Properties

Label 288.3.u.a.19.7
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 19.7
Character \(\chi\) \(=\) 288.19
Dual form 288.3.u.a.91.7

$q$-expansion

\(f(q)\) \(=\) \(q+(1.98676 + 0.229757i) q^{2} +(3.89442 + 0.912943i) q^{4} +(-4.18866 + 1.73500i) q^{5} +(3.93197 + 3.93197i) q^{7} +(7.52753 + 2.70857i) q^{8} +O(q^{10})\) \(q+(1.98676 + 0.229757i) q^{2} +(3.89442 + 0.912943i) q^{4} +(-4.18866 + 1.73500i) q^{5} +(3.93197 + 3.93197i) q^{7} +(7.52753 + 2.70857i) q^{8} +(-8.72048 + 2.48465i) q^{10} +(14.2355 - 5.89652i) q^{11} +(0.454935 + 0.188440i) q^{13} +(6.90848 + 8.71527i) q^{14} +(14.3331 + 7.11077i) q^{16} +26.5635i q^{17} +(-7.25040 + 17.5040i) q^{19} +(-17.8964 + 2.93282i) q^{20} +(29.6372 - 8.44428i) q^{22} +(-0.775848 + 0.775848i) q^{23} +(-3.14303 + 3.14303i) q^{25} +(0.860551 + 0.478910i) q^{26} +(11.7231 + 18.9024i) q^{28} +(17.9907 - 43.4334i) q^{29} -39.6852i q^{31} +(26.8426 + 17.4205i) q^{32} +(-6.10315 + 52.7753i) q^{34} +(-23.2916 - 9.64771i) q^{35} +(36.4715 - 15.1070i) q^{37} +(-18.4265 + 33.1104i) q^{38} +(-36.2296 + 1.71499i) q^{40} +(-38.9661 - 38.9661i) q^{41} +(-14.2899 + 5.91907i) q^{43} +(60.8221 - 9.96739i) q^{44} +(-1.71968 + 1.36317i) q^{46} -62.1759 q^{47} -18.0792i q^{49} +(-6.96658 + 5.52232i) q^{50} +(1.59968 + 1.14920i) q^{52} +(-11.4986 - 27.7600i) q^{53} +(-49.3970 + 49.3970i) q^{55} +(18.9480 + 40.2480i) q^{56} +(45.7223 - 82.1583i) q^{58} +(5.30584 + 12.8094i) q^{59} +(14.1407 - 34.1386i) q^{61} +(9.11794 - 78.8449i) q^{62} +(49.3273 + 40.7776i) q^{64} -2.23251 q^{65} +(26.1257 + 10.8216i) q^{67} +(-24.2510 + 103.450i) q^{68} +(-44.0583 - 24.5191i) q^{70} +(-17.7859 - 17.7859i) q^{71} +(12.8313 + 12.8313i) q^{73} +(75.9311 - 21.6344i) q^{74} +(-44.2163 + 61.5488i) q^{76} +(79.1584 + 32.7885i) q^{77} -144.157 q^{79} +(-72.3735 - 4.91674i) q^{80} +(-68.4635 - 86.3689i) q^{82} +(10.9897 - 26.5314i) q^{83} +(-46.0877 - 111.266i) q^{85} +(-29.7506 + 8.47657i) q^{86} +(123.129 - 5.82851i) q^{88} +(5.92267 - 5.92267i) q^{89} +(1.04785 + 2.52973i) q^{91} +(-3.72978 + 2.31318i) q^{92} +(-123.529 - 14.2853i) q^{94} -85.8978i q^{95} +66.9192 q^{97} +(4.15383 - 35.9191i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 28q + 4q^{2} - 4q^{4} + 4q^{5} - 4q^{7} + 4q^{8} + O(q^{10}) \) \( 28q + 4q^{2} - 4q^{4} + 4q^{5} - 4q^{7} + 4q^{8} - 44q^{10} + 4q^{11} - 4q^{13} + 20q^{14} + 16q^{16} - 4q^{19} - 76q^{20} + 144q^{22} + 68q^{23} - 4q^{25} - 96q^{26} + 56q^{28} + 4q^{29} + 24q^{32} - 48q^{34} - 92q^{35} - 4q^{37} + 396q^{38} - 408q^{40} + 4q^{41} + 92q^{43} + 188q^{44} - 36q^{46} + 8q^{47} - 308q^{50} + 420q^{52} + 164q^{53} + 252q^{55} - 552q^{56} + 528q^{58} - 124q^{59} - 68q^{61} - 216q^{62} - 232q^{64} + 8q^{65} - 164q^{67} + 368q^{68} - 664q^{70} + 260q^{71} - 4q^{73} + 532q^{74} - 516q^{76} - 220q^{77} - 520q^{79} - 312q^{80} + 636q^{82} + 484q^{83} + 96q^{85} - 688q^{86} + 672q^{88} + 4q^{89} - 196q^{91} - 616q^{92} + 40q^{94} - 8q^{97} + 328q^{98} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.98676 + 0.229757i 0.993380 + 0.114878i
\(3\) 0 0
\(4\) 3.89442 + 0.912943i 0.973606 + 0.228236i
\(5\) −4.18866 + 1.73500i −0.837732 + 0.347000i −0.759959 0.649971i \(-0.774781\pi\)
−0.0777729 + 0.996971i \(0.524781\pi\)
\(6\) 0 0
\(7\) 3.93197 + 3.93197i 0.561710 + 0.561710i 0.929793 0.368083i \(-0.119986\pi\)
−0.368083 + 0.929793i \(0.619986\pi\)
\(8\) 7.52753 + 2.70857i 0.940941 + 0.338571i
\(9\) 0 0
\(10\) −8.72048 + 2.48465i −0.872048 + 0.248465i
\(11\) 14.2355 5.89652i 1.29413 0.536048i 0.373919 0.927462i \(-0.378014\pi\)
0.920215 + 0.391414i \(0.128014\pi\)
\(12\) 0 0
\(13\) 0.454935 + 0.188440i 0.0349950 + 0.0144954i 0.400112 0.916466i \(-0.368971\pi\)
−0.365117 + 0.930962i \(0.618971\pi\)
\(14\) 6.90848 + 8.71527i 0.493463 + 0.622520i
\(15\) 0 0
\(16\) 14.3331 + 7.11077i 0.895817 + 0.444423i
\(17\) 26.5635i 1.56256i 0.624181 + 0.781280i \(0.285433\pi\)
−0.624181 + 0.781280i \(0.714567\pi\)
\(18\) 0 0
\(19\) −7.25040 + 17.5040i −0.381600 + 0.921264i 0.610057 + 0.792358i \(0.291147\pi\)
−0.991657 + 0.128906i \(0.958853\pi\)
\(20\) −17.8964 + 2.93282i −0.894818 + 0.146641i
\(21\) 0 0
\(22\) 29.6372 8.44428i 1.34715 0.383831i
\(23\) −0.775848 + 0.775848i −0.0337325 + 0.0337325i −0.723772 0.690039i \(-0.757593\pi\)
0.690039 + 0.723772i \(0.257593\pi\)
\(24\) 0 0
\(25\) −3.14303 + 3.14303i −0.125721 + 0.125721i
\(26\) 0.860551 + 0.478910i 0.0330981 + 0.0184196i
\(27\) 0 0
\(28\) 11.7231 + 18.9024i 0.418682 + 0.675086i
\(29\) 17.9907 43.4334i 0.620369 1.49770i −0.230901 0.972977i \(-0.574167\pi\)
0.851271 0.524727i \(-0.175833\pi\)
\(30\) 0 0
\(31\) 39.6852i 1.28017i −0.768306 0.640083i \(-0.778900\pi\)
0.768306 0.640083i \(-0.221100\pi\)
\(32\) 26.8426 + 17.4205i 0.838832 + 0.544391i
\(33\) 0 0
\(34\) −6.10315 + 52.7753i −0.179504 + 1.55222i
\(35\) −23.2916 9.64771i −0.665475 0.275649i
\(36\) 0 0
\(37\) 36.4715 15.1070i 0.985717 0.408297i 0.169177 0.985586i \(-0.445889\pi\)
0.816540 + 0.577288i \(0.195889\pi\)
\(38\) −18.4265 + 33.1104i −0.484907 + 0.871327i
\(39\) 0 0
\(40\) −36.2296 + 1.71499i −0.905740 + 0.0428746i
\(41\) −38.9661 38.9661i −0.950392 0.950392i 0.0484342 0.998826i \(-0.484577\pi\)
−0.998826 + 0.0484342i \(0.984577\pi\)
\(42\) 0 0
\(43\) −14.2899 + 5.91907i −0.332324 + 0.137653i −0.542605 0.839988i \(-0.682562\pi\)
0.210282 + 0.977641i \(0.432562\pi\)
\(44\) 60.8221 9.96739i 1.38232 0.226532i
\(45\) 0 0
\(46\) −1.71968 + 1.36317i −0.0373843 + 0.0296341i
\(47\) −62.1759 −1.32289 −0.661446 0.749993i \(-0.730057\pi\)
−0.661446 + 0.749993i \(0.730057\pi\)
\(48\) 0 0
\(49\) 18.0792i 0.368964i
\(50\) −6.96658 + 5.52232i −0.139332 + 0.110446i
\(51\) 0 0
\(52\) 1.59968 + 1.14920i 0.0307630 + 0.0220999i
\(53\) −11.4986 27.7600i −0.216954 0.523773i 0.777508 0.628874i \(-0.216484\pi\)
−0.994462 + 0.105100i \(0.966484\pi\)
\(54\) 0 0
\(55\) −49.3970 + 49.3970i −0.898128 + 0.898128i
\(56\) 18.9480 + 40.2480i 0.338357 + 0.718715i
\(57\) 0 0
\(58\) 45.7223 82.1583i 0.788316 1.41652i
\(59\) 5.30584 + 12.8094i 0.0899295 + 0.217109i 0.962445 0.271478i \(-0.0875124\pi\)
−0.872515 + 0.488587i \(0.837512\pi\)
\(60\) 0 0
\(61\) 14.1407 34.1386i 0.231814 0.559650i −0.764576 0.644533i \(-0.777052\pi\)
0.996391 + 0.0848835i \(0.0270518\pi\)
\(62\) 9.11794 78.8449i 0.147064 1.27169i
\(63\) 0 0
\(64\) 49.3273 + 40.7776i 0.770739 + 0.637151i
\(65\) −2.23251 −0.0343463
\(66\) 0 0
\(67\) 26.1257 + 10.8216i 0.389937 + 0.161517i 0.569033 0.822314i \(-0.307318\pi\)
−0.179097 + 0.983831i \(0.557318\pi\)
\(68\) −24.2510 + 103.450i −0.356632 + 1.52132i
\(69\) 0 0
\(70\) −44.0583 24.5191i −0.629404 0.350273i
\(71\) −17.7859 17.7859i −0.250505 0.250505i 0.570672 0.821178i \(-0.306683\pi\)
−0.821178 + 0.570672i \(0.806683\pi\)
\(72\) 0 0
\(73\) 12.8313 + 12.8313i 0.175771 + 0.175771i 0.789510 0.613738i \(-0.210335\pi\)
−0.613738 + 0.789510i \(0.710335\pi\)
\(74\) 75.9311 21.6344i 1.02610 0.292357i
\(75\) 0 0
\(76\) −44.2163 + 61.5488i −0.581793 + 0.809853i
\(77\) 79.1584 + 32.7885i 1.02803 + 0.425824i
\(78\) 0 0
\(79\) −144.157 −1.82477 −0.912383 0.409337i \(-0.865760\pi\)
−0.912383 + 0.409337i \(0.865760\pi\)
\(80\) −72.3735 4.91674i −0.904669 0.0614592i
\(81\) 0 0
\(82\) −68.4635 86.3689i −0.834921 1.05328i
\(83\) 10.9897 26.5314i 0.132406 0.319655i −0.843747 0.536741i \(-0.819655\pi\)
0.976153 + 0.217086i \(0.0696552\pi\)
\(84\) 0 0
\(85\) −46.0877 111.266i −0.542208 1.30901i
\(86\) −29.7506 + 8.47657i −0.345937 + 0.0985648i
\(87\) 0 0
\(88\) 123.129 5.82851i 1.39919 0.0662330i
\(89\) 5.92267 5.92267i 0.0665469 0.0665469i −0.673050 0.739597i \(-0.735016\pi\)
0.739597 + 0.673050i \(0.235016\pi\)
\(90\) 0 0
\(91\) 1.04785 + 2.52973i 0.0115148 + 0.0277993i
\(92\) −3.72978 + 2.31318i −0.0405411 + 0.0251432i
\(93\) 0 0
\(94\) −123.529 14.2853i −1.31413 0.151972i
\(95\) 85.8978i 0.904187i
\(96\) 0 0
\(97\) 66.9192 0.689889 0.344944 0.938623i \(-0.387898\pi\)
0.344944 + 0.938623i \(0.387898\pi\)
\(98\) 4.15383 35.9191i 0.0423860 0.366521i
\(99\) 0 0
\(100\) −15.1097 + 9.37089i −0.151097 + 0.0937089i
\(101\) −23.3697 + 9.68007i −0.231384 + 0.0958422i −0.495363 0.868686i \(-0.664965\pi\)
0.263979 + 0.964528i \(0.414965\pi\)
\(102\) 0 0
\(103\) −15.5454 15.5454i −0.150927 0.150927i 0.627605 0.778532i \(-0.284035\pi\)
−0.778532 + 0.627605i \(0.784035\pi\)
\(104\) 2.91413 + 2.65071i 0.0280205 + 0.0254876i
\(105\) 0 0
\(106\) −16.4668 57.7943i −0.155347 0.545229i
\(107\) −107.060 + 44.3456i −1.00056 + 0.414444i −0.822001 0.569485i \(-0.807143\pi\)
−0.178556 + 0.983930i \(0.557143\pi\)
\(108\) 0 0
\(109\) 82.3132 + 34.0952i 0.755167 + 0.312800i 0.726848 0.686799i \(-0.240985\pi\)
0.0283190 + 0.999599i \(0.490985\pi\)
\(110\) −109.489 + 86.7907i −0.995358 + 0.789006i
\(111\) 0 0
\(112\) 28.3979 + 84.3165i 0.253552 + 0.752826i
\(113\) 9.91566i 0.0877492i −0.999037 0.0438746i \(-0.986030\pi\)
0.999037 0.0438746i \(-0.0139702\pi\)
\(114\) 0 0
\(115\) 1.90367 4.59586i 0.0165536 0.0399640i
\(116\) 109.716 152.724i 0.945825 1.31658i
\(117\) 0 0
\(118\) 7.59837 + 26.6683i 0.0643930 + 0.226003i
\(119\) −104.447 + 104.447i −0.877705 + 0.877705i
\(120\) 0 0
\(121\) 82.3196 82.3196i 0.680327 0.680327i
\(122\) 35.9377 64.5763i 0.294571 0.529314i
\(123\) 0 0
\(124\) 36.2303 154.551i 0.292180 1.24638i
\(125\) 51.0869 123.335i 0.408695 0.986678i
\(126\) 0 0
\(127\) 59.4093i 0.467790i 0.972262 + 0.233895i \(0.0751471\pi\)
−0.972262 + 0.233895i \(0.924853\pi\)
\(128\) 88.6326 + 92.3486i 0.692442 + 0.721474i
\(129\) 0 0
\(130\) −4.43546 0.512935i −0.0341190 0.00394565i
\(131\) 176.426 + 73.0781i 1.34676 + 0.557848i 0.935390 0.353618i \(-0.115049\pi\)
0.411375 + 0.911466i \(0.365049\pi\)
\(132\) 0 0
\(133\) −97.3336 + 40.3169i −0.731832 + 0.303135i
\(134\) 49.4192 + 27.5026i 0.368800 + 0.205243i
\(135\) 0 0
\(136\) −71.9491 + 199.958i −0.529038 + 1.47028i
\(137\) 138.710 + 138.710i 1.01248 + 1.01248i 0.999921 + 0.0125608i \(0.00399832\pi\)
0.0125608 + 0.999921i \(0.496002\pi\)
\(138\) 0 0
\(139\) −63.7662 + 26.4128i −0.458750 + 0.190020i −0.600077 0.799943i \(-0.704863\pi\)
0.141327 + 0.989963i \(0.454863\pi\)
\(140\) −81.8997 58.8362i −0.584998 0.420259i
\(141\) 0 0
\(142\) −31.2498 39.4227i −0.220069 0.277624i
\(143\) 7.58736 0.0530584
\(144\) 0 0
\(145\) 213.142i 1.46994i
\(146\) 22.5446 + 28.4408i 0.154415 + 0.194800i
\(147\) 0 0
\(148\) 155.827 25.5366i 1.05289 0.172545i
\(149\) −41.3888 99.9214i −0.277777 0.670613i 0.721996 0.691897i \(-0.243225\pi\)
−0.999773 + 0.0212835i \(0.993225\pi\)
\(150\) 0 0
\(151\) 159.036 159.036i 1.05322 1.05322i 0.0547164 0.998502i \(-0.482575\pi\)
0.998502 0.0547164i \(-0.0174255\pi\)
\(152\) −101.988 + 112.124i −0.670976 + 0.737656i
\(153\) 0 0
\(154\) 149.735 + 83.3300i 0.972307 + 0.541104i
\(155\) 68.8537 + 166.228i 0.444218 + 1.07244i
\(156\) 0 0
\(157\) 31.5775 76.2349i 0.201131 0.485573i −0.790843 0.612020i \(-0.790357\pi\)
0.991973 + 0.126447i \(0.0403573\pi\)
\(158\) −286.404 33.1210i −1.81269 0.209626i
\(159\) 0 0
\(160\) −142.659 26.3967i −0.891619 0.164979i
\(161\) −6.10122 −0.0378958
\(162\) 0 0
\(163\) −192.658 79.8016i −1.18195 0.489581i −0.296826 0.954932i \(-0.595928\pi\)
−0.885126 + 0.465351i \(0.845928\pi\)
\(164\) −116.177 187.324i −0.708394 1.14222i
\(165\) 0 0
\(166\) 27.9296 50.1865i 0.168251 0.302329i
\(167\) −76.7432 76.7432i −0.459540 0.459540i 0.438964 0.898504i \(-0.355345\pi\)
−0.898504 + 0.438964i \(0.855345\pi\)
\(168\) 0 0
\(169\) −119.330 119.330i −0.706092 0.706092i
\(170\) −66.0011 231.647i −0.388242 1.36263i
\(171\) 0 0
\(172\) −61.0547 + 10.0055i −0.354969 + 0.0581716i
\(173\) −46.0052 19.0560i −0.265926 0.110150i 0.245737 0.969337i \(-0.420970\pi\)
−0.511663 + 0.859187i \(0.670970\pi\)
\(174\) 0 0
\(175\) −24.7166 −0.141238
\(176\) 245.967 + 16.7099i 1.39754 + 0.0949426i
\(177\) 0 0
\(178\) 13.1277 10.4062i 0.0737511 0.0584615i
\(179\) 29.4799 71.1707i 0.164692 0.397602i −0.819891 0.572520i \(-0.805966\pi\)
0.984583 + 0.174918i \(0.0559660\pi\)
\(180\) 0 0
\(181\) 46.7381 + 112.836i 0.258222 + 0.623402i 0.998821 0.0485445i \(-0.0154583\pi\)
−0.740599 + 0.671947i \(0.765458\pi\)
\(182\) 1.50060 + 5.26672i 0.00824506 + 0.0289380i
\(183\) 0 0
\(184\) −7.94165 + 3.73878i −0.0431611 + 0.0203194i
\(185\) −126.556 + 126.556i −0.684087 + 0.684087i
\(186\) 0 0
\(187\) 156.632 + 378.144i 0.837606 + 2.02216i
\(188\) −242.139 56.7630i −1.28797 0.301931i
\(189\) 0 0
\(190\) 19.7356 170.658i 0.103872 0.898201i
\(191\) 227.376i 1.19045i 0.803559 + 0.595226i \(0.202937\pi\)
−0.803559 + 0.595226i \(0.797063\pi\)
\(192\) 0 0
\(193\) −46.4565 −0.240707 −0.120354 0.992731i \(-0.538403\pi\)
−0.120354 + 0.992731i \(0.538403\pi\)
\(194\) 132.952 + 15.3751i 0.685321 + 0.0792533i
\(195\) 0 0
\(196\) 16.5053 70.4082i 0.0842107 0.359225i
\(197\) 186.490 77.2467i 0.946650 0.392115i 0.144680 0.989479i \(-0.453785\pi\)
0.801971 + 0.597363i \(0.203785\pi\)
\(198\) 0 0
\(199\) 54.5057 + 54.5057i 0.273898 + 0.273898i 0.830667 0.556769i \(-0.187959\pi\)
−0.556769 + 0.830667i \(0.687959\pi\)
\(200\) −32.1724 + 15.1461i −0.160862 + 0.0757307i
\(201\) 0 0
\(202\) −48.6541 + 13.8626i −0.240862 + 0.0686267i
\(203\) 241.518 100.040i 1.18974 0.492808i
\(204\) 0 0
\(205\) 230.822 + 95.6095i 1.12596 + 0.466388i
\(206\) −27.3134 34.4567i −0.132589 0.167266i
\(207\) 0 0
\(208\) 5.18066 + 5.93587i 0.0249070 + 0.0285378i
\(209\) 291.930i 1.39679i
\(210\) 0 0
\(211\) 35.0586 84.6390i 0.166155 0.401133i −0.818769 0.574123i \(-0.805343\pi\)
0.984923 + 0.172991i \(0.0553430\pi\)
\(212\) −19.4370 118.607i −0.0916839 0.559465i
\(213\) 0 0
\(214\) −222.890 + 63.5062i −1.04154 + 0.296758i
\(215\) 49.5860 49.5860i 0.230632 0.230632i
\(216\) 0 0
\(217\) 156.041 156.041i 0.719082 0.719082i
\(218\) 155.703 + 86.6510i 0.714233 + 0.397482i
\(219\) 0 0
\(220\) −237.470 + 147.276i −1.07941 + 0.669438i
\(221\) −5.00564 + 12.0847i −0.0226499 + 0.0546818i
\(222\) 0 0
\(223\) 428.136i 1.91989i 0.280181 + 0.959947i \(0.409606\pi\)
−0.280181 + 0.959947i \(0.590394\pi\)
\(224\) 37.0474 + 174.041i 0.165390 + 0.776970i
\(225\) 0 0
\(226\) 2.27819 19.7000i 0.0100805 0.0871683i
\(227\) 112.195 + 46.4728i 0.494252 + 0.204726i 0.615865 0.787852i \(-0.288807\pi\)
−0.121613 + 0.992578i \(0.538807\pi\)
\(228\) 0 0
\(229\) 128.033 53.0331i 0.559097 0.231586i −0.0851960 0.996364i \(-0.527152\pi\)
0.644293 + 0.764779i \(0.277152\pi\)
\(230\) 4.83806 8.69348i 0.0210350 0.0377977i
\(231\) 0 0
\(232\) 253.068 278.217i 1.09081 1.19921i
\(233\) 90.6042 + 90.6042i 0.388859 + 0.388859i 0.874280 0.485421i \(-0.161334\pi\)
−0.485421 + 0.874280i \(0.661334\pi\)
\(234\) 0 0
\(235\) 260.434 107.875i 1.10823 0.459043i
\(236\) 8.96891 + 54.7293i 0.0380039 + 0.231904i
\(237\) 0 0
\(238\) −231.508 + 183.514i −0.972724 + 0.771065i
\(239\) −283.775 −1.18734 −0.593672 0.804707i \(-0.702323\pi\)
−0.593672 + 0.804707i \(0.702323\pi\)
\(240\) 0 0
\(241\) 309.483i 1.28416i 0.766636 + 0.642082i \(0.221929\pi\)
−0.766636 + 0.642082i \(0.778071\pi\)
\(242\) 182.463 144.636i 0.753978 0.597668i
\(243\) 0 0
\(244\) 86.2364 120.041i 0.353428 0.491970i
\(245\) 31.3674 + 75.7277i 0.128030 + 0.309093i
\(246\) 0 0
\(247\) −6.59693 + 6.59693i −0.0267082 + 0.0267082i
\(248\) 107.490 298.731i 0.433427 1.20456i
\(249\) 0 0
\(250\) 129.834 233.299i 0.519337 0.933195i
\(251\) 33.9351 + 81.9265i 0.135199 + 0.326400i 0.976951 0.213465i \(-0.0684750\pi\)
−0.841751 + 0.539866i \(0.818475\pi\)
\(252\) 0 0
\(253\) −6.46975 + 15.6194i −0.0255721 + 0.0617366i
\(254\) −13.6497 + 118.032i −0.0537389 + 0.464693i
\(255\) 0 0
\(256\) 154.874 + 203.838i 0.604976 + 0.796244i
\(257\) −193.069 −0.751241 −0.375621 0.926774i \(-0.622570\pi\)
−0.375621 + 0.926774i \(0.622570\pi\)
\(258\) 0 0
\(259\) 202.805 + 84.0047i 0.783032 + 0.324342i
\(260\) −8.69435 2.03816i −0.0334398 0.00783906i
\(261\) 0 0
\(262\) 333.726 + 185.724i 1.27376 + 0.708869i
\(263\) 14.4799 + 14.4799i 0.0550568 + 0.0550568i 0.734099 0.679042i \(-0.237605\pi\)
−0.679042 + 0.734099i \(0.737605\pi\)
\(264\) 0 0
\(265\) 96.3271 + 96.3271i 0.363498 + 0.363498i
\(266\) −202.642 + 57.7369i −0.761810 + 0.217056i
\(267\) 0 0
\(268\) 91.8652 + 65.9954i 0.342781 + 0.246251i
\(269\) 125.951 + 52.1707i 0.468220 + 0.193943i 0.604303 0.796754i \(-0.293451\pi\)
−0.136083 + 0.990697i \(0.543451\pi\)
\(270\) 0 0
\(271\) −490.650 −1.81052 −0.905258 0.424863i \(-0.860322\pi\)
−0.905258 + 0.424863i \(0.860322\pi\)
\(272\) −188.887 + 380.737i −0.694438 + 1.39977i
\(273\) 0 0
\(274\) 243.714 + 307.453i 0.889466 + 1.12209i
\(275\) −26.2096 + 63.2755i −0.0953076 + 0.230093i
\(276\) 0 0
\(277\) −183.667 443.412i −0.663059 1.60076i −0.792985 0.609241i \(-0.791474\pi\)
0.129926 0.991524i \(-0.458526\pi\)
\(278\) −132.757 + 37.8252i −0.477542 + 0.136062i
\(279\) 0 0
\(280\) −149.197 135.710i −0.532846 0.484680i
\(281\) 164.474 164.474i 0.585316 0.585316i −0.351043 0.936359i \(-0.614173\pi\)
0.936359 + 0.351043i \(0.114173\pi\)
\(282\) 0 0
\(283\) −98.6436 238.147i −0.348564 0.841508i −0.996790 0.0800601i \(-0.974489\pi\)
0.648226 0.761448i \(-0.275511\pi\)
\(284\) −53.0282 85.5032i −0.186719 0.301068i
\(285\) 0 0
\(286\) 15.0743 + 1.74325i 0.0527072 + 0.00609527i
\(287\) 306.427i 1.06769i
\(288\) 0 0
\(289\) −416.621 −1.44159
\(290\) −48.9707 + 423.461i −0.168865 + 1.46021i
\(291\) 0 0
\(292\) 38.2563 + 61.6848i 0.131015 + 0.211249i
\(293\) 60.5536 25.0821i 0.206668 0.0856045i −0.276948 0.960885i \(-0.589323\pi\)
0.483616 + 0.875280i \(0.339323\pi\)
\(294\) 0 0
\(295\) −44.4487 44.4487i −0.150674 0.150674i
\(296\) 315.459 14.9327i 1.06574 0.0504484i
\(297\) 0 0
\(298\) −59.2719 208.029i −0.198899 0.698084i
\(299\) −0.499162 + 0.206759i −0.00166944 + 0.000691503i
\(300\) 0 0
\(301\) −79.4611 32.9139i −0.263990 0.109348i
\(302\) 352.506 279.427i 1.16724 0.925254i
\(303\) 0 0
\(304\) −228.388 + 199.330i −0.751275 + 0.655692i
\(305\) 167.529i 0.549276i
\(306\) 0 0
\(307\) 166.166 401.160i 0.541257 1.30671i −0.382580 0.923923i \(-0.624964\pi\)
0.923836 0.382787i \(-0.125036\pi\)
\(308\) 278.342 + 199.959i 0.903708 + 0.649218i
\(309\) 0 0
\(310\) 98.6038 + 346.074i 0.318077 + 1.11637i
\(311\) 261.640 261.640i 0.841288 0.841288i −0.147739 0.989026i \(-0.547199\pi\)
0.989026 + 0.147739i \(0.0471995\pi\)
\(312\) 0 0
\(313\) −301.723 + 301.723i −0.963972 + 0.963972i −0.999373 0.0354015i \(-0.988729\pi\)
0.0354015 + 0.999373i \(0.488729\pi\)
\(314\) 80.2525 144.205i 0.255581 0.459252i
\(315\) 0 0
\(316\) −561.407 131.607i −1.77660 0.416477i
\(317\) −11.4511 + 27.6454i −0.0361233 + 0.0872094i −0.940912 0.338652i \(-0.890029\pi\)
0.904788 + 0.425862i \(0.140029\pi\)
\(318\) 0 0
\(319\) 724.378i 2.27078i
\(320\) −277.364 85.2207i −0.866764 0.266315i
\(321\) 0 0
\(322\) −12.1217 1.40180i −0.0376449 0.00435341i
\(323\) −464.968 192.596i −1.43953 0.596273i
\(324\) 0 0
\(325\) −2.02215 + 0.837602i −0.00622200 + 0.00257724i
\(326\) −364.430 202.811i −1.11788 0.622120i
\(327\) 0 0
\(328\) −187.776 398.860i −0.572488 1.21604i
\(329\) −244.474 244.474i −0.743081 0.743081i
\(330\) 0 0
\(331\) −117.333 + 48.6009i −0.354480 + 0.146830i −0.552815 0.833304i \(-0.686447\pi\)
0.198335 + 0.980134i \(0.436447\pi\)
\(332\) 67.0201 93.2916i 0.201868 0.280999i
\(333\) 0 0
\(334\) −134.838 170.103i −0.403707 0.509289i
\(335\) −128.207 −0.382709
\(336\) 0 0
\(337\) 148.325i 0.440134i 0.975485 + 0.220067i \(0.0706276\pi\)
−0.975485 + 0.220067i \(0.929372\pi\)
\(338\) −209.662 264.496i −0.620303 0.782532i
\(339\) 0 0
\(340\) −77.9059 475.390i −0.229135 1.39821i
\(341\) −234.004 564.937i −0.686230 1.65671i
\(342\) 0 0
\(343\) 263.753 263.753i 0.768961 0.768961i
\(344\) −123.600 + 5.85080i −0.359302 + 0.0170081i
\(345\) 0 0
\(346\) −87.0230 48.4296i −0.251512 0.139970i
\(347\) 215.625 + 520.565i 0.621398 + 1.50019i 0.850062 + 0.526682i \(0.176564\pi\)
−0.228664 + 0.973505i \(0.573436\pi\)
\(348\) 0 0
\(349\) −92.9006 + 224.282i −0.266191 + 0.642641i −0.999298 0.0374720i \(-0.988070\pi\)
0.733107 + 0.680113i \(0.238070\pi\)
\(350\) −49.1060 5.67881i −0.140303 0.0162252i
\(351\) 0 0
\(352\) 484.838 + 89.7111i 1.37738 + 0.254861i
\(353\) −453.234 −1.28395 −0.641975 0.766726i \(-0.721885\pi\)
−0.641975 + 0.766726i \(0.721885\pi\)
\(354\) 0 0
\(355\) 105.357 + 43.6405i 0.296782 + 0.122931i
\(356\) 28.4725 17.6583i 0.0799788 0.0496021i
\(357\) 0 0
\(358\) 74.9214 134.626i 0.209278 0.376050i
\(359\) −175.857 175.857i −0.489852 0.489852i 0.418407 0.908259i \(-0.362588\pi\)
−0.908259 + 0.418407i \(0.862588\pi\)
\(360\) 0 0
\(361\) 1.44333 + 1.44333i 0.00399816 + 0.00399816i
\(362\) 66.9326 + 234.916i 0.184897 + 0.648939i
\(363\) 0 0
\(364\) 1.77127 + 10.8085i 0.00486612 + 0.0296936i
\(365\) −76.0082 31.4836i −0.208242 0.0862566i
\(366\) 0 0
\(367\) 115.194 0.313879 0.156939 0.987608i \(-0.449837\pi\)
0.156939 + 0.987608i \(0.449837\pi\)
\(368\) −16.6372 + 5.60340i −0.0452097 + 0.0152266i
\(369\) 0 0
\(370\) −280.514 + 222.359i −0.758145 + 0.600971i
\(371\) 63.9394 154.363i 0.172343 0.416074i
\(372\) 0 0
\(373\) −95.1961 229.824i −0.255217 0.616149i 0.743393 0.668855i \(-0.233215\pi\)
−0.998610 + 0.0527059i \(0.983215\pi\)
\(374\) 224.310 + 787.269i 0.599758 + 2.10500i
\(375\) 0 0
\(376\) −468.031 168.408i −1.24476 0.447893i
\(377\) 16.3692 16.3692i 0.0434197 0.0434197i
\(378\) 0 0
\(379\) 264.738 + 639.134i 0.698517 + 1.68637i 0.726873 + 0.686772i \(0.240973\pi\)
−0.0283560 + 0.999598i \(0.509027\pi\)
\(380\) 78.4198 334.522i 0.206368 0.880322i
\(381\) 0 0
\(382\) −52.2412 + 451.742i −0.136757 + 1.18257i
\(383\) 217.725i 0.568473i 0.958754 + 0.284236i \(0.0917401\pi\)
−0.958754 + 0.284236i \(0.908260\pi\)
\(384\) 0 0
\(385\) −388.455 −1.00897
\(386\) −92.2979 10.6737i −0.239114 0.0276521i
\(387\) 0 0
\(388\) 260.612 + 61.0934i 0.671680 + 0.157457i
\(389\) −452.405 + 187.392i −1.16299 + 0.481728i −0.878871 0.477060i \(-0.841703\pi\)
−0.284123 + 0.958788i \(0.591703\pi\)
\(390\) 0 0
\(391\) −20.6092 20.6092i −0.0527091 0.0527091i
\(392\) 48.9688 136.092i 0.124920 0.347173i
\(393\) 0 0
\(394\) 388.259 110.623i 0.985429 0.280770i
\(395\) 603.823 250.112i 1.52866 0.633194i
\(396\) 0 0
\(397\) −281.846 116.745i −0.709940 0.294067i −0.00166042 0.999999i \(-0.500529\pi\)
−0.708280 + 0.705932i \(0.750529\pi\)
\(398\) 95.7667 + 120.813i 0.240620 + 0.303550i
\(399\) 0 0
\(400\) −67.3987 + 22.6999i −0.168497 + 0.0567498i
\(401\) 173.814i 0.433452i 0.976232 + 0.216726i \(0.0695378\pi\)
−0.976232 + 0.216726i \(0.930462\pi\)
\(402\) 0 0
\(403\) 7.47829 18.0542i 0.0185565 0.0447995i
\(404\) −99.8490 + 16.3630i −0.247151 + 0.0405026i
\(405\) 0 0
\(406\) 502.823 143.265i 1.23848 0.352869i
\(407\) 430.110 430.110i 1.05678 1.05678i
\(408\) 0 0
\(409\) 322.065 322.065i 0.787446 0.787446i −0.193629 0.981075i \(-0.562026\pi\)
0.981075 + 0.193629i \(0.0620258\pi\)
\(410\) 436.620 + 242.986i 1.06493 + 0.592648i
\(411\) 0 0
\(412\) −46.3484 74.7326i −0.112496 0.181390i
\(413\) −29.5039 + 71.2287i −0.0714380 + 0.172467i
\(414\) 0 0
\(415\) 130.198i 0.313730i
\(416\) 8.92892 + 12.9834i 0.0214638 + 0.0312102i
\(417\) 0 0
\(418\) −67.0729 + 579.994i −0.160461 + 1.38755i
\(419\) −13.9903 5.79496i −0.0333896 0.0138304i 0.365926 0.930644i \(-0.380752\pi\)
−0.399316 + 0.916813i \(0.630752\pi\)
\(420\) 0 0
\(421\) −507.883 + 210.372i −1.20637 + 0.499696i −0.893053 0.449952i \(-0.851441\pi\)
−0.313320 + 0.949648i \(0.601441\pi\)
\(422\) 89.0994 160.102i 0.211136 0.379389i
\(423\) 0 0
\(424\) −11.3659 240.109i −0.0268064 0.566294i
\(425\) −83.4900 83.4900i −0.196447 0.196447i
\(426\) 0 0
\(427\) 189.833 78.6313i 0.444573 0.184148i
\(428\) −457.421 + 74.9610i −1.06874 + 0.175143i
\(429\) 0 0
\(430\) 109.908 87.1227i 0.255600 0.202611i
\(431\) −654.734 −1.51910 −0.759552 0.650447i \(-0.774582\pi\)
−0.759552 + 0.650447i \(0.774582\pi\)
\(432\) 0 0
\(433\) 366.488i 0.846392i −0.906038 0.423196i \(-0.860908\pi\)
0.906038 0.423196i \(-0.139092\pi\)
\(434\) 345.867 274.164i 0.796929 0.631715i
\(435\) 0 0
\(436\) 289.435 + 207.929i 0.663843 + 0.476900i
\(437\) −7.95524 19.2057i −0.0182042 0.0439489i
\(438\) 0 0
\(439\) 124.489 124.489i 0.283573 0.283573i −0.550959 0.834532i \(-0.685738\pi\)
0.834532 + 0.550959i \(0.185738\pi\)
\(440\) −505.633 + 238.042i −1.14917 + 0.541005i
\(441\) 0 0
\(442\) −12.7215 + 22.8593i −0.0287818 + 0.0517178i
\(443\) −147.480 356.047i −0.332911 0.803718i −0.998359 0.0572735i \(-0.981759\pi\)
0.665448 0.746445i \(-0.268241\pi\)
\(444\) 0 0
\(445\) −14.5322 + 35.0839i −0.0326567 + 0.0788402i
\(446\) −98.3673 + 850.604i −0.220554 + 1.90718i
\(447\) 0 0
\(448\) 33.6171 + 354.290i 0.0750381 + 0.790826i
\(449\) 689.326 1.53525 0.767623 0.640901i \(-0.221439\pi\)
0.767623 + 0.640901i \(0.221439\pi\)
\(450\) 0 0
\(451\) −784.465 324.936i −1.73939 0.720479i
\(452\) 9.05244 38.6158i 0.0200275 0.0854332i
\(453\) 0 0
\(454\) 212.228 + 118.108i 0.467462 + 0.260150i
\(455\) −8.77817 8.77817i −0.0192927 0.0192927i
\(456\) 0 0
\(457\) 86.4503 + 86.4503i 0.189169 + 0.189169i 0.795337 0.606168i \(-0.207294\pi\)
−0.606168 + 0.795337i \(0.707294\pi\)
\(458\) 266.556 75.9475i 0.582000 0.165824i
\(459\) 0 0
\(460\) 11.6094 16.1603i 0.0252379 0.0351310i
\(461\) 3.31579 + 1.37344i 0.00719259 + 0.00297927i 0.386277 0.922383i \(-0.373761\pi\)
−0.379084 + 0.925362i \(0.623761\pi\)
\(462\) 0 0
\(463\) 113.007 0.244075 0.122038 0.992525i \(-0.461057\pi\)
0.122038 + 0.992525i \(0.461057\pi\)
\(464\) 566.707 494.606i 1.22135 1.06596i
\(465\) 0 0
\(466\) 159.192 + 200.826i 0.341613 + 0.430956i
\(467\) 150.402 363.102i 0.322059 0.777520i −0.677075 0.735914i \(-0.736753\pi\)
0.999134 0.0416055i \(-0.0132473\pi\)
\(468\) 0 0
\(469\) 60.1753 + 145.276i 0.128306 + 0.309757i
\(470\) 542.204 154.485i 1.15363 0.328692i
\(471\) 0 0
\(472\) 5.24464 + 110.795i 0.0111115 + 0.234734i
\(473\) −168.522 + 168.522i −0.356282 + 0.356282i
\(474\) 0 0
\(475\) −32.2275 77.8040i −0.0678473 0.163798i
\(476\) −502.115 + 311.407i −1.05486 + 0.654215i
\(477\) 0 0
\(478\) −563.793 65.1993i −1.17948 0.136400i
\(479\) 205.624i 0.429278i 0.976693 + 0.214639i \(0.0688575\pi\)
−0.976693 + 0.214639i \(0.931142\pi\)
\(480\) 0 0
\(481\) 19.4390 0.0404136
\(482\) −71.1059 + 614.869i −0.147523 + 1.27566i
\(483\) 0 0
\(484\) 395.740 245.434i 0.817646 0.507096i
\(485\) −280.302 + 116.105i −0.577942 + 0.239391i
\(486\) 0 0
\(487\) 573.249 + 573.249i 1.17710 + 1.17710i 0.980479 + 0.196623i \(0.0629975\pi\)
0.196623 + 0.980479i \(0.437002\pi\)
\(488\) 198.911 218.678i 0.407605 0.448112i
\(489\) 0 0
\(490\) 44.9206 + 157.660i 0.0916747 + 0.321754i
\(491\) −421.115 + 174.432i −0.857669 + 0.355258i −0.767795 0.640695i \(-0.778646\pi\)
−0.0898735 + 0.995953i \(0.528646\pi\)
\(492\) 0 0
\(493\) 1153.74 + 477.897i 2.34025 + 0.969364i
\(494\) −14.6222 + 11.5908i −0.0295996 + 0.0234632i
\(495\) 0 0
\(496\) 282.192 568.810i 0.568936 1.14679i
\(497\) 139.867i 0.281423i
\(498\) 0 0
\(499\) 115.301 278.361i 0.231064 0.557837i −0.765239 0.643746i \(-0.777379\pi\)
0.996303 + 0.0859086i \(0.0273793\pi\)
\(500\) 311.552 433.678i 0.623103 0.867356i
\(501\) 0 0
\(502\) 48.5976 + 170.565i 0.0968080 + 0.339771i
\(503\) −526.474 + 526.474i −1.04667 + 1.04667i −0.0478110 + 0.998856i \(0.515225\pi\)
−0.998856 + 0.0478110i \(0.984775\pi\)
\(504\) 0 0
\(505\) 81.0930 81.0930i 0.160580 0.160580i
\(506\) −16.4425 + 29.5454i −0.0324950 + 0.0583902i
\(507\) 0 0
\(508\) −54.2373 + 231.365i −0.106766 + 0.455443i
\(509\) 98.1719 237.008i 0.192872 0.465634i −0.797628 0.603150i \(-0.793912\pi\)
0.990500 + 0.137516i \(0.0439119\pi\)
\(510\) 0 0
\(511\) 100.905i 0.197465i
\(512\) 260.864 + 440.561i 0.509499 + 0.860471i
\(513\) 0 0
\(514\) −383.582 44.3589i −0.746268 0.0863014i
\(515\) 92.0858 + 38.1432i 0.178807 + 0.0740644i
\(516\) 0 0
\(517\) −885.103 + 366.622i −1.71200 + 0.709133i
\(518\) 383.624 + 213.493i 0.740588 + 0.412149i
\(519\) 0 0
\(520\) −16.8053 6.04691i −0.0323179 0.0116287i
\(521\) 42.3980 + 42.3980i 0.0813781 + 0.0813781i 0.746624 0.665246i \(-0.231673\pi\)
−0.665246 + 0.746624i \(0.731673\pi\)
\(522\) 0 0
\(523\) 160.929 66.6589i 0.307703 0.127455i −0.223488 0.974707i \(-0.571744\pi\)
0.531192 + 0.847252i \(0.321744\pi\)
\(524\) 620.362 + 445.664i 1.18390 + 0.850504i
\(525\) 0 0
\(526\) 25.4413 + 32.0950i 0.0483674 + 0.0610171i
\(527\) 1054.18 2.00034
\(528\) 0 0
\(529\) 527.796i 0.997724i
\(530\) 169.247 + 213.511i 0.319334 + 0.402850i
\(531\) 0 0
\(532\) −415.865 + 68.1511i −0.781702 + 0.128103i
\(533\) −10.3843 25.0698i −0.0194827 0.0470353i
\(534\) 0 0
\(535\) 371.497 371.497i 0.694386 0.694386i
\(536\) 167.351 + 152.224i 0.312222 + 0.283999i
\(537\) 0 0
\(538\) 238.248 + 132.589i 0.442841 + 0.246448i
\(539\) −106.605 257.366i −0.197782 0.477488i
\(540\) 0 0
\(541\) −29.6178 + 71.5038i −0.0547465 + 0.132170i −0.948886 0.315618i \(-0.897788\pi\)
0.894140 + 0.447788i \(0.147788\pi\)
\(542\) −974.803 112.730i −1.79853 0.207989i
\(543\) 0 0
\(544\) −462.750 + 713.034i −0.850644 + 1.31072i
\(545\) −403.937 −0.741169
\(546\) 0 0
\(547\) 157.659 + 65.3046i 0.288225 + 0.119387i 0.522112 0.852877i \(-0.325144\pi\)
−0.233886 + 0.972264i \(0.575144\pi\)
\(548\) 413.561 + 666.830i 0.754674 + 1.21684i
\(549\) 0 0
\(550\) −66.6101 + 119.691i −0.121109 + 0.217621i
\(551\) 629.819 + 629.819i 1.14305 + 1.14305i
\(552\) 0 0
\(553\) −566.819 566.819i −1.02499 1.02499i
\(554\) −263.026 923.151i −0.474775 1.66634i
\(555\) 0 0
\(556\) −272.446 + 44.6479i −0.490011 + 0.0803019i
\(557\) 890.709 + 368.944i 1.59912 + 0.662376i 0.991291 0.131693i \(-0.0420413\pi\)
0.607827 + 0.794069i \(0.292041\pi\)
\(558\) 0 0
\(559\) −7.61638 −0.0136250
\(560\) −265.238 303.903i −0.473639 0.542684i
\(561\) 0 0
\(562\) 364.559 288.981i 0.648681 0.514201i
\(563\) −106.191 + 256.369i −0.188617 + 0.455362i −0.989694 0.143200i \(-0.954261\pi\)
0.801077 + 0.598562i \(0.204261\pi\)
\(564\) 0 0
\(565\) 17.2037 + 41.5333i 0.0304490 + 0.0735103i
\(566\) −141.265 495.804i −0.249585 0.875979i
\(567\) 0 0
\(568\) −85.7094 182.058i −0.150897 0.320525i
\(569\) 351.714 351.714i 0.618126 0.618126i −0.326925 0.945050i \(-0.606012\pi\)
0.945050 + 0.326925i \(0.106012\pi\)
\(570\) 0 0
\(571\) 179.708 + 433.854i 0.314725 + 0.759814i 0.999517 + 0.0310755i \(0.00989322\pi\)
−0.684792 + 0.728739i \(0.740107\pi\)
\(572\) 29.5484 + 6.92683i 0.0516580 + 0.0121098i
\(573\) 0 0
\(574\) 70.4037 608.796i 0.122654 1.06062i
\(575\) 4.87703i 0.00848179i
\(576\) 0 0
\(577\) 662.602 1.14836 0.574179 0.818730i \(-0.305321\pi\)
0.574179 + 0.818730i \(0.305321\pi\)
\(578\) −827.725 95.7214i −1.43205 0.165608i
\(579\) 0 0
\(580\) −194.586 + 830.064i −0.335493 + 1.43114i
\(581\) 147.532 61.1096i 0.253927 0.105180i
\(582\) 0 0
\(583\) −327.375 327.375i −0.561535 0.561535i
\(584\) 61.8335 + 131.342i 0.105879 + 0.224901i
\(585\) 0 0
\(586\) 126.068 35.9195i 0.215133 0.0612961i
\(587\) −650.448 + 269.424i −1.10809 + 0.458985i −0.860279 0.509824i \(-0.829711\pi\)
−0.247809 + 0.968809i \(0.579711\pi\)
\(588\) 0 0
\(589\) 694.650 + 287.733i 1.17937 + 0.488512i
\(590\) −78.0965 98.5213i −0.132367 0.166985i
\(591\) 0 0
\(592\) 630.172 + 42.8111i 1.06448 + 0.0723160i
\(593\) 430.692i 0.726293i −0.931732 0.363147i \(-0.881702\pi\)
0.931732 0.363147i \(-0.118298\pi\)
\(594\) 0 0
\(595\) 256.277 618.708i 0.430718 1.03985i
\(596\) −69.9630 426.922i −0.117388 0.716312i
\(597\) 0 0
\(598\) −1.03922 + 0.296095i −0.00173782 + 0.000495143i
\(599\) 16.0528 16.0528i 0.0267993 0.0267993i −0.693580 0.720379i \(-0.743968\pi\)
0.720379 + 0.693580i \(0.243968\pi\)
\(600\) 0 0
\(601\) 201.233 201.233i 0.334831 0.334831i −0.519587 0.854418i \(-0.673914\pi\)
0.854418 + 0.519587i \(0.173914\pi\)
\(602\) −150.308 83.6487i −0.249681 0.138951i
\(603\) 0 0
\(604\) 764.544 474.163i 1.26580 0.785038i
\(605\) −201.984 + 487.633i −0.333858 + 0.806005i
\(606\) 0 0
\(607\) 713.329i 1.17517i 0.809162 + 0.587586i \(0.199921\pi\)
−0.809162 + 0.587586i \(0.800079\pi\)
\(608\) −499.549 + 343.548i −0.821626 + 0.565046i
\(609\) 0 0
\(610\) −38.4910 + 332.840i −0.0630999 + 0.545639i
\(611\) −28.2860 11.7164i −0.0462946 0.0191759i
\(612\) 0 0
\(613\) −349.658 + 144.833i −0.570404 + 0.236269i −0.649195 0.760622i \(-0.724894\pi\)
0.0787907 + 0.996891i \(0.474894\pi\)
\(614\) 422.301 758.830i 0.687786 1.23588i
\(615\) 0 0
\(616\) 507.057 + 461.222i 0.823144 + 0.748737i
\(617\) −185.331 185.331i −0.300374 0.300374i 0.540786 0.841160i \(-0.318127\pi\)
−0.841160 + 0.540786i \(0.818127\pi\)
\(618\) 0 0
\(619\) −740.280 + 306.634i −1.19593 + 0.495370i −0.889681 0.456582i \(-0.849074\pi\)
−0.306248 + 0.951952i \(0.599074\pi\)
\(620\) 116.389 + 710.220i 0.187725 + 1.14552i
\(621\) 0 0
\(622\) 579.930 459.703i 0.932364 0.739072i
\(623\) 46.5755 0.0747601
\(624\) 0 0
\(625\) 494.120i 0.790591i
\(626\) −668.774 + 530.128i −1.06833 + 0.846850i
\(627\) 0 0
\(628\) 192.574 268.063i 0.306647 0.426851i
\(629\) 401.295 + 968.812i 0.637989 + 1.54024i
\(630\) 0 0
\(631\) 25.0415 25.0415i 0.0396854 0.0396854i −0.686986 0.726671i \(-0.741066\pi\)
0.726671 + 0.686986i \(0.241066\pi\)
\(632\) −1085.14 390.458i −1.71700 0.617813i
\(633\) 0 0
\(634\) −29.1023 + 52.2937i −0.0459026 + 0.0824822i
\(635\) −103.075 248.845i −0.162323 0.391882i
\(636\) 0 0
\(637\) 3.40686 8.22488i 0.00534828 0.0129119i
\(638\) 166.431 1439.16i 0.260863 2.25574i
\(639\) 0 0
\(640\) −531.476 233.039i −0.830432 0.364124i
\(641\) 150.813 0.235278 0.117639 0.993056i \(-0.462467\pi\)
0.117639 + 0.993056i \(0.462467\pi\)
\(642\) 0 0
\(643\) −635.355 263.173i −0.988110 0.409289i −0.170686 0.985325i \(-0.554598\pi\)
−0.817424 + 0.576037i \(0.804598\pi\)
\(644\) −23.7607 5.57007i −0.0368955 0.00864917i
\(645\) 0 0
\(646\) −879.530 489.472i −1.36150 0.757696i
\(647\) 460.454 + 460.454i 0.711675 + 0.711675i 0.966885 0.255211i \(-0.0821448\pi\)
−0.255211 + 0.966885i \(0.582145\pi\)
\(648\) 0 0
\(649\) 151.062 + 151.062i 0.232762 + 0.232762i
\(650\) −4.20997 + 1.19951i −0.00647688 + 0.00184540i
\(651\) 0 0
\(652\) −677.438 486.667i −1.03902 0.746422i
\(653\) −308.661 127.852i −0.472682 0.195791i 0.133609 0.991034i \(-0.457343\pi\)
−0.606291 + 0.795243i \(0.707343\pi\)
\(654\) 0 0
\(655\) −865.779 −1.32180
\(656\) −281.425 835.583i −0.429001 1.27375i
\(657\) 0 0
\(658\) −429.541 541.880i −0.652798 0.823526i
\(659\) 187.311 452.209i 0.284235 0.686205i −0.715690 0.698418i \(-0.753888\pi\)
0.999925 + 0.0122131i \(0.00388764\pi\)
\(660\) 0 0
\(661\) −279.659 675.156i −0.423084 1.02142i −0.981432 0.191809i \(-0.938564\pi\)
0.558348 0.829607i \(-0.311436\pi\)
\(662\) −244.279 + 69.6002i −0.369001 + 0.105136i
\(663\) 0 0
\(664\) 154.587 169.950i 0.232812 0.255948i
\(665\) 337.747 337.747i 0.507891 0.507891i
\(666\) 0 0
\(667\) 19.7397 + 47.6558i 0.0295947 + 0.0714479i
\(668\) −228.808 368.933i −0.342527 0.552294i
\(669\) 0 0
\(670\) −254.717 29.4565i −0.380175 0.0439649i
\(671\) 569.360i 0.848525i
\(672\) 0 0
\(673\) 74.6107 0.110863 0.0554314 0.998462i \(-0.482347\pi\)
0.0554314 + 0.998462i \(0.482347\pi\)
\(674\) −34.0787 + 294.686i −0.0505619 + 0.437220i
\(675\) 0 0
\(676\) −355.779 573.661i −0.526300 0.848611i
\(677\) 250.770 103.872i 0.370413 0.153430i −0.189709 0.981840i \(-0.560754\pi\)
0.560122 + 0.828410i \(0.310754\pi\)
\(678\) 0 0
\(679\) 263.124 + 263.124i 0.387517 + 0.387517i
\(680\) −45.5560 962.386i −0.0669942 1.41527i
\(681\) 0 0
\(682\) −335.112 1176.16i −0.491367 1.72457i
\(683\) −1198.32 + 496.359i −1.75449 + 0.726734i −0.757200 + 0.653183i \(0.773433\pi\)
−0.997291 + 0.0735510i \(0.976567\pi\)
\(684\) 0 0
\(685\) −821.671 340.347i −1.19952 0.496857i
\(686\) 584.614 463.415i 0.852207 0.675533i
\(687\) 0 0
\(688\) −246.907 16.7738i −0.358877 0.0243805i
\(689\) 14.7958i 0.0214743i
\(690\) 0 0
\(691\) −337.819 + 815.567i −0.488884 + 1.18027i 0.466398 + 0.884575i \(0.345551\pi\)
−0.955282 + 0.295696i \(0.904449\pi\)
\(692\) −161.767 116.212i −0.233767 0.167937i
\(693\) 0 0
\(694\) 308.792 + 1083.78i 0.444945 + 1.56164i
\(695\) 221.269 221.269i 0.318372 0.318372i
\(696\) 0 0
\(697\) 1035.08 1035.08i 1.48504 1.48504i
\(698\) −236.101 + 424.250i −0.338254 + 0.607807i
\(699\) 0 0
\(700\) −96.2570 22.5649i −0.137510 0.0322355i
\(701\) −487.432 + 1176.77i −0.695338 + 1.67870i 0.0383989 + 0.999262i \(0.487774\pi\)
−0.733737 + 0.679433i \(0.762226\pi\)
\(702\) 0 0
\(703\) 747.930i 1.06391i
\(704\) 942.644 + 289.629i 1.33898 + 0.411405i
\(705\) 0 0
\(706\) −900.467 104.134i −1.27545 0.147498i
\(707\) −129.951 53.8274i −0.183806 0.0761349i
\(708\) 0 0
\(709\) 949.384 393.248i 1.33905 0.554651i 0.405824 0.913951i \(-0.366985\pi\)
0.933222 + 0.359300i \(0.116985\pi\)
\(710\) 199.293 + 110.910i 0.280695 + 0.156211i
\(711\) 0 0
\(712\) 60.6250 28.5411i 0.0851475 0.0400858i
\(713\) 30.7896 + 30.7896i 0.0431832 + 0.0431832i
\(714\) 0 0
\(715\) −31.7809 + 13.1641i −0.0444487 + 0.0184113i
\(716\) 179.782 250.255i 0.251092 0.349519i
\(717\) 0 0
\(718\) −308.981 389.790i −0.430336 0.542882i
\(719\) −349.072 −0.485496 −0.242748 0.970089i \(-0.578049\pi\)
−0.242748 + 0.970089i \(0.578049\pi\)
\(720\) 0 0
\(721\) 122.248i 0.169554i
\(722\) 2.53594 + 3.19917i 0.00351239 + 0.00443099i
\(723\) 0 0
\(724\) 79.0054 + 482.100i 0.109123 + 0.665884i
\(725\) 79.9673 + 193.058i 0.110300 + 0.266287i
\(726\) 0 0
\(727\) −256.931 + 256.931i −0.353413 + 0.353413i −0.861378 0.507965i \(-0.830398\pi\)
0.507965 + 0.861378i \(0.330398\pi\)
\(728\) 1.03576 + 21.8808i 0.00142275 + 0.0300561i
\(729\) 0 0
\(730\) −143.776 80.0138i −0.196954 0.109608i
\(731\) −157.231 379.590i −0.215091 0.519275i
\(732\) 0 0
\(733\) 473.293 1142.63i 0.645694 1.55884i −0.173194 0.984888i \(-0.555409\pi\)
0.818887 0.573955i \(-0.194591\pi\)
\(734\) 228.862 + 26.4665i 0.311801 + 0.0360579i
\(735\) 0 0
\(736\) −34.3414 + 7.31011i −0.0466596 + 0.00993222i
\(737\) 435.722 0.591211
\(738\) 0 0
\(739\) −137.009 56.7511i −0.185398 0.0767945i 0.288053 0.957614i \(-0.406992\pi\)
−0.473451 + 0.880820i \(0.656992\pi\)
\(740\) −608.402 + 377.325i −0.822165 + 0.509898i
\(741\) 0 0
\(742\) 162.498 291.992i 0.219000 0.393521i
\(743\) 644.593 + 644.593i 0.867555 + 0.867555i 0.992201 0.124647i \(-0.0397797\pi\)
−0.124647 + 0.992201i \(0.539780\pi\)
\(744\) 0 0
\(745\) 346.727 + 346.727i 0.465405 + 0.465405i
\(746\) −136.328 478.476i −0.182746 0.641389i
\(747\) 0 0
\(748\) 264.769 + 1615.65i 0.353969 + 2.15996i
\(749\) −595.321 246.590i −0.794821 0.329225i
\(750\) 0 0
\(751\) −18.5402 −0.0246873 −0.0123437 0.999924i \(-0.503929\pi\)
−0.0123437 + 0.999924i \(0.503929\pi\)
\(752\) −891.171 442.119i −1.18507 0.587924i
\(753\) 0 0
\(754\) 36.2826 28.7608i 0.0481202 0.0381442i
\(755\) −390.220 + 942.075i −0.516848 + 1.24778i
\(756\) 0 0
\(757\) 100.854 + 243.482i 0.133228 + 0.321641i 0.976389 0.216021i \(-0.0693079\pi\)
−0.843161 + 0.537661i \(0.819308\pi\)
\(758\) 379.125 + 1330.63i 0.500165 + 1.75545i
\(759\) 0 0
\(760\) 232.660 646.598i 0.306132 0.850787i
\(761\) 272.267 272.267i 0.357775 0.357775i −0.505217 0.862992i \(-0.668588\pi\)
0.862992 + 0.505217i \(0.168588\pi\)
\(762\) 0 0
\(763\) 189.591 + 457.714i 0.248482 + 0.599888i
\(764\) −207.582 + 885.499i −0.271704 + 1.15903i
\(765\) 0 0
\(766\) −50.0238 + 432.567i −0.0653053 + 0.564709i
\(767\) 6.82730i 0.00890130i
\(768\) 0 0
\(769\) −341.927 −0.444638 −0.222319 0.974974i \(-0.571363\pi\)
−0.222319 + 0.974974i \(0.571363\pi\)
\(770\) −771.767 89.2503i −1.00229 0.115909i
\(771\) 0 0
\(772\) −180.921 42.4121i −0.234354 0.0549380i
\(773\) 366.728 151.904i 0.474421 0.196512i −0.132644 0.991164i \(-0.542347\pi\)
0.607065 + 0.794652i \(0.292347\pi\)
\(774\) 0 0
\(775\) 124.732 + 124.732i 0.160944 + 0.160944i
\(776\) 503.736 + 181.255i 0.649144 + 0.233576i
\(777\) 0 0
\(778\) −941.874 + 268.360i −1.21063 + 0.344936i
\(779\) 964.582 399.543i 1.23823 0.512892i
\(780\) 0 0
\(781\) −358.065 148.315i −0.458470 0.189904i
\(782\) −36.2105 45.6807i −0.0463050 0.0584153i
\(783\) 0 0
\(784\) 128.557 259.131i 0.163976 0.330524i
\(785\) 374.109i 0.476572i
\(786\) 0 0
\(787\) 167.684 404.824i 0.213067 0.514389i −0.780825 0.624750i \(-0.785201\pi\)
0.993892 + 0.110361i \(0.0352008\pi\)