Properties

Label 288.3.u.a.19.4
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 19.4
Character \(\chi\) \(=\) 288.19
Dual form 288.3.u.a.91.4

$q$-expansion

\(f(q)\) \(=\) \(q+(0.108191 + 1.99707i) q^{2} +(-3.97659 + 0.432130i) q^{4} +(2.81639 - 1.16659i) q^{5} +(-6.23443 - 6.23443i) q^{7} +(-1.29322 - 7.89478i) q^{8} +O(q^{10})\) \(q+(0.108191 + 1.99707i) q^{2} +(-3.97659 + 0.432130i) q^{4} +(2.81639 - 1.16659i) q^{5} +(-6.23443 - 6.23443i) q^{7} +(-1.29322 - 7.89478i) q^{8} +(2.63447 + 5.49832i) q^{10} +(8.06262 - 3.33965i) q^{11} +(13.3208 + 5.51766i) q^{13} +(11.7761 - 13.1251i) q^{14} +(15.6265 - 3.43680i) q^{16} -4.56488i q^{17} +(13.4421 - 32.4522i) q^{19} +(-10.6955 + 5.85609i) q^{20} +(7.54181 + 15.7403i) q^{22} +(6.75277 - 6.75277i) q^{23} +(-11.1065 + 11.1065i) q^{25} +(-9.57798 + 27.1996i) q^{26} +(27.4859 + 22.0977i) q^{28} +(0.266504 - 0.643399i) q^{29} +0.326715i q^{31} +(8.55419 + 30.8355i) q^{32} +(9.11639 - 0.493878i) q^{34} +(-24.8316 - 10.2856i) q^{35} +(31.5133 - 13.0532i) q^{37} +(66.2637 + 23.3339i) q^{38} +(-12.8522 - 20.7261i) q^{40} +(-15.7509 - 15.7509i) q^{41} +(4.83274 - 2.00179i) q^{43} +(-30.6186 + 16.7645i) q^{44} +(14.2164 + 12.7552i) q^{46} +49.7096 q^{47} +28.7362i q^{49} +(-23.3822 - 20.9789i) q^{50} +(-55.3558 - 16.1852i) q^{52} +(-4.45882 - 10.7645i) q^{53} +(18.8115 - 18.8115i) q^{55} +(-41.1569 + 57.2820i) q^{56} +(1.31375 + 0.462619i) q^{58} +(-13.1268 - 31.6909i) q^{59} +(-35.4023 + 85.4687i) q^{61} +(-0.652473 + 0.0353475i) q^{62} +(-60.6551 + 20.4194i) q^{64} +43.9535 q^{65} +(-41.3348 - 17.1214i) q^{67} +(1.97262 + 18.1527i) q^{68} +(17.8545 - 50.7033i) q^{70} +(-37.6381 - 37.6381i) q^{71} +(-52.2302 - 52.2302i) q^{73} +(29.4777 + 61.5220i) q^{74} +(-39.4303 + 134.858i) q^{76} +(-71.0866 - 29.4450i) q^{77} +26.9061 q^{79} +(40.0011 - 27.9091i) q^{80} +(29.7516 - 33.1598i) q^{82} +(-10.6315 + 25.6667i) q^{83} +(-5.32533 - 12.8565i) q^{85} +(4.52057 + 9.43475i) q^{86} +(-36.7926 - 59.3337i) q^{88} +(103.292 - 103.292i) q^{89} +(-48.6482 - 117.447i) q^{91} +(-23.9349 + 29.7711i) q^{92} +(5.37812 + 99.2736i) q^{94} -107.080i q^{95} +77.9778 q^{97} +(-57.3883 + 3.10900i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 28q + 4q^{2} - 4q^{4} + 4q^{5} - 4q^{7} + 4q^{8} + O(q^{10}) \) \( 28q + 4q^{2} - 4q^{4} + 4q^{5} - 4q^{7} + 4q^{8} - 44q^{10} + 4q^{11} - 4q^{13} + 20q^{14} + 16q^{16} - 4q^{19} - 76q^{20} + 144q^{22} + 68q^{23} - 4q^{25} - 96q^{26} + 56q^{28} + 4q^{29} + 24q^{32} - 48q^{34} - 92q^{35} - 4q^{37} + 396q^{38} - 408q^{40} + 4q^{41} + 92q^{43} + 188q^{44} - 36q^{46} + 8q^{47} - 308q^{50} + 420q^{52} + 164q^{53} + 252q^{55} - 552q^{56} + 528q^{58} - 124q^{59} - 68q^{61} - 216q^{62} - 232q^{64} + 8q^{65} - 164q^{67} + 368q^{68} - 664q^{70} + 260q^{71} - 4q^{73} + 532q^{74} - 516q^{76} - 220q^{77} - 520q^{79} - 312q^{80} + 636q^{82} + 484q^{83} + 96q^{85} - 688q^{86} + 672q^{88} + 4q^{89} - 196q^{91} - 616q^{92} + 40q^{94} - 8q^{97} + 328q^{98} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.108191 + 1.99707i 0.0540954 + 0.998536i
\(3\) 0 0
\(4\) −3.97659 + 0.432130i −0.994147 + 0.108032i
\(5\) 2.81639 1.16659i 0.563278 0.233318i −0.0828294 0.996564i \(-0.526396\pi\)
0.646108 + 0.763246i \(0.276396\pi\)
\(6\) 0 0
\(7\) −6.23443 6.23443i −0.890633 0.890633i 0.103950 0.994583i \(-0.466852\pi\)
−0.994583 + 0.103950i \(0.966852\pi\)
\(8\) −1.29322 7.89478i −0.161653 0.986848i
\(9\) 0 0
\(10\) 2.63447 + 5.49832i 0.263447 + 0.549832i
\(11\) 8.06262 3.33965i 0.732965 0.303604i 0.0151955 0.999885i \(-0.495163\pi\)
0.717770 + 0.696280i \(0.245163\pi\)
\(12\) 0 0
\(13\) 13.3208 + 5.51766i 1.02468 + 0.424436i 0.830789 0.556588i \(-0.187890\pi\)
0.193889 + 0.981023i \(0.437890\pi\)
\(14\) 11.7761 13.1251i 0.841150 0.937508i
\(15\) 0 0
\(16\) 15.6265 3.43680i 0.976658 0.214800i
\(17\) 4.56488i 0.268522i −0.990946 0.134261i \(-0.957134\pi\)
0.990946 0.134261i \(-0.0428661\pi\)
\(18\) 0 0
\(19\) 13.4421 32.4522i 0.707481 1.70801i 0.00128016 0.999999i \(-0.499593\pi\)
0.706201 0.708011i \(-0.250407\pi\)
\(20\) −10.6955 + 5.85609i −0.534776 + 0.292804i
\(21\) 0 0
\(22\) 7.54181 + 15.7403i 0.342810 + 0.715469i
\(23\) 6.75277 6.75277i 0.293599 0.293599i −0.544901 0.838500i \(-0.683433\pi\)
0.838500 + 0.544901i \(0.183433\pi\)
\(24\) 0 0
\(25\) −11.1065 + 11.1065i −0.444261 + 0.444261i
\(26\) −9.57798 + 27.1996i −0.368384 + 1.04614i
\(27\) 0 0
\(28\) 27.4859 + 22.0977i 0.981638 + 0.789203i
\(29\) 0.266504 0.643399i 0.00918981 0.0221862i −0.919218 0.393749i \(-0.871178\pi\)
0.928408 + 0.371563i \(0.121178\pi\)
\(30\) 0 0
\(31\) 0.326715i 0.0105392i 0.999986 + 0.00526959i \(0.00167737\pi\)
−0.999986 + 0.00526959i \(0.998323\pi\)
\(32\) 8.55419 + 30.8355i 0.267318 + 0.963608i
\(33\) 0 0
\(34\) 9.11639 0.493878i 0.268129 0.0145258i
\(35\) −24.8316 10.2856i −0.709475 0.293874i
\(36\) 0 0
\(37\) 31.5133 13.0532i 0.851710 0.352790i 0.0862502 0.996274i \(-0.472512\pi\)
0.765460 + 0.643484i \(0.222512\pi\)
\(38\) 66.2637 + 23.3339i 1.74378 + 0.614050i
\(39\) 0 0
\(40\) −12.8522 20.7261i −0.321305 0.518153i
\(41\) −15.7509 15.7509i −0.384169 0.384169i 0.488433 0.872601i \(-0.337569\pi\)
−0.872601 + 0.488433i \(0.837569\pi\)
\(42\) 0 0
\(43\) 4.83274 2.00179i 0.112389 0.0465531i −0.325780 0.945446i \(-0.605627\pi\)
0.438170 + 0.898892i \(0.355627\pi\)
\(44\) −30.6186 + 16.7645i −0.695877 + 0.381011i
\(45\) 0 0
\(46\) 14.2164 + 12.7552i 0.309051 + 0.277287i
\(47\) 49.7096 1.05765 0.528825 0.848731i \(-0.322633\pi\)
0.528825 + 0.848731i \(0.322633\pi\)
\(48\) 0 0
\(49\) 28.7362i 0.586454i
\(50\) −23.3822 20.9789i −0.467643 0.419578i
\(51\) 0 0
\(52\) −55.3558 16.1852i −1.06453 0.311253i
\(53\) −4.45882 10.7645i −0.0841286 0.203105i 0.876217 0.481917i \(-0.160059\pi\)
−0.960346 + 0.278812i \(0.910059\pi\)
\(54\) 0 0
\(55\) 18.8115 18.8115i 0.342027 0.342027i
\(56\) −41.1569 + 57.2820i −0.734946 + 1.02289i
\(57\) 0 0
\(58\) 1.31375 + 0.462619i 0.0226508 + 0.00797618i
\(59\) −13.1268 31.6909i −0.222488 0.537134i 0.772739 0.634724i \(-0.218886\pi\)
−0.995227 + 0.0975907i \(0.968886\pi\)
\(60\) 0 0
\(61\) −35.4023 + 85.4687i −0.580366 + 1.40113i 0.312116 + 0.950044i \(0.398962\pi\)
−0.892482 + 0.451083i \(0.851038\pi\)
\(62\) −0.652473 + 0.0353475i −0.0105238 + 0.000570122i
\(63\) 0 0
\(64\) −60.6551 + 20.4194i −0.947737 + 0.319054i
\(65\) 43.9535 0.676207
\(66\) 0 0
\(67\) −41.3348 17.1214i −0.616938 0.255544i 0.0522539 0.998634i \(-0.483359\pi\)
−0.669192 + 0.743090i \(0.733359\pi\)
\(68\) 1.97262 + 18.1527i 0.0290091 + 0.266951i
\(69\) 0 0
\(70\) 17.8545 50.7033i 0.255064 0.724333i
\(71\) −37.6381 37.6381i −0.530114 0.530114i 0.390492 0.920606i \(-0.372305\pi\)
−0.920606 + 0.390492i \(0.872305\pi\)
\(72\) 0 0
\(73\) −52.2302 52.2302i −0.715482 0.715482i 0.252195 0.967677i \(-0.418848\pi\)
−0.967677 + 0.252195i \(0.918848\pi\)
\(74\) 29.4777 + 61.5220i 0.398347 + 0.831379i
\(75\) 0 0
\(76\) −39.4303 + 134.858i −0.518820 + 1.77445i
\(77\) −71.0866 29.4450i −0.923203 0.382403i
\(78\) 0 0
\(79\) 26.9061 0.340583 0.170292 0.985394i \(-0.445529\pi\)
0.170292 + 0.985394i \(0.445529\pi\)
\(80\) 40.0011 27.9091i 0.500014 0.348864i
\(81\) 0 0
\(82\) 29.7516 33.1598i 0.362824 0.404388i
\(83\) −10.6315 + 25.6667i −0.128090 + 0.309237i −0.974894 0.222667i \(-0.928524\pi\)
0.846804 + 0.531905i \(0.178524\pi\)
\(84\) 0 0
\(85\) −5.32533 12.8565i −0.0626510 0.151253i
\(86\) 4.52057 + 9.43475i 0.0525647 + 0.109706i
\(87\) 0 0
\(88\) −36.7926 59.3337i −0.418097 0.674247i
\(89\) 103.292 103.292i 1.16058 1.16058i 0.176234 0.984348i \(-0.443609\pi\)
0.984348 0.176234i \(-0.0563914\pi\)
\(90\) 0 0
\(91\) −48.6482 117.447i −0.534596 1.29063i
\(92\) −23.9349 + 29.7711i −0.260162 + 0.323599i
\(93\) 0 0
\(94\) 5.37812 + 99.2736i 0.0572140 + 1.05610i
\(95\) 107.080i 1.12715i
\(96\) 0 0
\(97\) 77.9778 0.803895 0.401948 0.915663i \(-0.368333\pi\)
0.401948 + 0.915663i \(0.368333\pi\)
\(98\) −57.3883 + 3.10900i −0.585595 + 0.0317245i
\(99\) 0 0
\(100\) 39.3667 48.9656i 0.393667 0.489656i
\(101\) −104.064 + 43.1046i −1.03033 + 0.426778i −0.832833 0.553525i \(-0.813282\pi\)
−0.197500 + 0.980303i \(0.563282\pi\)
\(102\) 0 0
\(103\) −76.6571 76.6571i −0.744243 0.744243i 0.229148 0.973392i \(-0.426406\pi\)
−0.973392 + 0.229148i \(0.926406\pi\)
\(104\) 26.3339 112.301i 0.253211 1.07981i
\(105\) 0 0
\(106\) 21.0152 10.0692i 0.198256 0.0949925i
\(107\) 40.9728 16.9715i 0.382923 0.158612i −0.182914 0.983129i \(-0.558553\pi\)
0.565837 + 0.824517i \(0.308553\pi\)
\(108\) 0 0
\(109\) 102.183 + 42.3255i 0.937456 + 0.388307i 0.798502 0.601992i \(-0.205626\pi\)
0.138954 + 0.990299i \(0.455626\pi\)
\(110\) 39.6032 + 35.5327i 0.360029 + 0.323024i
\(111\) 0 0
\(112\) −118.849 75.9960i −1.06115 0.678536i
\(113\) 123.602i 1.09383i 0.837190 + 0.546913i \(0.184197\pi\)
−0.837190 + 0.546913i \(0.815803\pi\)
\(114\) 0 0
\(115\) 11.1408 26.8962i 0.0968761 0.233880i
\(116\) −0.781747 + 2.67370i −0.00673920 + 0.0230491i
\(117\) 0 0
\(118\) 61.8688 29.6438i 0.524312 0.251219i
\(119\) −28.4594 + 28.4594i −0.239155 + 0.239155i
\(120\) 0 0
\(121\) −31.7073 + 31.7073i −0.262044 + 0.262044i
\(122\) −174.517 61.4540i −1.43047 0.503721i
\(123\) 0 0
\(124\) −0.141183 1.29921i −0.00113857 0.0104775i
\(125\) −47.4883 + 114.647i −0.379906 + 0.917175i
\(126\) 0 0
\(127\) 133.213i 1.04892i 0.851434 + 0.524462i \(0.175734\pi\)
−0.851434 + 0.524462i \(0.824266\pi\)
\(128\) −47.3414 118.923i −0.369855 0.929090i
\(129\) 0 0
\(130\) 4.75536 + 87.7782i 0.0365797 + 0.675217i
\(131\) −228.056 94.4640i −1.74089 0.721100i −0.998704 0.0509041i \(-0.983790\pi\)
−0.742185 0.670195i \(-0.766210\pi\)
\(132\) 0 0
\(133\) −286.125 + 118.517i −2.15132 + 0.891104i
\(134\) 29.7207 84.4010i 0.221796 0.629858i
\(135\) 0 0
\(136\) −36.0387 + 5.90341i −0.264991 + 0.0434075i
\(137\) 111.817 + 111.817i 0.816180 + 0.816180i 0.985552 0.169372i \(-0.0541739\pi\)
−0.169372 + 0.985552i \(0.554174\pi\)
\(138\) 0 0
\(139\) 31.7750 13.1616i 0.228597 0.0946880i −0.265445 0.964126i \(-0.585519\pi\)
0.494042 + 0.869438i \(0.335519\pi\)
\(140\) 103.190 + 30.1711i 0.737070 + 0.215508i
\(141\) 0 0
\(142\) 71.0939 79.2381i 0.500661 0.558015i
\(143\) 125.828 0.879914
\(144\) 0 0
\(145\) 2.12296i 0.0146411i
\(146\) 98.6566 109.958i 0.675730 0.753138i
\(147\) 0 0
\(148\) −119.675 + 65.5251i −0.808613 + 0.442737i
\(149\) 108.344 + 261.565i 0.727140 + 1.75547i 0.651898 + 0.758307i \(0.273973\pi\)
0.0752422 + 0.997165i \(0.476027\pi\)
\(150\) 0 0
\(151\) 51.5292 51.5292i 0.341253 0.341253i −0.515585 0.856838i \(-0.672425\pi\)
0.856838 + 0.515585i \(0.172425\pi\)
\(152\) −273.587 64.1548i −1.79991 0.422071i
\(153\) 0 0
\(154\) 51.1129 145.151i 0.331902 0.942538i
\(155\) 0.381142 + 0.920157i 0.00245898 + 0.00593650i
\(156\) 0 0
\(157\) 39.3450 94.9872i 0.250605 0.605014i −0.747648 0.664095i \(-0.768817\pi\)
0.998253 + 0.0590811i \(0.0188171\pi\)
\(158\) 2.91099 + 53.7334i 0.0184240 + 0.340085i
\(159\) 0 0
\(160\) 60.0642 + 76.8655i 0.375401 + 0.480410i
\(161\) −84.1994 −0.522978
\(162\) 0 0
\(163\) −4.97467 2.06057i −0.0305194 0.0126416i 0.367372 0.930074i \(-0.380258\pi\)
−0.397891 + 0.917433i \(0.630258\pi\)
\(164\) 69.4413 + 55.8285i 0.423423 + 0.340417i
\(165\) 0 0
\(166\) −52.4085 18.4550i −0.315714 0.111174i
\(167\) 165.012 + 165.012i 0.988097 + 0.988097i 0.999930 0.0118333i \(-0.00376674\pi\)
−0.0118333 + 0.999930i \(0.503767\pi\)
\(168\) 0 0
\(169\) 27.4985 + 27.4985i 0.162713 + 0.162713i
\(170\) 25.0992 12.0260i 0.147642 0.0707413i
\(171\) 0 0
\(172\) −18.3528 + 10.0486i −0.106702 + 0.0584224i
\(173\) 115.760 + 47.9493i 0.669132 + 0.277163i 0.691275 0.722591i \(-0.257049\pi\)
−0.0221438 + 0.999755i \(0.507049\pi\)
\(174\) 0 0
\(175\) 138.486 0.791348
\(176\) 114.513 79.8967i 0.650642 0.453959i
\(177\) 0 0
\(178\) 217.456 + 195.106i 1.22166 + 1.09610i
\(179\) 44.8368 108.246i 0.250485 0.604724i −0.747758 0.663971i \(-0.768870\pi\)
0.998243 + 0.0592467i \(0.0188699\pi\)
\(180\) 0 0
\(181\) 80.3652 + 194.019i 0.444007 + 1.07193i 0.974530 + 0.224256i \(0.0719953\pi\)
−0.530524 + 0.847670i \(0.678005\pi\)
\(182\) 229.287 109.861i 1.25982 0.603630i
\(183\) 0 0
\(184\) −62.0445 44.5788i −0.337198 0.242276i
\(185\) 73.5260 73.5260i 0.397438 0.397438i
\(186\) 0 0
\(187\) −15.2451 36.8049i −0.0815245 0.196818i
\(188\) −197.675 + 21.4810i −1.05146 + 0.114261i
\(189\) 0 0
\(190\) 213.846 11.5850i 1.12550 0.0609738i
\(191\) 338.117i 1.77025i 0.465357 + 0.885123i \(0.345926\pi\)
−0.465357 + 0.885123i \(0.654074\pi\)
\(192\) 0 0
\(193\) 234.508 1.21507 0.607533 0.794295i \(-0.292159\pi\)
0.607533 + 0.794295i \(0.292159\pi\)
\(194\) 8.43648 + 155.727i 0.0434870 + 0.802718i
\(195\) 0 0
\(196\) −12.4178 114.272i −0.0633560 0.583022i
\(197\) −237.007 + 98.1713i −1.20308 + 0.498332i −0.891993 0.452050i \(-0.850693\pi\)
−0.311086 + 0.950382i \(0.600693\pi\)
\(198\) 0 0
\(199\) 39.2172 + 39.2172i 0.197071 + 0.197071i 0.798743 0.601672i \(-0.205499\pi\)
−0.601672 + 0.798743i \(0.705499\pi\)
\(200\) 102.047 + 73.3204i 0.510234 + 0.366602i
\(201\) 0 0
\(202\) −97.3416 203.159i −0.481889 1.00574i
\(203\) −5.67273 + 2.34972i −0.0279445 + 0.0115750i
\(204\) 0 0
\(205\) −62.7356 25.9859i −0.306027 0.126761i
\(206\) 144.796 161.383i 0.702894 0.783414i
\(207\) 0 0
\(208\) 227.121 + 40.4409i 1.09193 + 0.194427i
\(209\) 306.542i 1.46671i
\(210\) 0 0
\(211\) −79.9026 + 192.902i −0.378685 + 0.914227i 0.613528 + 0.789673i \(0.289750\pi\)
−0.992213 + 0.124554i \(0.960250\pi\)
\(212\) 22.3826 + 40.8794i 0.105578 + 0.192827i
\(213\) 0 0
\(214\) 38.3261 + 79.9894i 0.179094 + 0.373782i
\(215\) 11.2756 11.2756i 0.0524448 0.0524448i
\(216\) 0 0
\(217\) 2.03688 2.03688i 0.00938655 0.00938655i
\(218\) −73.4718 + 208.645i −0.337026 + 0.957089i
\(219\) 0 0
\(220\) −66.6766 + 82.9346i −0.303076 + 0.376976i
\(221\) 25.1875 60.8079i 0.113970 0.275149i
\(222\) 0 0
\(223\) 344.421i 1.54449i 0.635326 + 0.772244i \(0.280866\pi\)
−0.635326 + 0.772244i \(0.719134\pi\)
\(224\) 138.911 245.572i 0.620139 1.09630i
\(225\) 0 0
\(226\) −246.843 + 13.3726i −1.09222 + 0.0591709i
\(227\) −68.2639 28.2758i −0.300722 0.124563i 0.227220 0.973843i \(-0.427036\pi\)
−0.527942 + 0.849280i \(0.677036\pi\)
\(228\) 0 0
\(229\) −41.8202 + 17.3225i −0.182621 + 0.0756440i −0.472120 0.881534i \(-0.656511\pi\)
0.289499 + 0.957178i \(0.406511\pi\)
\(230\) 54.9189 + 19.3390i 0.238778 + 0.0840824i
\(231\) 0 0
\(232\) −5.42414 1.27194i −0.0233799 0.00548248i
\(233\) −203.044 203.044i −0.871432 0.871432i 0.121197 0.992629i \(-0.461327\pi\)
−0.992629 + 0.121197i \(0.961327\pi\)
\(234\) 0 0
\(235\) 140.002 57.9906i 0.595752 0.246768i
\(236\) 65.8944 + 120.349i 0.279214 + 0.509954i
\(237\) 0 0
\(238\) −59.9146 53.7565i −0.251742 0.225868i
\(239\) −87.6710 −0.366824 −0.183412 0.983036i \(-0.558714\pi\)
−0.183412 + 0.983036i \(0.558714\pi\)
\(240\) 0 0
\(241\) 15.4754i 0.0642135i 0.999484 + 0.0321067i \(0.0102216\pi\)
−0.999484 + 0.0321067i \(0.989778\pi\)
\(242\) −66.7522 59.8913i −0.275836 0.247485i
\(243\) 0 0
\(244\) 103.847 355.172i 0.425602 1.45562i
\(245\) 33.5233 + 80.9325i 0.136830 + 0.330337i
\(246\) 0 0
\(247\) 358.121 358.121i 1.44988 1.44988i
\(248\) 2.57934 0.422516i 0.0104006 0.00170369i
\(249\) 0 0
\(250\) −234.096 82.4338i −0.936383 0.329735i
\(251\) −95.9530 231.651i −0.382283 0.922913i −0.991524 0.129927i \(-0.958526\pi\)
0.609241 0.792985i \(-0.291474\pi\)
\(252\) 0 0
\(253\) 31.8932 76.9969i 0.126060 0.304336i
\(254\) −266.037 + 14.4125i −1.04739 + 0.0567420i
\(255\) 0 0
\(256\) 232.377 107.411i 0.907722 0.419573i
\(257\) 131.142 0.510282 0.255141 0.966904i \(-0.417878\pi\)
0.255141 + 0.966904i \(0.417878\pi\)
\(258\) 0 0
\(259\) −277.847 115.088i −1.07277 0.444355i
\(260\) −174.785 + 18.9936i −0.672250 + 0.0730523i
\(261\) 0 0
\(262\) 163.978 465.665i 0.625870 1.77735i
\(263\) 281.350 + 281.350i 1.06977 + 1.06977i 0.997376 + 0.0723955i \(0.0230644\pi\)
0.0723955 + 0.997376i \(0.476936\pi\)
\(264\) 0 0
\(265\) −25.1156 25.1156i −0.0947757 0.0947757i
\(266\) −267.643 558.590i −1.00618 2.09996i
\(267\) 0 0
\(268\) 171.770 + 50.2230i 0.640934 + 0.187399i
\(269\) −133.290 55.2107i −0.495503 0.205244i 0.120915 0.992663i \(-0.461417\pi\)
−0.616419 + 0.787419i \(0.711417\pi\)
\(270\) 0 0
\(271\) −368.673 −1.36042 −0.680208 0.733019i \(-0.738111\pi\)
−0.680208 + 0.733019i \(0.738111\pi\)
\(272\) −15.6886 71.3332i −0.0576787 0.262255i
\(273\) 0 0
\(274\) −211.208 + 235.404i −0.770834 + 0.859137i
\(275\) −52.4559 + 126.640i −0.190749 + 0.460508i
\(276\) 0 0
\(277\) 21.6001 + 52.1472i 0.0779786 + 0.188257i 0.958061 0.286564i \(-0.0925130\pi\)
−0.880083 + 0.474821i \(0.842513\pi\)
\(278\) 29.7225 + 62.0329i 0.106915 + 0.223140i
\(279\) 0 0
\(280\) −49.0896 + 209.342i −0.175320 + 0.747649i
\(281\) −85.0605 + 85.0605i −0.302706 + 0.302706i −0.842072 0.539365i \(-0.818664\pi\)
0.539365 + 0.842072i \(0.318664\pi\)
\(282\) 0 0
\(283\) 27.0948 + 65.4127i 0.0957414 + 0.231140i 0.964493 0.264107i \(-0.0850773\pi\)
−0.868752 + 0.495248i \(0.835077\pi\)
\(284\) 165.936 + 133.407i 0.584281 + 0.469742i
\(285\) 0 0
\(286\) 13.6134 + 251.287i 0.0475993 + 0.878626i
\(287\) 196.396i 0.684306i
\(288\) 0 0
\(289\) 268.162 0.927896
\(290\) 4.23971 0.229685i 0.0146197 0.000792018i
\(291\) 0 0
\(292\) 230.268 + 185.128i 0.788590 + 0.633999i
\(293\) 321.033 132.976i 1.09568 0.453844i 0.239694 0.970849i \(-0.422953\pi\)
0.855983 + 0.517005i \(0.172953\pi\)
\(294\) 0 0
\(295\) −73.9404 73.9404i −0.250645 0.250645i
\(296\) −143.806 231.910i −0.485831 0.783479i
\(297\) 0 0
\(298\) −510.643 + 244.669i −1.71357 + 0.821039i
\(299\) 127.212 52.6929i 0.425458 0.176231i
\(300\) 0 0
\(301\) −42.6094 17.6494i −0.141559 0.0586358i
\(302\) 108.483 + 97.3326i 0.359214 + 0.322293i
\(303\) 0 0
\(304\) 98.5222 553.313i 0.324086 1.82011i
\(305\) 282.013i 0.924634i
\(306\) 0 0
\(307\) −92.6973 + 223.791i −0.301946 + 0.728961i 0.697972 + 0.716125i \(0.254086\pi\)
−0.999918 + 0.0128360i \(0.995914\pi\)
\(308\) 295.406 + 86.3722i 0.959112 + 0.280429i
\(309\) 0 0
\(310\) −1.79638 + 0.860719i −0.00579479 + 0.00277651i
\(311\) 44.5768 44.5768i 0.143334 0.143334i −0.631799 0.775133i \(-0.717683\pi\)
0.775133 + 0.631799i \(0.217683\pi\)
\(312\) 0 0
\(313\) −27.9303 + 27.9303i −0.0892343 + 0.0892343i −0.750315 0.661081i \(-0.770098\pi\)
0.661081 + 0.750315i \(0.270098\pi\)
\(314\) 193.953 + 68.2980i 0.617685 + 0.217510i
\(315\) 0 0
\(316\) −106.994 + 11.6269i −0.338590 + 0.0367940i
\(317\) 125.850 303.829i 0.397003 0.958450i −0.591370 0.806400i \(-0.701413\pi\)
0.988373 0.152049i \(-0.0485873\pi\)
\(318\) 0 0
\(319\) 6.07751i 0.0190518i
\(320\) −147.008 + 128.269i −0.459399 + 0.400840i
\(321\) 0 0
\(322\) −9.10960 168.152i −0.0282907 0.522212i
\(323\) −148.140 61.3618i −0.458639 0.189975i
\(324\) 0 0
\(325\) −209.230 + 86.6660i −0.643785 + 0.266665i
\(326\) 3.57690 10.1577i 0.0109721 0.0311586i
\(327\) 0 0
\(328\) −103.981 + 144.719i −0.317014 + 0.441218i
\(329\) −309.911 309.911i −0.941978 0.941978i
\(330\) 0 0
\(331\) −169.515 + 70.2155i −0.512131 + 0.212131i −0.623756 0.781619i \(-0.714394\pi\)
0.111626 + 0.993750i \(0.464394\pi\)
\(332\) 31.1858 106.660i 0.0939330 0.321265i
\(333\) 0 0
\(334\) −311.688 + 347.394i −0.933198 + 1.04010i
\(335\) −136.389 −0.407131
\(336\) 0 0
\(337\) 67.3116i 0.199738i −0.995001 0.0998689i \(-0.968158\pi\)
0.995001 0.0998689i \(-0.0318423\pi\)
\(338\) −51.9414 + 57.8916i −0.153673 + 0.171277i
\(339\) 0 0
\(340\) 26.7323 + 48.8238i 0.0786245 + 0.143599i
\(341\) 1.09111 + 2.63418i 0.00319974 + 0.00772486i
\(342\) 0 0
\(343\) −126.333 + 126.333i −0.368318 + 0.368318i
\(344\) −22.0535 35.5646i −0.0641089 0.103386i
\(345\) 0 0
\(346\) −83.2340 + 236.368i −0.240561 + 0.683145i
\(347\) 107.157 + 258.699i 0.308809 + 0.745530i 0.999744 + 0.0226140i \(0.00719886\pi\)
−0.690935 + 0.722916i \(0.742801\pi\)
\(348\) 0 0
\(349\) 165.558 399.692i 0.474378 1.14525i −0.487831 0.872938i \(-0.662212\pi\)
0.962209 0.272311i \(-0.0877881\pi\)
\(350\) 14.9829 + 276.566i 0.0428083 + 0.790189i
\(351\) 0 0
\(352\) 171.949 + 220.047i 0.488491 + 0.625133i
\(353\) 574.524 1.62755 0.813773 0.581183i \(-0.197410\pi\)
0.813773 + 0.581183i \(0.197410\pi\)
\(354\) 0 0
\(355\) −149.912 62.0955i −0.422287 0.174917i
\(356\) −366.114 + 455.385i −1.02841 + 1.27917i
\(357\) 0 0
\(358\) 221.025 + 77.8311i 0.617389 + 0.217405i
\(359\) −499.243 499.243i −1.39065 1.39065i −0.823868 0.566782i \(-0.808188\pi\)
−0.566782 0.823868i \(-0.691812\pi\)
\(360\) 0 0
\(361\) −617.189 617.189i −1.70966 1.70966i
\(362\) −378.774 + 181.486i −1.04634 + 0.501343i
\(363\) 0 0
\(364\) 244.206 + 446.017i 0.670897 + 1.22532i
\(365\) −208.032 86.1696i −0.569950 0.236081i
\(366\) 0 0
\(367\) 295.566 0.805357 0.402679 0.915341i \(-0.368079\pi\)
0.402679 + 0.915341i \(0.368079\pi\)
\(368\) 82.3144 128.730i 0.223681 0.349811i
\(369\) 0 0
\(370\) 154.792 + 138.882i 0.418355 + 0.375356i
\(371\) −39.3126 + 94.9090i −0.105964 + 0.255819i
\(372\) 0 0
\(373\) −133.878 323.209i −0.358921 0.866512i −0.995452 0.0952612i \(-0.969631\pi\)
0.636531 0.771251i \(-0.280369\pi\)
\(374\) 71.8526 34.4275i 0.192119 0.0920521i
\(375\) 0 0
\(376\) −64.2856 392.446i −0.170972 1.04374i
\(377\) 7.10011 7.10011i 0.0188332 0.0188332i
\(378\) 0 0
\(379\) 170.642 + 411.967i 0.450244 + 1.08698i 0.972229 + 0.234030i \(0.0751915\pi\)
−0.521986 + 0.852954i \(0.674809\pi\)
\(380\) 46.2722 + 425.811i 0.121769 + 1.12056i
\(381\) 0 0
\(382\) −675.244 + 36.5812i −1.76765 + 0.0957622i
\(383\) 254.902i 0.665540i 0.943008 + 0.332770i \(0.107983\pi\)
−0.943008 + 0.332770i \(0.892017\pi\)
\(384\) 0 0
\(385\) −234.558 −0.609242
\(386\) 25.3716 + 468.328i 0.0657294 + 1.21329i
\(387\) 0 0
\(388\) −310.086 + 33.6965i −0.799190 + 0.0868467i
\(389\) −687.246 + 284.667i −1.76670 + 0.731791i −0.771247 + 0.636536i \(0.780367\pi\)
−0.995453 + 0.0952550i \(0.969633\pi\)
\(390\) 0 0
\(391\) −30.8256 30.8256i −0.0788379 0.0788379i
\(392\) 226.866 37.1624i 0.578741 0.0948020i
\(393\) 0 0
\(394\) −221.697 462.698i −0.562683 1.17436i
\(395\) 75.7781 31.3883i 0.191843 0.0794640i
\(396\) 0 0
\(397\) −56.8981 23.5679i −0.143320 0.0593651i 0.309871 0.950779i \(-0.399714\pi\)
−0.453191 + 0.891414i \(0.649714\pi\)
\(398\) −74.0766 + 82.5625i −0.186122 + 0.207443i
\(399\) 0 0
\(400\) −135.386 + 211.728i −0.338464 + 0.529319i
\(401\) 704.010i 1.75564i −0.478994 0.877818i \(-0.658999\pi\)
0.478994 0.877818i \(-0.341001\pi\)
\(402\) 0 0
\(403\) −1.80270 + 4.35211i −0.00447321 + 0.0107993i
\(404\) 395.192 216.378i 0.978197 0.535589i
\(405\) 0 0
\(406\) −5.30630 11.0746i −0.0130697 0.0272774i
\(407\) 210.486 210.486i 0.517166 0.517166i
\(408\) 0 0
\(409\) 528.488 528.488i 1.29215 1.29215i 0.358690 0.933457i \(-0.383224\pi\)
0.933457 0.358690i \(-0.116776\pi\)
\(410\) 45.1083 128.099i 0.110020 0.312436i
\(411\) 0 0
\(412\) 337.959 + 271.708i 0.820290 + 0.659485i
\(413\) −115.737 + 279.413i −0.280234 + 0.676544i
\(414\) 0 0
\(415\) 84.6901i 0.204072i
\(416\) −56.1909 + 457.953i −0.135074 + 1.10085i
\(417\) 0 0
\(418\) 612.186 33.1650i 1.46456 0.0793421i
\(419\) 153.485 + 63.5754i 0.366312 + 0.151731i 0.558244 0.829677i \(-0.311475\pi\)
−0.191932 + 0.981408i \(0.561475\pi\)
\(420\) 0 0
\(421\) −240.175 + 99.4838i −0.570487 + 0.236304i −0.649231 0.760591i \(-0.724909\pi\)
0.0787437 + 0.996895i \(0.474909\pi\)
\(422\) −393.884 138.701i −0.933373 0.328675i
\(423\) 0 0
\(424\) −79.2174 + 49.1224i −0.186834 + 0.115855i
\(425\) 50.7000 + 50.7000i 0.119294 + 0.119294i
\(426\) 0 0
\(427\) 753.562 312.136i 1.76478 0.730997i
\(428\) −155.598 + 85.1941i −0.363547 + 0.199052i
\(429\) 0 0
\(430\) 23.7381 + 21.2983i 0.0552050 + 0.0495310i
\(431\) 607.318 1.40909 0.704546 0.709659i \(-0.251151\pi\)
0.704546 + 0.709659i \(0.251151\pi\)
\(432\) 0 0
\(433\) 233.380i 0.538984i 0.963003 + 0.269492i \(0.0868557\pi\)
−0.963003 + 0.269492i \(0.913144\pi\)
\(434\) 4.28817 + 3.84743i 0.00988057 + 0.00886504i
\(435\) 0 0
\(436\) −424.629 124.155i −0.973919 0.284759i
\(437\) −128.371 309.914i −0.293754 0.709185i
\(438\) 0 0
\(439\) −496.850 + 496.850i −1.13178 + 1.13178i −0.141896 + 0.989882i \(0.545320\pi\)
−0.989882 + 0.141896i \(0.954680\pi\)
\(440\) −172.840 124.185i −0.392819 0.282239i
\(441\) 0 0
\(442\) 124.163 + 43.7223i 0.280911 + 0.0989193i
\(443\) −59.8483 144.487i −0.135098 0.326155i 0.841824 0.539752i \(-0.181482\pi\)
−0.976922 + 0.213597i \(0.931482\pi\)
\(444\) 0 0
\(445\) 170.411 411.409i 0.382947 0.924515i
\(446\) −687.833 + 37.2632i −1.54223 + 0.0835497i
\(447\) 0 0
\(448\) 505.454 + 250.847i 1.12825 + 0.559926i
\(449\) 15.4530 0.0344165 0.0172082 0.999852i \(-0.494522\pi\)
0.0172082 + 0.999852i \(0.494522\pi\)
\(450\) 0 0
\(451\) −179.596 74.3911i −0.398217 0.164947i
\(452\) −53.4122 491.516i −0.118169 1.08742i
\(453\) 0 0
\(454\) 49.0833 139.387i 0.108113 0.307020i
\(455\) −274.025 274.025i −0.602253 0.602253i
\(456\) 0 0
\(457\) −93.8365 93.8365i −0.205332 0.205332i 0.596948 0.802280i \(-0.296380\pi\)
−0.802280 + 0.596948i \(0.796380\pi\)
\(458\) −39.1188 81.6438i −0.0854122 0.178261i
\(459\) 0 0
\(460\) −32.6796 + 111.769i −0.0710426 + 0.242977i
\(461\) 574.348 + 237.903i 1.24588 + 0.516058i 0.905546 0.424248i \(-0.139462\pi\)
0.340329 + 0.940306i \(0.389462\pi\)
\(462\) 0 0
\(463\) 568.089 1.22697 0.613487 0.789705i \(-0.289766\pi\)
0.613487 + 0.789705i \(0.289766\pi\)
\(464\) 1.95330 10.9700i 0.00420971 0.0236423i
\(465\) 0 0
\(466\) 383.525 427.460i 0.823016 0.917296i
\(467\) 156.459 377.726i 0.335030 0.808835i −0.663147 0.748489i \(-0.730780\pi\)
0.998178 0.0603459i \(-0.0192204\pi\)
\(468\) 0 0
\(469\) 150.957 + 364.442i 0.321869 + 0.777061i
\(470\) 130.958 + 273.319i 0.278635 + 0.581530i
\(471\) 0 0
\(472\) −233.217 + 144.617i −0.494103 + 0.306391i
\(473\) 32.2793 32.2793i 0.0682437 0.0682437i
\(474\) 0 0
\(475\) 211.136 + 509.727i 0.444497 + 1.07311i
\(476\) 100.873 125.470i 0.211919 0.263592i
\(477\) 0 0
\(478\) −9.48520 175.085i −0.0198435 0.366287i
\(479\) 327.880i 0.684509i −0.939607 0.342254i \(-0.888810\pi\)
0.939607 0.342254i \(-0.111190\pi\)
\(480\) 0 0
\(481\) 491.806 1.02247
\(482\) −30.9056 + 1.67430i −0.0641194 + 0.00347365i
\(483\) 0 0
\(484\) 112.385 139.789i 0.232201 0.288820i
\(485\) 219.616 90.9680i 0.452817 0.187563i
\(486\) 0 0
\(487\) −147.493 147.493i −0.302861 0.302861i 0.539271 0.842132i \(-0.318700\pi\)
−0.842132 + 0.539271i \(0.818700\pi\)
\(488\) 720.540 + 168.963i 1.47652 + 0.346236i
\(489\) 0 0
\(490\) −158.001 + 75.7047i −0.322451 + 0.154499i
\(491\) −598.802 + 248.032i −1.21956 + 0.505157i −0.897269 0.441485i \(-0.854452\pi\)
−0.322288 + 0.946642i \(0.604452\pi\)
\(492\) 0 0
\(493\) −2.93704 1.21656i −0.00595748 0.00246767i
\(494\) 753.938 + 676.447i 1.52619 + 1.36933i
\(495\) 0 0
\(496\) 1.12285 + 5.10542i 0.00226382 + 0.0102932i
\(497\) 469.304i 0.944274i
\(498\) 0 0
\(499\) 58.1446 140.373i 0.116522 0.281309i −0.854849 0.518877i \(-0.826350\pi\)
0.971371 + 0.237568i \(0.0763502\pi\)
\(500\) 139.299 476.425i 0.278598 0.952849i
\(501\) 0 0
\(502\) 452.242 216.688i 0.900881 0.431648i
\(503\) 256.204 256.204i 0.509351 0.509351i −0.404976 0.914327i \(-0.632720\pi\)
0.914327 + 0.404976i \(0.132720\pi\)
\(504\) 0 0
\(505\) −242.799 + 242.799i −0.480789 + 0.480789i
\(506\) 157.219 + 55.3626i 0.310709 + 0.109412i
\(507\) 0 0
\(508\) −57.5655 529.735i −0.113318 1.04279i
\(509\) 229.271 553.510i 0.450435 1.08745i −0.521722 0.853115i \(-0.674710\pi\)
0.972157 0.234331i \(-0.0752898\pi\)
\(510\) 0 0
\(511\) 651.251i 1.27446i
\(512\) 239.648 + 452.452i 0.468062 + 0.883696i
\(513\) 0 0
\(514\) 14.1884 + 261.901i 0.0276039 + 0.509534i
\(515\) −305.324 126.469i −0.592861 0.245571i
\(516\) 0 0
\(517\) 400.789 166.012i 0.775221 0.321107i
\(518\) 199.778 567.331i 0.385672 1.09523i
\(519\) 0 0
\(520\) −56.8417 347.003i −0.109311 0.667314i
\(521\) −80.7376 80.7376i −0.154967 0.154967i 0.625365 0.780332i \(-0.284950\pi\)
−0.780332 + 0.625365i \(0.784950\pi\)
\(522\) 0 0
\(523\) 123.197 51.0300i 0.235559 0.0975717i −0.261781 0.965127i \(-0.584310\pi\)
0.497341 + 0.867555i \(0.334310\pi\)
\(524\) 947.707 + 277.095i 1.80860 + 0.528807i
\(525\) 0 0
\(526\) −531.436 + 592.315i −1.01034 + 1.12607i
\(527\) 1.49141 0.00283001
\(528\) 0 0
\(529\) 437.800i 0.827599i
\(530\) 47.4403 52.8748i 0.0895100 0.0997639i
\(531\) 0 0
\(532\) 1086.59 594.936i 2.04246 1.11830i
\(533\) −122.907 296.723i −0.230594 0.556704i
\(534\) 0 0
\(535\) 95.5966 95.5966i 0.178685 0.178685i
\(536\) −81.7149 + 348.471i −0.152453 + 0.650133i
\(537\) 0 0
\(538\) 95.8389 272.164i 0.178139 0.505881i
\(539\) 95.9689 + 231.689i 0.178050 + 0.429850i
\(540\) 0 0
\(541\) 184.993 446.613i 0.341947 0.825532i −0.655572 0.755132i \(-0.727573\pi\)
0.997519 0.0703996i \(-0.0224275\pi\)
\(542\) −39.8870 736.266i −0.0735923 1.35842i
\(543\) 0 0
\(544\) 140.760 39.0489i 0.258750 0.0717810i
\(545\) 337.163 0.618648
\(546\) 0 0
\(547\) −570.529 236.321i −1.04302 0.432031i −0.205622 0.978632i \(-0.565922\pi\)
−0.837394 + 0.546600i \(0.815922\pi\)
\(548\) −492.968 396.330i −0.899577 0.723230i
\(549\) 0 0
\(550\) −258.584 91.0569i −0.470152 0.165558i
\(551\) −17.2973 17.2973i −0.0313926 0.0313926i
\(552\) 0 0
\(553\) −167.744 167.744i −0.303335 0.303335i
\(554\) −101.805 + 48.7787i −0.183763 + 0.0880482i
\(555\) 0 0
\(556\) −120.669 + 66.0693i −0.217030 + 0.118830i
\(557\) −340.362 140.983i −0.611063 0.253111i 0.0556199 0.998452i \(-0.482286\pi\)
−0.666683 + 0.745341i \(0.732286\pi\)
\(558\) 0 0
\(559\) 75.4212 0.134922
\(560\) −423.381 75.3867i −0.756038 0.134619i
\(561\) 0 0
\(562\) −179.075 160.669i −0.318638 0.285888i
\(563\) −241.885 + 583.963i −0.429637 + 1.03723i 0.549766 + 0.835319i \(0.314717\pi\)
−0.979403 + 0.201916i \(0.935283\pi\)
\(564\) 0 0
\(565\) 144.193 + 348.113i 0.255209 + 0.616128i
\(566\) −127.702 + 61.1873i −0.225623 + 0.108105i
\(567\) 0 0
\(568\) −248.470 + 345.819i −0.437447 + 0.608836i
\(569\) −88.6373 + 88.6373i −0.155777 + 0.155777i −0.780693 0.624915i \(-0.785134\pi\)
0.624915 + 0.780693i \(0.285134\pi\)
\(570\) 0 0
\(571\) −160.453 387.367i −0.281003 0.678401i 0.718857 0.695158i \(-0.244666\pi\)
−0.999860 + 0.0167573i \(0.994666\pi\)
\(572\) −500.365 + 54.3739i −0.874764 + 0.0950592i
\(573\) 0 0
\(574\) −392.217 + 21.2482i −0.683304 + 0.0370178i
\(575\) 150.000i 0.260869i
\(576\) 0 0
\(577\) −501.285 −0.868778 −0.434389 0.900725i \(-0.643036\pi\)
−0.434389 + 0.900725i \(0.643036\pi\)
\(578\) 29.0126 + 535.538i 0.0501949 + 0.926537i
\(579\) 0 0
\(580\) 0.917395 + 8.44215i 0.00158172 + 0.0145554i
\(581\) 226.299 93.7360i 0.389498 0.161336i
\(582\) 0 0
\(583\) −71.8995 71.8995i −0.123327 0.123327i
\(584\) −344.800 + 479.891i −0.590412 + 0.821731i
\(585\) 0 0
\(586\) 300.296 + 626.739i 0.512451 + 1.06952i
\(587\) 805.600 333.691i 1.37240 0.568468i 0.429964 0.902846i \(-0.358526\pi\)
0.942439 + 0.334378i \(0.108526\pi\)
\(588\) 0 0
\(589\) 10.6026 + 4.39175i 0.0180010 + 0.00745628i
\(590\) 139.665 155.664i 0.236720 0.263837i
\(591\) 0 0
\(592\) 447.582 312.282i 0.756050 0.527503i
\(593\) 1035.33i 1.74591i 0.487798 + 0.872957i \(0.337800\pi\)
−0.487798 + 0.872957i \(0.662200\pi\)
\(594\) 0 0
\(595\) −46.9525 + 113.353i −0.0789117 + 0.190510i
\(596\) −543.869 993.319i −0.912532 1.66664i
\(597\) 0 0
\(598\) 118.995 + 248.351i 0.198988 + 0.415302i
\(599\) −361.938 + 361.938i −0.604237 + 0.604237i −0.941434 0.337197i \(-0.890521\pi\)
0.337197 + 0.941434i \(0.390521\pi\)
\(600\) 0 0
\(601\) −221.839 + 221.839i −0.369116 + 0.369116i −0.867155 0.498039i \(-0.834054\pi\)
0.498039 + 0.867155i \(0.334054\pi\)
\(602\) 30.6371 87.0034i 0.0508922 0.144524i
\(603\) 0 0
\(604\) −182.643 + 227.178i −0.302390 + 0.376122i
\(605\) −52.3109 + 126.290i −0.0864642 + 0.208743i
\(606\) 0 0
\(607\) 465.834i 0.767437i 0.923450 + 0.383719i \(0.125357\pi\)
−0.923450 + 0.383719i \(0.874643\pi\)
\(608\) 1115.67 + 136.892i 1.83498 + 0.225152i
\(609\) 0 0
\(610\) −563.201 + 30.5113i −0.923280 + 0.0500185i
\(611\) 662.172 + 274.281i 1.08375 + 0.448905i
\(612\) 0 0
\(613\) 292.579 121.190i 0.477290 0.197700i −0.131051 0.991376i \(-0.541835\pi\)
0.608341 + 0.793676i \(0.291835\pi\)
\(614\) −456.956 160.911i −0.744227 0.262070i
\(615\) 0 0
\(616\) −140.531 + 599.292i −0.228135 + 0.972877i
\(617\) 226.657 + 226.657i 0.367354 + 0.367354i 0.866511 0.499158i \(-0.166357\pi\)
−0.499158 + 0.866511i \(0.666357\pi\)
\(618\) 0 0
\(619\) 756.530 313.365i 1.22218 0.506244i 0.324078 0.946030i \(-0.394946\pi\)
0.898102 + 0.439787i \(0.144946\pi\)
\(620\) −1.91327 3.49438i −0.00308592 0.00563610i
\(621\) 0 0
\(622\) 93.8459 + 84.2003i 0.150878 + 0.135370i
\(623\) −1287.93 −2.06730
\(624\) 0 0
\(625\) 14.3854i 0.0230167i
\(626\) −58.8007 52.7570i −0.0939308 0.0842764i
\(627\) 0 0
\(628\) −115.412 + 394.727i −0.183777 + 0.628546i
\(629\) −59.5864 143.854i −0.0947320 0.228703i
\(630\) 0 0
\(631\) 338.810 338.810i 0.536941 0.536941i −0.385688 0.922629i \(-0.626036\pi\)
0.922629 + 0.385688i \(0.126036\pi\)
\(632\) −34.7956 212.418i −0.0550563 0.336104i
\(633\) 0 0
\(634\) 620.383 + 218.460i 0.978522 + 0.344574i
\(635\) 155.405 + 375.181i 0.244733 + 0.590837i
\(636\) 0 0
\(637\) −158.557 + 382.790i −0.248912 + 0.600927i
\(638\) 12.1372 0.657531i 0.0190239 0.00103061i
\(639\) 0 0
\(640\) −272.067 279.707i −0.425104 0.437042i
\(641\) −729.839 −1.13859 −0.569297 0.822132i \(-0.692785\pi\)
−0.569297 + 0.822132i \(0.692785\pi\)
\(642\) 0 0
\(643\) −370.578 153.498i −0.576327 0.238722i 0.0754293 0.997151i \(-0.475967\pi\)
−0.651756 + 0.758429i \(0.725967\pi\)
\(644\) 334.826 36.3850i 0.519917 0.0564985i
\(645\) 0 0
\(646\) 106.516 302.486i 0.164886 0.468244i
\(647\) 179.567 + 179.567i 0.277538 + 0.277538i 0.832126 0.554587i \(-0.187124\pi\)
−0.554587 + 0.832126i \(0.687124\pi\)
\(648\) 0 0
\(649\) −211.673 211.673i −0.326152 0.326152i
\(650\) −195.715 408.471i −0.301100 0.628417i
\(651\) 0 0
\(652\) 20.6726 + 6.04436i 0.0317065 + 0.00927049i
\(653\) 964.894 + 399.672i 1.47763 + 0.612056i 0.968585 0.248683i \(-0.0799976\pi\)
0.509048 + 0.860738i \(0.329998\pi\)
\(654\) 0 0
\(655\) −752.497 −1.14885
\(656\) −300.265 191.999i −0.457721 0.292682i
\(657\) 0 0
\(658\) 585.385 652.444i 0.889642 0.991556i
\(659\) −233.939 + 564.778i −0.354990 + 0.857023i 0.640998 + 0.767542i \(0.278521\pi\)
−0.995989 + 0.0894804i \(0.971479\pi\)
\(660\) 0 0
\(661\) 281.181 + 678.831i 0.425387 + 1.02698i 0.980732 + 0.195356i \(0.0625862\pi\)
−0.555345 + 0.831620i \(0.687414\pi\)
\(662\) −158.565 330.937i −0.239525 0.499905i
\(663\) 0 0
\(664\) 216.382 + 50.7405i 0.325876 + 0.0764165i
\(665\) −667.580 + 667.580i −1.00388 + 1.00388i
\(666\) 0 0
\(667\) −2.54508 6.14437i −0.00381571 0.00921195i
\(668\) −727.492 584.879i −1.08906 0.875567i
\(669\) 0 0
\(670\) −14.7560 272.378i −0.0220239 0.406534i
\(671\) 807.333i 1.20318i
\(672\) 0 0
\(673\) 705.345 1.04806 0.524031 0.851699i \(-0.324428\pi\)
0.524031 + 0.851699i \(0.324428\pi\)
\(674\) 134.426 7.28250i 0.199445 0.0108049i
\(675\) 0 0
\(676\) −121.233 97.4673i −0.179339 0.144182i
\(677\) 10.4550 4.33061i 0.0154432 0.00639676i −0.374948 0.927046i \(-0.622340\pi\)
0.390392 + 0.920649i \(0.372340\pi\)
\(678\) 0 0
\(679\) −486.147 486.147i −0.715976 0.715976i
\(680\) −94.6123 + 58.6687i −0.139136 + 0.0862775i
\(681\) 0 0
\(682\) −5.14259 + 2.46402i −0.00754046 + 0.00361294i
\(683\) 307.101 127.205i 0.449635 0.186245i −0.146363 0.989231i \(-0.546757\pi\)
0.595998 + 0.802986i \(0.296757\pi\)
\(684\) 0 0
\(685\) 445.364 + 184.476i 0.650166 + 0.269308i
\(686\) −265.964 238.628i −0.387703 0.347854i
\(687\) 0 0
\(688\) 68.6392 47.8901i 0.0997662 0.0696077i
\(689\) 167.995i 0.243824i
\(690\) 0 0
\(691\) −243.176 + 587.078i −0.351919 + 0.849607i 0.644465 + 0.764634i \(0.277080\pi\)
−0.996383 + 0.0849727i \(0.972920\pi\)
\(692\) −481.049 140.651i −0.695158 0.203253i
\(693\) 0 0
\(694\) −505.047 + 241.988i −0.727734 + 0.348686i
\(695\) 74.1366 74.1366i 0.106671 0.106671i
\(696\) 0 0
\(697\) −71.9010 + 71.9010i −0.103158 + 0.103158i
\(698\) 816.125 + 287.388i 1.16923 + 0.411730i
\(699\) 0 0
\(700\) −550.701 + 59.8438i −0.786716 + 0.0854912i
\(701\) −65.7383 + 158.706i −0.0937779 + 0.226400i −0.963807 0.266600i \(-0.914100\pi\)
0.870029 + 0.493000i \(0.164100\pi\)
\(702\) 0 0
\(703\) 1198.14i 1.70432i
\(704\) −420.846 + 367.201i −0.597792 + 0.521592i
\(705\) 0 0
\(706\) 62.1582 + 1147.37i 0.0880428 + 1.62516i
\(707\) 917.510 + 380.045i 1.29775 + 0.537546i
\(708\) 0 0
\(709\) −1029.00 + 426.228i −1.45135 + 0.601167i −0.962519 0.271214i \(-0.912575\pi\)
−0.488827 + 0.872381i \(0.662575\pi\)
\(710\) 107.790 306.103i 0.151817 0.431131i
\(711\) 0 0
\(712\) −949.046 681.887i −1.33293 0.957706i
\(713\) 2.20623 + 2.20623i 0.00309429 + 0.00309429i
\(714\) 0 0
\(715\) 354.380 146.789i 0.495637 0.205299i
\(716\) −131.521 + 449.824i −0.183689 + 0.628245i
\(717\) 0 0
\(718\) 943.011 1051.04i 1.31339 1.46384i
\(719\) 439.735 0.611592 0.305796 0.952097i \(-0.401077\pi\)
0.305796 + 0.952097i \(0.401077\pi\)
\(720\) 0 0
\(721\) 955.826i 1.32570i
\(722\) 1165.80 1299.34i 1.61468 1.79965i
\(723\) 0 0
\(724\) −403.421 736.805i −0.557211 1.01769i
\(725\) 4.18599 + 10.1059i 0.00577378 + 0.0139391i
\(726\) 0 0
\(727\) 137.308 137.308i 0.188869 0.188869i −0.606338 0.795207i \(-0.707362\pi\)
0.795207 + 0.606338i \(0.207362\pi\)
\(728\) −864.307 + 535.953i −1.18723 + 0.736199i
\(729\) 0 0
\(730\) 149.580 424.777i 0.204904 0.581886i
\(731\) −9.13791 22.0609i −0.0125006 0.0301790i
\(732\) 0 0
\(733\) 57.7693 139.467i 0.0788121 0.190269i −0.879562 0.475784i \(-0.842164\pi\)
0.958374 + 0.285514i \(0.0921645\pi\)
\(734\) 31.9775 + 590.267i 0.0435661 + 0.804178i
\(735\) 0 0
\(736\) 265.989 + 150.460i 0.361399 + 0.204430i
\(737\) −390.447 −0.529778
\(738\) 0 0
\(739\) 536.590 + 222.263i 0.726103 + 0.300762i 0.714950 0.699176i \(-0.246450\pi\)
0.0111538 + 0.999938i \(0.496450\pi\)
\(740\) −260.610 + 324.155i −0.352176 + 0.438048i
\(741\) 0 0
\(742\) −193.793 68.2418i −0.261177 0.0919700i
\(743\) −907.324 907.324i −1.22116 1.22116i −0.967219 0.253944i \(-0.918272\pi\)
−0.253944 0.967219i \(-0.581728\pi\)
\(744\) 0 0
\(745\) 610.278 + 610.278i 0.819165 + 0.819165i
\(746\) 630.987 302.331i 0.845827 0.405270i
\(747\) 0 0
\(748\) 76.5279 + 139.770i 0.102310 + 0.186858i
\(749\) −361.249 149.634i −0.482309 0.199779i
\(750\) 0 0
\(751\) −662.862 −0.882639 −0.441320 0.897350i \(-0.645489\pi\)
−0.441320 + 0.897350i \(0.645489\pi\)
\(752\) 776.788 170.842i 1.03296 0.227184i
\(753\) 0 0
\(754\) 14.9476 + 13.4113i 0.0198244 + 0.0177868i
\(755\) 85.0132 205.240i 0.112600 0.271841i
\(756\) 0 0
\(757\) 76.1190 + 183.767i 0.100553 + 0.242757i 0.966148 0.257988i \(-0.0830594\pi\)
−0.865595 + 0.500745i \(0.833059\pi\)
\(758\) −804.266 + 385.356i −1.06104 + 0.508385i
\(759\) 0 0
\(760\) −845.370 + 138.478i −1.11233 + 0.182208i
\(761\) −435.811 + 435.811i −0.572683 + 0.572683i −0.932877 0.360195i \(-0.882710\pi\)
0.360195 + 0.932877i \(0.382710\pi\)
\(762\) 0 0
\(763\) −373.176 900.926i −0.489090 1.18077i
\(764\) −146.110 1344.55i −0.191244 1.75989i
\(765\) 0 0
\(766\) −509.057 + 27.5780i −0.664565 + 0.0360026i
\(767\) 494.578i 0.644821i
\(768\) 0 0
\(769\) −1422.48 −1.84978 −0.924889 0.380237i \(-0.875843\pi\)
−0.924889 + 0.380237i \(0.875843\pi\)
\(770\) −25.3770 468.429i −0.0329572 0.608350i
\(771\) 0 0
\(772\) −932.540 + 101.338i −1.20795 + 0.131266i
\(773\) 0.439715 0.182136i 0.000568842 0.000235622i −0.382399 0.923997i \(-0.624902\pi\)
0.382968 + 0.923762i \(0.374902\pi\)
\(774\) 0 0
\(775\) −3.62867 3.62867i −0.00468215 0.00468215i
\(776\) −100.843 615.618i −0.129952 0.793322i
\(777\) 0 0
\(778\) −642.854 1341.68i −0.826290 1.72453i
\(779\) −722.878 + 299.426i −0.927956 + 0.384372i
\(780\) 0 0
\(781\) −429.160 177.764i −0.549500 0.227610i
\(782\) 58.2259 64.8960i 0.0744576 0.0829872i
\(783\) 0 0
\(784\) 98.7608 + 449.048i 0.125970 + 0.572765i
\(785\) 313.420i 0.399262i
\(786\) 0 0
\(787\) 23.0303 55.6002i 0.0292635 0.0706482i −0.908572 0.417728i \(-0.862827\pi\)
0.937836 + 0.347079i \(0.112827\pi\)