Properties

Label 288.3.u.a.19.5
Level $288$
Weight $3$
Character 288.19
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 19.5
Character \(\chi\) \(=\) 288.19
Dual form 288.3.u.a.91.5

$q$-expansion

\(f(q)\) \(=\) \(q+(0.360897 - 1.96717i) q^{2} +(-3.73951 - 1.41989i) q^{4} +(0.452310 - 0.187353i) q^{5} +(0.429965 + 0.429965i) q^{7} +(-4.14274 + 6.84381i) q^{8} +O(q^{10})\) \(q+(0.360897 - 1.96717i) q^{2} +(-3.73951 - 1.41989i) q^{4} +(0.452310 - 0.187353i) q^{5} +(0.429965 + 0.429965i) q^{7} +(-4.14274 + 6.84381i) q^{8} +(-0.205317 - 0.957385i) q^{10} +(-17.3350 + 7.18039i) q^{11} +(-19.9596 - 8.26755i) q^{13} +(1.00099 - 0.690640i) q^{14} +(11.9678 + 10.6194i) q^{16} -13.5961i q^{17} +(-3.45810 + 8.34859i) q^{19} +(-1.95744 + 0.0583763i) q^{20} +(7.86888 + 36.6922i) q^{22} +(16.8850 - 16.8850i) q^{23} +(-17.5082 + 17.5082i) q^{25} +(-23.4670 + 36.2802i) q^{26} +(-0.997353 - 2.21836i) q^{28} +(-13.8385 + 33.4091i) q^{29} +24.5614i q^{31} +(25.2093 - 19.7102i) q^{32} +(-26.7458 - 4.90679i) q^{34} +(0.275033 + 0.113922i) q^{35} +(9.89595 - 4.09904i) q^{37} +(15.1751 + 9.81565i) q^{38} +(-0.591598 + 3.87168i) q^{40} +(-14.4867 - 14.4867i) q^{41} +(17.8494 - 7.39348i) q^{43} +(75.0197 - 2.23730i) q^{44} +(-27.1219 - 39.3094i) q^{46} -43.6087 q^{47} -48.6303i q^{49} +(28.1229 + 40.7602i) q^{50} +(62.9001 + 59.2571i) q^{52} +(-28.0630 - 67.7501i) q^{53} +(-6.49552 + 6.49552i) q^{55} +(-4.72383 + 1.16136i) q^{56} +(60.7270 + 39.2799i) q^{58} +(-1.70130 - 4.10730i) q^{59} +(3.53360 - 8.53087i) q^{61} +(48.3165 + 8.86416i) q^{62} +(-29.6753 - 56.7043i) q^{64} -10.5769 q^{65} +(-0.300169 - 0.124334i) q^{67} +(-19.3050 + 50.8427i) q^{68} +(0.323363 - 0.499921i) q^{70} +(29.0914 + 29.0914i) q^{71} +(-68.2273 - 68.2273i) q^{73} +(-4.49208 - 20.9463i) q^{74} +(24.7857 - 26.3095i) q^{76} +(-10.5408 - 4.36612i) q^{77} +67.7588 q^{79} +(7.40274 + 2.56105i) q^{80} +(-33.7260 + 23.2695i) q^{82} +(16.4008 - 39.5950i) q^{83} +(-2.54727 - 6.14965i) q^{85} +(-8.10241 - 37.7811i) q^{86} +(22.6733 - 148.384i) q^{88} +(45.3745 - 45.3745i) q^{89} +(-5.02718 - 12.1367i) q^{91} +(-87.1165 + 39.1667i) q^{92} +(-15.7383 + 85.7857i) q^{94} +4.42403i q^{95} -119.312 q^{97} +(-95.6639 - 17.5505i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 28q + 4q^{2} - 4q^{4} + 4q^{5} - 4q^{7} + 4q^{8} + O(q^{10}) \) \( 28q + 4q^{2} - 4q^{4} + 4q^{5} - 4q^{7} + 4q^{8} - 44q^{10} + 4q^{11} - 4q^{13} + 20q^{14} + 16q^{16} - 4q^{19} - 76q^{20} + 144q^{22} + 68q^{23} - 4q^{25} - 96q^{26} + 56q^{28} + 4q^{29} + 24q^{32} - 48q^{34} - 92q^{35} - 4q^{37} + 396q^{38} - 408q^{40} + 4q^{41} + 92q^{43} + 188q^{44} - 36q^{46} + 8q^{47} - 308q^{50} + 420q^{52} + 164q^{53} + 252q^{55} - 552q^{56} + 528q^{58} - 124q^{59} - 68q^{61} - 216q^{62} - 232q^{64} + 8q^{65} - 164q^{67} + 368q^{68} - 664q^{70} + 260q^{71} - 4q^{73} + 532q^{74} - 516q^{76} - 220q^{77} - 520q^{79} - 312q^{80} + 636q^{82} + 484q^{83} + 96q^{85} - 688q^{86} + 672q^{88} + 4q^{89} - 196q^{91} - 616q^{92} + 40q^{94} - 8q^{97} + 328q^{98} + O(q^{100}) \)

Character values

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

\(n\) \(37\) \(65\) \(127\)
\(\chi(n)\) \(e\left(\frac{7}{8}\right)\) \(1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.360897 1.96717i 0.180449 0.983584i
\(3\) 0 0
\(4\) −3.73951 1.41989i −0.934877 0.354973i
\(5\) 0.452310 0.187353i 0.0904620 0.0374706i −0.336994 0.941507i \(-0.609410\pi\)
0.427456 + 0.904036i \(0.359410\pi\)
\(6\) 0 0
\(7\) 0.429965 + 0.429965i 0.0614236 + 0.0614236i 0.737151 0.675728i \(-0.236170\pi\)
−0.675728 + 0.737151i \(0.736170\pi\)
\(8\) −4.14274 + 6.84381i −0.517843 + 0.855476i
\(9\) 0 0
\(10\) −0.205317 0.957385i −0.0205317 0.0957385i
\(11\) −17.3350 + 7.18039i −1.57591 + 0.652763i −0.987759 0.155990i \(-0.950143\pi\)
−0.588149 + 0.808752i \(0.700143\pi\)
\(12\) 0 0
\(13\) −19.9596 8.26755i −1.53536 0.635965i −0.554761 0.832010i \(-0.687190\pi\)
−0.980595 + 0.196044i \(0.937190\pi\)
\(14\) 1.00099 0.690640i 0.0714991 0.0493315i
\(15\) 0 0
\(16\) 11.9678 + 10.6194i 0.747988 + 0.663712i
\(17\) 13.5961i 0.799770i −0.916565 0.399885i \(-0.869050\pi\)
0.916565 0.399885i \(-0.130950\pi\)
\(18\) 0 0
\(19\) −3.45810 + 8.34859i −0.182005 + 0.439399i −0.988380 0.152006i \(-0.951427\pi\)
0.806374 + 0.591405i \(0.201427\pi\)
\(20\) −1.95744 + 0.0583763i −0.0978718 + 0.00291881i
\(21\) 0 0
\(22\) 7.86888 + 36.6922i 0.357677 + 1.66783i
\(23\) 16.8850 16.8850i 0.734131 0.734131i −0.237304 0.971435i \(-0.576264\pi\)
0.971435 + 0.237304i \(0.0762639\pi\)
\(24\) 0 0
\(25\) −17.5082 + 17.5082i −0.700327 + 0.700327i
\(26\) −23.4670 + 36.2802i −0.902579 + 1.39539i
\(27\) 0 0
\(28\) −0.997353 2.21836i −0.0356197 0.0792271i
\(29\) −13.8385 + 33.4091i −0.477190 + 1.15204i 0.483732 + 0.875216i \(0.339281\pi\)
−0.960921 + 0.276821i \(0.910719\pi\)
\(30\) 0 0
\(31\) 24.5614i 0.792305i 0.918185 + 0.396152i \(0.129655\pi\)
−0.918185 + 0.396152i \(0.870345\pi\)
\(32\) 25.2093 19.7102i 0.787790 0.615944i
\(33\) 0 0
\(34\) −26.7458 4.90679i −0.786642 0.144317i
\(35\) 0.275033 + 0.113922i 0.00785807 + 0.00325492i
\(36\) 0 0
\(37\) 9.89595 4.09904i 0.267458 0.110785i −0.244924 0.969542i \(-0.578763\pi\)
0.512382 + 0.858757i \(0.328763\pi\)
\(38\) 15.1751 + 9.81565i 0.399344 + 0.258306i
\(39\) 0 0
\(40\) −0.591598 + 3.87168i −0.0147899 + 0.0967919i
\(41\) −14.4867 14.4867i −0.353334 0.353334i 0.508015 0.861348i \(-0.330380\pi\)
−0.861348 + 0.508015i \(0.830380\pi\)
\(42\) 0 0
\(43\) 17.8494 7.39348i 0.415103 0.171941i −0.165350 0.986235i \(-0.552875\pi\)
0.580453 + 0.814294i \(0.302875\pi\)
\(44\) 75.0197 2.23730i 1.70499 0.0508477i
\(45\) 0 0
\(46\) −27.1219 39.3094i −0.589607 0.854553i
\(47\) −43.6087 −0.927845 −0.463922 0.885876i \(-0.653558\pi\)
−0.463922 + 0.885876i \(0.653558\pi\)
\(48\) 0 0
\(49\) 48.6303i 0.992454i
\(50\) 28.1229 + 40.7602i 0.562458 + 0.815204i
\(51\) 0 0
\(52\) 62.9001 + 59.2571i 1.20962 + 1.13956i
\(53\) −28.0630 67.7501i −0.529490 1.27830i −0.931857 0.362825i \(-0.881812\pi\)
0.402367 0.915478i \(-0.368188\pi\)
\(54\) 0 0
\(55\) −6.49552 + 6.49552i −0.118100 + 0.118100i
\(56\) −4.72383 + 1.16136i −0.0843541 + 0.0207386i
\(57\) 0 0
\(58\) 60.7270 + 39.2799i 1.04702 + 0.677240i
\(59\) −1.70130 4.10730i −0.0288356 0.0696153i 0.908806 0.417219i \(-0.136995\pi\)
−0.937641 + 0.347604i \(0.886995\pi\)
\(60\) 0 0
\(61\) 3.53360 8.53087i 0.0579279 0.139850i −0.892266 0.451511i \(-0.850885\pi\)
0.950193 + 0.311661i \(0.100885\pi\)
\(62\) 48.3165 + 8.86416i 0.779299 + 0.142970i
\(63\) 0 0
\(64\) −29.6753 56.7043i −0.463677 0.886004i
\(65\) −10.5769 −0.162721
\(66\) 0 0
\(67\) −0.300169 0.124334i −0.00448013 0.00185573i 0.380442 0.924805i \(-0.375772\pi\)
−0.384922 + 0.922949i \(0.625772\pi\)
\(68\) −19.3050 + 50.8427i −0.283897 + 0.747686i
\(69\) 0 0
\(70\) 0.323363 0.499921i 0.00461947 0.00714173i
\(71\) 29.0914 + 29.0914i 0.409738 + 0.409738i 0.881647 0.471909i \(-0.156435\pi\)
−0.471909 + 0.881647i \(0.656435\pi\)
\(72\) 0 0
\(73\) −68.2273 68.2273i −0.934620 0.934620i 0.0633700 0.997990i \(-0.479815\pi\)
−0.997990 + 0.0633700i \(0.979815\pi\)
\(74\) −4.49208 20.9463i −0.0607037 0.283059i
\(75\) 0 0
\(76\) 24.7857 26.3095i 0.326127 0.346177i
\(77\) −10.5408 4.36612i −0.136893 0.0567029i
\(78\) 0 0
\(79\) 67.7588 0.857706 0.428853 0.903374i \(-0.358918\pi\)
0.428853 + 0.903374i \(0.358918\pi\)
\(80\) 7.40274 + 2.56105i 0.0925342 + 0.0320131i
\(81\) 0 0
\(82\) −33.7260 + 23.2695i −0.411292 + 0.283775i
\(83\) 16.4008 39.5950i 0.197600 0.477048i −0.793758 0.608234i \(-0.791878\pi\)
0.991358 + 0.131186i \(0.0418784\pi\)
\(84\) 0 0
\(85\) −2.54727 6.14965i −0.0299679 0.0723488i
\(86\) −8.10241 37.7811i −0.0942140 0.439315i
\(87\) 0 0
\(88\) 22.6733 148.384i 0.257651 1.68618i
\(89\) 45.3745 45.3745i 0.509825 0.509825i −0.404647 0.914473i \(-0.632606\pi\)
0.914473 + 0.404647i \(0.132606\pi\)
\(90\) 0 0
\(91\) −5.02718 12.1367i −0.0552438 0.133370i
\(92\) −87.1165 + 39.1667i −0.946919 + 0.425725i
\(93\) 0 0
\(94\) −15.7383 + 85.7857i −0.167428 + 0.912614i
\(95\) 4.42403i 0.0465688i
\(96\) 0 0
\(97\) −119.312 −1.23002 −0.615012 0.788518i \(-0.710849\pi\)
−0.615012 + 0.788518i \(0.710849\pi\)
\(98\) −95.6639 17.5505i −0.976163 0.179087i
\(99\) 0 0
\(100\) 90.3317 40.6122i 0.903317 0.406122i
\(101\) −98.7914 + 40.9207i −0.978133 + 0.405156i −0.813734 0.581238i \(-0.802569\pi\)
−0.164399 + 0.986394i \(0.552569\pi\)
\(102\) 0 0
\(103\) 127.634 + 127.634i 1.23916 + 1.23916i 0.960344 + 0.278817i \(0.0899423\pi\)
0.278817 + 0.960344i \(0.410058\pi\)
\(104\) 139.269 102.349i 1.33913 0.984130i
\(105\) 0 0
\(106\) −143.404 + 30.7538i −1.35286 + 0.290131i
\(107\) −94.9289 + 39.3208i −0.887186 + 0.367484i −0.779279 0.626677i \(-0.784415\pi\)
−0.107906 + 0.994161i \(0.534415\pi\)
\(108\) 0 0
\(109\) −27.8610 11.5404i −0.255605 0.105875i 0.251202 0.967935i \(-0.419174\pi\)
−0.506807 + 0.862060i \(0.669174\pi\)
\(110\) 10.4336 + 15.1220i 0.0948507 + 0.137473i
\(111\) 0 0
\(112\) 0.579776 + 9.71170i 0.00517658 + 0.0867116i
\(113\) 140.786i 1.24590i −0.782263 0.622948i \(-0.785935\pi\)
0.782263 0.622948i \(-0.214065\pi\)
\(114\) 0 0
\(115\) 4.47380 10.8007i 0.0389026 0.0939193i
\(116\) 99.1864 105.284i 0.855055 0.907623i
\(117\) 0 0
\(118\) −8.69375 + 1.86443i −0.0736758 + 0.0158003i
\(119\) 5.84584 5.84584i 0.0491247 0.0491247i
\(120\) 0 0
\(121\) 163.384 163.384i 1.35028 1.35028i
\(122\) −15.5064 10.0300i −0.127102 0.0822128i
\(123\) 0 0
\(124\) 34.8746 91.8477i 0.281247 0.740707i
\(125\) −9.32274 + 22.5071i −0.0745819 + 0.180057i
\(126\) 0 0
\(127\) 163.979i 1.29117i −0.763687 0.645587i \(-0.776613\pi\)
0.763687 0.645587i \(-0.223387\pi\)
\(128\) −122.257 + 37.9120i −0.955130 + 0.296187i
\(129\) 0 0
\(130\) −3.81717 + 20.8065i −0.0293629 + 0.160050i
\(131\) 11.2279 + 4.65074i 0.0857090 + 0.0355018i 0.425126 0.905134i \(-0.360230\pi\)
−0.339417 + 0.940636i \(0.610230\pi\)
\(132\) 0 0
\(133\) −5.07646 + 2.10274i −0.0381689 + 0.0158101i
\(134\) −0.352916 + 0.545611i −0.00263370 + 0.00407172i
\(135\) 0 0
\(136\) 93.0490 + 56.3251i 0.684184 + 0.414155i
\(137\) −21.2983 21.2983i −0.155462 0.155462i 0.625090 0.780552i \(-0.285062\pi\)
−0.780552 + 0.625090i \(0.785062\pi\)
\(138\) 0 0
\(139\) −154.836 + 64.1351i −1.11393 + 0.461404i −0.862288 0.506418i \(-0.830969\pi\)
−0.251639 + 0.967821i \(0.580969\pi\)
\(140\) −0.866729 0.816529i −0.00619092 0.00583235i
\(141\) 0 0
\(142\) 67.7268 46.7287i 0.476949 0.329076i
\(143\) 405.364 2.83471
\(144\) 0 0
\(145\) 17.7039i 0.122096i
\(146\) −158.838 + 109.592i −1.08793 + 0.750627i
\(147\) 0 0
\(148\) −42.8262 + 1.27720i −0.289366 + 0.00862971i
\(149\) 90.9258 + 219.514i 0.610240 + 1.47325i 0.862737 + 0.505653i \(0.168748\pi\)
−0.252497 + 0.967598i \(0.581252\pi\)
\(150\) 0 0
\(151\) −82.0484 + 82.0484i −0.543367 + 0.543367i −0.924514 0.381147i \(-0.875529\pi\)
0.381147 + 0.924514i \(0.375529\pi\)
\(152\) −42.8101 58.2526i −0.281645 0.383241i
\(153\) 0 0
\(154\) −12.3930 + 19.1597i −0.0804742 + 0.124414i
\(155\) 4.60166 + 11.1094i 0.0296881 + 0.0716735i
\(156\) 0 0
\(157\) −52.8906 + 127.689i −0.336883 + 0.813307i 0.661129 + 0.750272i \(0.270078\pi\)
−0.998011 + 0.0630341i \(0.979922\pi\)
\(158\) 24.4540 133.293i 0.154772 0.843627i
\(159\) 0 0
\(160\) 7.70964 13.6382i 0.0481853 0.0852385i
\(161\) 14.5199 0.0901859
\(162\) 0 0
\(163\) 54.8297 + 22.7112i 0.336379 + 0.139333i 0.544478 0.838775i \(-0.316728\pi\)
−0.208099 + 0.978108i \(0.566728\pi\)
\(164\) 33.6035 + 74.7426i 0.204900 + 0.455747i
\(165\) 0 0
\(166\) −71.9710 46.5528i −0.433560 0.280439i
\(167\) 98.7296 + 98.7296i 0.591195 + 0.591195i 0.937954 0.346759i \(-0.112718\pi\)
−0.346759 + 0.937954i \(0.612718\pi\)
\(168\) 0 0
\(169\) 210.533 + 210.533i 1.24576 + 1.24576i
\(170\) −13.0167 + 2.79151i −0.0765688 + 0.0164207i
\(171\) 0 0
\(172\) −77.2460 + 2.30369i −0.449105 + 0.0133936i
\(173\) 6.09221 + 2.52348i 0.0352151 + 0.0145866i 0.400221 0.916418i \(-0.368933\pi\)
−0.365006 + 0.931005i \(0.618933\pi\)
\(174\) 0 0
\(175\) −15.0558 −0.0860332
\(176\) −283.713 98.1534i −1.61201 0.557690i
\(177\) 0 0
\(178\) −72.8837 105.635i −0.409459 0.593454i
\(179\) −80.6673 + 194.748i −0.450655 + 1.08798i 0.521418 + 0.853301i \(0.325403\pi\)
−0.972073 + 0.234677i \(0.924597\pi\)
\(180\) 0 0
\(181\) −59.7464 144.241i −0.330091 0.796910i −0.998584 0.0531918i \(-0.983061\pi\)
0.668493 0.743718i \(-0.266939\pi\)
\(182\) −25.6892 + 5.50922i −0.141150 + 0.0302704i
\(183\) 0 0
\(184\) 45.6075 + 185.508i 0.247867 + 1.00820i
\(185\) 3.70807 3.70807i 0.0200436 0.0200436i
\(186\) 0 0
\(187\) 97.6252 + 235.688i 0.522060 + 1.26036i
\(188\) 163.075 + 61.9196i 0.867421 + 0.329360i
\(189\) 0 0
\(190\) 8.70282 + 1.59662i 0.0458043 + 0.00840327i
\(191\) 107.812i 0.564460i 0.959347 + 0.282230i \(0.0910741\pi\)
−0.959347 + 0.282230i \(0.908926\pi\)
\(192\) 0 0
\(193\) −174.830 −0.905855 −0.452927 0.891547i \(-0.649620\pi\)
−0.452927 + 0.891547i \(0.649620\pi\)
\(194\) −43.0595 + 234.707i −0.221956 + 1.20983i
\(195\) 0 0
\(196\) −69.0497 + 181.853i −0.352294 + 0.927822i
\(197\) 108.472 44.9304i 0.550618 0.228073i −0.0899887 0.995943i \(-0.528683\pi\)
0.640606 + 0.767870i \(0.278683\pi\)
\(198\) 0 0
\(199\) 190.347 + 190.347i 0.956516 + 0.956516i 0.999093 0.0425770i \(-0.0135568\pi\)
−0.0425770 + 0.999093i \(0.513557\pi\)
\(200\) −47.2907 192.355i −0.236453 0.961773i
\(201\) 0 0
\(202\) 44.8445 + 209.108i 0.222002 + 1.03519i
\(203\) −20.3148 + 8.41467i −0.100073 + 0.0414516i
\(204\) 0 0
\(205\) −9.26659 3.83835i −0.0452029 0.0187237i
\(206\) 297.140 205.014i 1.44242 0.995215i
\(207\) 0 0
\(208\) −151.077 310.904i −0.726331 1.49473i
\(209\) 169.553i 0.811259i
\(210\) 0 0
\(211\) 86.6725 209.246i 0.410770 0.991686i −0.574162 0.818742i \(-0.694672\pi\)
0.984932 0.172944i \(-0.0553281\pi\)
\(212\) 8.74400 + 293.198i 0.0412453 + 1.38301i
\(213\) 0 0
\(214\) 43.0911 + 200.932i 0.201360 + 0.938934i
\(215\) 6.68829 6.68829i 0.0311083 0.0311083i
\(216\) 0 0
\(217\) −10.5606 + 10.5606i −0.0486662 + 0.0486662i
\(218\) −32.7569 + 50.6423i −0.150261 + 0.232304i
\(219\) 0 0
\(220\) 33.5130 15.0671i 0.152332 0.0684869i
\(221\) −112.406 + 271.373i −0.508626 + 1.22793i
\(222\) 0 0
\(223\) 103.845i 0.465671i 0.972516 + 0.232836i \(0.0748004\pi\)
−0.972516 + 0.232836i \(0.925200\pi\)
\(224\) 19.3138 + 2.36441i 0.0862223 + 0.0105554i
\(225\) 0 0
\(226\) −276.951 50.8094i −1.22544 0.224820i
\(227\) −106.086 43.9421i −0.467338 0.193578i 0.136572 0.990630i \(-0.456391\pi\)
−0.603910 + 0.797052i \(0.706391\pi\)
\(228\) 0 0
\(229\) 46.1162 19.1019i 0.201381 0.0834146i −0.279714 0.960083i \(-0.590240\pi\)
0.481094 + 0.876669i \(0.340240\pi\)
\(230\) −19.6322 12.6987i −0.0853576 0.0552116i
\(231\) 0 0
\(232\) −171.316 233.113i −0.738431 1.00480i
\(233\) 62.7031 + 62.7031i 0.269112 + 0.269112i 0.828742 0.559630i \(-0.189057\pi\)
−0.559630 + 0.828742i \(0.689057\pi\)
\(234\) 0 0
\(235\) −19.7247 + 8.17022i −0.0839347 + 0.0347669i
\(236\) 0.530099 + 17.7749i 0.00224618 + 0.0753175i
\(237\) 0 0
\(238\) −9.39001 13.6095i −0.0394538 0.0571828i
\(239\) −306.080 −1.28067 −0.640335 0.768095i \(-0.721205\pi\)
−0.640335 + 0.768095i \(0.721205\pi\)
\(240\) 0 0
\(241\) 245.242i 1.01760i −0.860884 0.508801i \(-0.830089\pi\)
0.860884 0.508801i \(-0.169911\pi\)
\(242\) −262.439 380.369i −1.08446 1.57177i
\(243\) 0 0
\(244\) −25.3268 + 26.8839i −0.103799 + 0.110180i
\(245\) −9.11102 21.9960i −0.0371878 0.0897794i
\(246\) 0 0
\(247\) 138.045 138.045i 0.558886 0.558886i
\(248\) −168.094 101.752i −0.677797 0.410290i
\(249\) 0 0
\(250\) 40.9107 + 26.4621i 0.163643 + 0.105849i
\(251\) −132.845 320.715i −0.529261 1.27775i −0.932008 0.362438i \(-0.881944\pi\)
0.402747 0.915311i \(-0.368056\pi\)
\(252\) 0 0
\(253\) −171.461 + 413.942i −0.677710 + 1.63614i
\(254\) −322.574 59.1796i −1.26998 0.232990i
\(255\) 0 0
\(256\) 30.4572 + 254.182i 0.118973 + 0.992897i
\(257\) 108.814 0.423399 0.211700 0.977335i \(-0.432100\pi\)
0.211700 + 0.977335i \(0.432100\pi\)
\(258\) 0 0
\(259\) 6.01735 + 2.49247i 0.0232330 + 0.00962343i
\(260\) 39.5523 + 15.0180i 0.152124 + 0.0577617i
\(261\) 0 0
\(262\) 13.2009 20.4087i 0.0503851 0.0778958i
\(263\) 150.151 + 150.151i 0.570916 + 0.570916i 0.932384 0.361468i \(-0.117724\pi\)
−0.361468 + 0.932384i \(0.617724\pi\)
\(264\) 0 0
\(265\) −25.3863 25.3863i −0.0957975 0.0957975i
\(266\) 2.30436 + 10.7451i 0.00866301 + 0.0403952i
\(267\) 0 0
\(268\) 0.945942 + 0.891155i 0.00352963 + 0.00332520i
\(269\) 255.485 + 105.825i 0.949758 + 0.393403i 0.803140 0.595791i \(-0.203161\pi\)
0.146618 + 0.989193i \(0.453161\pi\)
\(270\) 0 0
\(271\) −261.648 −0.965492 −0.482746 0.875760i \(-0.660361\pi\)
−0.482746 + 0.875760i \(0.660361\pi\)
\(272\) 144.382 162.716i 0.530817 0.598219i
\(273\) 0 0
\(274\) −49.5839 + 34.2109i −0.180963 + 0.124857i
\(275\) 177.789 429.220i 0.646504 1.56080i
\(276\) 0 0
\(277\) 120.123 + 290.003i 0.433658 + 1.04694i 0.978098 + 0.208143i \(0.0667420\pi\)
−0.544440 + 0.838799i \(0.683258\pi\)
\(278\) 70.2848 + 327.734i 0.252823 + 1.17890i
\(279\) 0 0
\(280\) −1.91905 + 1.41032i −0.00685375 + 0.00503685i
\(281\) −21.7898 + 21.7898i −0.0775437 + 0.0775437i −0.744815 0.667271i \(-0.767462\pi\)
0.667271 + 0.744815i \(0.267462\pi\)
\(282\) 0 0
\(283\) −155.937 376.466i −0.551016 1.33027i −0.916717 0.399537i \(-0.869171\pi\)
0.365702 0.930732i \(-0.380829\pi\)
\(284\) −67.4809 150.094i −0.237609 0.528501i
\(285\) 0 0
\(286\) 146.295 797.420i 0.511520 2.78818i
\(287\) 12.4575i 0.0434060i
\(288\) 0 0
\(289\) 104.146 0.360368
\(290\) 34.8266 + 6.38930i 0.120092 + 0.0220321i
\(291\) 0 0
\(292\) 158.261 + 352.012i 0.541990 + 1.20552i
\(293\) 37.2090 15.4125i 0.126993 0.0526023i −0.318282 0.947996i \(-0.603106\pi\)
0.445275 + 0.895394i \(0.353106\pi\)
\(294\) 0 0
\(295\) −1.53903 1.53903i −0.00521705 0.00521705i
\(296\) −12.9434 + 84.7072i −0.0437276 + 0.286173i
\(297\) 0 0
\(298\) 464.637 99.6443i 1.55918 0.334377i
\(299\) −476.616 + 197.421i −1.59403 + 0.660271i
\(300\) 0 0
\(301\) 10.8536 + 4.49569i 0.0360584 + 0.0149359i
\(302\) 131.792 + 191.014i 0.436397 + 0.632497i
\(303\) 0 0
\(304\) −130.043 + 63.1915i −0.427772 + 0.207867i
\(305\) 4.52063i 0.0148217i
\(306\) 0 0
\(307\) −101.089 + 244.049i −0.329279 + 0.794949i 0.669368 + 0.742931i \(0.266565\pi\)
−0.998646 + 0.0520174i \(0.983435\pi\)
\(308\) 33.2178 + 31.2939i 0.107850 + 0.101603i
\(309\) 0 0
\(310\) 23.5148 5.04289i 0.0758541 0.0162674i
\(311\) 181.395 181.395i 0.583264 0.583264i −0.352534 0.935799i \(-0.614680\pi\)
0.935799 + 0.352534i \(0.114680\pi\)
\(312\) 0 0
\(313\) 110.963 110.963i 0.354513 0.354513i −0.507273 0.861786i \(-0.669346\pi\)
0.861786 + 0.507273i \(0.169346\pi\)
\(314\) 232.098 + 150.127i 0.739166 + 0.478113i
\(315\) 0 0
\(316\) −253.384 96.2102i −0.801850 0.304463i
\(317\) −134.161 + 323.892i −0.423219 + 1.02174i 0.558172 + 0.829725i \(0.311503\pi\)
−0.981392 + 0.192017i \(0.938497\pi\)
\(318\) 0 0
\(319\) 678.512i 2.12700i
\(320\) −24.0462 20.0881i −0.0751443 0.0627755i
\(321\) 0 0
\(322\) 5.24020 28.5631i 0.0162739 0.0887054i
\(323\) 113.508 + 47.0166i 0.351419 + 0.145562i
\(324\) 0 0
\(325\) 494.207 204.707i 1.52064 0.629868i
\(326\) 64.4647 99.6629i 0.197744 0.305714i
\(327\) 0 0
\(328\) 159.159 39.1294i 0.485240 0.119297i
\(329\) −18.7502 18.7502i −0.0569915 0.0569915i
\(330\) 0 0
\(331\) −580.238 + 240.342i −1.75298 + 0.726110i −0.755506 + 0.655141i \(0.772609\pi\)
−0.997479 + 0.0709686i \(0.977391\pi\)
\(332\) −117.551 + 124.778i −0.354071 + 0.375839i
\(333\) 0 0
\(334\) 229.849 158.587i 0.688171 0.474810i
\(335\) −0.159064 −0.000474817
\(336\) 0 0
\(337\) 130.257i 0.386519i −0.981148 0.193259i \(-0.938094\pi\)
0.981148 0.193259i \(-0.0619059\pi\)
\(338\) 490.136 338.174i 1.45011 1.00051i
\(339\) 0 0
\(340\) 0.793689 + 26.6135i 0.00233438 + 0.0782750i
\(341\) −176.361 425.772i −0.517187 1.24860i
\(342\) 0 0
\(343\) 41.9776 41.9776i 0.122384 0.122384i
\(344\) −23.3461 + 152.787i −0.0678666 + 0.444149i
\(345\) 0 0
\(346\) 7.16277 11.0737i 0.0207016 0.0320049i
\(347\) 54.6775 + 132.003i 0.157572 + 0.380412i 0.982874 0.184279i \(-0.0589951\pi\)
−0.825302 + 0.564692i \(0.808995\pi\)
\(348\) 0 0
\(349\) −46.7936 + 112.970i −0.134079 + 0.323696i −0.976632 0.214918i \(-0.931052\pi\)
0.842553 + 0.538613i \(0.181052\pi\)
\(350\) −5.43360 + 29.6173i −0.0155246 + 0.0846209i
\(351\) 0 0
\(352\) −295.476 + 522.689i −0.839420 + 1.48491i
\(353\) −382.113 −1.08247 −0.541236 0.840871i \(-0.682043\pi\)
−0.541236 + 0.840871i \(0.682043\pi\)
\(354\) 0 0
\(355\) 18.6087 + 7.70798i 0.0524189 + 0.0217126i
\(356\) −234.105 + 105.251i −0.657598 + 0.295650i
\(357\) 0 0
\(358\) 353.990 + 228.970i 0.988798 + 0.639582i
\(359\) 81.2910 + 81.2910i 0.226437 + 0.226437i 0.811203 0.584765i \(-0.198813\pi\)
−0.584765 + 0.811203i \(0.698813\pi\)
\(360\) 0 0
\(361\) 197.525 + 197.525i 0.547161 + 0.547161i
\(362\) −305.308 + 65.4753i −0.843392 + 0.180871i
\(363\) 0 0
\(364\) 1.56639 + 52.5233i 0.00430328 + 0.144295i
\(365\) −43.6425 18.0773i −0.119568 0.0495268i
\(366\) 0 0
\(367\) 456.145 1.24290 0.621452 0.783453i \(-0.286543\pi\)
0.621452 + 0.783453i \(0.286543\pi\)
\(368\) 381.385 22.7682i 1.03637 0.0618701i
\(369\) 0 0
\(370\) −5.95617 8.63263i −0.0160977 0.0233314i
\(371\) 17.0640 41.1963i 0.0459947 0.111041i
\(372\) 0 0
\(373\) −184.108 444.476i −0.493588 1.19163i −0.952882 0.303342i \(-0.901898\pi\)
0.459294 0.888284i \(-0.348102\pi\)
\(374\) 498.871 106.986i 1.33388 0.286059i
\(375\) 0 0
\(376\) 180.660 298.450i 0.480478 0.793749i
\(377\) 552.423 552.423i 1.46531 1.46531i
\(378\) 0 0
\(379\) −108.900 262.908i −0.287336 0.693690i 0.712634 0.701536i \(-0.247502\pi\)
−0.999969 + 0.00784682i \(0.997502\pi\)
\(380\) 6.28165 16.5437i 0.0165307 0.0435361i
\(381\) 0 0
\(382\) 212.084 + 38.9090i 0.555194 + 0.101856i
\(383\) 476.810i 1.24493i −0.782646 0.622467i \(-0.786131\pi\)
0.782646 0.622467i \(-0.213869\pi\)
\(384\) 0 0
\(385\) −5.58569 −0.0145083
\(386\) −63.0957 + 343.920i −0.163460 + 0.890985i
\(387\) 0 0
\(388\) 446.169 + 169.411i 1.14992 + 0.436625i
\(389\) 71.5472 29.6358i 0.183926 0.0761846i −0.288820 0.957383i \(-0.593263\pi\)
0.472746 + 0.881199i \(0.343263\pi\)
\(390\) 0 0
\(391\) −229.570 229.570i −0.587136 0.587136i
\(392\) 332.816 + 201.463i 0.849020 + 0.513936i
\(393\) 0 0
\(394\) −49.2386 229.597i −0.124971 0.582734i
\(395\) 30.6480 12.6948i 0.0775898 0.0321388i
\(396\) 0 0
\(397\) 120.360 + 49.8545i 0.303173 + 0.125578i 0.529084 0.848570i \(-0.322536\pi\)
−0.225911 + 0.974148i \(0.572536\pi\)
\(398\) 443.140 305.749i 1.11342 0.768212i
\(399\) 0 0
\(400\) −395.461 + 23.6085i −0.988652 + 0.0590213i
\(401\) 174.015i 0.433953i 0.976177 + 0.216976i \(0.0696195\pi\)
−0.976177 + 0.216976i \(0.930381\pi\)
\(402\) 0 0
\(403\) 203.063 490.237i 0.503878 1.21647i
\(404\) 427.534 12.7503i 1.05825 0.0315601i
\(405\) 0 0
\(406\) 9.22151 + 42.9995i 0.0227131 + 0.105910i
\(407\) −142.114 + 142.114i −0.349173 + 0.349173i
\(408\) 0 0
\(409\) −108.736 + 108.736i −0.265857 + 0.265857i −0.827428 0.561571i \(-0.810197\pi\)
0.561571 + 0.827428i \(0.310197\pi\)
\(410\) −10.8950 + 16.8437i −0.0265731 + 0.0410822i
\(411\) 0 0
\(412\) −296.061 658.513i −0.718594 1.59833i
\(413\) 1.03450 2.49749i 0.00250483 0.00604720i
\(414\) 0 0
\(415\) 20.9819i 0.0505589i
\(416\) −666.123 + 184.989i −1.60126 + 0.444686i
\(417\) 0 0
\(418\) −333.540 61.1913i −0.797942 0.146391i
\(419\) −370.373 153.414i −0.883946 0.366142i −0.105920 0.994375i \(-0.533779\pi\)
−0.778026 + 0.628232i \(0.783779\pi\)
\(420\) 0 0
\(421\) −600.339 + 248.669i −1.42598 + 0.590662i −0.956357 0.292202i \(-0.905612\pi\)
−0.469628 + 0.882864i \(0.655612\pi\)
\(422\) −380.342 246.016i −0.901284 0.582975i
\(423\) 0 0
\(424\) 579.926 + 88.6135i 1.36775 + 0.208994i
\(425\) 238.043 + 238.043i 0.560101 + 0.560101i
\(426\) 0 0
\(427\) 5.18730 2.14865i 0.0121482 0.00503197i
\(428\) 410.818 12.2518i 0.959856 0.0286256i
\(429\) 0 0
\(430\) −10.7432 15.5708i −0.0249842 0.0362111i
\(431\) −289.906 −0.672636 −0.336318 0.941749i \(-0.609182\pi\)
−0.336318 + 0.941749i \(0.609182\pi\)
\(432\) 0 0
\(433\) 314.414i 0.726129i 0.931764 + 0.363064i \(0.118269\pi\)
−0.931764 + 0.363064i \(0.881731\pi\)
\(434\) 16.9631 + 24.5857i 0.0390856 + 0.0566490i
\(435\) 0 0
\(436\) 87.8002 + 82.7149i 0.201377 + 0.189713i
\(437\) 82.5760 + 199.356i 0.188961 + 0.456192i
\(438\) 0 0
\(439\) −579.455 + 579.455i −1.31994 + 1.31994i −0.406125 + 0.913818i \(0.633120\pi\)
−0.913818 + 0.406125i \(0.866880\pi\)
\(440\) −17.5448 71.3634i −0.0398745 0.162189i
\(441\) 0 0
\(442\) 493.269 + 319.060i 1.11599 + 0.721855i
\(443\) −107.736 260.098i −0.243197 0.587130i 0.754400 0.656415i \(-0.227928\pi\)
−0.997597 + 0.0692856i \(0.977928\pi\)
\(444\) 0 0
\(445\) 12.0223 29.0244i 0.0270164 0.0652233i
\(446\) 204.280 + 37.4773i 0.458027 + 0.0840297i
\(447\) 0 0
\(448\) 11.6215 37.1402i 0.0259408 0.0829022i
\(449\) −470.997 −1.04899 −0.524496 0.851413i \(-0.675746\pi\)
−0.524496 + 0.851413i \(0.675746\pi\)
\(450\) 0 0
\(451\) 355.147 + 147.107i 0.787465 + 0.326179i
\(452\) −199.901 + 526.471i −0.442260 + 1.16476i
\(453\) 0 0
\(454\) −124.728 + 192.830i −0.274730 + 0.424735i
\(455\) −4.54769 4.54769i −0.00999493 0.00999493i
\(456\) 0 0
\(457\) 447.868 + 447.868i 0.980018 + 0.980018i 0.999804 0.0197861i \(-0.00629852\pi\)
−0.0197861 + 0.999804i \(0.506299\pi\)
\(458\) −20.9335 97.6121i −0.0457064 0.213127i
\(459\) 0 0
\(460\) −32.0657 + 34.0370i −0.0697080 + 0.0739935i
\(461\) −253.222 104.888i −0.549288 0.227523i 0.0907394 0.995875i \(-0.471077\pi\)
−0.640027 + 0.768352i \(0.721077\pi\)
\(462\) 0 0
\(463\) −653.753 −1.41199 −0.705996 0.708215i \(-0.749501\pi\)
−0.705996 + 0.708215i \(0.749501\pi\)
\(464\) −520.401 + 252.877i −1.12155 + 0.544994i
\(465\) 0 0
\(466\) 145.977 100.718i 0.313255 0.216133i
\(467\) −39.3875 + 95.0899i −0.0843416 + 0.203619i −0.960424 0.278544i \(-0.910148\pi\)
0.876082 + 0.482162i \(0.160148\pi\)
\(468\) 0 0
\(469\) −0.0756028 0.182521i −0.000161200 0.000389171i
\(470\) 8.95363 + 41.7503i 0.0190503 + 0.0888305i
\(471\) 0 0
\(472\) 35.1576 + 5.37213i 0.0744865 + 0.0113816i
\(473\) −256.332 + 256.332i −0.541927 + 0.541927i
\(474\) 0 0
\(475\) −85.6236 206.714i −0.180260 0.435187i
\(476\) −30.1610 + 13.5601i −0.0633635 + 0.0284876i
\(477\) 0 0
\(478\) −110.464 + 602.112i −0.231095 + 1.25965i
\(479\) 857.713i 1.79063i −0.445432 0.895316i \(-0.646950\pi\)
0.445432 0.895316i \(-0.353050\pi\)
\(480\) 0 0
\(481\) −231.408 −0.481099
\(482\) −482.433 88.5072i −1.00090 0.183625i
\(483\) 0 0
\(484\) −842.963 + 378.988i −1.74166 + 0.783033i
\(485\) −53.9661 + 22.3535i −0.111270 + 0.0460897i
\(486\) 0 0
\(487\) 12.5467 + 12.5467i 0.0257633 + 0.0257633i 0.719871 0.694108i \(-0.244201\pi\)
−0.694108 + 0.719871i \(0.744201\pi\)
\(488\) 43.7448 + 59.5245i 0.0896410 + 0.121976i
\(489\) 0 0
\(490\) −46.5579 + 9.98464i −0.0950161 + 0.0203768i
\(491\) −91.7015 + 37.9840i −0.186765 + 0.0773605i −0.474106 0.880468i \(-0.657229\pi\)
0.287341 + 0.957828i \(0.407229\pi\)
\(492\) 0 0
\(493\) 454.233 + 188.149i 0.921365 + 0.381642i
\(494\) −221.737 321.377i −0.448861 0.650561i
\(495\) 0 0
\(496\) −260.828 + 293.947i −0.525862 + 0.592635i
\(497\) 25.0166i 0.0503352i
\(498\) 0 0
\(499\) 193.677 467.577i 0.388130 0.937029i −0.602206 0.798341i \(-0.705711\pi\)
0.990336 0.138688i \(-0.0442886\pi\)
\(500\) 66.8201 70.9281i 0.133640 0.141856i
\(501\) 0 0
\(502\) −678.844 + 145.582i −1.35228 + 0.290005i
\(503\) −659.583 + 659.583i −1.31130 + 1.31130i −0.390840 + 0.920459i \(0.627816\pi\)
−0.920459 + 0.390840i \(0.872184\pi\)
\(504\) 0 0
\(505\) −37.0177 + 37.0177i −0.0733024 + 0.0733024i
\(506\) 752.415 + 486.683i 1.48699 + 0.961823i
\(507\) 0 0
\(508\) −232.832 + 613.201i −0.458332 + 1.20709i
\(509\) 133.178 321.521i 0.261647 0.631671i −0.737394 0.675463i \(-0.763944\pi\)
0.999041 + 0.0437918i \(0.0139438\pi\)
\(510\) 0 0
\(511\) 58.6707i 0.114815i
\(512\) 511.010 + 31.8190i 0.998067 + 0.0621466i
\(513\) 0 0
\(514\) 39.2705 214.055i 0.0764018 0.416449i
\(515\) 81.6425 + 33.8174i 0.158529 + 0.0656649i
\(516\) 0 0
\(517\) 755.957 313.127i 1.46220 0.605662i
\(518\) 7.07475 10.9376i 0.0136578 0.0211151i
\(519\) 0 0
\(520\) 43.8173 72.3862i 0.0842641 0.139204i
\(521\) −71.2918 71.2918i −0.136837 0.136837i 0.635371 0.772207i \(-0.280847\pi\)
−0.772207 + 0.635371i \(0.780847\pi\)
\(522\) 0 0
\(523\) −376.338 + 155.884i −0.719576 + 0.298058i −0.712261 0.701915i \(-0.752329\pi\)
−0.00731529 + 0.999973i \(0.502329\pi\)
\(524\) −35.3832 33.3338i −0.0675252 0.0636142i
\(525\) 0 0
\(526\) 349.562 241.183i 0.664566 0.458523i
\(527\) 333.940 0.633662
\(528\) 0 0
\(529\) 41.2074i 0.0778968i
\(530\) −59.1011 + 40.7774i −0.111511 + 0.0769384i
\(531\) 0 0
\(532\) 21.9691 0.655181i 0.0412953 0.00123154i
\(533\) 169.379 + 408.918i 0.317785 + 0.767201i
\(534\) 0 0
\(535\) −35.5704 + 35.5704i −0.0664867 + 0.0664867i
\(536\) 2.09444 1.53921i 0.00390754 0.00287167i
\(537\) 0 0
\(538\) 300.380 464.390i 0.558327 0.863178i
\(539\) 349.184 + 843.005i 0.647837 + 1.56402i
\(540\) 0 0
\(541\) −131.242 + 316.846i −0.242591 + 0.585667i −0.997539 0.0701185i \(-0.977662\pi\)
0.754948 + 0.655785i \(0.227662\pi\)
\(542\) −94.4281 + 514.706i −0.174222 + 0.949643i
\(543\) 0 0
\(544\) −267.982 342.748i −0.492614 0.630051i
\(545\) −14.7639 −0.0270898
\(546\) 0 0
\(547\) −57.6667 23.8863i −0.105424 0.0436679i 0.329348 0.944209i \(-0.393171\pi\)
−0.434772 + 0.900541i \(0.643171\pi\)
\(548\) 49.4039 + 109.886i 0.0901531 + 0.200523i
\(549\) 0 0
\(550\) −780.184 504.645i −1.41852 0.917536i
\(551\) −231.064 231.064i −0.419354 0.419354i
\(552\) 0 0
\(553\) 29.1339 + 29.1339i 0.0526834 + 0.0526834i
\(554\) 613.837 131.641i 1.10801 0.237620i
\(555\) 0 0
\(556\) 670.075 19.9835i 1.20517 0.0359416i
\(557\) −403.952 167.322i −0.725228 0.300399i −0.0106383 0.999943i \(-0.503386\pi\)
−0.714589 + 0.699544i \(0.753386\pi\)
\(558\) 0 0
\(559\) −417.394 −0.746680
\(560\) 2.08175 + 4.28408i 0.00371742 + 0.00765014i
\(561\) 0 0
\(562\) 35.0003 + 50.7280i 0.0622781 + 0.0902634i
\(563\) −2.60893 + 6.29851i −0.00463398 + 0.0111874i −0.926180 0.377083i \(-0.876927\pi\)
0.921546 + 0.388270i \(0.126927\pi\)
\(564\) 0 0
\(565\) −26.3767 63.6791i −0.0466845 0.112706i
\(566\) −796.850 + 170.890i −1.40786 + 0.301925i
\(567\) 0 0
\(568\) −319.614 + 78.5777i −0.562702 + 0.138341i
\(569\) −225.325 + 225.325i −0.396002 + 0.396002i −0.876820 0.480818i \(-0.840340\pi\)
0.480818 + 0.876820i \(0.340340\pi\)
\(570\) 0 0
\(571\) 203.081 + 490.280i 0.355658 + 0.858634i 0.995900 + 0.0904608i \(0.0288340\pi\)
−0.640242 + 0.768173i \(0.721166\pi\)
\(572\) −1515.86 575.573i −2.65011 1.00625i
\(573\) 0 0
\(574\) −24.5061 4.49589i −0.0426935 0.00783256i
\(575\) 591.252i 1.02826i
\(576\) 0 0
\(577\) −1017.81 −1.76396 −0.881980 0.471286i \(-0.843790\pi\)
−0.881980 + 0.471286i \(0.843790\pi\)
\(578\) 37.5861 204.873i 0.0650278 0.354452i
\(579\) 0 0
\(580\) 25.1377 66.2040i 0.0433408 0.114145i
\(581\) 24.0762 9.97270i 0.0414393 0.0171647i
\(582\) 0 0
\(583\) 972.943 + 972.943i 1.66886 + 1.66886i
\(584\) 749.582 184.286i 1.28353 0.315558i
\(585\) 0 0
\(586\) −16.8903 78.7587i −0.0288230 0.134400i
\(587\) 721.215 298.737i 1.22865 0.508922i 0.328498 0.944505i \(-0.393458\pi\)
0.900149 + 0.435583i \(0.143458\pi\)
\(588\) 0 0
\(589\) −205.053 84.9359i −0.348138 0.144204i
\(590\) −3.58296 + 2.47210i −0.00607282 + 0.00419000i
\(591\) 0 0
\(592\) 161.962 + 56.0324i 0.273585 + 0.0946493i
\(593\) 525.499i 0.886170i −0.896479 0.443085i \(-0.853884\pi\)
0.896479 0.443085i \(-0.146116\pi\)
\(594\) 0 0
\(595\) 1.54890 3.73937i 0.00260319 0.00628465i
\(596\) −28.3311 949.980i −0.0475354 1.59393i
\(597\) 0 0
\(598\) 216.351 + 1008.83i 0.361791 + 1.68701i
\(599\) 359.176 359.176i 0.599626 0.599626i −0.340587 0.940213i \(-0.610626\pi\)
0.940213 + 0.340587i \(0.110626\pi\)
\(600\) 0 0
\(601\) 163.858 163.858i 0.272642 0.272642i −0.557521 0.830163i \(-0.688247\pi\)
0.830163 + 0.557521i \(0.188247\pi\)
\(602\) 12.7608 19.7283i 0.0211974 0.0327713i
\(603\) 0 0
\(604\) 423.320 190.321i 0.700862 0.315101i
\(605\) 43.2897 104.511i 0.0715533 0.172745i
\(606\) 0 0
\(607\) 208.191i 0.342984i −0.985186 0.171492i \(-0.945141\pi\)
0.985186 0.171492i \(-0.0548587\pi\)
\(608\) 77.3762 + 278.622i 0.127263 + 0.458259i
\(609\) 0 0
\(610\) −8.89284 1.63148i −0.0145784 0.00267456i
\(611\) 870.414 + 360.537i 1.42457 + 0.590077i
\(612\) 0 0
\(613\) 643.217 266.429i 1.04929 0.434632i 0.209654 0.977776i \(-0.432766\pi\)
0.839640 + 0.543144i \(0.182766\pi\)
\(614\) 443.604 + 286.935i 0.722481 + 0.467321i
\(615\) 0 0
\(616\) 73.5485 54.0511i 0.119397 0.0877453i
\(617\) 526.767 + 526.767i 0.853755 + 0.853755i 0.990593 0.136838i \(-0.0436941\pi\)
−0.136838 + 0.990593i \(0.543694\pi\)
\(618\) 0 0
\(619\) −316.799 + 131.222i −0.511791 + 0.211991i −0.623607 0.781738i \(-0.714333\pi\)
0.111816 + 0.993729i \(0.464333\pi\)
\(620\) −1.43381 48.0775i −0.00231259 0.0775443i
\(621\) 0 0
\(622\) −291.370 422.300i −0.468441 0.678939i
\(623\) 39.0188 0.0626306
\(624\) 0 0
\(625\) 607.081i 0.971330i
\(626\) −178.236 258.328i −0.284722 0.412665i
\(627\) 0 0
\(628\) 379.089 402.395i 0.603645 0.640757i
\(629\) −55.7309 134.546i −0.0886024 0.213905i
\(630\) 0 0
\(631\) 515.138 515.138i 0.816383 0.816383i −0.169199 0.985582i \(-0.554118\pi\)
0.985582 + 0.169199i \(0.0541179\pi\)
\(632\) −280.707 + 463.728i −0.444157 + 0.733747i
\(633\) 0 0
\(634\) 588.732 + 380.808i 0.928600 + 0.600644i
\(635\) −30.7220 74.1694i −0.0483810 0.116802i
\(636\) 0 0
\(637\) −402.053 + 970.642i −0.631167 + 1.52377i
\(638\) −1334.75 244.873i −2.09208 0.383814i
\(639\) 0 0
\(640\) −48.1950 + 40.0531i −0.0753046 + 0.0625830i
\(641\) 827.282 1.29061 0.645306 0.763925i \(-0.276730\pi\)
0.645306 + 0.763925i \(0.276730\pi\)
\(642\) 0 0
\(643\) 300.259 + 124.371i 0.466965 + 0.193423i 0.603744 0.797178i \(-0.293675\pi\)
−0.136779 + 0.990602i \(0.543675\pi\)
\(644\) −54.2974 20.6167i −0.0843127 0.0320135i
\(645\) 0 0
\(646\) 133.454 206.322i 0.206586 0.319383i
\(647\) 182.325 + 182.325i 0.281800 + 0.281800i 0.833827 0.552027i \(-0.186145\pi\)
−0.552027 + 0.833827i \(0.686145\pi\)
\(648\) 0 0
\(649\) 58.9840 + 58.9840i 0.0908845 + 0.0908845i
\(650\) −224.336 1046.07i −0.345132 1.60933i
\(651\) 0 0
\(652\) −172.789 162.781i −0.265013 0.249664i
\(653\) 83.4520 + 34.5670i 0.127798 + 0.0529356i 0.445666 0.895199i \(-0.352967\pi\)
−0.317868 + 0.948135i \(0.602967\pi\)
\(654\) 0 0
\(655\) 5.94981 0.00908368
\(656\) −19.5342 327.214i −0.0297778 0.498801i
\(657\) 0 0
\(658\) −43.6517 + 30.1179i −0.0663400 + 0.0457719i
\(659\) −36.4182 + 87.9213i −0.0552628 + 0.133416i −0.949099 0.314976i \(-0.898003\pi\)
0.893837 + 0.448393i \(0.148003\pi\)
\(660\) 0 0
\(661\) −420.501 1015.18i −0.636159 1.53582i −0.831757 0.555140i \(-0.812665\pi\)
0.195597 0.980684i \(-0.437335\pi\)
\(662\) 263.388 + 1228.16i 0.397867 + 1.85523i
\(663\) 0 0
\(664\) 203.036 + 276.276i 0.305777 + 0.416078i
\(665\) −1.90218 + 1.90218i −0.00286042 + 0.00286042i
\(666\) 0 0
\(667\) 330.450 + 797.776i 0.495427 + 1.19607i
\(668\) −229.015 509.385i −0.342836 0.762553i
\(669\) 0 0
\(670\) −0.0574056 + 0.312905i −8.56800e−5 + 0.000467022i
\(671\) 173.255i 0.258205i
\(672\) 0 0
\(673\) 80.3370 0.119372 0.0596858 0.998217i \(-0.480990\pi\)
0.0596858 + 0.998217i \(0.480990\pi\)
\(674\) −256.237 47.0094i −0.380174 0.0697468i
\(675\) 0 0
\(676\) −488.356 1086.23i −0.722421 1.60684i
\(677\) 944.061 391.043i 1.39448 0.577611i 0.446165 0.894951i \(-0.352789\pi\)
0.948312 + 0.317339i \(0.102789\pi\)
\(678\) 0 0
\(679\) −51.3001 51.3001i −0.0755524 0.0755524i
\(680\) 52.6397 + 8.04342i 0.0774113 + 0.0118286i
\(681\) 0 0
\(682\) −901.214 + 193.271i −1.32143 + 0.283389i
\(683\) 173.921 72.0404i 0.254643 0.105476i −0.251711 0.967803i \(-0.580993\pi\)
0.506353 + 0.862326i \(0.330993\pi\)
\(684\) 0 0
\(685\) −13.6237 5.64314i −0.0198887 0.00823816i
\(686\) −67.4274 97.7266i −0.0982907 0.142459i
\(687\) 0 0
\(688\) 292.133 + 101.066i 0.424612 + 0.146899i
\(689\) 1584.28i 2.29939i
\(690\) 0 0
\(691\) 185.902 448.807i 0.269033 0.649503i −0.730405 0.683014i \(-0.760669\pi\)
0.999438 + 0.0335109i \(0.0106688\pi\)
\(692\) −19.1988 18.0868i −0.0277439 0.0261370i
\(693\) 0 0
\(694\) 279.405 59.9203i 0.402601 0.0863404i
\(695\) −58.0179 + 58.0179i −0.0834790 + 0.0834790i
\(696\) 0 0
\(697\) −196.962 + 196.962i −0.282586 + 0.282586i
\(698\) 205.343 + 132.821i 0.294188 + 0.190289i
\(699\) 0 0
\(700\) 56.3013 + 21.3776i 0.0804304 + 0.0305395i
\(701\) 150.886 364.271i 0.215244 0.519645i −0.778970 0.627061i \(-0.784258\pi\)
0.994214 + 0.107416i \(0.0342576\pi\)
\(702\) 0 0
\(703\) 96.7921i 0.137684i
\(704\) 921.580 + 769.887i 1.30906 + 1.09359i
\(705\) 0 0
\(706\) −137.903 + 751.680i −0.195331 + 1.06470i
\(707\) −60.0713 24.8824i −0.0849665 0.0351943i
\(708\) 0 0
\(709\) −457.191 + 189.375i −0.644839 + 0.267101i −0.681043 0.732243i \(-0.738473\pi\)
0.0362043 + 0.999344i \(0.488473\pi\)
\(710\) 21.8787 33.8247i 0.0308151 0.0476404i
\(711\) 0 0
\(712\) 122.559 + 498.509i 0.172134 + 0.700153i
\(713\) 414.720 + 414.720i 0.581656 + 0.581656i
\(714\) 0 0
\(715\) 183.350 75.9462i 0.256434 0.106218i
\(716\) 578.177 613.723i 0.807510 0.857155i
\(717\) 0 0
\(718\) 189.251 130.575i 0.263581 0.181860i
\(719\) −1277.00 −1.77608 −0.888039 0.459768i \(-0.847932\pi\)
−0.888039 + 0.459768i \(0.847932\pi\)
\(720\) 0 0
\(721\) 109.756i 0.152227i
\(722\) 459.851 317.279i 0.636913 0.439444i
\(723\) 0 0
\(724\) 18.6161 + 624.222i 0.0257128 + 0.862186i
\(725\) −342.646 827.219i −0.472614 1.14099i
\(726\) 0 0
\(727\) 470.863 470.863i 0.647679 0.647679i −0.304753 0.952432i \(-0.598574\pi\)
0.952432 + 0.304753i \(0.0985738\pi\)
\(728\) 103.888 + 15.8742i 0.142703 + 0.0218052i
\(729\) 0 0
\(730\) −51.3115 + 79.3280i −0.0702898 + 0.108669i
\(731\) −100.522 242.683i −0.137514 0.331987i
\(732\) 0 0
\(733\) 364.452 879.866i 0.497206 1.20036i −0.453776 0.891116i \(-0.649923\pi\)
0.950982 0.309246i \(-0.100077\pi\)
\(734\) 164.622 897.315i 0.224280 1.22250i
\(735\) 0 0
\(736\) 92.8520 758.466i 0.126158 1.03052i
\(737\) 6.09619 0.00827163
\(738\) 0 0
\(739\) 1146.65 + 474.958i 1.55162 + 0.642704i 0.983609 0.180314i \(-0.0577112\pi\)
0.568016 + 0.823018i \(0.307711\pi\)
\(740\) −19.1314 + 8.60129i −0.0258533 + 0.0116234i
\(741\) 0 0
\(742\) −74.8816 48.4355i −0.100919 0.0652769i
\(743\) −512.021 512.021i −0.689126 0.689126i 0.272913 0.962039i \(-0.412013\pi\)
−0.962039 + 0.272913i \(0.912013\pi\)
\(744\) 0 0
\(745\) 82.2533 + 82.2533i 0.110407 + 0.110407i
\(746\) −940.804 + 201.762i −1.26113 + 0.270458i
\(747\) 0 0
\(748\) −30.4185 1019.97i −0.0406665 1.36360i
\(749\) −57.7227 23.9095i −0.0770663 0.0319219i
\(750\) 0 0
\(751\) 335.629 0.446910 0.223455 0.974714i \(-0.428266\pi\)
0.223455 + 0.974714i \(0.428266\pi\)
\(752\) −521.901 463.098i −0.694017 0.615822i
\(753\) 0 0
\(754\) −887.341 1286.08i −1.17684 1.70567i
\(755\) −21.7393 + 52.4833i −0.0287938 + 0.0695143i
\(756\) 0 0
\(757\) −139.805 337.518i −0.184682 0.445863i 0.804238 0.594307i \(-0.202573\pi\)
−0.988921 + 0.148444i \(0.952573\pi\)
\(758\) −556.487 + 119.342i −0.734152 + 0.157444i
\(759\) 0 0
\(760\) −30.2772 18.3276i −0.0398385 0.0241153i
\(761\) −495.581 + 495.581i −0.651223 + 0.651223i −0.953288 0.302064i \(-0.902324\pi\)
0.302064 + 0.953288i \(0.402324\pi\)
\(762\) 0 0
\(763\) −7.01728 16.9412i −0.00919696 0.0222034i
\(764\) 153.081 403.163i 0.200368 0.527700i
\(765\) 0 0
\(766\) −937.965 172.079i −1.22450 0.224647i
\(767\) 96.0458i 0.125223i
\(768\) 0 0
\(769\) 372.267 0.484092 0.242046 0.970265i \(-0.422181\pi\)
0.242046 + 0.970265i \(0.422181\pi\)
\(770\) −2.01586 + 10.9880i −0.00261800 + 0.0142701i
\(771\) 0 0
\(772\) 653.778 + 248.240i 0.846862 + 0.321554i
\(773\) 534.778 221.512i 0.691822 0.286562i −0.00893708 0.999960i \(-0.502845\pi\)
0.700759 + 0.713398i \(0.252845\pi\)
\(774\) 0 0
\(775\) −430.026 430.026i −0.554873 0.554873i
\(776\) 494.280 816.550i 0.636959 1.05226i
\(777\) 0 0
\(778\) −32.4775 151.441i −0.0417448 0.194654i
\(779\) 171.040 70.8470i 0.219563 0.0909461i
\(780\) 0 0
\(781\) −713.187 295.412i −0.913172 0.378248i
\(782\) −534.455 + 368.752i −0.683446 + 0.471550i
\(783\) 0 0
\(784\) 516.424 581.998i 0.658704 0.742344i
\(785\) 67.6643i 0.0861965i
\(786\) 0 0
\(787\) −280.233 + 676.541i −0.356077 + 0.859646i 0.639767 + 0.768569i \(0.279031\pi\)