Properties

Label 288.3.u.a.163.3
Level $288$
Weight $3$
Character 288.163
Analytic conductor $7.847$
Analytic rank $0$
Dimension $28$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 288 = 2^{5} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 288.u (of order \(8\), degree \(4\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(7.84743161358\)
Analytic rank: \(0\)
Dimension: \(28\)
Relative dimension: \(7\) over \(\Q(\zeta_{8})\)
Twist minimal: no (minimal twist has level 32)
Sato-Tate group: $\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label 163.3
Character \(\chi\) \(=\) 288.163
Dual form 288.3.u.a.235.3

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.682385 + 1.87999i) q^{2} +(-3.06870 - 2.56575i) q^{4} +(-1.34740 - 3.25291i) q^{5} +(0.583225 + 0.583225i) q^{7} +(6.91761 - 4.01829i) q^{8} +O(q^{10})\) \(q+(-0.682385 + 1.87999i) q^{2} +(-3.06870 - 2.56575i) q^{4} +(-1.34740 - 3.25291i) q^{5} +(0.583225 + 0.583225i) q^{7} +(6.91761 - 4.01829i) q^{8} +(7.03487 - 0.313357i) q^{10} +(3.03620 + 7.33003i) q^{11} +(-6.38385 + 15.4120i) q^{13} +(-1.49444 + 0.698471i) q^{14} +(2.83386 + 15.7470i) q^{16} +19.0889i q^{17} +(-29.6679 - 12.2888i) q^{19} +(-4.21138 + 13.4393i) q^{20} +(-15.8522 + 0.706111i) q^{22} +(-15.2998 + 15.2998i) q^{23} +(8.91173 - 8.91173i) q^{25} +(-24.6181 - 22.5185i) q^{26} +(-0.293334 - 3.28615i) q^{28} +(20.5148 + 8.49749i) q^{29} +53.6582i q^{31} +(-31.5380 - 5.41792i) q^{32} +(-35.8868 - 13.0260i) q^{34} +(1.11134 - 2.68301i) q^{35} +(-3.80237 - 9.17973i) q^{37} +(43.3477 - 47.3895i) q^{38} +(-22.3919 - 17.0881i) q^{40} +(-14.5108 - 14.5108i) q^{41} +(20.3685 + 49.1739i) q^{43} +(9.48983 - 30.2838i) q^{44} +(-18.3230 - 39.2037i) q^{46} -4.73351 q^{47} -48.3197i q^{49} +(10.6727 + 22.8352i) q^{50} +(59.1334 - 30.9154i) q^{52} +(-61.4006 + 25.4330i) q^{53} +(19.7530 - 19.7530i) q^{55} +(6.37809 + 1.69095i) q^{56} +(-29.9741 + 32.7689i) q^{58} +(-42.4656 + 17.5898i) q^{59} +(-27.7452 - 11.4924i) q^{61} +(-100.877 - 36.6155i) q^{62} +(31.7067 - 55.5939i) q^{64} +58.7354 q^{65} +(-9.42323 + 22.7497i) q^{67} +(48.9772 - 58.5780i) q^{68} +(4.28567 + 3.92015i) q^{70} +(95.1299 + 95.1299i) q^{71} +(37.1241 + 37.1241i) q^{73} +(19.8524 - 0.884295i) q^{74} +(59.5118 + 113.831i) q^{76} +(-2.50427 + 6.04584i) q^{77} -70.3394 q^{79} +(47.4053 - 30.4358i) q^{80} +(37.1821 - 17.3782i) q^{82} +(-14.5221 - 6.01526i) q^{83} +(62.0944 - 25.7203i) q^{85} +(-106.345 + 4.73698i) q^{86} +(50.4574 + 38.5060i) q^{88} +(60.8411 - 60.8411i) q^{89} +(-12.7119 + 5.26543i) q^{91} +(86.2059 - 7.69507i) q^{92} +(3.23007 - 8.89893i) q^{94} +113.065i q^{95} +31.8287 q^{97} +(90.8404 + 32.9726i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 28q + 4q^{2} - 4q^{4} + 4q^{5} - 4q^{7} + 4q^{8} + O(q^{10}) \) \( 28q + 4q^{2} - 4q^{4} + 4q^{5} - 4q^{7} + 4q^{8} - 44q^{10} + 4q^{11} - 4q^{13} + 20q^{14} + 16q^{16} - 4q^{19} - 76q^{20} + 144q^{22} + 68q^{23} - 4q^{25} - 96q^{26} + 56q^{28} + 4q^{29} + 24q^{32} - 48q^{34} - 92q^{35} - 4q^{37} + 396q^{38} - 408q^{40} + 4q^{41} + 92q^{43} + 188q^{44} - 36q^{46} + 8q^{47} - 308q^{50} + 420q^{52} + 164q^{53} + 252q^{55} - 552q^{56} + 528q^{58} - 124q^{59} - 68q^{61} - 216q^{62} - 232q^{64} + 8q^{65} - 164q^{67} + 368q^{68} - 664q^{70} + 260q^{71} - 4q^{73} + 532q^{74} - 516q^{76} - 220q^{77} - 520q^{79} - 312q^{80} + 636q^{82} + 484q^{83} + 96q^{85} - 688q^{86} + 672q^{88} + 4q^{89} - 196q^{91} - 616q^{92} + 40q^{94} - 8q^{97} + 328q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/288\mathbb{Z}\right)^\times\).

\(n\) \(37\) \(65\) \(127\)
\(\chi(n)\) \(e\left(\frac{3}{8}\right)\) \(1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.682385 + 1.87999i −0.341192 + 0.939993i
\(3\) 0 0
\(4\) −3.06870 2.56575i −0.767175 0.641437i
\(5\) −1.34740 3.25291i −0.269480 0.650582i 0.729979 0.683469i \(-0.239530\pi\)
−0.999459 + 0.0328874i \(0.989530\pi\)
\(6\) 0 0
\(7\) 0.583225 + 0.583225i 0.0833178 + 0.0833178i 0.747537 0.664220i \(-0.231236\pi\)
−0.664220 + 0.747537i \(0.731236\pi\)
\(8\) 6.91761 4.01829i 0.864701 0.502286i
\(9\) 0 0
\(10\) 7.03487 0.313357i 0.703487 0.0313357i
\(11\) 3.03620 + 7.33003i 0.276018 + 0.666366i 0.999718 0.0237484i \(-0.00756007\pi\)
−0.723700 + 0.690115i \(0.757560\pi\)
\(12\) 0 0
\(13\) −6.38385 + 15.4120i −0.491065 + 1.18554i 0.463113 + 0.886299i \(0.346732\pi\)
−0.954179 + 0.299238i \(0.903268\pi\)
\(14\) −1.49444 + 0.698471i −0.106746 + 0.0498908i
\(15\) 0 0
\(16\) 2.83386 + 15.7470i 0.177116 + 0.984190i
\(17\) 19.0889i 1.12287i 0.827519 + 0.561437i \(0.189751\pi\)
−0.827519 + 0.561437i \(0.810249\pi\)
\(18\) 0 0
\(19\) −29.6679 12.2888i −1.56147 0.646781i −0.576123 0.817363i \(-0.695435\pi\)
−0.985343 + 0.170582i \(0.945435\pi\)
\(20\) −4.21138 + 13.4393i −0.210569 + 0.671965i
\(21\) 0 0
\(22\) −15.8522 + 0.706111i −0.720555 + 0.0320959i
\(23\) −15.2998 + 15.2998i −0.665208 + 0.665208i −0.956603 0.291395i \(-0.905881\pi\)
0.291395 + 0.956603i \(0.405881\pi\)
\(24\) 0 0
\(25\) 8.91173 8.91173i 0.356469 0.356469i
\(26\) −24.6181 22.5185i −0.946849 0.866094i
\(27\) 0 0
\(28\) −0.293334 3.28615i −0.0104762 0.117363i
\(29\) 20.5148 + 8.49749i 0.707405 + 0.293017i 0.707231 0.706983i \(-0.249944\pi\)
0.000174983 1.00000i \(0.499944\pi\)
\(30\) 0 0
\(31\) 53.6582i 1.73091i 0.500988 + 0.865454i \(0.332970\pi\)
−0.500988 + 0.865454i \(0.667030\pi\)
\(32\) −31.5380 5.41792i −0.985563 0.169310i
\(33\) 0 0
\(34\) −35.8868 13.0260i −1.05549 0.383116i
\(35\) 1.11134 2.68301i 0.0317526 0.0766575i
\(36\) 0 0
\(37\) −3.80237 9.17973i −0.102767 0.248101i 0.864130 0.503268i \(-0.167869\pi\)
−0.966897 + 0.255168i \(0.917869\pi\)
\(38\) 43.3477 47.3895i 1.14073 1.24709i
\(39\) 0 0
\(40\) −22.3919 17.0881i −0.559798 0.427203i
\(41\) −14.5108 14.5108i −0.353922 0.353922i 0.507644 0.861567i \(-0.330516\pi\)
−0.861567 + 0.507644i \(0.830516\pi\)
\(42\) 0 0
\(43\) 20.3685 + 49.1739i 0.473686 + 1.14358i 0.962522 + 0.271203i \(0.0874214\pi\)
−0.488837 + 0.872375i \(0.662579\pi\)
\(44\) 9.48983 30.2838i 0.215678 0.688268i
\(45\) 0 0
\(46\) −18.3230 39.2037i −0.398327 0.852255i
\(47\) −4.73351 −0.100713 −0.0503565 0.998731i \(-0.516036\pi\)
−0.0503565 + 0.998731i \(0.516036\pi\)
\(48\) 0 0
\(49\) 48.3197i 0.986116i
\(50\) 10.6727 + 22.8352i 0.213454 + 0.456703i
\(51\) 0 0
\(52\) 59.1334 30.9154i 1.13718 0.594527i
\(53\) −61.4006 + 25.4330i −1.15850 + 0.479867i −0.877376 0.479803i \(-0.840708\pi\)
−0.281126 + 0.959671i \(0.590708\pi\)
\(54\) 0 0
\(55\) 19.7530 19.7530i 0.359145 0.359145i
\(56\) 6.37809 + 1.69095i 0.113894 + 0.0301956i
\(57\) 0 0
\(58\) −29.9741 + 32.7689i −0.516795 + 0.564981i
\(59\) −42.4656 + 17.5898i −0.719757 + 0.298133i −0.712335 0.701840i \(-0.752362\pi\)
−0.00742152 + 0.999972i \(0.502362\pi\)
\(60\) 0 0
\(61\) −27.7452 11.4924i −0.454839 0.188400i 0.143489 0.989652i \(-0.454168\pi\)
−0.598328 + 0.801251i \(0.704168\pi\)
\(62\) −100.877 36.6155i −1.62704 0.590573i
\(63\) 0 0
\(64\) 31.7067 55.5939i 0.495417 0.868655i
\(65\) 58.7354 0.903621
\(66\) 0 0
\(67\) −9.42323 + 22.7497i −0.140645 + 0.339548i −0.978469 0.206393i \(-0.933828\pi\)
0.837824 + 0.545940i \(0.183828\pi\)
\(68\) 48.9772 58.5780i 0.720254 0.861442i
\(69\) 0 0
\(70\) 4.28567 + 3.92015i 0.0612238 + 0.0560022i
\(71\) 95.1299 + 95.1299i 1.33986 + 1.33986i 0.896193 + 0.443664i \(0.146322\pi\)
0.443664 + 0.896193i \(0.353678\pi\)
\(72\) 0 0
\(73\) 37.1241 + 37.1241i 0.508550 + 0.508550i 0.914081 0.405531i \(-0.132913\pi\)
−0.405531 + 0.914081i \(0.632913\pi\)
\(74\) 19.8524 0.884295i 0.268276 0.0119499i
\(75\) 0 0
\(76\) 59.5118 + 113.831i 0.783050 + 1.49778i
\(77\) −2.50427 + 6.04584i −0.0325230 + 0.0785174i
\(78\) 0 0
\(79\) −70.3394 −0.890372 −0.445186 0.895438i \(-0.646862\pi\)
−0.445186 + 0.895438i \(0.646862\pi\)
\(80\) 47.4053 30.4358i 0.592567 0.380448i
\(81\) 0 0
\(82\) 37.1821 17.3782i 0.453440 0.211929i
\(83\) −14.5221 6.01526i −0.174965 0.0724730i 0.293481 0.955965i \(-0.405186\pi\)
−0.468447 + 0.883492i \(0.655186\pi\)
\(84\) 0 0
\(85\) 62.0944 25.7203i 0.730522 0.302592i
\(86\) −106.345 + 4.73698i −1.23657 + 0.0550812i
\(87\) 0 0
\(88\) 50.4574 + 38.5060i 0.573380 + 0.437568i
\(89\) 60.8411 60.8411i 0.683608 0.683608i −0.277204 0.960811i \(-0.589408\pi\)
0.960811 + 0.277204i \(0.0894076\pi\)
\(90\) 0 0
\(91\) −12.7119 + 5.26543i −0.139691 + 0.0578618i
\(92\) 86.2059 7.69507i 0.937020 0.0836420i
\(93\) 0 0
\(94\) 3.23007 8.89893i 0.0343625 0.0946695i
\(95\) 113.065i 1.19016i
\(96\) 0 0
\(97\) 31.8287 0.328131 0.164066 0.986449i \(-0.447539\pi\)
0.164066 + 0.986449i \(0.447539\pi\)
\(98\) 90.8404 + 32.9726i 0.926943 + 0.336455i
\(99\) 0 0
\(100\) −50.2127 + 4.48218i −0.502127 + 0.0448218i
\(101\) −11.0397 26.6521i −0.109304 0.263883i 0.859758 0.510702i \(-0.170615\pi\)
−0.969061 + 0.246820i \(0.920615\pi\)
\(102\) 0 0
\(103\) 56.0862 + 56.0862i 0.544526 + 0.544526i 0.924852 0.380326i \(-0.124188\pi\)
−0.380326 + 0.924852i \(0.624188\pi\)
\(104\) 17.7688 + 132.266i 0.170854 + 1.27179i
\(105\) 0 0
\(106\) −5.91480 132.787i −0.0558000 1.25271i
\(107\) −5.85623 14.1382i −0.0547311 0.132133i 0.894149 0.447770i \(-0.147782\pi\)
−0.948880 + 0.315637i \(0.897782\pi\)
\(108\) 0 0
\(109\) 37.6258 90.8367i 0.345191 0.833364i −0.651983 0.758233i \(-0.726063\pi\)
0.997174 0.0751304i \(-0.0239373\pi\)
\(110\) 23.6562 + 50.6144i 0.215056 + 0.460131i
\(111\) 0 0
\(112\) −7.53128 + 10.8368i −0.0672436 + 0.0967575i
\(113\) 82.4104i 0.729295i −0.931146 0.364648i \(-0.881189\pi\)
0.931146 0.364648i \(-0.118811\pi\)
\(114\) 0 0
\(115\) 70.3837 + 29.1539i 0.612032 + 0.253512i
\(116\) −41.1512 78.7120i −0.354752 0.678552i
\(117\) 0 0
\(118\) −4.09077 91.8379i −0.0346675 0.778287i
\(119\) −11.1331 + 11.1331i −0.0935555 + 0.0935555i
\(120\) 0 0
\(121\) 41.0491 41.0491i 0.339249 0.339249i
\(122\) 40.5385 44.3183i 0.332283 0.363265i
\(123\) 0 0
\(124\) 137.673 164.661i 1.11027 1.32791i
\(125\) −122.319 50.6664i −0.978556 0.405331i
\(126\) 0 0
\(127\) 60.4972i 0.476356i 0.971221 + 0.238178i \(0.0765502\pi\)
−0.971221 + 0.238178i \(0.923450\pi\)
\(128\) 82.8797 + 97.5446i 0.647498 + 0.762067i
\(129\) 0 0
\(130\) −40.0801 + 110.422i −0.308309 + 0.849398i
\(131\) 56.4124 136.192i 0.430629 1.03963i −0.548456 0.836179i \(-0.684784\pi\)
0.979085 0.203451i \(-0.0652157\pi\)
\(132\) 0 0
\(133\) −10.1359 24.4702i −0.0762096 0.183986i
\(134\) −36.3389 33.2396i −0.271185 0.248057i
\(135\) 0 0
\(136\) 76.7046 + 132.049i 0.564005 + 0.970951i
\(137\) 139.949 + 139.949i 1.02152 + 1.02152i 0.999763 + 0.0217604i \(0.00692709\pi\)
0.0217604 + 0.999763i \(0.493073\pi\)
\(138\) 0 0
\(139\) −2.63118 6.35223i −0.0189293 0.0456995i 0.914132 0.405416i \(-0.132873\pi\)
−0.933062 + 0.359717i \(0.882873\pi\)
\(140\) −10.2943 + 5.38195i −0.0735308 + 0.0384425i
\(141\) 0 0
\(142\) −243.758 + 113.928i −1.71661 + 0.802308i
\(143\) −132.353 −0.925545
\(144\) 0 0
\(145\) 78.1822i 0.539187i
\(146\) −95.1258 + 44.4599i −0.651547 + 0.304520i
\(147\) 0 0
\(148\) −11.8845 + 37.9258i −0.0803010 + 0.256255i
\(149\) 134.849 55.8563i 0.905027 0.374874i 0.118876 0.992909i \(-0.462071\pi\)
0.786151 + 0.618035i \(0.212071\pi\)
\(150\) 0 0
\(151\) −131.423 + 131.423i −0.870353 + 0.870353i −0.992511 0.122158i \(-0.961019\pi\)
0.122158 + 0.992511i \(0.461019\pi\)
\(152\) −254.611 + 34.2048i −1.67507 + 0.225031i
\(153\) 0 0
\(154\) −9.65723 8.83358i −0.0627093 0.0573609i
\(155\) 174.545 72.2990i 1.12610 0.466445i
\(156\) 0 0
\(157\) −151.775 62.8673i −0.966720 0.400429i −0.157230 0.987562i \(-0.550256\pi\)
−0.809490 + 0.587133i \(0.800256\pi\)
\(158\) 47.9985 132.237i 0.303788 0.836944i
\(159\) 0 0
\(160\) 24.8703 + 109.890i 0.155439 + 0.686815i
\(161\) −17.8464 −0.110847
\(162\) 0 0
\(163\) 75.6492 182.633i 0.464106 1.12045i −0.502591 0.864524i \(-0.667620\pi\)
0.966696 0.255926i \(-0.0823802\pi\)
\(164\) 7.29825 + 81.7605i 0.0445015 + 0.498540i
\(165\) 0 0
\(166\) 21.2183 23.1967i 0.127821 0.139739i
\(167\) −148.515 148.515i −0.889310 0.889310i 0.105147 0.994457i \(-0.466469\pi\)
−0.994457 + 0.105147i \(0.966469\pi\)
\(168\) 0 0
\(169\) −77.2745 77.2745i −0.457246 0.457246i
\(170\) 5.98163 + 134.288i 0.0351860 + 0.789928i
\(171\) 0 0
\(172\) 63.6630 203.160i 0.370134 1.18116i
\(173\) −14.9093 + 35.9942i −0.0861808 + 0.208059i −0.961094 0.276220i \(-0.910918\pi\)
0.874914 + 0.484279i \(0.160918\pi\)
\(174\) 0 0
\(175\) 10.3951 0.0594005
\(176\) −106.822 + 68.5834i −0.606944 + 0.389678i
\(177\) 0 0
\(178\) 72.8634 + 155.897i 0.409345 + 0.875829i
\(179\) −276.876 114.686i −1.54679 0.640703i −0.564062 0.825733i \(-0.690762\pi\)
−0.982733 + 0.185029i \(0.940762\pi\)
\(180\) 0 0
\(181\) −82.1686 + 34.0354i −0.453970 + 0.188041i −0.597939 0.801542i \(-0.704014\pi\)
0.143969 + 0.989582i \(0.454014\pi\)
\(182\) −1.22455 27.4912i −0.00672830 0.151051i
\(183\) 0 0
\(184\) −44.3590 + 167.317i −0.241081 + 0.909331i
\(185\) −24.7375 + 24.7375i −0.133716 + 0.133716i
\(186\) 0 0
\(187\) −139.922 + 57.9576i −0.748246 + 0.309933i
\(188\) 14.5257 + 12.1450i 0.0772645 + 0.0646010i
\(189\) 0 0
\(190\) −212.560 77.1537i −1.11874 0.406072i
\(191\) 178.857i 0.936426i 0.883616 + 0.468213i \(0.155102\pi\)
−0.883616 + 0.468213i \(0.844898\pi\)
\(192\) 0 0
\(193\) 197.034 1.02090 0.510450 0.859908i \(-0.329479\pi\)
0.510450 + 0.859908i \(0.329479\pi\)
\(194\) −21.7194 + 59.8376i −0.111956 + 0.308441i
\(195\) 0 0
\(196\) −123.976 + 148.279i −0.632532 + 0.756524i
\(197\) −62.3398 150.502i −0.316446 0.763968i −0.999437 0.0335413i \(-0.989321\pi\)
0.682992 0.730426i \(-0.260679\pi\)
\(198\) 0 0
\(199\) 22.3835 + 22.3835i 0.112480 + 0.112480i 0.761107 0.648627i \(-0.224656\pi\)
−0.648627 + 0.761107i \(0.724656\pi\)
\(200\) 25.8380 97.4578i 0.129190 0.487289i
\(201\) 0 0
\(202\) 57.6390 2.56744i 0.285342 0.0127101i
\(203\) 7.00877 + 16.9207i 0.0345260 + 0.0833530i
\(204\) 0 0
\(205\) −27.6505 + 66.7542i −0.134881 + 0.325630i
\(206\) −143.714 + 67.1690i −0.697640 + 0.326063i
\(207\) 0 0
\(208\) −260.784 56.8513i −1.25377 0.273324i
\(209\) 254.778i 1.21903i
\(210\) 0 0
\(211\) −315.926 130.861i −1.49728 0.620194i −0.524394 0.851476i \(-0.675708\pi\)
−0.972887 + 0.231282i \(0.925708\pi\)
\(212\) 253.675 + 79.4924i 1.19658 + 0.374964i
\(213\) 0 0
\(214\) 30.5758 1.36195i 0.142878 0.00636425i
\(215\) 132.514 132.514i 0.616343 0.616343i
\(216\) 0 0
\(217\) −31.2948 + 31.2948i −0.144216 + 0.144216i
\(218\) 145.096 + 132.722i 0.665580 + 0.608814i
\(219\) 0 0
\(220\) −111.297 + 9.93480i −0.505896 + 0.0451582i
\(221\) −294.197 121.860i −1.33121 0.551405i
\(222\) 0 0
\(223\) 103.995i 0.466346i 0.972435 + 0.233173i \(0.0749109\pi\)
−0.972435 + 0.233173i \(0.925089\pi\)
\(224\) −15.2339 21.5536i −0.0680084 0.0962215i
\(225\) 0 0
\(226\) 154.930 + 56.2356i 0.685533 + 0.248830i
\(227\) −19.9655 + 48.2010i −0.0879538 + 0.212339i −0.961736 0.273979i \(-0.911660\pi\)
0.873782 + 0.486318i \(0.161660\pi\)
\(228\) 0 0
\(229\) 52.0405 + 125.637i 0.227251 + 0.548633i 0.995841 0.0911090i \(-0.0290412\pi\)
−0.768590 + 0.639742i \(0.779041\pi\)
\(230\) −102.838 + 112.426i −0.447120 + 0.488810i
\(231\) 0 0
\(232\) 176.059 23.6519i 0.758873 0.101948i
\(233\) 0.497550 + 0.497550i 0.00213541 + 0.00213541i 0.708174 0.706038i \(-0.249519\pi\)
−0.706038 + 0.708174i \(0.749519\pi\)
\(234\) 0 0
\(235\) 6.37793 + 15.3977i 0.0271401 + 0.0655220i
\(236\) 175.446 + 54.9782i 0.743413 + 0.232958i
\(237\) 0 0
\(238\) −13.3330 28.5271i −0.0560211 0.119862i
\(239\) 80.2602 0.335817 0.167908 0.985803i \(-0.446299\pi\)
0.167908 + 0.985803i \(0.446299\pi\)
\(240\) 0 0
\(241\) 9.94799i 0.0412780i −0.999787 0.0206390i \(-0.993430\pi\)
0.999787 0.0206390i \(-0.00657006\pi\)
\(242\) 49.1605 + 105.183i 0.203142 + 0.434641i
\(243\) 0 0
\(244\) 55.6550 + 106.454i 0.228094 + 0.436287i
\(245\) −157.180 + 65.1059i −0.641549 + 0.265738i
\(246\) 0 0
\(247\) 378.790 378.790i 1.53356 1.53356i
\(248\) 215.614 + 371.186i 0.869412 + 1.49672i
\(249\) 0 0
\(250\) 178.721 195.385i 0.714884 0.781540i
\(251\) 37.4569 15.5152i 0.149231 0.0618134i −0.306818 0.951768i \(-0.599264\pi\)
0.456049 + 0.889955i \(0.349264\pi\)
\(252\) 0 0
\(253\) −158.601 65.6947i −0.626881 0.259663i
\(254\) −113.734 41.2824i −0.447772 0.162529i
\(255\) 0 0
\(256\) −239.938 + 89.2499i −0.937260 + 0.348632i
\(257\) 351.412 1.36736 0.683680 0.729782i \(-0.260378\pi\)
0.683680 + 0.729782i \(0.260378\pi\)
\(258\) 0 0
\(259\) 3.13621 7.57148i 0.0121089 0.0292335i
\(260\) −180.241 150.700i −0.693236 0.579616i
\(261\) 0 0
\(262\) 217.543 + 198.990i 0.830318 + 0.759502i
\(263\) 347.609 + 347.609i 1.32171 + 1.32171i 0.912393 + 0.409316i \(0.134233\pi\)
0.409316 + 0.912393i \(0.365767\pi\)
\(264\) 0 0
\(265\) 165.462 + 165.462i 0.624386 + 0.624386i
\(266\) 52.9202 2.35724i 0.198948 0.00886182i
\(267\) 0 0
\(268\) 87.2871 45.6344i 0.325698 0.170278i
\(269\) −77.8419 + 187.927i −0.289375 + 0.698613i −0.999988 0.00497024i \(-0.998418\pi\)
0.710613 + 0.703584i \(0.248418\pi\)
\(270\) 0 0
\(271\) −380.417 −1.40375 −0.701876 0.712299i \(-0.747654\pi\)
−0.701876 + 0.712299i \(0.747654\pi\)
\(272\) −300.593 + 54.0952i −1.10512 + 0.198879i
\(273\) 0 0
\(274\) −358.601 + 167.603i −1.30876 + 0.611689i
\(275\) 92.3810 + 38.2655i 0.335931 + 0.139147i
\(276\) 0 0
\(277\) 130.082 53.8819i 0.469612 0.194519i −0.135312 0.990803i \(-0.543204\pi\)
0.604924 + 0.796284i \(0.293204\pi\)
\(278\) 13.7376 0.611918i 0.0494158 0.00220114i
\(279\) 0 0
\(280\) −3.09331 23.0257i −0.0110475 0.0822348i
\(281\) 40.5881 40.5881i 0.144442 0.144442i −0.631188 0.775630i \(-0.717432\pi\)
0.775630 + 0.631188i \(0.217432\pi\)
\(282\) 0 0
\(283\) 442.450 183.269i 1.56343 0.647593i 0.577748 0.816215i \(-0.303932\pi\)
0.985681 + 0.168622i \(0.0539316\pi\)
\(284\) −47.8458 536.005i −0.168471 1.88734i
\(285\) 0 0
\(286\) 90.3156 248.822i 0.315789 0.870006i
\(287\) 16.9261i 0.0589761i
\(288\) 0 0
\(289\) −75.3848 −0.260847
\(290\) 146.981 + 53.3503i 0.506833 + 0.183967i
\(291\) 0 0
\(292\) −18.6717 209.174i −0.0639441 0.716350i
\(293\) 141.261 + 341.035i 0.482120 + 1.16394i 0.958600 + 0.284756i \(0.0919127\pi\)
−0.476479 + 0.879186i \(0.658087\pi\)
\(294\) 0 0
\(295\) 114.436 + 114.436i 0.387920 + 0.387920i
\(296\) −63.1901 48.2228i −0.213480 0.162915i
\(297\) 0 0
\(298\) 12.9902 + 291.630i 0.0435912 + 0.978623i
\(299\) −138.128 333.471i −0.461968 1.11529i
\(300\) 0 0
\(301\) −16.8000 + 40.5588i −0.0558140 + 0.134747i
\(302\) −157.393 336.755i −0.521168 1.11508i
\(303\) 0 0
\(304\) 109.438 502.006i 0.359994 1.65134i
\(305\) 105.737i 0.346680i
\(306\) 0 0
\(307\) 27.5569 + 11.4145i 0.0897620 + 0.0371807i 0.427113 0.904198i \(-0.359531\pi\)
−0.337351 + 0.941379i \(0.609531\pi\)
\(308\) 23.1970 12.1276i 0.0753148 0.0393752i
\(309\) 0 0
\(310\) 16.8142 + 377.478i 0.0542392 + 1.21767i
\(311\) −262.516 + 262.516i −0.844102 + 0.844102i −0.989389 0.145288i \(-0.953589\pi\)
0.145288 + 0.989389i \(0.453589\pi\)
\(312\) 0 0
\(313\) −346.338 + 346.338i −1.10651 + 1.10651i −0.112907 + 0.993606i \(0.536016\pi\)
−0.993606 + 0.112907i \(0.963984\pi\)
\(314\) 221.759 242.435i 0.706238 0.772087i
\(315\) 0 0
\(316\) 215.851 + 180.473i 0.683071 + 0.571118i
\(317\) −37.8371 15.6726i −0.119360 0.0494405i 0.322204 0.946670i \(-0.395576\pi\)
−0.441564 + 0.897230i \(0.645576\pi\)
\(318\) 0 0
\(319\) 176.174i 0.552269i
\(320\) −223.564 28.2317i −0.698636 0.0882241i
\(321\) 0 0
\(322\) 12.1781 33.5510i 0.0378203 0.104196i
\(323\) 234.580 566.326i 0.726253 1.75333i
\(324\) 0 0
\(325\) 80.4563 + 194.239i 0.247558 + 0.597657i
\(326\) 291.726 + 266.846i 0.894866 + 0.818545i
\(327\) 0 0
\(328\) −158.689 42.0715i −0.483807 0.128267i
\(329\) −2.76070 2.76070i −0.00839118 0.00839118i
\(330\) 0 0
\(331\) 123.850 + 298.999i 0.374168 + 0.903321i 0.993034 + 0.117825i \(0.0375921\pi\)
−0.618867 + 0.785496i \(0.712408\pi\)
\(332\) 29.1304 + 55.7192i 0.0877422 + 0.167829i
\(333\) 0 0
\(334\) 380.550 177.862i 1.13937 0.532520i
\(335\) 86.6995 0.258805
\(336\) 0 0
\(337\) 553.901i 1.64362i −0.569759 0.821812i \(-0.692963\pi\)
0.569759 0.821812i \(-0.307037\pi\)
\(338\) 198.006 92.5441i 0.585817 0.273799i
\(339\) 0 0
\(340\) −256.541 80.3905i −0.754532 0.236443i
\(341\) −393.316 + 162.917i −1.15342 + 0.477762i
\(342\) 0 0
\(343\) 56.7593 56.7593i 0.165479 0.165479i
\(344\) 338.496 + 258.319i 0.984000 + 0.750928i
\(345\) 0 0
\(346\) −57.4947 52.5912i −0.166170 0.151998i
\(347\) −149.596 + 61.9645i −0.431111 + 0.178572i −0.587677 0.809095i \(-0.699958\pi\)
0.156566 + 0.987667i \(0.449958\pi\)
\(348\) 0 0
\(349\) −354.488 146.834i −1.01572 0.420727i −0.188184 0.982134i \(-0.560260\pi\)
−0.827540 + 0.561407i \(0.810260\pi\)
\(350\) −7.09345 + 19.5426i −0.0202670 + 0.0558361i
\(351\) 0 0
\(352\) −56.0421 247.624i −0.159211 0.703478i
\(353\) 360.254 1.02055 0.510275 0.860011i \(-0.329544\pi\)
0.510275 + 0.860011i \(0.329544\pi\)
\(354\) 0 0
\(355\) 181.271 437.627i 0.510622 1.23275i
\(356\) −342.806 + 30.6002i −0.962939 + 0.0859556i
\(357\) 0 0
\(358\) 404.544 442.264i 1.13001 1.23537i
\(359\) −92.0047 92.0047i −0.256280 0.256280i 0.567259 0.823539i \(-0.308004\pi\)
−0.823539 + 0.567259i \(0.808004\pi\)
\(360\) 0 0
\(361\) 473.901 + 473.901i 1.31275 + 1.31275i
\(362\) −7.91541 177.701i −0.0218658 0.490887i
\(363\) 0 0
\(364\) 52.5187 + 16.4574i 0.144282 + 0.0452127i
\(365\) 70.7404 170.782i 0.193809 0.467897i
\(366\) 0 0
\(367\) 254.513 0.693496 0.346748 0.937958i \(-0.387286\pi\)
0.346748 + 0.937958i \(0.387286\pi\)
\(368\) −284.284 197.569i −0.772510 0.536872i
\(369\) 0 0
\(370\) −29.6257 63.3867i −0.0800695 0.171315i
\(371\) −50.6435 20.9772i −0.136505 0.0565424i
\(372\) 0 0
\(373\) 440.477 182.452i 1.18090 0.489147i 0.296122 0.955150i \(-0.404307\pi\)
0.884783 + 0.466004i \(0.154307\pi\)
\(374\) −13.4789 302.601i −0.0360397 0.809093i
\(375\) 0 0
\(376\) −32.7446 + 19.0206i −0.0870866 + 0.0505867i
\(377\) −261.926 + 261.926i −0.694765 + 0.694765i
\(378\) 0 0
\(379\) 124.964 51.7618i 0.329720 0.136575i −0.211681 0.977339i \(-0.567894\pi\)
0.541402 + 0.840764i \(0.317894\pi\)
\(380\) 290.096 346.962i 0.763411 0.913059i
\(381\) 0 0
\(382\) −336.250 122.050i −0.880235 0.319502i
\(383\) 182.483i 0.476458i −0.971209 0.238229i \(-0.923433\pi\)
0.971209 0.238229i \(-0.0765669\pi\)
\(384\) 0 0
\(385\) 23.0408 0.0598463
\(386\) −134.453 + 370.421i −0.348323 + 0.959639i
\(387\) 0 0
\(388\) −97.6728 81.6645i −0.251734 0.210476i
\(389\) 134.979 + 325.868i 0.346990 + 0.837708i 0.996972 + 0.0777583i \(0.0247763\pi\)
−0.649982 + 0.759949i \(0.725224\pi\)
\(390\) 0 0
\(391\) −292.055 292.055i −0.746945 0.746945i
\(392\) −194.163 334.257i −0.495313 0.852696i
\(393\) 0 0
\(394\) 325.481 14.4980i 0.826093 0.0367970i
\(395\) 94.7752 + 228.808i 0.239937 + 0.579260i
\(396\) 0 0
\(397\) −272.283 + 657.350i −0.685852 + 1.65579i 0.0671236 + 0.997745i \(0.478618\pi\)
−0.752976 + 0.658048i \(0.771382\pi\)
\(398\) −57.3549 + 26.8066i −0.144108 + 0.0673532i
\(399\) 0 0
\(400\) 165.588 + 115.079i 0.413970 + 0.287697i
\(401\) 74.4996i 0.185785i 0.995676 + 0.0928923i \(0.0296112\pi\)
−0.995676 + 0.0928923i \(0.970389\pi\)
\(402\) 0 0
\(403\) −826.978 342.546i −2.05206 0.849989i
\(404\) −34.5052 + 110.113i −0.0854090 + 0.272556i
\(405\) 0 0
\(406\) −36.5933 + 1.62999i −0.0901313 + 0.00401475i
\(407\) 55.7429 55.7429i 0.136961 0.136961i
\(408\) 0 0
\(409\) −289.633 + 289.633i −0.708149 + 0.708149i −0.966146 0.257997i \(-0.916938\pi\)
0.257997 + 0.966146i \(0.416938\pi\)
\(410\) −106.629 97.5347i −0.260070 0.237889i
\(411\) 0 0
\(412\) −28.2087 316.015i −0.0684678 0.767027i
\(413\) −35.0258 14.5082i −0.0848083 0.0351288i
\(414\) 0 0
\(415\) 55.3441i 0.133359i
\(416\) 284.835 451.476i 0.684699 1.08528i
\(417\) 0 0
\(418\) 478.979 + 173.856i 1.14588 + 0.415924i
\(419\) −234.290 + 565.626i −0.559165 + 1.34994i 0.351264 + 0.936277i \(0.385752\pi\)
−0.910428 + 0.413667i \(0.864248\pi\)
\(420\) 0 0
\(421\) 205.463 + 496.031i 0.488035 + 1.17822i 0.955707 + 0.294319i \(0.0950929\pi\)
−0.467672 + 0.883902i \(0.654907\pi\)
\(422\) 461.600 504.640i 1.09384 1.19583i
\(423\) 0 0
\(424\) −322.549 + 422.661i −0.760728 + 0.996842i
\(425\) 170.115 + 170.115i 0.400270 + 0.400270i
\(426\) 0 0
\(427\) −9.47901 22.8843i −0.0221991 0.0535933i
\(428\) −18.3040 + 58.4115i −0.0427664 + 0.136476i
\(429\) 0 0
\(430\) 158.699 + 339.549i 0.369067 + 0.789649i
\(431\) 94.1706 0.218493 0.109247 0.994015i \(-0.465156\pi\)
0.109247 + 0.994015i \(0.465156\pi\)
\(432\) 0 0
\(433\) 66.2703i 0.153049i −0.997068 0.0765246i \(-0.975618\pi\)
0.997068 0.0765246i \(-0.0243824\pi\)
\(434\) −37.4787 80.1888i −0.0863564 0.184767i
\(435\) 0 0
\(436\) −348.526 + 182.212i −0.799372 + 0.417918i
\(437\) 641.928 265.895i 1.46894 0.608456i
\(438\) 0 0
\(439\) 393.404 393.404i 0.896137 0.896137i −0.0989551 0.995092i \(-0.531550\pi\)
0.995092 + 0.0989551i \(0.0315500\pi\)
\(440\) 57.2701 216.016i 0.130159 0.490946i
\(441\) 0 0
\(442\) 429.852 469.931i 0.972515 1.06319i
\(443\) −124.298 + 51.4859i −0.280583 + 0.116221i −0.518537 0.855055i \(-0.673523\pi\)
0.237954 + 0.971276i \(0.423523\pi\)
\(444\) 0 0
\(445\) −279.888 115.933i −0.628961 0.260524i
\(446\) −195.510 70.9647i −0.438362 0.159114i
\(447\) 0 0
\(448\) 50.9159 13.9317i 0.113652 0.0310974i
\(449\) −621.505 −1.38420 −0.692099 0.721802i \(-0.743314\pi\)
−0.692099 + 0.721802i \(0.743314\pi\)
\(450\) 0 0
\(451\) 62.3070 150.422i 0.138153 0.333531i
\(452\) −211.444 + 252.893i −0.467797 + 0.559498i
\(453\) 0 0
\(454\) −76.9931 70.4265i −0.169588 0.155124i
\(455\) 34.2559 + 34.2559i 0.0752877 + 0.0752877i
\(456\) 0 0
\(457\) −121.890 121.890i −0.266718 0.266718i 0.561058 0.827776i \(-0.310394\pi\)
−0.827776 + 0.561058i \(0.810394\pi\)
\(458\) −271.708 + 12.1028i −0.593248 + 0.0264253i
\(459\) 0 0
\(460\) −141.185 270.052i −0.306924 0.587069i
\(461\) −92.0148 + 222.143i −0.199598 + 0.481873i −0.991709 0.128505i \(-0.958982\pi\)
0.792111 + 0.610378i \(0.208982\pi\)
\(462\) 0 0
\(463\) −133.158 −0.287598 −0.143799 0.989607i \(-0.545932\pi\)
−0.143799 + 0.989607i \(0.545932\pi\)
\(464\) −75.6743 + 347.127i −0.163091 + 0.748119i
\(465\) 0 0
\(466\) −1.27491 + 0.595867i −0.00273586 + 0.00127869i
\(467\) 414.267 + 171.595i 0.887082 + 0.367441i 0.779239 0.626727i \(-0.215606\pi\)
0.107843 + 0.994168i \(0.465606\pi\)
\(468\) 0 0
\(469\) −18.7640 + 7.77232i −0.0400086 + 0.0165721i
\(470\) −33.2996 + 1.48328i −0.0708503 + 0.00315591i
\(471\) 0 0
\(472\) −223.080 + 292.319i −0.472626 + 0.619320i
\(473\) −298.603 + 298.603i −0.631296 + 0.631296i
\(474\) 0 0
\(475\) −373.907 + 154.877i −0.787172 + 0.326058i
\(476\) 62.7289 5.59942i 0.131783 0.0117635i
\(477\) 0 0
\(478\) −54.7683 + 150.888i −0.114578 + 0.315665i
\(479\) 293.655i 0.613059i 0.951861 + 0.306530i \(0.0991679\pi\)
−0.951861 + 0.306530i \(0.900832\pi\)
\(480\) 0 0
\(481\) 165.752 0.344598
\(482\) 18.7021 + 6.78836i 0.0388010 + 0.0140837i
\(483\) 0 0
\(484\) −231.289 + 20.6458i −0.477870 + 0.0426565i
\(485\) −42.8860 103.536i −0.0884247 0.213476i
\(486\) 0 0
\(487\) 468.368 + 468.368i 0.961741 + 0.961741i 0.999295 0.0375532i \(-0.0119564\pi\)
−0.0375532 + 0.999295i \(0.511956\pi\)
\(488\) −238.110 + 31.9881i −0.487931 + 0.0655493i
\(489\) 0 0
\(490\) −15.1413 339.923i −0.0309006 0.693720i
\(491\) 120.443 + 290.775i 0.245301 + 0.592210i 0.997794 0.0663911i \(-0.0211485\pi\)
−0.752492 + 0.658601i \(0.771149\pi\)
\(492\) 0 0
\(493\) −162.207 + 391.603i −0.329021 + 0.794328i
\(494\) 453.640 + 970.602i 0.918300 + 1.96478i
\(495\) 0 0
\(496\) −844.957 + 152.060i −1.70354 + 0.306572i
\(497\) 110.964i 0.223268i
\(498\) 0 0
\(499\) 572.626 + 237.190i 1.14755 + 0.475330i 0.873711 0.486446i \(-0.161707\pi\)
0.273837 + 0.961776i \(0.411707\pi\)
\(500\) 245.365 + 469.321i 0.490729 + 0.938642i
\(501\) 0 0
\(502\) 3.60827 + 81.0058i 0.00718779 + 0.161366i
\(503\) 397.129 397.129i 0.789520 0.789520i −0.191895 0.981415i \(-0.561463\pi\)
0.981415 + 0.191895i \(0.0614634\pi\)
\(504\) 0 0
\(505\) −71.8222 + 71.8222i −0.142222 + 0.142222i
\(506\) 231.732 253.339i 0.457968 0.500669i
\(507\) 0 0
\(508\) 155.221 185.648i 0.305553 0.365449i
\(509\) 16.5014 + 6.83509i 0.0324192 + 0.0134285i 0.398834 0.917023i \(-0.369415\pi\)
−0.366415 + 0.930452i \(0.619415\pi\)
\(510\) 0 0
\(511\) 43.3034i 0.0847425i
\(512\) −4.05825 511.984i −0.00792626 0.999969i
\(513\) 0 0
\(514\) −239.798 + 660.649i −0.466533 + 1.28531i
\(515\) 106.873 258.014i 0.207520 0.500998i
\(516\) 0 0
\(517\) −14.3719 34.6968i −0.0277986 0.0671117i
\(518\) 12.0942 + 11.0627i 0.0233478 + 0.0213566i
\(519\) 0 0
\(520\) 406.308 236.016i 0.781362 0.453877i
\(521\) 11.8175 + 11.8175i 0.0226824 + 0.0226824i 0.718357 0.695675i \(-0.244894\pi\)
−0.695675 + 0.718357i \(0.744894\pi\)
\(522\) 0 0
\(523\) 141.420 + 341.417i 0.270401 + 0.652806i 0.999501 0.0316019i \(-0.0100609\pi\)
−0.729100 + 0.684408i \(0.760061\pi\)
\(524\) −522.546 + 273.191i −0.997225 + 0.521357i
\(525\) 0 0
\(526\) −890.705 + 416.298i −1.69335 + 0.791441i
\(527\) −1024.27 −1.94359
\(528\) 0 0
\(529\) 60.8334i 0.114997i
\(530\) −423.976 + 198.158i −0.799955 + 0.373883i
\(531\) 0 0
\(532\) −31.6804 + 101.098i −0.0595495 + 0.190034i
\(533\) 316.275 131.006i 0.593387 0.245789i
\(534\) 0 0
\(535\) −38.0996 + 38.0996i −0.0712142 + 0.0712142i
\(536\) 26.2286 + 195.239i 0.0489340 + 0.364251i
\(537\) 0 0
\(538\) −300.182 274.580i −0.557959 0.510372i
\(539\) 354.185 146.708i 0.657115 0.272186i
\(540\) 0 0
\(541\) −117.048 48.4829i −0.216355 0.0896172i 0.271874 0.962333i \(-0.412357\pi\)
−0.488229 + 0.872716i \(0.662357\pi\)
\(542\) 259.591 715.178i 0.478949 1.31952i
\(543\) 0 0
\(544\) 103.422 602.025i 0.190114 1.10666i
\(545\) −346.180 −0.635193
\(546\) 0 0
\(547\) −113.911 + 275.005i −0.208247 + 0.502752i −0.993147 0.116870i \(-0.962714\pi\)
0.784901 + 0.619622i \(0.212714\pi\)
\(548\) −70.3876 788.534i −0.128445 1.43893i
\(549\) 0 0
\(550\) −134.978 + 147.563i −0.245415 + 0.268297i
\(551\) −504.205 504.205i −0.915072 0.915072i
\(552\) 0 0
\(553\) −41.0237 41.0237i −0.0741838 0.0741838i
\(554\) 12.5310 + 281.321i 0.0226191 + 0.507800i
\(555\) 0 0
\(556\) −8.22392 + 26.2440i −0.0147912 + 0.0472015i
\(557\) −87.2197 + 210.567i −0.156588 + 0.378037i −0.982631 0.185570i \(-0.940587\pi\)
0.826043 + 0.563607i \(0.190587\pi\)
\(558\) 0 0
\(559\) −887.896 −1.58836
\(560\) 45.3989 + 9.89703i 0.0810695 + 0.0176733i
\(561\) 0 0
\(562\) 48.6084 + 104.002i 0.0864918 + 0.185057i
\(563\) −697.221 288.798i −1.23840 0.512963i −0.335188 0.942151i \(-0.608800\pi\)
−0.903215 + 0.429188i \(0.858800\pi\)
\(564\) 0 0
\(565\) −268.074 + 111.040i −0.474466 + 0.196530i
\(566\) 42.6218 + 956.861i 0.0753035 + 1.69057i
\(567\) 0 0
\(568\) 1040.33 + 275.812i 1.83157 + 0.485584i
\(569\) 252.850 252.850i 0.444376 0.444376i −0.449104 0.893480i \(-0.648257\pi\)
0.893480 + 0.449104i \(0.148257\pi\)
\(570\) 0 0
\(571\) 352.993 146.215i 0.618202 0.256068i −0.0515290 0.998672i \(-0.516409\pi\)
0.669731 + 0.742604i \(0.266409\pi\)
\(572\) 406.152 + 339.584i 0.710055 + 0.593679i
\(573\) 0 0
\(574\) 31.8209 + 11.5501i 0.0554371 + 0.0201222i
\(575\) 272.695i 0.474252i
\(576\) 0 0
\(577\) −197.099 −0.341593 −0.170797 0.985306i \(-0.554634\pi\)
−0.170797 + 0.985306i \(0.554634\pi\)
\(578\) 51.4414 141.722i 0.0889990 0.245194i
\(579\) 0 0
\(580\) −200.596 + 239.918i −0.345855 + 0.413651i
\(581\) −4.96141 11.9779i −0.00853944 0.0206160i
\(582\) 0 0
\(583\) −372.849 372.849i −0.639535 0.639535i
\(584\) 405.986 + 107.635i 0.695181 + 0.184306i
\(585\) 0 0
\(586\) −737.536 + 32.8523i −1.25859 + 0.0560620i
\(587\) 238.745 + 576.382i 0.406721 + 0.981912i 0.985994 + 0.166778i \(0.0533365\pi\)
−0.579273 + 0.815134i \(0.696664\pi\)
\(588\) 0 0
\(589\) 659.396 1591.92i 1.11952 2.70276i
\(590\) −293.228 + 137.049i −0.496997 + 0.232287i
\(591\) 0 0
\(592\) 133.778 85.8901i 0.225977 0.145085i
\(593\) 276.598i 0.466438i −0.972424 0.233219i \(-0.925074\pi\)
0.972424 0.233219i \(-0.0749260\pi\)
\(594\) 0 0
\(595\) 51.2157 + 21.2142i 0.0860768 + 0.0356542i
\(596\) −557.124 174.582i −0.934772 0.292923i
\(597\) 0 0
\(598\) 721.179 32.1237i 1.20598 0.0537186i
\(599\) 710.727 710.727i 1.18652 1.18652i 0.208501 0.978022i \(-0.433141\pi\)
0.978022 0.208501i \(-0.0668585\pi\)
\(600\) 0 0
\(601\) −215.219 + 215.219i −0.358102 + 0.358102i −0.863113 0.505011i \(-0.831488\pi\)
0.505011 + 0.863113i \(0.331488\pi\)
\(602\) −64.7860 59.2605i −0.107618 0.0984394i
\(603\) 0 0
\(604\) 740.498 66.0997i 1.22599 0.109437i
\(605\) −188.839 78.2195i −0.312130 0.129288i
\(606\) 0 0
\(607\) 683.779i 1.12649i −0.826290 0.563245i \(-0.809553\pi\)
0.826290 0.563245i \(-0.190447\pi\)
\(608\) 869.086 + 548.303i 1.42942 + 0.901815i
\(609\) 0 0
\(610\) −198.785 72.1536i −0.325877 0.118285i
\(611\) 30.2180 72.9527i 0.0494566 0.119399i
\(612\) 0 0
\(613\) −296.111 714.875i −0.483052 1.16619i −0.958152 0.286259i \(-0.907588\pi\)
0.475100 0.879932i \(-0.342412\pi\)
\(614\) −40.2635 + 44.0176i −0.0655757 + 0.0716900i
\(615\) 0 0
\(616\) 6.97039 + 51.8856i 0.0113156 + 0.0842299i
\(617\) 275.822 + 275.822i 0.447037 + 0.447037i 0.894368 0.447331i \(-0.147626\pi\)
−0.447331 + 0.894368i \(0.647626\pi\)
\(618\) 0 0
\(619\) 201.130 + 485.570i 0.324927 + 0.784443i 0.998954 + 0.0457357i \(0.0145632\pi\)
−0.674027 + 0.738707i \(0.735437\pi\)
\(620\) −721.128 225.975i −1.16311 0.364476i
\(621\) 0 0
\(622\) −314.389 672.663i −0.505449 1.08145i
\(623\) 70.9681 0.113913
\(624\) 0 0
\(625\) 151.085i 0.241735i
\(626\) −414.775 887.448i −0.662581 1.41765i
\(627\) 0 0
\(628\) 304.451 + 582.338i 0.484794 + 0.927289i
\(629\) 175.231 72.5829i 0.278586 0.115394i
\(630\) 0 0
\(631\) 48.9545 48.9545i 0.0775823 0.0775823i −0.667251 0.744833i \(-0.732529\pi\)
0.744833 + 0.667251i \(0.232529\pi\)
\(632\) −486.580 + 282.644i −0.769906 + 0.447222i
\(633\) 0 0
\(634\) 55.2838 60.4385i 0.0871984 0.0953288i
\(635\) 196.792 81.5139i 0.309909 0.128368i
\(636\) 0 0
\(637\) 744.702 + 308.466i 1.16908 + 0.484248i
\(638\) −331.205 120.218i −0.519129 0.188430i
\(639\) 0 0
\(640\) 205.632 401.032i 0.321299 0.626612i
\(641\) −320.295 −0.499680 −0.249840 0.968287i \(-0.580378\pi\)
−0.249840 + 0.968287i \(0.580378\pi\)
\(642\) 0 0
\(643\) 39.8184 96.1302i 0.0619260 0.149503i −0.889887 0.456180i \(-0.849217\pi\)
0.951813 + 0.306677i \(0.0992173\pi\)
\(644\) 54.7653 + 45.7894i 0.0850394 + 0.0711016i
\(645\) 0 0
\(646\) 904.612 + 827.459i 1.40033 + 1.28090i
\(647\) 134.372 + 134.372i 0.207684 + 0.207684i 0.803282 0.595598i \(-0.203085\pi\)
−0.595598 + 0.803282i \(0.703085\pi\)
\(648\) 0 0
\(649\) −257.868 257.868i −0.397331 0.397331i
\(650\) −420.068 + 18.7113i −0.646259 + 0.0287865i
\(651\) 0 0
\(652\) −700.736 + 366.350i −1.07475 + 0.561887i
\(653\) 358.760 866.123i 0.549403 1.32638i −0.368521 0.929619i \(-0.620136\pi\)
0.917924 0.396756i \(-0.129864\pi\)
\(654\) 0 0
\(655\) −519.029 −0.792410
\(656\) 187.381 269.624i 0.285641 0.411012i
\(657\) 0 0
\(658\) 7.07394 3.30622i 0.0107507 0.00502465i
\(659\) −596.224 246.964i −0.904741 0.374756i −0.118700 0.992930i \(-0.537873\pi\)
−0.786041 + 0.618174i \(0.787873\pi\)
\(660\) 0 0
\(661\) 16.3196 6.75978i 0.0246892 0.0102266i −0.370305 0.928910i \(-0.620747\pi\)
0.394994 + 0.918684i \(0.370747\pi\)
\(662\) −646.628 + 28.8030i −0.976779 + 0.0435090i
\(663\) 0 0
\(664\) −124.629 + 16.7429i −0.187695 + 0.0252152i
\(665\) −65.9422 + 65.9422i −0.0991612 + 0.0991612i
\(666\) 0 0
\(667\) −443.881 + 183.862i −0.665489 + 0.275655i
\(668\) 74.6959 + 836.799i 0.111820 + 1.25269i
\(669\) 0 0
\(670\) −59.1625 + 162.994i −0.0883022 + 0.243275i
\(671\) 238.266i 0.355091i
\(672\) 0 0
\(673\) −334.752 −0.497403 −0.248701 0.968580i \(-0.580004\pi\)
−0.248701 + 0.968580i \(0.580004\pi\)
\(674\) 1041.33 + 377.974i 1.54500 + 0.560792i
\(675\) 0 0
\(676\) 38.8654 + 435.399i 0.0574932 + 0.644082i
\(677\) −294.364 710.658i −0.434807 1.04972i −0.977717 0.209926i \(-0.932678\pi\)
0.542911 0.839790i \(-0.317322\pi\)
\(678\) 0 0
\(679\) 18.5633 + 18.5633i 0.0273392 + 0.0273392i
\(680\) 326.193 427.436i 0.479695 0.628583i
\(681\) 0 0
\(682\) −37.8886 850.601i −0.0555551 1.24721i
\(683\) 118.311 + 285.628i 0.173223 + 0.418196i 0.986518 0.163655i \(-0.0523285\pi\)
−0.813295 + 0.581851i \(0.802328\pi\)
\(684\) 0 0
\(685\) 266.674 643.807i 0.389305 0.939865i
\(686\) 67.9750 + 145.438i 0.0990889 + 0.212009i
\(687\) 0 0
\(688\) −716.621 + 460.095i −1.04160 + 0.668743i
\(689\) 1108.67i 1.60909i
\(690\) 0 0
\(691\) −13.1275 5.43758i −0.0189978 0.00786914i 0.373164 0.927765i \(-0.378273\pi\)
−0.392162 + 0.919896i \(0.628273\pi\)
\(692\) 138.104 72.2020i 0.199573 0.104338i
\(693\) 0 0
\(694\) −14.4107 323.522i −0.0207647 0.466169i
\(695\) −17.1180 + 17.1180i −0.0246302 + 0.0246302i
\(696\) 0 0
\(697\) 276.995 276.995i 0.397410 0.397410i
\(698\) 517.942 566.235i 0.742038 0.811225i
\(699\) 0 0
\(700\) −31.8994 26.6712i −0.0455706 0.0381017i
\(701\) 100.100 + 41.4627i 0.142796 + 0.0591480i 0.452937 0.891543i \(-0.350376\pi\)
−0.310141 + 0.950691i \(0.600376\pi\)
\(702\) 0 0
\(703\) 319.070i 0.453869i
\(704\) 503.773 + 63.6166i 0.715587 + 0.0903645i
\(705\) 0 0
\(706\) −245.832 + 677.273i −0.348204 + 0.959310i
\(707\) 9.10558 21.9828i 0.0128792 0.0310931i
\(708\) 0 0
\(709\) 273.663 + 660.681i 0.385985 + 0.931849i 0.990781 + 0.135470i \(0.0432543\pi\)
−0.604797 + 0.796380i \(0.706746\pi\)
\(710\) 699.036 + 639.417i 0.984558 + 0.900587i
\(711\) 0 0
\(712\) 176.398 665.352i 0.247750 0.934483i
\(713\) −820.958 820.958i −1.15141 1.15141i
\(714\) 0 0
\(715\) 178.332 + 430.532i 0.249416 + 0.602143i
\(716\) 555.395 + 1062.33i 0.775692 + 1.48370i
\(717\) 0 0
\(718\) 235.750 110.185i 0.328343 0.153461i
\(719\) 532.079 0.740026 0.370013 0.929026i \(-0.379353\pi\)
0.370013 + 0.929026i \(0.379353\pi\)
\(720\) 0 0
\(721\) 65.4218i 0.0907375i
\(722\) −1214.31 + 567.545i −1.68187 + 0.786074i
\(723\) 0 0
\(724\) 339.477 + 106.380i 0.468891 + 0.146933i
\(725\) 258.549 107.095i 0.356620 0.147717i
\(726\) 0 0
\(727\) 305.054 305.054i 0.419606 0.419606i −0.465462 0.885068i \(-0.654112\pi\)
0.885068 + 0.465462i \(0.154112\pi\)
\(728\) −66.7777 + 87.5042i −0.0917276 + 0.120198i
\(729\) 0 0
\(730\) 272.797 + 249.530i 0.373694 + 0.341823i
\(731\) −938.673 + 388.811i −1.28409 + 0.531889i
\(732\) 0 0
\(733\) 344.710 + 142.783i 0.470272 + 0.194793i 0.605218 0.796060i \(-0.293086\pi\)
−0.134946 + 0.990853i \(0.543086\pi\)
\(734\) −173.676 + 478.481i −0.236616 + 0.651882i
\(735\) 0 0
\(736\) 565.418 399.632i 0.768230 0.542978i
\(737\) −195.367 −0.265084
\(738\) 0 0
\(739\) 107.676 259.954i 0.145706 0.351765i −0.834131 0.551567i \(-0.814030\pi\)
0.979836 + 0.199803i \(0.0640301\pi\)
\(740\) 139.382 12.4418i 0.188354 0.0168132i
\(741\) 0 0
\(742\) 73.9953 80.8946i 0.0997241 0.109022i
\(743\) 470.112 + 470.112i 0.632721 + 0.632721i 0.948750 0.316029i \(-0.102350\pi\)
−0.316029 + 0.948750i \(0.602350\pi\)
\(744\) 0 0
\(745\) −363.391 363.391i −0.487773 0.487773i
\(746\) 42.4317 + 952.594i 0.0568790 + 1.27694i
\(747\) 0 0
\(748\) 578.083 + 181.150i 0.772839 + 0.242179i
\(749\) 4.83025 11.6612i 0.00644893 0.0155691i
\(750\) 0 0
\(751\) 844.801 1.12490 0.562451 0.826831i \(-0.309859\pi\)
0.562451 + 0.826831i \(0.309859\pi\)
\(752\) −13.4141 74.5387i −0.0178379 0.0991207i
\(753\) 0 0
\(754\) −313.684 671.153i −0.416026 0.890123i
\(755\) 604.588 + 250.428i 0.800778 + 0.331693i
\(756\) 0 0
\(757\) 1050.78 435.247i 1.38808 0.574962i 0.441452 0.897285i \(-0.354464\pi\)
0.946630 + 0.322322i \(0.104464\pi\)
\(758\) 12.0379 + 270.252i 0.0158812 + 0.356533i
\(759\) 0 0
\(760\) 454.327 + 782.139i 0.597799 + 1.02913i
\(761\) 44.1359 44.1359i 0.0579972 0.0579972i −0.677513 0.735511i \(-0.736942\pi\)
0.735511 + 0.677513i \(0.236942\pi\)
\(762\) 0 0
\(763\) 74.9225 31.0339i 0.0981946 0.0406735i
\(764\) 458.903 548.860i 0.600659 0.718403i
\(765\) 0 0
\(766\) 343.066 + 124.524i 0.447867 + 0.162564i
\(767\) 766.771i 0.999701i
\(768\) 0 0
\(769\) 794.025 1.03254 0.516271 0.856425i \(-0.327320\pi\)
0.516271 + 0.856425i \(0.327320\pi\)
\(770\) −15.7227 + 43.3164i −0.0204191 + 0.0562551i
\(771\) 0 0
\(772\) −604.637 505.539i −0.783209 0.654843i
\(773\) 395.664 + 955.218i 0.511856 + 1.23573i 0.942803 + 0.333351i \(0.108180\pi\)
−0.430947 + 0.902377i \(0.641820\pi\)
\(774\) 0 0
\(775\) 478.187 + 478.187i 0.617016 + 0.617016i
\(776\) 220.179 127.897i 0.283735 0.164816i
\(777\) 0 0
\(778\) −704.736 + 31.3913i −0.905830 + 0.0403487i
\(779\) 252.184 + 608.826i 0.323728 + 0.781548i
\(780\) 0 0
\(781\) −408.472 + 986.138i −0.523011 + 1.26266i
\(782\) 748.355 349.766i 0.956975 0.447271i
\(783\) 0 0
\(784\) 760.892 136.931i 0.970526 0.174657i
\(785\) 578.418i 0.736838i
\(786\) 0 0
\(787\) −445.085 184.360i −0.565547 0.234257i 0.0815444 0.996670i \(-0.474015\pi\)
−0.647091 + 0.762413i \(0.724015\pi\)