Properties

Label 288.3.u.a.163.6
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 163.6
Character \(\chi\) \(=\) 288.163
Dual form 288.3.u.a.235.6

$q$-expansion

\(f(q)\) \(=\) \(q+(1.46783 - 1.35848i) q^{2} +(0.309042 - 3.98804i) q^{4} +(-1.74699 - 4.21761i) q^{5} +(-0.392379 - 0.392379i) q^{7} +(-4.96407 - 6.27359i) q^{8} +O(q^{10})\) \(q+(1.46783 - 1.35848i) q^{2} +(0.309042 - 3.98804i) q^{4} +(-1.74699 - 4.21761i) q^{5} +(-0.392379 - 0.392379i) q^{7} +(-4.96407 - 6.27359i) q^{8} +(-8.29385 - 3.81747i) q^{10} +(-2.90924 - 7.02353i) q^{11} +(-4.50555 + 10.8774i) q^{13} +(-1.10898 - 0.0429045i) q^{14} +(-15.8090 - 2.46495i) q^{16} -10.5402i q^{17} +(-1.88707 - 0.781651i) q^{19} +(-17.3599 + 5.66366i) q^{20} +(-13.8116 - 6.35718i) q^{22} +(0.445453 - 0.445453i) q^{23} +(2.94139 - 2.94139i) q^{25} +(8.16334 + 22.0868i) q^{26} +(-1.68608 + 1.44356i) q^{28} +(-0.741814 - 0.307270i) q^{29} -47.6947i q^{31} +(-26.5535 + 17.8581i) q^{32} +(-14.3187 - 15.4712i) q^{34} +(-0.969419 + 2.34038i) q^{35} +(14.5080 + 35.0255i) q^{37} +(-3.83176 + 1.41623i) q^{38} +(-17.7874 + 31.8965i) q^{40} +(11.3365 + 11.3365i) q^{41} +(-14.6421 - 35.3493i) q^{43} +(-28.9092 + 9.43161i) q^{44} +(0.0487080 - 1.25899i) q^{46} +80.5164 q^{47} -48.6921i q^{49} +(0.321625 - 8.31328i) q^{50} +(41.9870 + 21.3299i) q^{52} +(66.6128 - 27.5919i) q^{53} +(-24.5401 + 24.5401i) q^{55} +(-0.513828 + 4.40942i) q^{56} +(-1.50628 + 0.556724i) q^{58} +(-65.0706 + 26.9531i) q^{59} +(87.4322 + 36.2156i) q^{61} +(-64.7925 - 70.0077i) q^{62} +(-14.7160 + 62.2852i) q^{64} +53.7476 q^{65} +(-7.12379 + 17.1984i) q^{67} +(-42.0348 - 3.25737i) q^{68} +(1.75643 + 4.75222i) q^{70} +(14.8103 + 14.8103i) q^{71} +(18.6720 + 18.6720i) q^{73} +(68.8769 + 31.7025i) q^{74} +(-3.70044 + 7.28417i) q^{76} +(-1.61436 + 3.89741i) q^{77} -36.2398 q^{79} +(17.2220 + 70.9824i) q^{80} +(32.0406 + 1.23959i) q^{82} +(-27.0868 - 11.2197i) q^{83} +(-44.4545 + 18.4137i) q^{85} +(-69.5135 - 31.9955i) q^{86} +(-29.6211 + 53.1167i) q^{88} +(56.4944 - 56.4944i) q^{89} +(6.03592 - 2.50016i) q^{91} +(-1.63882 - 1.91415i) q^{92} +(118.184 - 109.380i) q^{94} +9.32448i q^{95} +158.579 q^{97} +(-66.1474 - 71.4716i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 28q + 4q^{2} - 4q^{4} + 4q^{5} - 4q^{7} + 4q^{8} + O(q^{10}) \) \( 28q + 4q^{2} - 4q^{4} + 4q^{5} - 4q^{7} + 4q^{8} - 44q^{10} + 4q^{11} - 4q^{13} + 20q^{14} + 16q^{16} - 4q^{19} - 76q^{20} + 144q^{22} + 68q^{23} - 4q^{25} - 96q^{26} + 56q^{28} + 4q^{29} + 24q^{32} - 48q^{34} - 92q^{35} - 4q^{37} + 396q^{38} - 408q^{40} + 4q^{41} + 92q^{43} + 188q^{44} - 36q^{46} + 8q^{47} - 308q^{50} + 420q^{52} + 164q^{53} + 252q^{55} - 552q^{56} + 528q^{58} - 124q^{59} - 68q^{61} - 216q^{62} - 232q^{64} + 8q^{65} - 164q^{67} + 368q^{68} - 664q^{70} + 260q^{71} - 4q^{73} + 532q^{74} - 516q^{76} - 220q^{77} - 520q^{79} - 312q^{80} + 636q^{82} + 484q^{83} + 96q^{85} - 688q^{86} + 672q^{88} + 4q^{89} - 196q^{91} - 616q^{92} + 40q^{94} - 8q^{97} + 328q^{98} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.46783 1.35848i 0.733914 0.679242i
\(3\) 0 0
\(4\) 0.309042 3.98804i 0.0772606 0.997011i
\(5\) −1.74699 4.21761i −0.349399 0.843523i −0.996691 0.0812812i \(-0.974099\pi\)
0.647293 0.762242i \(-0.275901\pi\)
\(6\) 0 0
\(7\) −0.392379 0.392379i −0.0560541 0.0560541i 0.678524 0.734578i \(-0.262620\pi\)
−0.734578 + 0.678524i \(0.762620\pi\)
\(8\) −4.96407 6.27359i −0.620509 0.784199i
\(9\) 0 0
\(10\) −8.29385 3.81747i −0.829385 0.381747i
\(11\) −2.90924 7.02353i −0.264477 0.638503i 0.734729 0.678361i \(-0.237309\pi\)
−0.999205 + 0.0398581i \(0.987309\pi\)
\(12\) 0 0
\(13\) −4.50555 + 10.8774i −0.346581 + 0.836720i 0.650438 + 0.759559i \(0.274585\pi\)
−0.997019 + 0.0771604i \(0.975415\pi\)
\(14\) −1.10898 0.0429045i −0.0792132 0.00306461i
\(15\) 0 0
\(16\) −15.8090 2.46495i −0.988062 0.154059i
\(17\) 10.5402i 0.620012i −0.950735 0.310006i \(-0.899669\pi\)
0.950735 0.310006i \(-0.100331\pi\)
\(18\) 0 0
\(19\) −1.88707 0.781651i −0.0993196 0.0411395i 0.332470 0.943114i \(-0.392118\pi\)
−0.431790 + 0.901974i \(0.642118\pi\)
\(20\) −17.3599 + 5.66366i −0.867996 + 0.283183i
\(21\) 0 0
\(22\) −13.8116 6.35718i −0.627801 0.288963i
\(23\) 0.445453 0.445453i 0.0193675 0.0193675i −0.697357 0.716724i \(-0.745641\pi\)
0.716724 + 0.697357i \(0.245641\pi\)
\(24\) 0 0
\(25\) 2.94139 2.94139i 0.117656 0.117656i
\(26\) 8.16334 + 22.0868i 0.313975 + 0.849493i
\(27\) 0 0
\(28\) −1.68608 + 1.44356i −0.0602173 + 0.0515558i
\(29\) −0.741814 0.307270i −0.0255798 0.0105955i 0.369857 0.929089i \(-0.379407\pi\)
−0.395437 + 0.918493i \(0.629407\pi\)
\(30\) 0 0
\(31\) 47.6947i 1.53854i −0.638924 0.769270i \(-0.720620\pi\)
0.638924 0.769270i \(-0.279380\pi\)
\(32\) −26.5535 + 17.8581i −0.829796 + 0.558067i
\(33\) 0 0
\(34\) −14.3187 15.4712i −0.421138 0.455036i
\(35\) −0.969419 + 2.34038i −0.0276977 + 0.0668681i
\(36\) 0 0
\(37\) 14.5080 + 35.0255i 0.392109 + 0.946635i 0.989480 + 0.144670i \(0.0462120\pi\)
−0.597371 + 0.801965i \(0.703788\pi\)
\(38\) −3.83176 + 1.41623i −0.100836 + 0.0372692i
\(39\) 0 0
\(40\) −17.7874 + 31.8965i −0.444685 + 0.797412i
\(41\) 11.3365 + 11.3365i 0.276501 + 0.276501i 0.831711 0.555209i \(-0.187362\pi\)
−0.555209 + 0.831711i \(0.687362\pi\)
\(42\) 0 0
\(43\) −14.6421 35.3493i −0.340515 0.822076i −0.997664 0.0683149i \(-0.978238\pi\)
0.657149 0.753761i \(-0.271762\pi\)
\(44\) −28.9092 + 9.43161i −0.657028 + 0.214355i
\(45\) 0 0
\(46\) 0.0487080 1.25899i 0.00105887 0.0273694i
\(47\) 80.5164 1.71312 0.856558 0.516051i \(-0.172598\pi\)
0.856558 + 0.516051i \(0.172598\pi\)
\(48\) 0 0
\(49\) 48.6921i 0.993716i
\(50\) 0.321625 8.31328i 0.00643251 0.166266i
\(51\) 0 0
\(52\) 41.9870 + 21.3299i 0.807442 + 0.410190i
\(53\) 66.6128 27.5919i 1.25685 0.520602i 0.347905 0.937530i \(-0.386893\pi\)
0.908940 + 0.416927i \(0.136893\pi\)
\(54\) 0 0
\(55\) −24.5401 + 24.5401i −0.446184 + 0.446184i
\(56\) −0.513828 + 4.40942i −0.00917551 + 0.0787396i
\(57\) 0 0
\(58\) −1.50628 + 0.556724i −0.0259703 + 0.00959869i
\(59\) −65.0706 + 26.9531i −1.10289 + 0.456833i −0.858484 0.512840i \(-0.828594\pi\)
−0.244408 + 0.969673i \(0.578594\pi\)
\(60\) 0 0
\(61\) 87.4322 + 36.2156i 1.43331 + 0.593698i 0.958168 0.286208i \(-0.0923948\pi\)
0.475147 + 0.879906i \(0.342395\pi\)
\(62\) −64.7925 70.0077i −1.04504 1.12916i
\(63\) 0 0
\(64\) −14.7160 + 62.2852i −0.229937 + 0.973205i
\(65\) 53.7476 0.826887
\(66\) 0 0
\(67\) −7.12379 + 17.1984i −0.106325 + 0.256692i −0.968084 0.250627i \(-0.919363\pi\)
0.861759 + 0.507319i \(0.169363\pi\)
\(68\) −42.0348 3.25737i −0.618159 0.0479025i
\(69\) 0 0
\(70\) 1.75643 + 4.75222i 0.0250919 + 0.0678889i
\(71\) 14.8103 + 14.8103i 0.208596 + 0.208596i 0.803671 0.595074i \(-0.202877\pi\)
−0.595074 + 0.803671i \(0.702877\pi\)
\(72\) 0 0
\(73\) 18.6720 + 18.6720i 0.255781 + 0.255781i 0.823336 0.567555i \(-0.192110\pi\)
−0.567555 + 0.823336i \(0.692110\pi\)
\(74\) 68.8769 + 31.7025i 0.930769 + 0.428412i
\(75\) 0 0
\(76\) −3.70044 + 7.28417i −0.0486901 + 0.0958443i
\(77\) −1.61436 + 3.89741i −0.0209657 + 0.0506157i
\(78\) 0 0
\(79\) −36.2398 −0.458732 −0.229366 0.973340i \(-0.573665\pi\)
−0.229366 + 0.973340i \(0.573665\pi\)
\(80\) 17.2220 + 70.9824i 0.215275 + 0.887281i
\(81\) 0 0
\(82\) 32.0406 + 1.23959i 0.390739 + 0.0151170i
\(83\) −27.0868 11.2197i −0.326347 0.135177i 0.213494 0.976944i \(-0.431516\pi\)
−0.539841 + 0.841767i \(0.681516\pi\)
\(84\) 0 0
\(85\) −44.4545 + 18.4137i −0.522994 + 0.216631i
\(86\) −69.5135 31.9955i −0.808297 0.372041i
\(87\) 0 0
\(88\) −29.6211 + 53.1167i −0.336603 + 0.603599i
\(89\) 56.4944 56.4944i 0.634769 0.634769i −0.314491 0.949260i \(-0.601834\pi\)
0.949260 + 0.314491i \(0.101834\pi\)
\(90\) 0 0
\(91\) 6.03592 2.50016i 0.0663288 0.0274743i
\(92\) −1.63882 1.91415i −0.0178133 0.0208060i
\(93\) 0 0
\(94\) 118.184 109.380i 1.25728 1.16362i
\(95\) 9.32448i 0.0981525i
\(96\) 0 0
\(97\) 158.579 1.63484 0.817419 0.576043i \(-0.195404\pi\)
0.817419 + 0.576043i \(0.195404\pi\)
\(98\) −66.1474 71.4716i −0.674974 0.729302i
\(99\) 0 0
\(100\) −10.8214 12.6394i −0.108214 0.126394i
\(101\) 53.8420 + 129.986i 0.533089 + 1.28699i 0.929468 + 0.368903i \(0.120267\pi\)
−0.396379 + 0.918087i \(0.629733\pi\)
\(102\) 0 0
\(103\) 9.94607 + 9.94607i 0.0965638 + 0.0965638i 0.753738 0.657175i \(-0.228249\pi\)
−0.657175 + 0.753738i \(0.728249\pi\)
\(104\) 90.6060 25.7300i 0.871211 0.247404i
\(105\) 0 0
\(106\) 60.2930 130.993i 0.568802 1.23578i
\(107\) −68.8129 166.129i −0.643111 1.55261i −0.822461 0.568822i \(-0.807399\pi\)
0.179350 0.983785i \(-0.442601\pi\)
\(108\) 0 0
\(109\) 3.61301 8.72257i 0.0331469 0.0800236i −0.906439 0.422336i \(-0.861210\pi\)
0.939586 + 0.342313i \(0.111210\pi\)
\(110\) −2.68333 + 69.3580i −0.0243939 + 0.630528i
\(111\) 0 0
\(112\) 5.23591 + 7.17030i 0.0467492 + 0.0640205i
\(113\) 85.8345i 0.759598i 0.925069 + 0.379799i \(0.124007\pi\)
−0.925069 + 0.379799i \(0.875993\pi\)
\(114\) 0 0
\(115\) −2.65695 1.10055i −0.0231039 0.00956997i
\(116\) −1.45466 + 2.86343i −0.0125401 + 0.0246847i
\(117\) 0 0
\(118\) −58.8971 + 127.960i −0.499128 + 1.08441i
\(119\) −4.13575 + 4.13575i −0.0347542 + 0.0347542i
\(120\) 0 0
\(121\) 44.6936 44.6936i 0.369369 0.369369i
\(122\) 177.534 65.6169i 1.45520 0.537844i
\(123\) 0 0
\(124\) −190.209 14.7397i −1.53394 0.118869i
\(125\) −122.985 50.9419i −0.983877 0.407535i
\(126\) 0 0
\(127\) 17.2873i 0.136120i −0.997681 0.0680601i \(-0.978319\pi\)
0.997681 0.0680601i \(-0.0216810\pi\)
\(128\) 63.0128 + 111.415i 0.492288 + 0.870432i
\(129\) 0 0
\(130\) 78.8923 73.0153i 0.606864 0.561656i
\(131\) 40.2223 97.1053i 0.307041 0.741262i −0.692758 0.721171i \(-0.743604\pi\)
0.999798 0.0200911i \(-0.00639562\pi\)
\(132\) 0 0
\(133\) 0.433744 + 1.04715i 0.00326123 + 0.00787331i
\(134\) 12.9072 + 34.9218i 0.0963223 + 0.260610i
\(135\) 0 0
\(136\) −66.1250 + 52.3224i −0.486213 + 0.384723i
\(137\) −25.5351 25.5351i −0.186387 0.186387i 0.607745 0.794132i \(-0.292074\pi\)
−0.794132 + 0.607745i \(0.792074\pi\)
\(138\) 0 0
\(139\) −52.2202 126.071i −0.375685 0.906984i −0.992764 0.120083i \(-0.961684\pi\)
0.617079 0.786901i \(-0.288316\pi\)
\(140\) 9.03396 + 4.58936i 0.0645283 + 0.0327812i
\(141\) 0 0
\(142\) 41.8587 + 1.61943i 0.294779 + 0.0114045i
\(143\) 89.5052 0.625910
\(144\) 0 0
\(145\) 3.66548i 0.0252792i
\(146\) 52.7730 + 2.04169i 0.361459 + 0.0139842i
\(147\) 0 0
\(148\) 144.167 47.0343i 0.974100 0.317799i
\(149\) −151.298 + 62.6697i −1.01542 + 0.420602i −0.827430 0.561569i \(-0.810198\pi\)
−0.187993 + 0.982170i \(0.560198\pi\)
\(150\) 0 0
\(151\) −123.292 + 123.292i −0.816505 + 0.816505i −0.985600 0.169095i \(-0.945916\pi\)
0.169095 + 0.985600i \(0.445916\pi\)
\(152\) 4.46380 + 15.7189i 0.0293671 + 0.103414i
\(153\) 0 0
\(154\) 2.92496 + 7.91381i 0.0189933 + 0.0513883i
\(155\) −201.158 + 83.3223i −1.29779 + 0.537563i
\(156\) 0 0
\(157\) 107.069 + 44.3494i 0.681968 + 0.282480i 0.696649 0.717412i \(-0.254673\pi\)
−0.0146813 + 0.999892i \(0.504673\pi\)
\(158\) −53.1939 + 49.2312i −0.336670 + 0.311590i
\(159\) 0 0
\(160\) 121.707 + 80.7943i 0.760671 + 0.504964i
\(161\) −0.349573 −0.00217126
\(162\) 0 0
\(163\) −48.6441 + 117.437i −0.298430 + 0.720474i 0.701539 + 0.712631i \(0.252497\pi\)
−0.999969 + 0.00784306i \(0.997503\pi\)
\(164\) 48.7141 41.7072i 0.297037 0.254312i
\(165\) 0 0
\(166\) −55.0006 + 20.3284i −0.331329 + 0.122460i
\(167\) −88.6392 88.6392i −0.530774 0.530774i 0.390029 0.920803i \(-0.372465\pi\)
−0.920803 + 0.390029i \(0.872465\pi\)
\(168\) 0 0
\(169\) 21.4841 + 21.4841i 0.127125 + 0.127125i
\(170\) −40.2370 + 87.4189i −0.236688 + 0.514229i
\(171\) 0 0
\(172\) −145.499 + 47.4691i −0.845927 + 0.275983i
\(173\) −87.2836 + 210.721i −0.504530 + 1.21804i 0.442463 + 0.896787i \(0.354105\pi\)
−0.946993 + 0.321255i \(0.895895\pi\)
\(174\) 0 0
\(175\) −2.30827 −0.0131901
\(176\) 28.6795 + 118.206i 0.162952 + 0.671625i
\(177\) 0 0
\(178\) 6.17737 159.671i 0.0347043 0.897028i
\(179\) 5.53118 + 2.29109i 0.0309005 + 0.0127994i 0.398080 0.917351i \(-0.369677\pi\)
−0.367180 + 0.930150i \(0.619677\pi\)
\(180\) 0 0
\(181\) −273.836 + 113.427i −1.51291 + 0.626666i −0.976155 0.217075i \(-0.930348\pi\)
−0.536751 + 0.843741i \(0.680348\pi\)
\(182\) 5.46327 11.8695i 0.0300180 0.0652171i
\(183\) 0 0
\(184\) −5.00586 0.583331i −0.0272057 0.00317028i
\(185\) 122.379 122.379i 0.661506 0.661506i
\(186\) 0 0
\(187\) −74.0295 + 30.6640i −0.395880 + 0.163979i
\(188\) 24.8830 321.103i 0.132356 1.70800i
\(189\) 0 0
\(190\) 12.6672 + 13.6867i 0.0666693 + 0.0720355i
\(191\) 140.503i 0.735620i 0.929901 + 0.367810i \(0.119892\pi\)
−0.929901 + 0.367810i \(0.880108\pi\)
\(192\) 0 0
\(193\) −159.719 −0.827560 −0.413780 0.910377i \(-0.635792\pi\)
−0.413780 + 0.910377i \(0.635792\pi\)
\(194\) 232.767 215.427i 1.19983 1.11045i
\(195\) 0 0
\(196\) −194.186 15.0479i −0.990746 0.0767751i
\(197\) 23.3511 + 56.3745i 0.118533 + 0.286165i 0.971999 0.234984i \(-0.0755037\pi\)
−0.853466 + 0.521149i \(0.825504\pi\)
\(198\) 0 0
\(199\) 138.741 + 138.741i 0.697191 + 0.697191i 0.963804 0.266613i \(-0.0859044\pi\)
−0.266613 + 0.963804i \(0.585904\pi\)
\(200\) −33.0543 3.85181i −0.165272 0.0192591i
\(201\) 0 0
\(202\) 255.615 + 117.654i 1.26542 + 0.582444i
\(203\) 0.170506 + 0.411638i 0.000839931 + 0.00202777i
\(204\) 0 0
\(205\) 28.0083 67.6180i 0.136626 0.329844i
\(206\) 28.1107 + 1.08755i 0.136460 + 0.00527937i
\(207\) 0 0
\(208\) 98.0403 160.854i 0.471348 0.773337i
\(209\) 15.5279i 0.0742963i
\(210\) 0 0
\(211\) −194.276 80.4718i −0.920740 0.381383i −0.128582 0.991699i \(-0.541043\pi\)
−0.792158 + 0.610316i \(0.791043\pi\)
\(212\) −89.4516 274.182i −0.421942 1.29331i
\(213\) 0 0
\(214\) −326.689 150.368i −1.52658 0.702653i
\(215\) −123.510 + 123.510i −0.574464 + 0.574464i
\(216\) 0 0
\(217\) −18.7144 + 18.7144i −0.0862414 + 0.0862414i
\(218\) −6.54620 17.7115i −0.0300284 0.0812452i
\(219\) 0 0
\(220\) 90.2831 + 105.451i 0.410378 + 0.479323i
\(221\) 114.650 + 47.4894i 0.518776 + 0.214884i
\(222\) 0 0
\(223\) 285.957i 1.28232i −0.767408 0.641160i \(-0.778454\pi\)
0.767408 0.641160i \(-0.221546\pi\)
\(224\) 17.4262 + 3.41187i 0.0777954 + 0.0152316i
\(225\) 0 0
\(226\) 116.605 + 125.990i 0.515951 + 0.557480i
\(227\) −8.02885 + 19.3834i −0.0353694 + 0.0853893i −0.940577 0.339580i \(-0.889715\pi\)
0.905208 + 0.424969i \(0.139715\pi\)
\(228\) 0 0
\(229\) −66.9028 161.518i −0.292152 0.705317i 0.707848 0.706365i \(-0.249666\pi\)
−0.999999 + 0.00104819i \(0.999666\pi\)
\(230\) −5.39503 + 1.99402i −0.0234566 + 0.00866963i
\(231\) 0 0
\(232\) 1.75474 + 6.17915i 0.00756352 + 0.0266343i
\(233\) −282.286 282.286i −1.21153 1.21153i −0.970525 0.241001i \(-0.922524\pi\)
−0.241001 0.970525i \(-0.577476\pi\)
\(234\) 0 0
\(235\) −140.662 339.587i −0.598560 1.44505i
\(236\) 87.3807 + 267.834i 0.370257 + 1.13489i
\(237\) 0 0
\(238\) −0.452223 + 11.6889i −0.00190010 + 0.0491131i
\(239\) −13.1618 −0.0550704 −0.0275352 0.999621i \(-0.508766\pi\)
−0.0275352 + 0.999621i \(0.508766\pi\)
\(240\) 0 0
\(241\) 231.745i 0.961599i 0.876830 + 0.480800i \(0.159654\pi\)
−0.876830 + 0.480800i \(0.840346\pi\)
\(242\) 4.88701 126.318i 0.0201943 0.521976i
\(243\) 0 0
\(244\) 171.450 337.491i 0.702663 1.38316i
\(245\) −205.364 + 85.0647i −0.838222 + 0.347203i
\(246\) 0 0
\(247\) 17.0046 17.0046i 0.0688445 0.0688445i
\(248\) −299.217 + 236.760i −1.20652 + 0.954678i
\(249\) 0 0
\(250\) −249.724 + 92.2986i −0.998896 + 0.369194i
\(251\) −131.701 + 54.5521i −0.524703 + 0.217339i −0.629281 0.777177i \(-0.716651\pi\)
0.104578 + 0.994517i \(0.466651\pi\)
\(252\) 0 0
\(253\) −4.42459 1.83272i −0.0174885 0.00724397i
\(254\) −23.4845 25.3748i −0.0924586 0.0999006i
\(255\) 0 0
\(256\) 243.848 + 77.9367i 0.952531 + 0.304440i
\(257\) 70.0955 0.272745 0.136373 0.990658i \(-0.456456\pi\)
0.136373 + 0.990658i \(0.456456\pi\)
\(258\) 0 0
\(259\) 8.05061 19.4359i 0.0310834 0.0750420i
\(260\) 16.6103 214.348i 0.0638858 0.824415i
\(261\) 0 0
\(262\) −72.8765 197.175i −0.278155 0.752577i
\(263\) 245.883 + 245.883i 0.934916 + 0.934916i 0.998008 0.0630921i \(-0.0200962\pi\)
−0.0630921 + 0.998008i \(0.520096\pi\)
\(264\) 0 0
\(265\) −232.744 232.744i −0.878280 0.878280i
\(266\) 2.05920 + 0.947803i 0.00774135 + 0.00356317i
\(267\) 0 0
\(268\) 66.3862 + 33.7250i 0.247710 + 0.125840i
\(269\) −7.33716 + 17.7135i −0.0272757 + 0.0658493i −0.936931 0.349516i \(-0.886346\pi\)
0.909655 + 0.415365i \(0.136346\pi\)
\(270\) 0 0
\(271\) 327.600 1.20886 0.604429 0.796659i \(-0.293401\pi\)
0.604429 + 0.796659i \(0.293401\pi\)
\(272\) −25.9811 + 166.630i −0.0955187 + 0.612610i
\(273\) 0 0
\(274\) −72.1701 2.79213i −0.263394 0.0101902i
\(275\) −29.2161 12.1017i −0.106240 0.0440063i
\(276\) 0 0
\(277\) −31.9345 + 13.2277i −0.115287 + 0.0477535i −0.439581 0.898203i \(-0.644873\pi\)
0.324294 + 0.945956i \(0.394873\pi\)
\(278\) −247.916 114.110i −0.891783 0.410468i
\(279\) 0 0
\(280\) 19.4949 5.53609i 0.0696246 0.0197718i
\(281\) 263.413 263.413i 0.937413 0.937413i −0.0607409 0.998154i \(-0.519346\pi\)
0.998154 + 0.0607409i \(0.0193463\pi\)
\(282\) 0 0
\(283\) −268.113 + 111.056i −0.947397 + 0.392425i −0.802252 0.596986i \(-0.796365\pi\)
−0.145145 + 0.989410i \(0.546365\pi\)
\(284\) 63.6413 54.4873i 0.224089 0.191857i
\(285\) 0 0
\(286\) 131.378 121.591i 0.459365 0.425145i
\(287\) 8.89644i 0.0309980i
\(288\) 0 0
\(289\) 177.904 0.615585
\(290\) 4.97950 + 5.38030i 0.0171707 + 0.0185528i
\(291\) 0 0
\(292\) 80.2353 68.6944i 0.274778 0.235255i
\(293\) −44.7772 108.102i −0.152823 0.368948i 0.828863 0.559451i \(-0.188988\pi\)
−0.981687 + 0.190503i \(0.938988\pi\)
\(294\) 0 0
\(295\) 227.356 + 227.356i 0.770698 + 0.770698i
\(296\) 147.717 264.887i 0.499043 0.894887i
\(297\) 0 0
\(298\) −136.944 + 297.524i −0.459543 + 0.998404i
\(299\) 2.83834 + 6.85237i 0.00949279 + 0.0229176i
\(300\) 0 0
\(301\) −8.12503 + 19.6155i −0.0269934 + 0.0651679i
\(302\) −13.4814 + 348.462i −0.0446403 + 1.15385i
\(303\) 0 0
\(304\) 27.9060 + 17.0087i 0.0917960 + 0.0559495i
\(305\) 432.024i 1.41647i
\(306\) 0 0
\(307\) 430.497 + 178.318i 1.40227 + 0.580839i 0.950340 0.311215i \(-0.100736\pi\)
0.451930 + 0.892054i \(0.350736\pi\)
\(308\) 15.0441 + 7.64260i 0.0488446 + 0.0248136i
\(309\) 0 0
\(310\) −182.073 + 395.573i −0.587333 + 1.27604i
\(311\) 61.3250 61.3250i 0.197187 0.197187i −0.601606 0.798793i \(-0.705472\pi\)
0.798793 + 0.601606i \(0.205472\pi\)
\(312\) 0 0
\(313\) 129.308 129.308i 0.413124 0.413124i −0.469701 0.882826i \(-0.655638\pi\)
0.882826 + 0.469701i \(0.155638\pi\)
\(314\) 217.407 80.3541i 0.692379 0.255905i
\(315\) 0 0
\(316\) −11.1996 + 144.526i −0.0354419 + 0.457361i
\(317\) 286.711 + 118.760i 0.904452 + 0.374636i 0.785930 0.618315i \(-0.212184\pi\)
0.118522 + 0.992951i \(0.462184\pi\)
\(318\) 0 0
\(319\) 6.10408i 0.0191350i
\(320\) 288.403 46.7454i 0.901261 0.146079i
\(321\) 0 0
\(322\) −0.513113 + 0.474889i −0.00159352 + 0.00147481i
\(323\) −8.23877 + 19.8901i −0.0255070 + 0.0615794i
\(324\) 0 0
\(325\) 18.7420 + 45.2471i 0.0576676 + 0.139222i
\(326\) 88.1354 + 238.460i 0.270354 + 0.731472i
\(327\) 0 0
\(328\) 14.8455 127.396i 0.0452606 0.388403i
\(329\) −31.5929 31.5929i −0.0960271 0.0960271i
\(330\) 0 0
\(331\) 123.164 + 297.345i 0.372098 + 0.898324i 0.993395 + 0.114748i \(0.0366061\pi\)
−0.621297 + 0.783575i \(0.713394\pi\)
\(332\) −53.1158 + 104.556i −0.159987 + 0.314928i
\(333\) 0 0
\(334\) −250.522 9.69223i −0.750066 0.0290187i
\(335\) 84.9812 0.253675
\(336\) 0 0
\(337\) 263.653i 0.782354i 0.920315 + 0.391177i \(0.127932\pi\)
−0.920315 + 0.391177i \(0.872068\pi\)
\(338\) 60.7209 + 2.34918i 0.179648 + 0.00695023i
\(339\) 0 0
\(340\) 59.6962 + 182.977i 0.175577 + 0.538168i
\(341\) −334.985 + 138.755i −0.982362 + 0.406908i
\(342\) 0 0
\(343\) −38.3323 + 38.3323i −0.111756 + 0.111756i
\(344\) −149.082 + 267.335i −0.433379 + 0.777137i
\(345\) 0 0
\(346\) 158.144 + 427.876i 0.457064 + 1.23664i
\(347\) 388.417 160.888i 1.11936 0.463653i 0.255208 0.966886i \(-0.417856\pi\)
0.864151 + 0.503233i \(0.167856\pi\)
\(348\) 0 0
\(349\) 448.277 + 185.683i 1.28446 + 0.532042i 0.917330 0.398127i \(-0.130340\pi\)
0.367132 + 0.930169i \(0.380340\pi\)
\(350\) −3.38815 + 3.13575i −0.00968044 + 0.00895930i
\(351\) 0 0
\(352\) 202.678 + 134.546i 0.575789 + 0.382232i
\(353\) 106.951 0.302976 0.151488 0.988459i \(-0.451593\pi\)
0.151488 + 0.988459i \(0.451593\pi\)
\(354\) 0 0
\(355\) 36.5908 88.3379i 0.103073 0.248839i
\(356\) −207.843 242.761i −0.583829 0.681914i
\(357\) 0 0
\(358\) 11.2312 4.15109i 0.0313722 0.0115952i
\(359\) 208.761 + 208.761i 0.581508 + 0.581508i 0.935317 0.353810i \(-0.115114\pi\)
−0.353810 + 0.935317i \(0.615114\pi\)
\(360\) 0 0
\(361\) −252.315 252.315i −0.698935 0.698935i
\(362\) −247.856 + 538.492i −0.684685 + 1.48755i
\(363\) 0 0
\(364\) −8.10539 24.8442i −0.0222676 0.0682532i
\(365\) 46.1315 111.371i 0.126388 0.305127i
\(366\) 0 0
\(367\) 711.002 1.93734 0.968668 0.248361i \(-0.0798919\pi\)
0.968668 + 0.248361i \(0.0798919\pi\)
\(368\) −8.14019 + 5.94415i −0.0221201 + 0.0161526i
\(369\) 0 0
\(370\) 13.3815 345.880i 0.0361661 0.934811i
\(371\) −36.9639 15.3110i −0.0996332 0.0412694i
\(372\) 0 0
\(373\) −587.430 + 243.321i −1.57488 + 0.652336i −0.987592 0.157043i \(-0.949804\pi\)
−0.587287 + 0.809379i \(0.699804\pi\)
\(374\) −67.0060 + 145.577i −0.179160 + 0.389244i
\(375\) 0 0
\(376\) −399.689 505.128i −1.06300 1.34342i
\(377\) 6.68456 6.68456i 0.0177309 0.0177309i
\(378\) 0 0
\(379\) −34.5203 + 14.2988i −0.0910825 + 0.0377276i −0.427759 0.903893i \(-0.640697\pi\)
0.336677 + 0.941620i \(0.390697\pi\)
\(380\) 37.1864 + 2.88166i 0.0978591 + 0.00758332i
\(381\) 0 0
\(382\) 190.872 + 206.235i 0.499664 + 0.539882i
\(383\) 347.623i 0.907631i −0.891096 0.453815i \(-0.850063\pi\)
0.891096 0.453815i \(-0.149937\pi\)
\(384\) 0 0
\(385\) 19.2580 0.0500209
\(386\) −234.440 + 216.976i −0.607359 + 0.562114i
\(387\) 0 0
\(388\) 49.0077 632.421i 0.126309 1.62995i
\(389\) 60.7529 + 146.670i 0.156177 + 0.377045i 0.982529 0.186109i \(-0.0595878\pi\)
−0.826352 + 0.563154i \(0.809588\pi\)
\(390\) 0 0
\(391\) −4.69517 4.69517i −0.0120081 0.0120081i
\(392\) −305.474 + 241.711i −0.779271 + 0.616610i
\(393\) 0 0
\(394\) 110.859 + 51.0260i 0.281368 + 0.129508i
\(395\) 63.3107 + 152.846i 0.160280 + 0.386951i
\(396\) 0 0
\(397\) 179.460 433.255i 0.452041 1.09132i −0.519505 0.854468i \(-0.673883\pi\)
0.971545 0.236855i \(-0.0761165\pi\)
\(398\) 392.126 + 15.1706i 0.985240 + 0.0381171i
\(399\) 0 0
\(400\) −53.7507 + 39.2500i −0.134377 + 0.0981250i
\(401\) 680.550i 1.69713i 0.529089 + 0.848566i \(0.322534\pi\)
−0.529089 + 0.848566i \(0.677466\pi\)
\(402\) 0 0
\(403\) 518.792 + 214.891i 1.28733 + 0.533228i
\(404\) 535.029 174.553i 1.32433 0.432062i
\(405\) 0 0
\(406\) 0.809477 + 0.372584i 0.00199379 + 0.000917696i
\(407\) 203.795 203.795i 0.500725 0.500725i
\(408\) 0 0
\(409\) 239.915 239.915i 0.586589 0.586589i −0.350117 0.936706i \(-0.613858\pi\)
0.936706 + 0.350117i \(0.113858\pi\)
\(410\) −50.7466 137.301i −0.123772 0.334879i
\(411\) 0 0
\(412\) 42.7391 36.5916i 0.103736 0.0888146i
\(413\) 36.1082 + 14.9565i 0.0874289 + 0.0362143i
\(414\) 0 0
\(415\) 133.843i 0.322512i
\(416\) −74.6112 369.292i −0.179354 0.887722i
\(417\) 0 0
\(418\) 21.0944 + 22.7923i 0.0504652 + 0.0545271i
\(419\) −33.5102 + 80.9009i −0.0799767 + 0.193081i −0.958810 0.284048i \(-0.908322\pi\)
0.878833 + 0.477129i \(0.158322\pi\)
\(420\) 0 0
\(421\) 37.2975 + 90.0441i 0.0885926 + 0.213882i 0.961966 0.273170i \(-0.0880723\pi\)
−0.873373 + 0.487052i \(0.838072\pi\)
\(422\) −394.484 + 145.802i −0.934796 + 0.345503i
\(423\) 0 0
\(424\) −503.771 280.933i −1.18814 0.662579i
\(425\) −31.0028 31.0028i −0.0729479 0.0729479i
\(426\) 0 0
\(427\) −20.0963 48.5167i −0.0470639 0.113622i
\(428\) −683.796 + 223.088i −1.59765 + 0.521233i
\(429\) 0 0
\(430\) −13.5051 + 349.077i −0.0314073 + 0.811808i
\(431\) 509.094 1.18119 0.590596 0.806967i \(-0.298893\pi\)
0.590596 + 0.806967i \(0.298893\pi\)
\(432\) 0 0
\(433\) 66.0083i 0.152444i 0.997091 + 0.0762220i \(0.0242858\pi\)
−0.997091 + 0.0762220i \(0.975714\pi\)
\(434\) −2.04632 + 52.8927i −0.00471502 + 0.121873i
\(435\) 0 0
\(436\) −33.6694 17.1045i −0.0772235 0.0392305i
\(437\) −1.18879 + 0.492414i −0.00272035 + 0.00112681i
\(438\) 0 0
\(439\) −39.8501 + 39.8501i −0.0907747 + 0.0907747i −0.751036 0.660261i \(-0.770446\pi\)
0.660261 + 0.751036i \(0.270446\pi\)
\(440\) 275.774 + 32.1358i 0.626758 + 0.0730360i
\(441\) 0 0
\(442\) 232.800 86.0433i 0.526696 0.194668i
\(443\) 193.778 80.2656i 0.437423 0.181187i −0.153094 0.988212i \(-0.548924\pi\)
0.590517 + 0.807025i \(0.298924\pi\)
\(444\) 0 0
\(445\) −336.967 139.576i −0.757229 0.313655i
\(446\) −388.468 419.736i −0.871005 0.941113i
\(447\) 0 0
\(448\) 30.2136 18.6651i 0.0674410 0.0416632i
\(449\) −124.217 −0.276652 −0.138326 0.990387i \(-0.544172\pi\)
−0.138326 + 0.990387i \(0.544172\pi\)
\(450\) 0 0
\(451\) 46.6418 112.603i 0.103419 0.249675i
\(452\) 342.312 + 26.5265i 0.757327 + 0.0586870i
\(453\) 0 0
\(454\) 14.5470 + 39.3585i 0.0320419 + 0.0866928i
\(455\) −21.0894 21.0894i −0.0463504 0.0463504i
\(456\) 0 0
\(457\) −573.100 573.100i −1.25405 1.25405i −0.953889 0.300159i \(-0.902960\pi\)
−0.300159 0.953889i \(-0.597040\pi\)
\(458\) −317.621 146.194i −0.693495 0.319200i
\(459\) 0 0
\(460\) −5.21014 + 10.2559i −0.0113264 + 0.0222955i
\(461\) 86.0707 207.793i 0.186704 0.450744i −0.802617 0.596495i \(-0.796560\pi\)
0.989321 + 0.145750i \(0.0465596\pi\)
\(462\) 0 0
\(463\) −555.587 −1.19997 −0.599986 0.800010i \(-0.704827\pi\)
−0.599986 + 0.800010i \(0.704827\pi\)
\(464\) 10.9699 + 6.68616i 0.0236421 + 0.0144098i
\(465\) 0 0
\(466\) −797.827 30.8664i −1.71208 0.0662370i
\(467\) 319.806 + 132.468i 0.684809 + 0.283657i 0.697835 0.716258i \(-0.254147\pi\)
−0.0130269 + 0.999915i \(0.504147\pi\)
\(468\) 0 0
\(469\) 9.54349 3.95304i 0.0203486 0.00842866i
\(470\) −667.791 307.369i −1.42083 0.653977i
\(471\) 0 0
\(472\) 492.108 + 274.429i 1.04260 + 0.581418i
\(473\) −205.679 + 205.679i −0.434839 + 0.434839i
\(474\) 0 0
\(475\) −7.84975 + 3.25147i −0.0165258 + 0.00684521i
\(476\) 15.2154 + 17.7717i 0.0319652 + 0.0373355i
\(477\) 0 0
\(478\) −19.3193 + 17.8801i −0.0404170 + 0.0374061i
\(479\) 239.576i 0.500159i −0.968225 0.250079i \(-0.919543\pi\)
0.968225 0.250079i \(-0.0804567\pi\)
\(480\) 0 0
\(481\) −446.351 −0.927965
\(482\) 314.822 + 340.163i 0.653159 + 0.705732i
\(483\) 0 0
\(484\) −164.428 192.052i −0.339727 0.396802i
\(485\) −277.037 668.826i −0.571210 1.37902i
\(486\) 0 0
\(487\) −269.525 269.525i −0.553439 0.553439i 0.373992 0.927432i \(-0.377989\pi\)
−0.927432 + 0.373992i \(0.877989\pi\)
\(488\) −206.818 728.291i −0.423807 1.49240i
\(489\) 0 0
\(490\) −185.881 + 403.845i −0.379348 + 0.824173i
\(491\) −285.394 689.002i −0.581250 1.40326i −0.891680 0.452666i \(-0.850473\pi\)
0.310430 0.950596i \(-0.399527\pi\)
\(492\) 0 0
\(493\) −3.23869 + 7.81888i −0.00656934 + 0.0158598i
\(494\) 1.85936 48.0603i 0.00376389 0.0972881i
\(495\) 0 0
\(496\) −117.565 + 754.005i −0.237026 + 1.52017i
\(497\) 11.6225i 0.0233854i
\(498\) 0 0
\(499\) 581.267 + 240.769i 1.16486 + 0.482503i 0.879492 0.475914i \(-0.157883\pi\)
0.285373 + 0.958417i \(0.407883\pi\)
\(500\) −241.166 + 474.725i −0.482332 + 0.949449i
\(501\) 0 0
\(502\) −119.206 + 258.986i −0.237461 + 0.515909i
\(503\) −204.189 + 204.189i −0.405942 + 0.405942i −0.880321 0.474379i \(-0.842673\pi\)
0.474379 + 0.880321i \(0.342673\pi\)
\(504\) 0 0
\(505\) 454.169 454.169i 0.899345 0.899345i
\(506\) −8.98426 + 3.32061i −0.0177555 + 0.00656246i
\(507\) 0 0
\(508\) −68.9424 5.34250i −0.135713 0.0105167i
\(509\) 397.562 + 164.676i 0.781066 + 0.323528i 0.737345 0.675516i \(-0.236079\pi\)
0.0437202 + 0.999044i \(0.486079\pi\)
\(510\) 0 0
\(511\) 14.6530i 0.0286751i
\(512\) 463.803 216.866i 0.905865 0.423566i
\(513\) 0 0
\(514\) 102.888 95.2236i 0.200172 0.185260i
\(515\) 24.5730 59.3244i 0.0477145 0.115193i
\(516\) 0 0
\(517\) −234.242 565.510i −0.453079 1.09383i
\(518\) −14.5864 39.4652i −0.0281591 0.0761876i
\(519\) 0 0
\(520\) −266.807 337.191i −0.513091 0.648444i
\(521\) 333.835 + 333.835i 0.640759 + 0.640759i 0.950742 0.309983i \(-0.100324\pi\)
−0.309983 + 0.950742i \(0.600324\pi\)
\(522\) 0 0
\(523\) −211.672 511.022i −0.404727 0.977097i −0.986502 0.163748i \(-0.947642\pi\)
0.581775 0.813350i \(-0.302358\pi\)
\(524\) −374.830 190.418i −0.715324 0.363393i
\(525\) 0 0
\(526\) 694.942 + 26.8860i 1.32118 + 0.0511141i
\(527\) −502.712 −0.953913
\(528\) 0 0
\(529\) 528.603i 0.999250i
\(530\) −657.808 25.4494i −1.24115 0.0480177i
\(531\) 0 0
\(532\) 4.31013 1.40618i 0.00810174 0.00264319i
\(533\) −174.389 + 72.2343i −0.327184 + 0.135524i
\(534\) 0 0
\(535\) −580.452 + 580.452i −1.08496 + 1.08496i
\(536\) 143.259 40.6821i 0.267273 0.0758994i
\(537\) 0 0
\(538\) 13.2938 + 35.9677i 0.0247096 + 0.0668545i
\(539\) −341.990 + 141.657i −0.634490 + 0.262815i
\(540\) 0 0
\(541\) −529.582 219.360i −0.978896 0.405472i −0.164879 0.986314i \(-0.552723\pi\)
−0.814016 + 0.580842i \(0.802723\pi\)
\(542\) 480.861 445.040i 0.887198 0.821107i
\(543\) 0 0
\(544\) 188.228 + 279.879i 0.346008 + 0.514484i
\(545\) −43.1003 −0.0790832
\(546\) 0 0
\(547\) −68.4960 + 165.364i −0.125221 + 0.302311i −0.974041 0.226371i \(-0.927314\pi\)
0.848820 + 0.528682i \(0.177314\pi\)
\(548\) −109.726 + 93.9435i −0.200231 + 0.171430i
\(549\) 0 0
\(550\) −59.3243 + 21.9264i −0.107862 + 0.0398662i
\(551\) 1.15968 + 1.15968i 0.00210468 + 0.00210468i
\(552\) 0 0
\(553\) 14.2197 + 14.2197i 0.0257138 + 0.0257138i
\(554\) −28.9048 + 62.7986i −0.0521747 + 0.113355i
\(555\) 0 0
\(556\) −518.914 + 169.295i −0.933299 + 0.304488i
\(557\) 308.610 745.049i 0.554057 1.33761i −0.360351 0.932817i \(-0.617343\pi\)
0.914408 0.404794i \(-0.132657\pi\)
\(558\) 0 0
\(559\) 450.477 0.805863
\(560\) 21.0945 34.6095i 0.0376687 0.0618027i
\(561\) 0 0
\(562\) 28.8028 744.487i 0.0512506 1.32471i
\(563\) 347.195 + 143.813i 0.616687 + 0.255440i 0.669085 0.743186i \(-0.266686\pi\)
−0.0523978 + 0.998626i \(0.516686\pi\)
\(564\) 0 0
\(565\) 362.017 149.952i 0.640738 0.265402i
\(566\) −242.676 + 527.239i −0.428757 + 0.931518i
\(567\) 0 0
\(568\) 19.3945 166.434i 0.0341452 0.293017i
\(569\) −717.322 + 717.322i −1.26067 + 1.26067i −0.309903 + 0.950768i \(0.600297\pi\)
−0.950768 + 0.309903i \(0.899703\pi\)
\(570\) 0 0
\(571\) −327.041 + 135.465i −0.572751 + 0.237241i −0.650210 0.759754i \(-0.725319\pi\)
0.0774591 + 0.996996i \(0.475319\pi\)
\(572\) 27.6609 356.951i 0.0483582 0.624039i
\(573\) 0 0
\(574\) −12.0857 13.0584i −0.0210552 0.0227499i
\(575\) 2.62050i 0.00455740i
\(576\) 0 0
\(577\) 531.710 0.921507 0.460754 0.887528i \(-0.347579\pi\)
0.460754 + 0.887528i \(0.347579\pi\)
\(578\) 261.133 241.680i 0.451787 0.418131i
\(579\) 0 0
\(580\) 14.6181 + 1.13279i 0.0252036 + 0.00195309i
\(581\) 6.22591 + 15.0307i 0.0107158 + 0.0258703i
\(582\) 0 0
\(583\) −387.585 387.585i −0.664812 0.664812i
\(584\) 24.4514 209.830i 0.0418689 0.359298i
\(585\) 0 0
\(586\) −212.580 97.8456i −0.362764 0.166972i
\(587\) −105.581 254.894i −0.179865 0.434232i 0.808073 0.589082i \(-0.200510\pi\)
−0.987938 + 0.154850i \(0.950510\pi\)
\(588\) 0 0
\(589\) −37.2806 + 90.0034i −0.0632948 + 0.152807i
\(590\) 642.579 + 24.8602i 1.08912 + 0.0421359i
\(591\) 0 0
\(592\) −143.021 589.479i −0.241590 0.995742i
\(593\) 405.861i 0.684419i −0.939624 0.342210i \(-0.888825\pi\)
0.939624 0.342210i \(-0.111175\pi\)
\(594\) 0 0
\(595\) 24.6681 + 10.2179i 0.0414590 + 0.0171729i
\(596\) 203.172 + 622.751i 0.340892 + 1.04488i
\(597\) 0 0
\(598\) 13.4750 + 6.20226i 0.0225335 + 0.0103717i
\(599\) −561.484 + 561.484i −0.937370 + 0.937370i −0.998151 0.0607815i \(-0.980641\pi\)
0.0607815 + 0.998151i \(0.480641\pi\)
\(600\) 0 0
\(601\) −358.762 + 358.762i −0.596941 + 0.596941i −0.939497 0.342556i \(-0.888707\pi\)
0.342556 + 0.939497i \(0.388707\pi\)
\(602\) 14.7213 + 39.8300i 0.0244539 + 0.0661628i
\(603\) 0 0
\(604\) 453.592 + 529.797i 0.750981 + 0.877148i
\(605\) −266.580 110.421i −0.440628 0.182514i
\(606\) 0 0
\(607\) 571.923i 0.942213i −0.882076 0.471107i \(-0.843855\pi\)
0.882076 0.471107i \(-0.156145\pi\)
\(608\) 64.0672 12.9440i 0.105374 0.0212895i
\(609\) 0 0
\(610\) −586.897 634.137i −0.962126 1.03957i
\(611\) −362.771 + 875.806i −0.593733 + 1.43340i
\(612\) 0 0
\(613\) 401.254 + 968.712i 0.654574 + 1.58028i 0.806068 + 0.591823i \(0.201591\pi\)
−0.151494 + 0.988458i \(0.548409\pi\)
\(614\) 874.137 323.083i 1.42368 0.526194i
\(615\) 0 0
\(616\) 32.4645 9.21918i 0.0527022 0.0149662i
\(617\) 151.870 + 151.870i 0.246143 + 0.246143i 0.819386 0.573242i \(-0.194315\pi\)
−0.573242 + 0.819386i \(0.694315\pi\)
\(618\) 0 0
\(619\) 146.518 + 353.725i 0.236701 + 0.571446i 0.996938 0.0781999i \(-0.0249173\pi\)
−0.760237 + 0.649646i \(0.774917\pi\)
\(620\) 270.127 + 827.977i 0.435688 + 1.33545i
\(621\) 0 0
\(622\) 6.70557 173.324i 0.0107807 0.278656i
\(623\) −44.3344 −0.0711628
\(624\) 0 0
\(625\) 503.703i 0.805924i
\(626\) 14.1391 365.465i 0.0225865 0.583809i
\(627\) 0 0
\(628\) 209.956 413.290i 0.334325 0.658105i
\(629\) 369.176 152.918i 0.586925 0.243112i
\(630\) 0 0
\(631\) −682.535 + 682.535i −1.08167 + 1.08167i −0.0853189 + 0.996354i \(0.527191\pi\)
−0.996354 + 0.0853189i \(0.972809\pi\)
\(632\) 179.897 + 227.354i 0.284647 + 0.359737i
\(633\) 0 0
\(634\) 582.176 215.174i 0.918259 0.339391i
\(635\) −72.9111 + 30.2007i −0.114821 + 0.0475602i
\(636\) 0 0
\(637\) 529.641 + 219.385i 0.831462 + 0.344403i
\(638\) 8.29229 + 8.95974i 0.0129973 + 0.0140435i
\(639\) 0 0
\(640\) 359.824 460.406i 0.562225 0.719384i
\(641\) −38.9310 −0.0607348 −0.0303674 0.999539i \(-0.509668\pi\)
−0.0303674 + 0.999539i \(0.509668\pi\)
\(642\) 0 0
\(643\) 318.631 769.243i 0.495538 1.19633i −0.456326 0.889813i \(-0.650835\pi\)
0.951864 0.306522i \(-0.0991652\pi\)
\(644\) −0.108033 + 1.39411i −0.000167753 + 0.00216477i
\(645\) 0 0
\(646\) 14.9273 + 40.3876i 0.0231073 + 0.0625194i
\(647\) 157.445 + 157.445i 0.243346 + 0.243346i 0.818233 0.574887i \(-0.194954\pi\)
−0.574887 + 0.818233i \(0.694954\pi\)
\(648\) 0 0
\(649\) 378.612 + 378.612i 0.583378 + 0.583378i
\(650\) 88.9774 + 40.9543i 0.136888 + 0.0630067i
\(651\) 0 0
\(652\) 453.312 + 230.288i 0.695264 + 0.353202i
\(653\) 15.6861 37.8696i 0.0240216 0.0579933i −0.911414 0.411492i \(-0.865008\pi\)
0.935435 + 0.353498i \(0.115008\pi\)
\(654\) 0 0
\(655\) −479.821 −0.732551
\(656\) −151.275 207.163i −0.230603 0.315798i
\(657\) 0 0
\(658\) −89.2915 3.45452i −0.135701 0.00525003i
\(659\) −187.169 77.5281i −0.284020 0.117645i 0.236125 0.971723i \(-0.424122\pi\)
−0.520146 + 0.854078i \(0.674122\pi\)
\(660\) 0 0
\(661\) 30.1818 12.5017i 0.0456608 0.0189133i −0.359736 0.933054i \(-0.617133\pi\)
0.405397 + 0.914141i \(0.367133\pi\)
\(662\) 584.723 + 269.135i 0.883267 + 0.406548i
\(663\) 0 0
\(664\) 64.0729 + 225.627i 0.0964954 + 0.339800i
\(665\) 3.65873 3.65873i 0.00550184 0.00550184i
\(666\) 0 0
\(667\) −0.467318 + 0.193569i −0.000700627 + 0.000290209i
\(668\) −380.890 + 326.104i −0.570195 + 0.488179i
\(669\) 0 0
\(670\) 124.738 115.446i 0.186176 0.172307i
\(671\) 719.443i 1.07219i
\(672\) 0 0
\(673\) −327.878 −0.487189 −0.243595 0.969877i \(-0.578327\pi\)
−0.243595 + 0.969877i \(0.578327\pi\)
\(674\) 358.169 + 386.998i 0.531408 + 0.574181i
\(675\) 0 0
\(676\) 92.3192 79.0402i 0.136567 0.116923i
\(677\) −117.661 284.058i −0.173797 0.419583i 0.812846 0.582478i \(-0.197917\pi\)
−0.986643 + 0.162895i \(0.947917\pi\)
\(678\) 0 0
\(679\) −62.2231 62.2231i −0.0916393 0.0916393i
\(680\) 336.195 + 187.483i 0.494405 + 0.275710i
\(681\) 0 0
\(682\) −303.204 + 658.741i −0.444581 + 0.965897i
\(683\) 324.811 + 784.162i 0.475564 + 1.14811i 0.961669 + 0.274213i \(0.0884175\pi\)
−0.486104 + 0.873901i \(0.661583\pi\)
\(684\) 0 0
\(685\) −63.0875 + 152.307i −0.0920985 + 0.222345i
\(686\) −4.19143 + 108.339i −0.00610996 + 0.157929i
\(687\) 0 0
\(688\) 144.343 + 594.928i 0.209801 + 0.864721i
\(689\) 848.888i 1.23206i
\(690\) 0 0
\(691\) 826.286 + 342.259i 1.19578 + 0.495309i 0.889634 0.456674i \(-0.150959\pi\)
0.306149 + 0.951984i \(0.400959\pi\)
\(692\) 813.391 + 413.213i 1.17542 + 0.597128i
\(693\) 0 0
\(694\) 351.567 763.815i 0.506580 1.10060i
\(695\) −440.490 + 440.490i −0.633798 + 0.633798i
\(696\) 0 0
\(697\) 119.490 119.490i 0.171434 0.171434i
\(698\) 910.241 336.427i 1.30407 0.481988i
\(699\) 0 0
\(700\) −0.713355 + 9.20550i −0.00101908 + 0.0131507i
\(701\) −430.597 178.359i −0.614260 0.254435i 0.0537885 0.998552i \(-0.482870\pi\)
−0.668049 + 0.744117i \(0.732870\pi\)
\(702\) 0 0
\(703\) 77.4359i 0.110151i
\(704\) 480.274 77.8444i 0.682207 0.110574i
\(705\) 0 0
\(706\) 156.985 145.291i 0.222359 0.205794i
\(707\) 29.8773 72.1301i 0.0422592 0.102023i
\(708\) 0 0
\(709\) −77.1066 186.152i −0.108754 0.262555i 0.860128 0.510078i \(-0.170384\pi\)
−0.968882 + 0.247523i \(0.920384\pi\)
\(710\) −66.2967 179.373i −0.0933756 0.252638i
\(711\) 0 0
\(712\) −634.866 73.9807i −0.891665 0.103906i
\(713\) −21.2458 21.2458i −0.0297977 0.0297977i
\(714\) 0 0
\(715\) −156.365 377.498i −0.218692 0.527970i
\(716\) 10.8463 21.3506i 0.0151485 0.0298192i
\(717\) 0 0
\(718\) 590.025 + 22.8270i 0.821762 + 0.0317924i
\(719\) −809.898 −1.12642 −0.563212 0.826313i \(-0.690434\pi\)
−0.563212 + 0.826313i \(0.690434\pi\)
\(720\) 0 0
\(721\) 7.80525i 0.0108256i
\(722\) −713.122 27.5894i −0.987704 0.0382124i
\(723\) 0 0
\(724\) 367.723 + 1127.12i 0.507905 + 1.55680i
\(725\) −3.08576 + 1.27817i −0.00425623 + 0.00176299i
\(726\) 0 0
\(727\) 542.456 542.456i 0.746156 0.746156i −0.227599 0.973755i \(-0.573087\pi\)
0.973755 + 0.227599i \(0.0730875\pi\)
\(728\) −45.6477 25.4559i −0.0627029 0.0349670i
\(729\) 0 0
\(730\) −83.5830 226.143i −0.114497 0.309785i
\(731\) −372.588 + 154.331i −0.509697 + 0.211123i
\(732\) 0 0
\(733\) 562.276 + 232.903i 0.767089 + 0.317739i 0.731693 0.681635i \(-0.238731\pi\)
0.0353965 + 0.999373i \(0.488731\pi\)
\(734\) 1043.63 965.885i 1.42184 1.31592i
\(735\) 0 0
\(736\) −3.87337 + 19.7833i −0.00526273 + 0.0268795i
\(737\) 141.518 0.192019
\(738\) 0 0
\(739\) −305.819 + 738.312i −0.413828 + 0.999070i 0.570272 + 0.821456i \(0.306838\pi\)
−0.984100 + 0.177614i \(0.943162\pi\)
\(740\) −450.231 525.871i −0.608420 0.710637i
\(741\) 0 0
\(742\) −75.0564 + 27.7410i −0.101154 + 0.0373868i
\(743\) −581.334 581.334i −0.782414 0.782414i 0.197823 0.980238i \(-0.436613\pi\)
−0.980238 + 0.197823i \(0.936613\pi\)
\(744\) 0 0
\(745\) 528.633 + 528.633i 0.709574 + 0.709574i
\(746\) −531.698 + 1155.17i −0.712732 + 1.54848i
\(747\) 0 0
\(748\) 99.4112 + 304.709i 0.132903 + 0.407365i
\(749\) −38.1847 + 92.1861i −0.0509810 + 0.123079i
\(750\) 0 0
\(751\) −187.901 −0.250201 −0.125100 0.992144i \(-0.539925\pi\)
−0.125100 + 0.992144i \(0.539925\pi\)
\(752\) −1272.88 198.469i −1.69266 0.263922i
\(753\) 0 0
\(754\) 0.730922 18.8927i 0.000969392 0.0250566i
\(755\) 735.390 + 304.608i 0.974026 + 0.403455i
\(756\) 0 0
\(757\) −168.645 + 69.8549i −0.222780 + 0.0922786i −0.491282 0.871001i \(-0.663472\pi\)
0.268502 + 0.963279i \(0.413472\pi\)
\(758\) −31.2452 + 67.8833i −0.0412206 + 0.0895559i
\(759\) 0 0
\(760\) 58.4980 46.2874i 0.0769711 0.0609045i
\(761\) −391.406 + 391.406i −0.514331 + 0.514331i −0.915850 0.401520i \(-0.868482\pi\)
0.401520 + 0.915850i \(0.368482\pi\)
\(762\) 0 0
\(763\) −4.84022 + 2.00488i −0.00634367 + 0.00262763i
\(764\) 560.334 + 43.4215i 0.733421 + 0.0568345i
\(765\) 0 0
\(766\) −472.240 510.250i −0.616501 0.666123i
\(767\) 829.235i 1.08114i
\(768\) 0 0
\(769\) 184.433 0.239835 0.119918 0.992784i \(-0.461737\pi\)
0.119918 + 0.992784i \(0.461737\pi\)
\(770\) 28.2675 26.1617i 0.0367110 0.0339763i
\(771\) 0 0
\(772\) −49.3600 + 636.967i −0.0639378 + 0.825087i
\(773\) 140.532 + 339.275i 0.181801 + 0.438907i 0.988338 0.152277i \(-0.0486607\pi\)
−0.806537 + 0.591184i \(0.798661\pi\)
\(774\) 0 0
\(775\) −140.289 140.289i −0.181018 0.181018i
\(776\) −787.199 994.862i −1.01443 1.28204i
\(777\) 0 0
\(778\) 288.424 + 132.755i 0.370725 + 0.170637i
\(779\) −12.5317 30.2541i −0.0160869 0.0388371i
\(780\) 0 0
\(781\) 60.9340 147.108i 0.0780206 0.188358i
\(782\) −13.2700 0.513392i −0.0169693 0.000656512i
\(783\) 0 0
\(784\) −120.024 + 769.772i −0.153091 + 0.981852i
\(785\) 529.054i 0.673954i
\(786\) 0 0
\(787\) −926.743 383.870i −1.17756 0.487763i −0.293878 0.955843i \(-0.594946\pi\)
−0.883686