) 0 0
\(327\) 264.553 + 479.920i 0.809031 + 1.46765i
\(328\) 0 0
\(329\) 13.4296 + 7.75358i 0.0408194 + 0.0235671i
\(330\) 0 0
\(331\) 32.6901 56.6210i 0.0987617 0.171060i −0.812411 0.583086i \(-0.801845\pi\)
0.911172 + 0.412025i \(0.135178\pi\)
\(332\) 0 0
\(333\) −198.787 378.137i −0.596958 1.13555i
\(334\) 0 0
\(335\) 117.125 + 67.6223i 0.349628 + 0.201858i
\(336\) 0 0
\(337\) 154.265 0.457759 0.228880 0.973455i \(-0.426494\pi\)
0.228880 + 0.973455i \(0.426494\pi\)
\(338\) 0 0
\(339\) −9.84475 + 497.122i −0.0290405 + 1.46644i
\(340\) 0 0
\(341\) 43.5524i 0.127720i
\(342\) 0 0
\(343\) 42.9089 0.125099
\(344\) 0 0
\(345\) −137.366 249.193i −0.398163 0.722299i
\(346\) 0 0
\(347\) 46.1796i 0.133082i 0.997784 + 0.0665412i \(0.0211964\pi\)
−0.997784 + 0.0665412i \(0.978804\pi\)
\(348\) 0 0
\(349\) 291.074 504.156i 0.834024 1.44457i −0.0607982 0.998150i \(-0.519365\pi\)
0.894822 0.446422i \(-0.147302\pi\)
\(350\) 0 0
\(351\) −279.860 + 424.373i −0.797321 + 1.20904i
\(352\) 0 0
\(353\) 127.757 + 73.7605i 0.361918 + 0.208953i 0.669922 0.742432i \(-0.266328\pi\)
−0.308004 + 0.951385i \(0.599661\pi\)
\(354\) 0 0
\(355\) 343.966 595.767i 0.968918 1.67822i
\(356\) 0 0
\(357\) 1.18087 59.6293i 0.00330775 0.167029i
\(358\) 0 0
\(359\) −334.186 192.943i −0.930881 0.537445i −0.0437911 0.999041i \(-0.513944\pi\)
−0.887090 + 0.461596i \(0.847277\pi\)
\(360\) 0 0
\(361\) −38.9227 + 358.896i −0.107819 + 0.994171i
\(362\) 0 0
\(363\) 268.928 + 5.32570i 0.740847 + 0.0146714i
\(364\) 0 0
\(365\) −97.0824 56.0505i −0.265979 0.153563i
\(366\) 0 0
\(367\) −8.62992 −0.0235148 −0.0117574 0.999931i \(-0.503743\pi\)
−0.0117574 + 0.999931i \(0.503743\pi\)
\(368\) 0 0
\(369\) 293.265 154.170i 0.794756 0.417804i
\(370\) 0 0
\(371\) 183.369i 0.494256i
\(372\) 0 0
\(373\) −26.3653 45.6661i −0.0706846 0.122429i 0.828517 0.559964i \(-0.189185\pi\)
−0.899202 + 0.437535i \(0.855852\pi\)
\(374\) 0 0
\(375\) −267.663 161.684i −0.713767 0.431159i
\(376\) 0 0
\(377\) −200.468 115.740i −0.531746 0.307004i
\(378\) 0 0
\(379\) 442.574 1.16774 0.583871 0.811846i \(-0.301537\pi\)
0.583871 + 0.811846i \(0.301537\pi\)
\(380\) 0 0
\(381\) 666.112 + 13.1913i 1.74832 + 0.0346229i
\(382\) 0 0
\(383\) 306.590i 0.800497i 0.916407 + 0.400249i \(0.131076\pi\)
−0.916407 + 0.400249i \(0.868924\pi\)
\(384\) 0 0
\(385\) 158.594 + 274.692i 0.411932 + 0.713486i
\(386\) 0 0
\(387\) −194.878 + 308.636i −0.503561 + 0.797509i
\(388\) 0 0
\(389\) 597.805i 1.53677i −0.639986 0.768387i \(-0.721060\pi\)
0.639986 0.768387i \(-0.278940\pi\)
\(390\) 0 0
\(391\) 16.6402 + 28.8217i 0.0425580 + 0.0737127i
\(392\) 0 0
\(393\) 348.562 + 210.553i 0.886927 + 0.535757i
\(394\) 0 0
\(395\) −50.1246 + 28.9394i −0.126898 + 0.0732644i
\(396\) 0 0
\(397\) −322.145 + 557.971i −0.811447 + 1.40547i 0.100404 + 0.994947i \(0.467987\pi\)
−0.911851 + 0.410521i \(0.865347\pi\)
\(398\) 0 0
\(399\) −189.824 + 544.202i −0.475748 + 1.36392i
\(400\) 0 0
\(401\) 644.375i 1.60692i −0.595359 0.803460i \(-0.702990\pi\)
0.595359 0.803460i \(-0.297010\pi\)
\(402\) 0 0
\(403\) −146.473 −0.363456
\(404\) 0 0
\(405\) −373.878 257.325i −0.923155 0.635369i
\(406\) 0 0
\(407\) −230.130 132.865i −0.565429 0.326451i
\(408\) 0 0
\(409\) 139.081 240.895i 0.340050 0.588984i −0.644391 0.764696i \(-0.722889\pi\)
0.984442 + 0.175711i \(0.0562226\pi\)
\(410\) 0 0
\(411\) −40.9590 24.7417i −0.0996569 0.0601988i
\(412\) 0 0
\(413\) 220.422 + 127.261i 0.533710 + 0.308138i
\(414\) 0 0
\(415\) 126.428 218.980i 0.304647 0.527664i
\(416\) 0 0
\(417\) −270.152 490.076i −0.647846 1.17524i
\(418\) 0 0
\(419\) 171.805 99.1919i 0.410037 0.236735i −0.280769 0.959775i \(-0.590589\pi\)
0.690806 + 0.723041i \(0.257256\pi\)
\(420\) 0 0
\(421\) −353.818 612.830i −0.840422 1.45565i −0.889538 0.456861i \(-0.848974\pi\)
0.0491163 0.998793i \(-0.484359\pi\)
\(422\) 0 0
\(423\) −12.2171 + 6.42257i −0.0288821 + 0.0151834i
\(424\) 0 0
\(425\) −10.8933 6.28927i −0.0256314 0.0147983i
\(426\) 0 0
\(427\) −321.401 + 556.683i −0.752696 + 1.30371i
\(428\) 0 0
\(429\) −6.26066 + 316.139i −0.0145936 + 0.736922i
\(430\) 0 0
\(431\) −548.645 + 316.760i −1.27296 + 0.734942i −0.975543 0.219807i \(-0.929457\pi\)
−0.297414 + 0.954749i \(0.596124\pi\)
\(432\) 0 0
\(433\) 159.871 + 276.905i 0.369217 + 0.639503i 0.989443 0.144920i \(-0.0462926\pi\)
−0.620226 + 0.784423i \(0.712959\pi\)
\(434\) 0 0
\(435\) 106.862 176.906i 0.245660 0.406681i
\(436\) 0 0
\(437\) −66.3469 314.697i −0.151824 0.720131i
\(438\) 0 0
\(439\) −295.486 511.797i −0.673089 1.16582i −0.977024 0.213131i \(-0.931634\pi\)
0.303935 0.952693i \(-0.401699\pi\)
\(440\) 0 0
\(441\) −255.838 + 405.181i −0.580132 + 0.918778i
\(442\) 0 0
\(443\) 665.786i 1.50290i −0.659789 0.751451i \(-0.729354\pi\)
0.659789 0.751451i \(-0.270646\pi\)
\(444\) 0 0
\(445\) −457.865 793.045i −1.02891 1.78212i
\(446\) 0 0
\(447\) −392.445 237.060i −0.877952 0.530336i
\(448\) 0 0
\(449\) 649.827i 1.44728i 0.690180 + 0.723638i \(0.257531\pi\)
−0.690180 + 0.723638i \(0.742469\pi\)
\(450\) 0 0
\(451\) 103.044 178.478i 0.228479 0.395738i
\(452\) 0 0
\(453\) −278.004 504.322i −0.613696 1.11329i
\(454\) 0 0
\(455\) 923.829 533.373i 2.03039 1.17225i
\(456\) 0 0
\(457\) −135.270 + 234.294i −0.295995 + 0.512678i −0.975216 0.221256i \(-0.928984\pi\)
0.679221 + 0.733934i \(0.262318\pi\)
\(458\) 0 0
\(459\) 44.3158 + 29.2248i 0.0965486 + 0.0636706i
\(460\) 0 0
\(461\) −523.868 + 302.456i −1.13637 + 0.656086i −0.945530 0.325535i \(-0.894456\pi\)
−0.190844 + 0.981620i \(0.561122\pi\)
\(462\) 0 0
\(463\) −114.322 198.011i −0.246915 0.427669i 0.715753 0.698353i \(-0.246084\pi\)
−0.962668 + 0.270684i \(0.912750\pi\)
\(464\) 0 0
\(465\) 2.58935 130.752i 0.00556848 0.281187i
\(466\) 0 0
\(467\) 778.065i 1.66609i 0.553203 + 0.833046i \(0.313405\pi\)
−0.553203 + 0.833046i \(0.686595\pi\)
\(468\) 0 0
\(469\) 122.028 + 211.358i 0.260187 + 0.450657i
\(470\) 0 0
\(471\) −72.1233 + 119.398i −0.153128 + 0.253498i
\(472\) 0 0
\(473\) 227.046i 0.480012i
\(474\) 0 0
\(475\) 81.1876 + 90.4686i 0.170921 + 0.190460i
\(476\) 0 0
\(477\) −138.004 87.1378i −0.289316 0.182679i
\(478\) 0 0
\(479\) 54.6238i 0.114037i −0.998373 0.0570186i \(-0.981841\pi\)
0.998373 0.0570186i \(-0.0181594\pi\)
\(480\) 0 0
\(481\) −446.845 + 773.958i −0.928992 + 1.60906i
\(482\) 0 0
\(483\) 10.1667 513.378i 0.0210490 1.06289i
\(484\) 0 0
\(485\) 874.107 504.666i 1.80228 1.04055i
\(486\) 0 0
\(487\) −243.924 −0.500871 −0.250436 0.968133i \(-0.580574\pi\)
−0.250436 + 0.968133i \(0.580574\pi\)
\(488\) 0 0
\(489\) −75.6882 + 125.299i −0.154782 + 0.256235i
\(490\) 0 0
\(491\) 736.116i 1.49922i −0.661881 0.749609i \(-0.730242\pi\)
0.661881 0.749609i \(-0.269758\pi\)
\(492\) 0 0
\(493\) −12.0864 + 20.9342i −0.0245160 + 0.0424629i
\(494\) 0 0
\(495\) −282.098 11.1774i −0.569894 0.0225806i
\(496\) 0 0
\(497\) 1075.09 620.704i 2.16316 1.24890i
\(498\) 0 0
\(499\) −181.451 −0.363630 −0.181815 0.983333i \(-0.558197\pi\)
−0.181815 + 0.983333i \(0.558197\pi\)
\(500\) 0 0
\(501\) −99.8482 + 55.0407i −0.199298 + 0.109862i
\(502\) 0 0
\(503\) 373.769 215.795i 0.743079 0.429017i −0.0801088 0.996786i \(-0.525527\pi\)
0.823188 + 0.567769i \(0.192193\pi\)
\(504\) 0 0
\(505\) −834.567 −1.65261
\(506\) 0 0
\(507\) 556.321 + 11.0171i 1.09728 + 0.0217300i
\(508\) 0 0
\(509\) 245.195 + 141.563i 0.481719 + 0.278120i 0.721132 0.692797i \(-0.243622\pi\)
−0.239414 + 0.970918i \(0.576955\pi\)
\(510\) 0 0
\(511\) −101.146 175.190i −0.197937 0.342838i
\(512\) 0 0
\(513\) −319.362 401.469i −0.622537 0.782590i
\(514\) 0 0
\(515\) −47.0917 + 27.1884i −0.0914402 + 0.0527930i
\(516\) 0 0
\(517\) −4.29272 + 7.43521i −0.00830314 + 0.0143815i
\(518\) 0 0
\(519\) 7.59106 383.320i 0.0146263 0.738573i
\(520\) 0 0
\(521\) 84.5401i 0.162265i −0.996703 0.0811326i \(-0.974146\pi\)
0.996703 0.0811326i \(-0.0258537\pi\)
\(522\) 0 0
\(523\) 496.389 + 859.771i 0.949119 + 1.64392i 0.747286 + 0.664503i \(0.231357\pi\)
0.201833 + 0.979420i \(0.435310\pi\)
\(524\) 0 0
\(525\) 93.6895 + 169.960i 0.178456 + 0.323733i
\(526\) 0 0
\(527\) 15.2957i 0.0290240i
\(528\) 0 0
\(529\) −121.236 209.988i −0.229180 0.396952i
\(530\) 0 0
\(531\) −200.522 + 105.415i −0.377631 + 0.198521i
\(532\) 0 0
\(533\) −600.246 346.552i −1.12616 0.650191i
\(534\) 0 0
\(535\) −935.580 −1.74875
\(536\) 0 0
\(537\) −118.187 71.3921i −0.220088 0.132946i
\(538\) 0 0
\(539\) 298.068i 0.553002i
\(540\) 0 0
\(541\) 343.707 + 595.317i 0.635317 + 1.10040i 0.986448 + 0.164075i \(0.0524640\pi\)
−0.351131 + 0.936326i \(0.614203\pi\)
\(542\) 0 0
\(543\) −467.630 9.26071i −0.861198 0.0170547i
\(544\) 0 0
\(545\) 886.430 + 511.781i 1.62648 + 0.939047i
\(546\) 0 0
\(547\) 408.784 0.747320 0.373660 0.927566i \(-0.378103\pi\)
0.373660 + 0.927566i \(0.378103\pi\)
\(548\) 0 0
\(549\) −266.229 506.425i −0.484934 0.922450i
\(550\) 0 0
\(551\) 173.858 156.022i 0.315531 0.283162i
\(552\) 0 0
\(553\) −104.445 −0.188870
\(554\) 0 0
\(555\) −682.991 412.568i −1.23061 0.743365i
\(556\) 0 0
\(557\) 255.992 147.797i 0.459590 0.265344i −0.252282 0.967654i \(-0.581181\pi\)
0.711872 + 0.702309i \(0.247848\pi\)
\(558\) 0 0
\(559\) 763.587 1.36599
\(560\) 0 0
\(561\) 33.0134 + 0.653780i 0.0588474 + 0.00116538i
\(562\) 0 0
\(563\) 404.587 233.589i 0.718628 0.414900i −0.0956197 0.995418i \(-0.530483\pi\)
0.814247 + 0.580518i \(0.197150\pi\)
\(564\) 0 0
\(565\) 464.350 + 804.279i 0.821859 + 1.42350i
\(566\) 0 0
\(567\) −352.113 739.484i −0.621011 1.30420i
\(568\) 0 0
\(569\) −968.689 559.273i −1.70244 0.982904i −0.943278 0.332003i \(-0.892276\pi\)
−0.759162 0.650902i \(-0.774391\pi\)
\(570\) 0 0
\(571\) 154.236 + 267.144i 0.270115 + 0.467853i 0.968891 0.247488i \(-0.0796049\pi\)
−0.698776 + 0.715341i \(0.746272\pi\)
\(572\) 0 0
\(573\) 290.821 160.313i 0.507541 0.279779i
\(574\) 0 0
\(575\) −93.7861 54.1474i −0.163106 0.0941694i
\(576\) 0 0
\(577\) −619.239 −1.07320 −0.536602 0.843835i \(-0.680292\pi\)
−0.536602 + 0.843835i \(0.680292\pi\)
\(578\) 0 0
\(579\) 172.270 285.186i 0.297529 0.492549i
\(580\) 0 0
\(581\) 395.161 228.146i 0.680140 0.392679i
\(582\) 0 0
\(583\) −101.521 −0.174136
\(584\) 0 0
\(585\) −37.5912 + 948.735i −0.0642585 + 1.62177i
\(586\) 0 0
\(587\) 145.340 83.9120i 0.247598 0.142951i −0.371066 0.928606i \(-0.621008\pi\)
0.618664 + 0.785656i \(0.287674\pi\)
\(588\) 0 0
\(589\) 45.9097 140.504i 0.0779452 0.238547i
\(590\) 0 0
\(591\) −701.395 423.685i −1.18679 0.716895i
\(592\) 0 0
\(593\) −182.164 + 105.172i −0.307191 + 0.177357i −0.645669 0.763618i \(-0.723421\pi\)
0.338478 + 0.940974i \(0.390088\pi\)
\(594\) 0 0
\(595\) −55.6983 96.4724i −0.0936107 0.162138i
\(596\) 0 0
\(597\) 282.248 + 5.58949i 0.472777 + 0.00936263i
\(598\) 0 0
\(599\) 802.647 + 463.408i 1.33998 + 0.773636i 0.986804 0.161921i \(-0.0517691\pi\)
0.353174 + 0.935558i \(0.385102\pi\)
\(600\) 0 0
\(601\) 41.3839 71.6790i 0.0688584 0.119266i −0.829541 0.558446i \(-0.811398\pi\)
0.898399 + 0.439180i \(0.144731\pi\)
\(602\) 0 0
\(603\) −217.056 8.60032i −0.359961 0.0142626i
\(604\) 0 0
\(605\) 435.090 251.199i 0.719157 0.415205i
\(606\) 0 0
\(607\) −95.3438 165.140i −0.157074 0.272060i 0.776738 0.629823i \(-0.216873\pi\)
−0.933812 + 0.357764i \(0.883539\pi\)
\(608\) 0 0
\(609\) 326.620 180.048i 0.536322 0.295645i
\(610\) 0 0
\(611\) 25.0057 + 14.4370i 0.0409258 + 0.0236285i
\(612\) 0 0
\(613\) 122.066 211.425i 0.199129 0.344902i −0.749117 0.662438i \(-0.769522\pi\)
0.948246 + 0.317535i \(0.102855\pi\)
\(614\) 0 0
\(615\) 319.968 529.695i 0.520273 0.861293i
\(616\) 0 0
\(617\) 110.470 + 63.7797i 0.179043 + 0.103371i 0.586843 0.809701i \(-0.300371\pi\)
−0.407800 + 0.913071i \(0.633704\pi\)
\(618\) 0 0
\(619\) 594.759 1030.15i 0.960838 1.66422i 0.240433 0.970666i \(-0.422711\pi\)
0.720405 0.693554i \(-0.243956\pi\)
\(620\) 0 0
\(621\) 381.537 + 251.611i 0.614391 + 0.405170i
\(622\) 0 0
\(623\) 1652.48i 2.65246i
\(624\) 0 0
\(625\) −744.012 −1.19042
\(626\) 0 0
\(627\) −301.295 105.095i −0.480534 0.167615i
\(628\) 0 0
\(629\) 80.8219 + 46.6625i 0.128493 + 0.0741853i
\(630\) 0 0
\(631\) 309.854 + 536.683i 0.491052 + 0.850527i 0.999947 0.0103016i \(-0.00327917\pi\)
−0.508895 + 0.860829i \(0.669946\pi\)
\(632\) 0 0
\(633\) −88.9053 + 147.180i −0.140451 + 0.232511i
\(634\) 0 0
\(635\) 1077.68 622.200i 1.69714 0.979842i
\(636\) 0 0
\(637\) 1002.45 1.57370
\(638\) 0 0
\(639\) −43.7462 + 1104.07i −0.0684604 + 1.72782i
\(640\) 0 0
\(641\) −426.376 + 246.168i −0.665173 + 0.384038i −0.794245 0.607597i \(-0.792133\pi\)
0.129072 + 0.991635i \(0.458800\pi\)
\(642\) 0 0
\(643\) 1166.57 1.81426 0.907128 0.420855i \(-0.138270\pi\)
0.907128 + 0.420855i \(0.138270\pi\)
\(644\) 0 0
\(645\) −13.4987 + 681.631i −0.0209282 + 1.05679i
\(646\) 0 0
\(647\) 558.344i 0.862974i 0.902119 + 0.431487i \(0.142011\pi\)
−0.902119 + 0.431487i \(0.857989\pi\)
\(648\) 0 0
\(649\) −70.4573 + 122.036i −0.108563 + 0.188036i
\(650\) 0 0
\(651\) 122.021 202.001i 0.187436 0.310294i
\(652\) 0 0
\(653\) −819.423 + 473.094i −1.25486 + 0.724493i −0.972070 0.234690i \(-0.924593\pi\)
−0.282788 + 0.959182i \(0.591259\pi\)
\(654\) 0 0
\(655\) 760.601 1.16122
\(656\) 0 0
\(657\) 179.913 + 7.12860i 0.273840 + 0.0108502i
\(658\) 0 0
\(659\) 516.029i 0.783049i −0.920168 0.391525i \(-0.871948\pi\)
0.920168 0.391525i \(-0.128052\pi\)
\(660\) 0 0
\(661\) −237.002 + 410.499i −0.358551 + 0.621028i −0.987719 0.156241i \(-0.950062\pi\)
0.629168 + 0.777269i \(0.283396\pi\)
\(662\) 0 0
\(663\) 2.19875 111.029i 0.00331637 0.167464i
\(664\) 0 0
\(665\) 222.078 + 1053.36i 0.333951 + 1.58400i
\(666\) 0 0
\(667\) −104.058 + 180.233i −0.156008 + 0.270215i
\(668\) 0 0
\(669\) −29.2852 0.579949i −0.0437746 0.000866890i
\(670\) 0 0
\(671\) −308.205 177.942i −0.459321 0.265189i
\(672\) 0 0
\(673\) 180.204 312.122i 0.267762 0.463777i −0.700522 0.713631i \(-0.747049\pi\)
0.968284 + 0.249854i \(0.0803826\pi\)
\(674\) 0 0
\(675\) −172.434 10.2551i −0.255457 0.0151927i
\(676\) 0 0
\(677\) 633.100 + 365.521i 0.935156 + 0.539912i 0.888438 0.458996i \(-0.151791\pi\)
0.0467173 + 0.998908i \(0.485124\pi\)
\(678\) 0 0
\(679\) 1821.39 2.68246
\(680\) 0 0
\(681\) −213.299 + 117.580i −0.313214 + 0.172658i
\(682\) 0 0
\(683\) 222.822i 0.326240i −0.986606 0.163120i \(-0.947844\pi\)
0.986606 0.163120i \(-0.0521558\pi\)
\(684\) 0 0
\(685\) −89.3770 −0.130477
\(686\) 0 0
\(687\) −548.006 10.8524i −0.797679 0.0157968i
\(688\) 0 0
\(689\) 341.430i 0.495545i
\(690\) 0 0
\(691\) −520.364 + 901.297i −0.753060 + 1.30434i 0.193273 + 0.981145i \(0.438090\pi\)
−0.946333 + 0.323193i \(0.895244\pi\)
\(692\) 0 0
\(693\) −430.773 271.998i −0.621607 0.392493i
\(694\) 0 0
\(695\) −905.189 522.611i −1.30243 0.751959i
\(696\) 0 0
\(697\) −36.1893 + 62.6817i −0.0519215 + 0.0899306i
\(698\) 0 0
\(699\) 434.813 239.688i 0.622050 0.342901i
\(700\) 0 0
\(701\) 1023.92 + 591.162i 1.46066 + 0.843313i 0.999042 0.0437659i \(-0.0139356\pi\)
0.461619 + 0.887079i \(0.347269\pi\)
\(702\) 0 0
\(703\) −602.363 671.222i −0.856846 0.954797i
\(704\) 0 0
\(705\) −13.3296 + 22.0666i −0.0189072 + 0.0313002i
\(706\) 0 0
\(707\) −1304.25 753.009i −1.84477 1.06508i
\(708\) 0 0
\(709\) −665.458 −0.938587 −0.469294 0.883042i \(-0.655491\pi\)
−0.469294 + 0.883042i \(0.655491\pi\)
\(710\) 0 0
\(711\) 49.6329 78.6056i 0.0698072 0.110556i
\(712\) 0 0
\(713\) 131.688i 0.184696i
\(714\) 0 0
\(715\) 295.299 + 511.472i 0.413005 + 0.715346i
\(716\) 0 0
\(717\) 15.1889 766.982i 0.0211840 1.06971i
\(718\) 0 0
\(719\) −627.535 362.307i −0.872788 0.503904i −0.00451422 0.999990i \(-0.501437\pi\)
−0.868274 + 0.496085i \(0.834770\pi\)
\(720\) 0 0
\(721\) −98.1257 −0.136097
\(722\) 0 0
\(723\) −394.200 + 652.584i −0.545228 + 0.902605i
\(724\) 0 0
\(725\) 78.6585i 0.108495i
\(726\) 0 0
\(727\) 703.528 + 1218.55i 0.967714 + 1.67613i 0.702140 + 0.712039i \(0.252228\pi\)
0.265574 + 0.964090i \(0.414439\pi\)
\(728\) 0 0
\(729\) 723.861 + 86.4055i 0.992951 + 0.118526i
\(730\) 0 0
\(731\) 79.7388i 0.109082i
\(732\) 0 0
\(733\) −86.4814 149.790i −0.117983 0.204352i 0.800985 0.598684i \(-0.204309\pi\)
−0.918968 + 0.394332i \(0.870976\pi\)
\(734\) 0 0
\(735\) −17.7212 + 894.854i −0.0241105 + 1.21749i
\(736\) 0 0
\(737\) −117.017 + 67.5600i −0.158775 + 0.0916689i
\(738\) 0 0
\(739\) −66.6721 + 115.480i −0.0902194 + 0.156265i −0.907603 0.419829i \(-0.862090\pi\)
0.817384 + 0.576093i \(0.195423\pi\)
\(740\) 0 0
\(741\) −353.448 + 1013.30i −0.476989 + 1.36747i
\(742\) 0 0
\(743\) 422.459i 0.568586i 0.958737 + 0.284293i \(0.0917588\pi\)
−0.958737 + 0.284293i \(0.908241\pi\)
\(744\) 0 0
\(745\) −856.357 −1.14947
\(746\) 0 0
\(747\) −16.0794 + 405.814i −0.0215253 + 0.543259i
\(748\) 0 0
\(749\) −1462.11 844.151i −1.95209 1.12704i
\(750\) 0 0
\(751\) −141.310 + 244.755i −0.188162 + 0.325906i −0.944637 0.328116i \(-0.893586\pi\)
0.756476 + 0.654022i \(0.226920\pi\)
\(752\) 0 0
\(753\) −3.41258 + 172.322i −0.00453198 + 0.228847i
\(754\) 0 0
\(755\) −931.500 537.802i −1.23378 0.712321i
\(756\) 0 0
\(757\) 82.4999 142.894i 0.108983 0.188764i −0.806376 0.591404i \(-0.798574\pi\)
0.915358 + 0.402640i \(0.131907\pi\)
\(758\) 0 0
\(759\) 284.229 + 5.62872i 0.374478 + 0.00741596i
\(760\) 0 0
\(761\) −1122.72 + 648.202i −1.47532 + 0.851776i −0.999613 0.0278273i \(-0.991141\pi\)
−0.475707 + 0.879604i \(0.657808\pi\)
\(762\) 0 0
\(763\) 923.534 + 1599.61i 1.21040 + 2.09647i
\(764\) 0 0
\(765\) 99.0732 + 3.92553i 0.129507 + 0.00513141i
\(766\) 0 0
\(767\) 410.423 + 236.958i 0.535101 + 0.308941i
\(768\) 0 0
\(769\) −390.911 + 677.077i −0.508336 + 0.880464i 0.491617 + 0.870812i \(0.336406\pi\)
−0.999953 + 0.00965296i \(0.996927\pi\)
\(770\) 0 0
\(771\) −1186.06 + 653.811i −1.53835 + 0.848004i
\(772\) 0 0
\(773\) −722.493 + 417.131i −0.934661 + 0.539627i −0.888283 0.459297i \(-0.848101\pi\)
−0.0463781 + 0.998924i \(0.514768\pi\)
\(774\) 0 0
\(775\) −24.8862 43.1041i −0.0321112 0.0556182i
\(776\) 0 0
\(777\) −695.119 1261.00i −0.894619 1.62291i
\(778\) 0 0
\(779\) 520.568 467.164i 0.668252 0.599697i
\(780\) 0 0
\(781\) 343.649 + 595.218i 0.440012 + 0.762123i
\(782\) 0 0
\(783\) −19.7077 + 331.374i −0.0251694 + 0.423210i
\(784\) 0 0
\(785\) 260.538i 0.331896i
\(786\) 0 0
\(787\) 282.861 + 489.930i 0.359417 + 0.622529i 0.987864 0.155324i \(-0.0496422\pi\)
−0.628446 + 0.777853i \(0.716309\pi\)
\(788\) 0 0
\(789\) 25.5175 1288.53i 0.0323415 1.63312i
\(790\) 0 0
\(791\) 1675.89i 2.11869i
\(792\) 0 0
\(793\) −598.444 + 1036.54i −0.754658 + 1.30711i
\(794\) 0 0
\(795\) −304.785 6.03580i −0.383377 0.00759220i
\(796\) 0 0