Properties

Label 288.3.u.a.163.2
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 163.2
Character \(\chi\) \(=\) 288.163
Dual form 288.3.u.a.235.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.20513 - 1.59614i) q^{2} +(-1.09531 + 3.84712i) q^{4} +(0.642823 + 1.55191i) q^{5} +(-4.95044 - 4.95044i) q^{7} +(7.46052 - 2.88803i) q^{8} +O(q^{10})\) \(q+(-1.20513 - 1.59614i) q^{2} +(-1.09531 + 3.84712i) q^{4} +(0.642823 + 1.55191i) q^{5} +(-4.95044 - 4.95044i) q^{7} +(7.46052 - 2.88803i) q^{8} +(1.70238 - 2.89629i) q^{10} +(4.27221 + 10.3140i) q^{11} +(1.68327 - 4.06379i) q^{13} +(-1.93564 + 13.8675i) q^{14} +(-13.6006 - 8.42755i) q^{16} -28.6469i q^{17} +(17.5460 + 7.26778i) q^{19} +(-6.67447 + 0.773195i) q^{20} +(11.3140 - 19.2488i) q^{22} +(24.3334 - 24.3334i) q^{23} +(15.6825 - 15.6825i) q^{25} +(-8.51493 + 2.21067i) q^{26} +(24.4672 - 13.6227i) q^{28} +(-8.57286 - 3.55100i) q^{29} +5.73273i q^{31} +(2.93903 + 31.8647i) q^{32} +(-45.7244 + 34.5233i) q^{34} +(4.50039 - 10.8649i) q^{35} +(-26.1364 - 63.0989i) q^{37} +(-9.54487 - 36.7644i) q^{38} +(9.27775 + 9.72157i) q^{40} +(14.2561 + 14.2561i) q^{41} +(-10.1365 - 24.4717i) q^{43} +(-44.3587 + 5.13867i) q^{44} +(-68.1643 - 9.51443i) q^{46} -57.9804 q^{47} +0.0137567i q^{49} +(-43.9308 - 6.13190i) q^{50} +(13.7902 + 10.9268i) q^{52} +(46.3830 - 19.2124i) q^{53} +(-13.2602 + 13.2602i) q^{55} +(-51.2299 - 22.6358i) q^{56} +(4.66357 + 17.9629i) q^{58} +(27.6347 - 11.4467i) q^{59} +(76.3985 + 31.6453i) q^{61} +(9.15022 - 6.90870i) q^{62} +(47.3186 - 43.0924i) q^{64} +7.38868 q^{65} +(-36.1949 + 87.3821i) q^{67} +(110.208 + 31.3771i) q^{68} +(-22.7654 + 5.91042i) q^{70} +(5.39666 + 5.39666i) q^{71} +(-25.4031 - 25.4031i) q^{73} +(-69.2166 + 117.760i) q^{74} +(-47.1782 + 59.5410i) q^{76} +(29.9097 - 72.2084i) q^{77} +50.1674 q^{79} +(4.33602 - 26.5244i) q^{80} +(5.57420 - 39.9353i) q^{82} +(100.805 + 41.7550i) q^{83} +(44.4574 - 18.4149i) q^{85} +(-26.8443 + 45.6709i) q^{86} +(61.6601 + 64.6097i) q^{88} +(-10.6266 + 10.6266i) q^{89} +(-28.4505 + 11.7846i) q^{91} +(66.9607 + 120.266i) q^{92} +(69.8741 + 92.5446i) q^{94} +31.9017i q^{95} -14.3055 q^{97} +(0.0219576 - 0.0165786i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 28q + 4q^{2} - 4q^{4} + 4q^{5} - 4q^{7} + 4q^{8} + O(q^{10}) \) \( 28q + 4q^{2} - 4q^{4} + 4q^{5} - 4q^{7} + 4q^{8} - 44q^{10} + 4q^{11} - 4q^{13} + 20q^{14} + 16q^{16} - 4q^{19} - 76q^{20} + 144q^{22} + 68q^{23} - 4q^{25} - 96q^{26} + 56q^{28} + 4q^{29} + 24q^{32} - 48q^{34} - 92q^{35} - 4q^{37} + 396q^{38} - 408q^{40} + 4q^{41} + 92q^{43} + 188q^{44} - 36q^{46} + 8q^{47} - 308q^{50} + 420q^{52} + 164q^{53} + 252q^{55} - 552q^{56} + 528q^{58} - 124q^{59} - 68q^{61} - 216q^{62} - 232q^{64} + 8q^{65} - 164q^{67} + 368q^{68} - 664q^{70} + 260q^{71} - 4q^{73} + 532q^{74} - 516q^{76} - 220q^{77} - 520q^{79} - 312q^{80} + 636q^{82} + 484q^{83} + 96q^{85} - 688q^{86} + 672q^{88} + 4q^{89} - 196q^{91} - 616q^{92} + 40q^{94} - 8q^{97} + 328q^{98} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.20513 1.59614i −0.602567 0.798069i
\(3\) 0 0
\(4\) −1.09531 + 3.84712i −0.273827 + 0.961779i
\(5\) 0.642823 + 1.55191i 0.128565 + 0.310382i 0.975034 0.222055i \(-0.0712763\pi\)
−0.846470 + 0.532437i \(0.821276\pi\)
\(6\) 0 0
\(7\) −4.95044 4.95044i −0.707206 0.707206i 0.258741 0.965947i \(-0.416692\pi\)
−0.965947 + 0.258741i \(0.916692\pi\)
\(8\) 7.46052 2.88803i 0.932564 0.361004i
\(9\) 0 0
\(10\) 1.70238 2.89629i 0.170238 0.289629i
\(11\) 4.27221 + 10.3140i 0.388383 + 0.937640i 0.990283 + 0.139068i \(0.0444106\pi\)
−0.601900 + 0.798572i \(0.705589\pi\)
\(12\) 0 0
\(13\) 1.68327 4.06379i 0.129483 0.312599i −0.845821 0.533467i \(-0.820889\pi\)
0.975304 + 0.220868i \(0.0708890\pi\)
\(14\) −1.93564 + 13.8675i −0.138260 + 0.990538i
\(15\) 0 0
\(16\) −13.6006 8.42755i −0.850038 0.526722i
\(17\) 28.6469i 1.68511i −0.538609 0.842556i \(-0.681050\pi\)
0.538609 0.842556i \(-0.318950\pi\)
\(18\) 0 0
\(19\) 17.5460 + 7.26778i 0.923473 + 0.382515i 0.793199 0.608963i \(-0.208414\pi\)
0.130274 + 0.991478i \(0.458414\pi\)
\(20\) −6.67447 + 0.773195i −0.333724 + 0.0386597i
\(21\) 0 0
\(22\) 11.3140 19.2488i 0.514274 0.874947i
\(23\) 24.3334 24.3334i 1.05797 1.05797i 0.0597590 0.998213i \(-0.480967\pi\)
0.998213 0.0597590i \(-0.0190332\pi\)
\(24\) 0 0
\(25\) 15.6825 15.6825i 0.627298 0.627298i
\(26\) −8.51493 + 2.21067i −0.327497 + 0.0850256i
\(27\) 0 0
\(28\) 24.4672 13.6227i 0.873828 0.486524i
\(29\) −8.57286 3.55100i −0.295616 0.122448i 0.229946 0.973203i \(-0.426145\pi\)
−0.525562 + 0.850755i \(0.676145\pi\)
\(30\) 0 0
\(31\) 5.73273i 0.184927i 0.995716 + 0.0924634i \(0.0294741\pi\)
−0.995716 + 0.0924634i \(0.970526\pi\)
\(32\) 2.93903 + 31.8647i 0.0918446 + 0.995773i
\(33\) 0 0
\(34\) −45.7244 + 34.5233i −1.34483 + 1.01539i
\(35\) 4.50039 10.8649i 0.128583 0.310426i
\(36\) 0 0
\(37\) −26.1364 63.0989i −0.706390 1.70538i −0.708831 0.705379i \(-0.750777\pi\)
0.00244114 0.999997i \(-0.499223\pi\)
\(38\) −9.54487 36.7644i −0.251181 0.967485i
\(39\) 0 0
\(40\) 9.27775 + 9.72157i 0.231944 + 0.243039i
\(41\) 14.2561 + 14.2561i 0.347711 + 0.347711i 0.859256 0.511545i \(-0.170927\pi\)
−0.511545 + 0.859256i \(0.670927\pi\)
\(42\) 0 0
\(43\) −10.1365 24.4717i −0.235733 0.569109i 0.761100 0.648634i \(-0.224660\pi\)
−0.996833 + 0.0795253i \(0.974660\pi\)
\(44\) −44.3587 + 5.13867i −1.00815 + 0.116788i
\(45\) 0 0
\(46\) −68.1643 9.51443i −1.48183 0.206835i
\(47\) −57.9804 −1.23363 −0.616813 0.787110i \(-0.711576\pi\)
−0.616813 + 0.787110i \(0.711576\pi\)
\(48\) 0 0
\(49\) 0.0137567i 0.000280749i
\(50\) −43.9308 6.13190i −0.878616 0.122638i
\(51\) 0 0
\(52\) 13.7902 + 10.9268i 0.265195 + 0.210132i
\(53\) 46.3830 19.2124i 0.875150 0.362499i 0.100536 0.994933i \(-0.467944\pi\)
0.774614 + 0.632434i \(0.217944\pi\)
\(54\) 0 0
\(55\) −13.2602 + 13.2602i −0.241094 + 0.241094i
\(56\) −51.2299 22.6358i −0.914819 0.404211i
\(57\) 0 0
\(58\) 4.66357 + 17.9629i 0.0804064 + 0.309705i
\(59\) 27.6347 11.4467i 0.468384 0.194011i −0.135992 0.990710i \(-0.543422\pi\)
0.604377 + 0.796699i \(0.293422\pi\)
\(60\) 0 0
\(61\) 76.3985 + 31.6453i 1.25243 + 0.518775i 0.907579 0.419881i \(-0.137928\pi\)
0.344855 + 0.938656i \(0.387928\pi\)
\(62\) 9.15022 6.90870i 0.147584 0.111431i
\(63\) 0 0
\(64\) 47.3186 43.0924i 0.739353 0.673318i
\(65\) 7.38868 0.113672
\(66\) 0 0
\(67\) −36.1949 + 87.3821i −0.540222 + 1.30421i 0.384345 + 0.923190i \(0.374427\pi\)
−0.924566 + 0.381021i \(0.875573\pi\)
\(68\) 110.208 + 31.3771i 1.62070 + 0.461429i
\(69\) 0 0
\(70\) −22.7654 + 5.91042i −0.325221 + 0.0844346i
\(71\) 5.39666 + 5.39666i 0.0760092 + 0.0760092i 0.744089 0.668080i \(-0.232884\pi\)
−0.668080 + 0.744089i \(0.732884\pi\)
\(72\) 0 0
\(73\) −25.4031 25.4031i −0.347988 0.347988i 0.511372 0.859360i \(-0.329137\pi\)
−0.859360 + 0.511372i \(0.829137\pi\)
\(74\) −69.2166 + 117.760i −0.935360 + 1.59135i
\(75\) 0 0
\(76\) −47.1782 + 59.5410i −0.620766 + 0.783434i
\(77\) 29.9097 72.2084i 0.388438 0.937771i
\(78\) 0 0
\(79\) 50.1674 0.635030 0.317515 0.948253i \(-0.397152\pi\)
0.317515 + 0.948253i \(0.397152\pi\)
\(80\) 4.33602 26.5244i 0.0542003 0.331554i
\(81\) 0 0
\(82\) 5.57420 39.9353i 0.0679781 0.487016i
\(83\) 100.805 + 41.7550i 1.21452 + 0.503072i 0.895665 0.444730i \(-0.146700\pi\)
0.318859 + 0.947802i \(0.396700\pi\)
\(84\) 0 0
\(85\) 44.4574 18.4149i 0.523029 0.216646i
\(86\) −26.8443 + 45.6709i −0.312143 + 0.531057i
\(87\) 0 0
\(88\) 61.6601 + 64.6097i 0.700683 + 0.734202i
\(89\) −10.6266 + 10.6266i −0.119400 + 0.119400i −0.764282 0.644882i \(-0.776906\pi\)
0.644882 + 0.764282i \(0.276906\pi\)
\(90\) 0 0
\(91\) −28.4505 + 11.7846i −0.312643 + 0.129501i
\(92\) 66.9607 + 120.266i 0.727834 + 1.30724i
\(93\) 0 0
\(94\) 69.8741 + 92.5446i 0.743341 + 0.984517i
\(95\) 31.9017i 0.335807i
\(96\) 0 0
\(97\) −14.3055 −0.147479 −0.0737395 0.997278i \(-0.523493\pi\)
−0.0737395 + 0.997278i \(0.523493\pi\)
\(98\) 0.0219576 0.0165786i 0.000224057 0.000169170i
\(99\) 0 0
\(100\) 43.1551 + 77.5094i 0.431551 + 0.775094i
\(101\) −51.6638 124.728i −0.511523 1.23493i −0.942997 0.332801i \(-0.892006\pi\)
0.431474 0.902125i \(-0.357994\pi\)
\(102\) 0 0
\(103\) 4.87593 + 4.87593i 0.0473392 + 0.0473392i 0.730380 0.683041i \(-0.239343\pi\)
−0.683041 + 0.730380i \(0.739343\pi\)
\(104\) 0.821771 35.1793i 0.00790164 0.338262i
\(105\) 0 0
\(106\) −86.5634 50.8800i −0.816635 0.480000i
\(107\) 4.55603 + 10.9992i 0.0425797 + 0.102797i 0.943739 0.330692i \(-0.107282\pi\)
−0.901159 + 0.433489i \(0.857282\pi\)
\(108\) 0 0
\(109\) 11.0098 26.5800i 0.101007 0.243853i −0.865295 0.501263i \(-0.832869\pi\)
0.966302 + 0.257410i \(0.0828690\pi\)
\(110\) 37.1454 + 5.18478i 0.337685 + 0.0471344i
\(111\) 0 0
\(112\) 25.6089 + 109.049i 0.228651 + 0.973653i
\(113\) 120.275i 1.06438i 0.846624 + 0.532191i \(0.178631\pi\)
−0.846624 + 0.532191i \(0.821369\pi\)
\(114\) 0 0
\(115\) 53.4052 + 22.1212i 0.464393 + 0.192358i
\(116\) 23.0510 29.0914i 0.198716 0.250788i
\(117\) 0 0
\(118\) −51.5739 30.3140i −0.437067 0.256898i
\(119\) −141.815 + 141.815i −1.19172 + 1.19172i
\(120\) 0 0
\(121\) −2.56759 + 2.56759i −0.0212197 + 0.0212197i
\(122\) −41.5601 160.079i −0.340657 1.31212i
\(123\) 0 0
\(124\) −22.0545 6.27910i −0.177859 0.0506379i
\(125\) 73.2166 + 30.3273i 0.585733 + 0.242619i
\(126\) 0 0
\(127\) 128.040i 1.00819i 0.863648 + 0.504095i \(0.168174\pi\)
−0.863648 + 0.504095i \(0.831826\pi\)
\(128\) −125.807 23.5949i −0.982863 0.184335i
\(129\) 0 0
\(130\) −8.90435 11.7933i −0.0684950 0.0907181i
\(131\) −20.1358 + 48.6121i −0.153708 + 0.371084i −0.981911 0.189345i \(-0.939364\pi\)
0.828203 + 0.560429i \(0.189364\pi\)
\(132\) 0 0
\(133\) −50.8816 122.839i −0.382569 0.923602i
\(134\) 183.093 47.5351i 1.36637 0.354740i
\(135\) 0 0
\(136\) −82.7331 213.721i −0.608331 1.57148i
\(137\) 1.66083 + 1.66083i 0.0121228 + 0.0121228i 0.713142 0.701019i \(-0.247271\pi\)
−0.701019 + 0.713142i \(0.747271\pi\)
\(138\) 0 0
\(139\) 75.6997 + 182.755i 0.544602 + 1.31479i 0.921445 + 0.388508i \(0.127009\pi\)
−0.376843 + 0.926277i \(0.622991\pi\)
\(140\) 36.8692 + 29.2139i 0.263352 + 0.208671i
\(141\) 0 0
\(142\) 2.11011 15.1175i 0.0148599 0.106461i
\(143\) 49.1053 0.343394
\(144\) 0 0
\(145\) 15.5870i 0.107496i
\(146\) −9.93270 + 71.1609i −0.0680322 + 0.487404i
\(147\) 0 0
\(148\) 271.376 31.4372i 1.83362 0.212413i
\(149\) 16.1203 6.67724i 0.108190 0.0448137i −0.327932 0.944701i \(-0.606352\pi\)
0.436122 + 0.899888i \(0.356352\pi\)
\(150\) 0 0
\(151\) −127.344 + 127.344i −0.843335 + 0.843335i −0.989291 0.145956i \(-0.953374\pi\)
0.145956 + 0.989291i \(0.453374\pi\)
\(152\) 151.892 + 3.54811i 0.999287 + 0.0233429i
\(153\) 0 0
\(154\) −151.300 + 39.2808i −0.982465 + 0.255070i
\(155\) −8.89669 + 3.68513i −0.0573980 + 0.0237750i
\(156\) 0 0
\(157\) −236.255 97.8598i −1.50481 0.623311i −0.530328 0.847793i \(-0.677931\pi\)
−0.974478 + 0.224482i \(0.927931\pi\)
\(158\) −60.4584 80.0740i −0.382648 0.506797i
\(159\) 0 0
\(160\) −47.5620 + 25.0445i −0.297262 + 0.156528i
\(161\) −240.922 −1.49641
\(162\) 0 0
\(163\) 38.0947 91.9687i 0.233710 0.564225i −0.762898 0.646518i \(-0.776224\pi\)
0.996608 + 0.0822932i \(0.0262244\pi\)
\(164\) −70.4599 + 39.2302i −0.429634 + 0.239209i
\(165\) 0 0
\(166\) −54.8373 211.220i −0.330345 1.27241i
\(167\) −223.831 223.831i −1.34031 1.34031i −0.895750 0.444558i \(-0.853361\pi\)
−0.444558 0.895750i \(-0.646639\pi\)
\(168\) 0 0
\(169\) 105.820 + 105.820i 0.626154 + 0.626154i
\(170\) −82.9698 48.7678i −0.488058 0.286869i
\(171\) 0 0
\(172\) 105.248 12.1923i 0.611907 0.0708855i
\(173\) −13.2654 + 32.0254i −0.0766784 + 0.185118i −0.957571 0.288199i \(-0.906944\pi\)
0.880892 + 0.473317i \(0.156944\pi\)
\(174\) 0 0
\(175\) −155.270 −0.887259
\(176\) 28.8173 176.281i 0.163735 1.00160i
\(177\) 0 0
\(178\) 29.7680 + 4.15504i 0.167236 + 0.0233429i
\(179\) 13.8305 + 5.72877i 0.0772652 + 0.0320043i 0.420981 0.907069i \(-0.361686\pi\)
−0.343716 + 0.939074i \(0.611686\pi\)
\(180\) 0 0
\(181\) 153.596 63.6217i 0.848599 0.351501i 0.0843605 0.996435i \(-0.473115\pi\)
0.764238 + 0.644934i \(0.223115\pi\)
\(182\) 53.0964 + 31.2089i 0.291739 + 0.171477i
\(183\) 0 0
\(184\) 111.264 251.815i 0.604695 1.36856i
\(185\) 81.1228 81.1228i 0.438502 0.438502i
\(186\) 0 0
\(187\) 295.465 122.386i 1.58003 0.654469i
\(188\) 63.5063 223.057i 0.337800 1.18647i
\(189\) 0 0
\(190\) 50.9195 38.4458i 0.267997 0.202346i
\(191\) 2.00135i 0.0104783i 0.999986 + 0.00523914i \(0.00166768\pi\)
−0.999986 + 0.00523914i \(0.998332\pi\)
\(192\) 0 0
\(193\) −107.502 −0.557003 −0.278502 0.960436i \(-0.589838\pi\)
−0.278502 + 0.960436i \(0.589838\pi\)
\(194\) 17.2400 + 22.8335i 0.0888659 + 0.117698i
\(195\) 0 0
\(196\) −0.0529236 0.0150678i −0.000270018 7.68765e-5i
\(197\) −35.9828 86.8701i −0.182654 0.440965i 0.805858 0.592109i \(-0.201704\pi\)
−0.988512 + 0.151144i \(0.951704\pi\)
\(198\) 0 0
\(199\) −228.742 228.742i −1.14946 1.14946i −0.986659 0.162799i \(-0.947948\pi\)
−0.162799 0.986659i \(-0.552052\pi\)
\(200\) 71.7079 162.291i 0.358539 0.811453i
\(201\) 0 0
\(202\) −136.820 + 232.776i −0.677329 + 1.15236i
\(203\) 24.8605 + 60.0185i 0.122465 + 0.295658i
\(204\) 0 0
\(205\) −12.9601 + 31.2885i −0.0632200 + 0.152627i
\(206\) 1.90651 13.6588i 0.00925489 0.0663049i
\(207\) 0 0
\(208\) −57.1413 + 41.0841i −0.274718 + 0.197520i
\(209\) 212.019i 1.01445i
\(210\) 0 0
\(211\) −244.800 101.400i −1.16019 0.480567i −0.282252 0.959340i \(-0.591082\pi\)
−0.877938 + 0.478773i \(0.841082\pi\)
\(212\) 23.1090 + 199.484i 0.109005 + 0.940963i
\(213\) 0 0
\(214\) 12.0657 20.5276i 0.0563816 0.0959233i
\(215\) 31.4619 31.4619i 0.146335 0.146335i
\(216\) 0 0
\(217\) 28.3796 28.3796i 0.130781 0.130781i
\(218\) −55.6935 + 14.4593i −0.255475 + 0.0663270i
\(219\) 0 0
\(220\) −36.4895 65.5375i −0.165861 0.297898i
\(221\) −116.415 48.2206i −0.526764 0.218193i
\(222\) 0 0
\(223\) 110.575i 0.495853i −0.968779 0.247927i \(-0.920251\pi\)
0.968779 0.247927i \(-0.0797492\pi\)
\(224\) 143.195 172.294i 0.639264 0.769170i
\(225\) 0 0
\(226\) 191.976 144.948i 0.849449 0.641361i
\(227\) −153.333 + 370.178i −0.675475 + 1.63074i 0.0966861 + 0.995315i \(0.469176\pi\)
−0.772161 + 0.635427i \(0.780824\pi\)
\(228\) 0 0
\(229\) −24.0559 58.0760i −0.105047 0.253607i 0.862612 0.505865i \(-0.168827\pi\)
−0.967660 + 0.252258i \(0.918827\pi\)
\(230\) −29.0520 111.901i −0.126313 0.486526i
\(231\) 0 0
\(232\) −74.2134 1.73359i −0.319885 0.00747236i
\(233\) 104.978 + 104.978i 0.450547 + 0.450547i 0.895536 0.444989i \(-0.146792\pi\)
−0.444989 + 0.895536i \(0.646792\pi\)
\(234\) 0 0
\(235\) −37.2711 89.9804i −0.158600 0.382895i
\(236\) 13.7682 + 118.851i 0.0583397 + 0.503608i
\(237\) 0 0
\(238\) 397.262 + 55.4501i 1.66917 + 0.232984i
\(239\) −122.643 −0.513151 −0.256576 0.966524i \(-0.582594\pi\)
−0.256576 + 0.966524i \(0.582594\pi\)
\(240\) 0 0
\(241\) 188.784i 0.783335i 0.920107 + 0.391668i \(0.128102\pi\)
−0.920107 + 0.391668i \(0.871898\pi\)
\(242\) 7.19251 + 1.00394i 0.0297211 + 0.00414850i
\(243\) 0 0
\(244\) −205.423 + 259.253i −0.841897 + 1.06251i
\(245\) −0.0213492 + 0.00884311i −8.71395e−5 + 3.60943e-5i
\(246\) 0 0
\(247\) 59.0694 59.0694i 0.239147 0.239147i
\(248\) 16.5563 + 42.7691i 0.0667592 + 0.172456i
\(249\) 0 0
\(250\) −39.8292 153.412i −0.159317 0.613649i
\(251\) 355.365 147.197i 1.41580 0.586443i 0.461997 0.886881i \(-0.347133\pi\)
0.953801 + 0.300439i \(0.0971330\pi\)
\(252\) 0 0
\(253\) 354.932 + 147.018i 1.40289 + 0.581098i
\(254\) 204.370 154.305i 0.804604 0.607501i
\(255\) 0 0
\(256\) 113.953 + 229.239i 0.445129 + 0.895467i
\(257\) −84.4316 −0.328528 −0.164264 0.986416i \(-0.552525\pi\)
−0.164264 + 0.986416i \(0.552525\pi\)
\(258\) 0 0
\(259\) −182.981 + 441.754i −0.706489 + 1.70561i
\(260\) −8.09287 + 28.4251i −0.0311264 + 0.109327i
\(261\) 0 0
\(262\) 101.858 26.4446i 0.388770 0.100933i
\(263\) 37.2079 + 37.2079i 0.141475 + 0.141475i 0.774297 0.632822i \(-0.218104\pi\)
−0.632822 + 0.774297i \(0.718104\pi\)
\(264\) 0 0
\(265\) 59.6320 + 59.6320i 0.225027 + 0.225027i
\(266\) −134.749 + 229.252i −0.506575 + 0.861848i
\(267\) 0 0
\(268\) −296.525 234.956i −1.10644 0.876702i
\(269\) 90.5201 218.535i 0.336506 0.812398i −0.661540 0.749910i \(-0.730097\pi\)
0.998046 0.0624874i \(-0.0199033\pi\)
\(270\) 0 0
\(271\) 312.612 1.15355 0.576775 0.816903i \(-0.304311\pi\)
0.576775 + 0.816903i \(0.304311\pi\)
\(272\) −241.423 + 389.615i −0.887585 + 1.43241i
\(273\) 0 0
\(274\) 0.649390 4.65243i 0.00237004 0.0169797i
\(275\) 228.748 + 94.7506i 0.831812 + 0.344548i
\(276\) 0 0
\(277\) −199.434 + 82.6083i −0.719978 + 0.298225i −0.712426 0.701747i \(-0.752404\pi\)
−0.00755172 + 0.999971i \(0.502404\pi\)
\(278\) 200.474 341.071i 0.721130 1.22688i
\(279\) 0 0
\(280\) 2.19708 94.0550i 0.00784672 0.335911i
\(281\) −237.700 + 237.700i −0.845909 + 0.845909i −0.989620 0.143711i \(-0.954096\pi\)
0.143711 + 0.989620i \(0.454096\pi\)
\(282\) 0 0
\(283\) 58.7408 24.3312i 0.207565 0.0859761i −0.276479 0.961020i \(-0.589168\pi\)
0.484044 + 0.875044i \(0.339168\pi\)
\(284\) −26.6726 + 14.8506i −0.0939174 + 0.0522907i
\(285\) 0 0
\(286\) −59.1785 78.3788i −0.206918 0.274052i
\(287\) 141.148i 0.491807i
\(288\) 0 0
\(289\) −531.645 −1.83960
\(290\) −24.8790 + 18.7844i −0.0857895 + 0.0647738i
\(291\) 0 0
\(292\) 125.553 69.9045i 0.429976 0.239399i
\(293\) −47.5607 114.822i −0.162323 0.391883i 0.821701 0.569919i \(-0.193026\pi\)
−0.984024 + 0.178036i \(0.943026\pi\)
\(294\) 0 0
\(295\) 35.5284 + 35.5284i 0.120435 + 0.120435i
\(296\) −377.223 395.268i −1.27440 1.33536i
\(297\) 0 0
\(298\) −30.0849 17.6832i −0.100956 0.0593396i
\(299\) −57.9258 139.845i −0.193732 0.467710i
\(300\) 0 0
\(301\) −70.9655 + 171.326i −0.235766 + 0.569189i
\(302\) 356.724 + 49.7918i 1.18120 + 0.164874i
\(303\) 0 0
\(304\) −177.386 246.716i −0.583508 0.811565i
\(305\) 138.906i 0.455429i
\(306\) 0 0
\(307\) 407.254 + 168.690i 1.32656 + 0.549480i 0.929673 0.368387i \(-0.120090\pi\)
0.396889 + 0.917867i \(0.370090\pi\)
\(308\) 245.034 + 194.156i 0.795564 + 0.630378i
\(309\) 0 0
\(310\) 16.6037 + 9.75926i 0.0535602 + 0.0314815i
\(311\) −149.458 + 149.458i −0.480572 + 0.480572i −0.905314 0.424742i \(-0.860365\pi\)
0.424742 + 0.905314i \(0.360365\pi\)
\(312\) 0 0
\(313\) 295.452 295.452i 0.943937 0.943937i −0.0545726 0.998510i \(-0.517380\pi\)
0.998510 + 0.0545726i \(0.0173796\pi\)
\(314\) 128.521 + 495.029i 0.409301 + 1.57652i
\(315\) 0 0
\(316\) −54.9486 + 193.000i −0.173888 + 0.610758i
\(317\) 222.852 + 92.3084i 0.703004 + 0.291194i 0.705406 0.708803i \(-0.250765\pi\)
−0.00240221 + 0.999997i \(0.500765\pi\)
\(318\) 0 0
\(319\) 103.591i 0.324738i
\(320\) 97.2930 + 45.7335i 0.304041 + 0.142917i
\(321\) 0 0
\(322\) 290.343 + 384.544i 0.901686 + 1.19424i
\(323\) 208.199 502.638i 0.644580 1.55615i
\(324\) 0 0
\(325\) −37.3323 90.1281i −0.114868 0.277317i
\(326\) −192.704 + 50.0302i −0.591116 + 0.153467i
\(327\) 0 0
\(328\) 147.530 + 65.1860i 0.449788 + 0.198738i
\(329\) 287.029 + 287.029i 0.872427 + 0.872427i
\(330\) 0 0
\(331\) −200.624 484.350i −0.606115 1.46329i −0.867192 0.497974i \(-0.834077\pi\)
0.261076 0.965318i \(-0.415923\pi\)
\(332\) −271.049 + 342.076i −0.816413 + 1.03035i
\(333\) 0 0
\(334\) −87.5189 + 627.012i −0.262033 + 1.87728i
\(335\) −158.876 −0.474257
\(336\) 0 0
\(337\) 248.089i 0.736169i 0.929792 + 0.368085i \(0.119986\pi\)
−0.929792 + 0.368085i \(0.880014\pi\)
\(338\) 41.3760 296.431i 0.122414 0.877014i
\(339\) 0 0
\(340\) 22.1496 + 191.203i 0.0651460 + 0.562361i
\(341\) −59.1276 + 24.4914i −0.173395 + 0.0718224i
\(342\) 0 0
\(343\) −242.504 + 242.504i −0.707007 + 0.707007i
\(344\) −146.299 153.297i −0.425286 0.445631i
\(345\) 0 0
\(346\) 67.1035 17.4216i 0.193941 0.0503514i
\(347\) 101.462 42.0270i 0.292398 0.121115i −0.231662 0.972796i \(-0.574416\pi\)
0.524061 + 0.851681i \(0.324416\pi\)
\(348\) 0 0
\(349\) 489.895 + 202.921i 1.40371 + 0.581436i 0.950712 0.310076i \(-0.100354\pi\)
0.452998 + 0.891512i \(0.350354\pi\)
\(350\) 187.121 + 247.833i 0.534632 + 0.708093i
\(351\) 0 0
\(352\) −316.098 + 166.446i −0.898006 + 0.472859i
\(353\) 185.627 0.525856 0.262928 0.964815i \(-0.415312\pi\)
0.262928 + 0.964815i \(0.415312\pi\)
\(354\) 0 0
\(355\) −4.90604 + 11.8442i −0.0138198 + 0.0333640i
\(356\) −29.2424 52.5211i −0.0821415 0.147531i
\(357\) 0 0
\(358\) −7.52366 28.9793i −0.0210158 0.0809476i
\(359\) −222.847 222.847i −0.620743 0.620743i 0.324978 0.945722i \(-0.394643\pi\)
−0.945722 + 0.324978i \(0.894643\pi\)
\(360\) 0 0
\(361\) −0.224842 0.224842i −0.000622830 0.000622830i
\(362\) −286.653 168.488i −0.791859 0.465437i
\(363\) 0 0
\(364\) −14.1746 122.360i −0.0389413 0.336154i
\(365\) 23.0937 55.7530i 0.0632703 0.152748i
\(366\) 0 0
\(367\) 532.771 1.45169 0.725846 0.687857i \(-0.241448\pi\)
0.725846 + 0.687857i \(0.241448\pi\)
\(368\) −536.019 + 125.878i −1.45657 + 0.342060i
\(369\) 0 0
\(370\) −227.247 31.7193i −0.614181 0.0857279i
\(371\) −324.726 134.506i −0.875273 0.362550i
\(372\) 0 0
\(373\) −277.629 + 114.998i −0.744313 + 0.308305i −0.722419 0.691456i \(-0.756970\pi\)
−0.0218944 + 0.999760i \(0.506970\pi\)
\(374\) −551.419 324.112i −1.47438 0.866609i
\(375\) 0 0
\(376\) −432.564 + 167.449i −1.15043 + 0.445343i
\(377\) −28.8610 + 28.8610i −0.0765543 + 0.0765543i
\(378\) 0 0
\(379\) 306.344 126.892i 0.808296 0.334807i 0.0600223 0.998197i \(-0.480883\pi\)
0.748274 + 0.663390i \(0.230883\pi\)
\(380\) −122.730 34.9421i −0.322972 0.0919530i
\(381\) 0 0
\(382\) 3.19443 2.41190i 0.00836239 0.00631387i
\(383\) 163.336i 0.426465i 0.977001 + 0.213233i \(0.0683992\pi\)
−0.977001 + 0.213233i \(0.931601\pi\)
\(384\) 0 0
\(385\) 131.288 0.341007
\(386\) 129.554 + 171.587i 0.335632 + 0.444527i
\(387\) 0 0
\(388\) 15.6689 55.0348i 0.0403837 0.141842i
\(389\) 27.0717 + 65.3568i 0.0695930 + 0.168012i 0.954849 0.297092i \(-0.0960168\pi\)
−0.885256 + 0.465104i \(0.846017\pi\)
\(390\) 0 0
\(391\) −697.075 697.075i −1.78280 1.78280i
\(392\) 0.0397297 + 0.102632i 0.000101351 + 0.000261816i
\(393\) 0 0
\(394\) −95.2925 + 162.124i −0.241859 + 0.411481i
\(395\) 32.2487 + 77.8553i 0.0816423 + 0.197102i
\(396\) 0 0
\(397\) −153.949 + 371.666i −0.387781 + 0.936187i 0.602628 + 0.798022i \(0.294120\pi\)
−0.990409 + 0.138165i \(0.955880\pi\)
\(398\) −89.4390 + 640.769i −0.224721 + 1.60997i
\(399\) 0 0
\(400\) −345.456 + 81.1263i −0.863639 + 0.202816i
\(401\) 287.838i 0.717801i −0.933376 0.358900i \(-0.883152\pi\)
0.933376 0.358900i \(-0.116848\pi\)
\(402\) 0 0
\(403\) 23.2966 + 9.64976i 0.0578079 + 0.0239448i
\(404\) 536.429 62.1419i 1.32779 0.153816i
\(405\) 0 0
\(406\) 65.8375 112.011i 0.162161 0.275889i
\(407\) 539.144 539.144i 1.32468 1.32468i
\(408\) 0 0
\(409\) −134.641 + 134.641i −0.329195 + 0.329195i −0.852280 0.523085i \(-0.824781\pi\)
0.523085 + 0.852280i \(0.324781\pi\)
\(410\) 65.5593 17.0207i 0.159901 0.0415138i
\(411\) 0 0
\(412\) −24.0989 + 13.4176i −0.0584925 + 0.0325671i
\(413\) −193.470 80.1378i −0.468450 0.194038i
\(414\) 0 0
\(415\) 183.282i 0.441644i
\(416\) 134.439 + 41.6936i 0.323170 + 0.100225i
\(417\) 0 0
\(418\) 338.412 255.512i 0.809598 0.611272i
\(419\) −94.1979 + 227.414i −0.224816 + 0.542754i −0.995532 0.0944249i \(-0.969899\pi\)
0.770716 + 0.637179i \(0.219899\pi\)
\(420\) 0 0
\(421\) −151.850 366.598i −0.360689 0.870779i −0.995200 0.0978656i \(-0.968798\pi\)
0.634511 0.772914i \(-0.281202\pi\)
\(422\) 133.169 + 512.935i 0.315567 + 1.21549i
\(423\) 0 0
\(424\) 290.555 277.290i 0.685270 0.653986i
\(425\) −449.254 449.254i −1.05707 1.05707i
\(426\) 0 0
\(427\) −221.548 534.864i −0.518848 1.25261i
\(428\) −47.3056 + 5.48005i −0.110527 + 0.0128039i
\(429\) 0 0
\(430\) −88.1333 12.3017i −0.204961 0.0286087i
\(431\) 691.406 1.60419 0.802095 0.597196i \(-0.203719\pi\)
0.802095 + 0.597196i \(0.203719\pi\)
\(432\) 0 0
\(433\) 580.011i 1.33952i 0.742579 + 0.669758i \(0.233602\pi\)
−0.742579 + 0.669758i \(0.766398\pi\)
\(434\) −79.4988 11.0965i −0.183177 0.0255680i
\(435\) 0 0
\(436\) 90.1971 + 71.4691i 0.206874 + 0.163920i
\(437\) 603.802 250.103i 1.38170 0.572318i
\(438\) 0 0
\(439\) 411.067 411.067i 0.936371 0.936371i −0.0617227 0.998093i \(-0.519659\pi\)
0.998093 + 0.0617227i \(0.0196594\pi\)
\(440\) −60.6321 + 137.224i −0.137800 + 0.311872i
\(441\) 0 0
\(442\) 63.3287 + 243.926i 0.143278 + 0.551869i
\(443\) 34.4767 14.2807i 0.0778256 0.0322364i −0.343431 0.939178i \(-0.611589\pi\)
0.421257 + 0.906941i \(0.361589\pi\)
\(444\) 0 0
\(445\) −23.3226 9.66052i −0.0524102 0.0217090i
\(446\) −176.493 + 133.258i −0.395725 + 0.298785i
\(447\) 0 0
\(448\) −447.574 20.9216i −0.999049 0.0467001i
\(449\) −185.456 −0.413043 −0.206521 0.978442i \(-0.566214\pi\)
−0.206521 + 0.978442i \(0.566214\pi\)
\(450\) 0 0
\(451\) −86.1331 + 207.944i −0.190982 + 0.461073i
\(452\) −462.712 131.738i −1.02370 0.291456i
\(453\) 0 0
\(454\) 775.642 201.374i 1.70846 0.443555i
\(455\) −36.5772 36.5772i −0.0803895 0.0803895i
\(456\) 0 0
\(457\) 386.211 + 386.211i 0.845100 + 0.845100i 0.989517 0.144417i \(-0.0461306\pi\)
−0.144417 + 0.989517i \(0.546131\pi\)
\(458\) −63.7067 + 108.386i −0.139098 + 0.236650i
\(459\) 0 0
\(460\) −143.598 + 181.227i −0.312169 + 0.393971i
\(461\) −268.824 + 648.999i −0.583133 + 1.40781i 0.306826 + 0.951766i \(0.400733\pi\)
−0.889958 + 0.456042i \(0.849267\pi\)
\(462\) 0 0
\(463\) 49.4705 0.106848 0.0534238 0.998572i \(-0.482987\pi\)
0.0534238 + 0.998572i \(0.482987\pi\)
\(464\) 86.6700 + 120.544i 0.186789 + 0.259793i
\(465\) 0 0
\(466\) 41.0466 294.070i 0.0880828 0.631052i
\(467\) 192.753 + 79.8411i 0.412748 + 0.170966i 0.579388 0.815052i \(-0.303292\pi\)
−0.166640 + 0.986018i \(0.553292\pi\)
\(468\) 0 0
\(469\) 611.761 253.400i 1.30439 0.540297i
\(470\) −98.7044 + 167.928i −0.210009 + 0.357294i
\(471\) 0 0
\(472\) 173.111 165.208i 0.366760 0.350016i
\(473\) 209.097 209.097i 0.442065 0.442065i
\(474\) 0 0
\(475\) 389.141 161.187i 0.819244 0.339342i
\(476\) −390.247 700.909i −0.819847 1.47250i
\(477\) 0 0
\(478\) 147.801 + 195.755i 0.309208 + 0.409530i
\(479\) 256.988i 0.536509i 0.963348 + 0.268254i \(0.0864468\pi\)
−0.963348 + 0.268254i \(0.913553\pi\)
\(480\) 0 0
\(481\) −300.415 −0.624564
\(482\) 301.325 227.510i 0.625155 0.472012i
\(483\) 0 0
\(484\) −7.06551 12.6901i −0.0145982 0.0262192i
\(485\) −9.19588 22.2008i −0.0189606 0.0457749i
\(486\) 0 0
\(487\) −10.7898 10.7898i −0.0221557 0.0221557i 0.695942 0.718098i \(-0.254987\pi\)
−0.718098 + 0.695942i \(0.754987\pi\)
\(488\) 661.365 + 15.4492i 1.35526 + 0.0316581i
\(489\) 0 0
\(490\) 0.0398434 + 0.0234191i 8.13131e−5 + 4.77940e-5i
\(491\) −58.0314 140.100i −0.118190 0.285336i 0.853702 0.520761i \(-0.174352\pi\)
−0.971893 + 0.235425i \(0.924352\pi\)
\(492\) 0 0
\(493\) −101.725 + 245.586i −0.206339 + 0.498146i
\(494\) −165.469 23.0964i −0.334958 0.0467538i
\(495\) 0 0
\(496\) 48.3128 77.9686i 0.0974049 0.157195i
\(497\) 53.4317i 0.107508i
\(498\) 0 0
\(499\) −72.1133 29.8703i −0.144516 0.0598603i 0.309253 0.950980i \(-0.399921\pi\)
−0.453769 + 0.891119i \(0.649921\pi\)
\(500\) −196.867 + 248.455i −0.393735 + 0.496910i
\(501\) 0 0
\(502\) −663.210 389.820i −1.32113 0.776533i
\(503\) −151.600 + 151.600i −0.301393 + 0.301393i −0.841559 0.540166i \(-0.818361\pi\)
0.540166 + 0.841559i \(0.318361\pi\)
\(504\) 0 0
\(505\) 160.355 160.355i 0.317535 0.317535i
\(506\) −193.080 743.697i −0.381582 1.46976i
\(507\) 0 0
\(508\) −492.585 140.243i −0.969656 0.276069i
\(509\) 562.711 + 233.082i 1.10552 + 0.457922i 0.859393 0.511315i \(-0.170842\pi\)
0.246128 + 0.969237i \(0.420842\pi\)
\(510\) 0 0
\(511\) 251.513i 0.492198i
\(512\) 228.569 458.149i 0.446424 0.894822i
\(513\) 0 0
\(514\) 101.751 + 134.764i 0.197960 + 0.262188i
\(515\) −4.43266 + 10.7014i −0.00860710 + 0.0207794i
\(516\) 0 0
\(517\) −247.705 598.012i −0.479119 1.15670i
\(518\) 925.616 240.311i 1.78690 0.463920i
\(519\) 0 0
\(520\) 55.1234 21.3387i 0.106006 0.0410360i
\(521\) 224.985 + 224.985i 0.431833 + 0.431833i 0.889252 0.457418i \(-0.151226\pi\)
−0.457418 + 0.889252i \(0.651226\pi\)
\(522\) 0 0
\(523\) −9.30771 22.4708i −0.0177968 0.0429652i 0.914731 0.404063i \(-0.132402\pi\)
−0.932528 + 0.361097i \(0.882402\pi\)
\(524\) −164.961 130.710i −0.314812 0.249446i
\(525\) 0 0
\(526\) 14.5484 104.229i 0.0276586 0.198155i
\(527\) 164.225 0.311622
\(528\) 0 0
\(529\) 655.224i 1.23861i
\(530\) 23.3163 167.045i 0.0439931 0.315180i
\(531\) 0 0
\(532\) 528.307 61.2010i 0.993059 0.115039i
\(533\) 81.9309 33.9369i 0.153717 0.0636715i
\(534\) 0 0
\(535\) −14.1411 + 14.1411i −0.0264320 + 0.0264320i
\(536\) −17.6702 + 756.447i −0.0329669 + 1.41128i
\(537\) 0 0
\(538\) −457.901 + 118.881i −0.851116 + 0.220969i
\(539\) −0.141887 + 0.0587715i −0.000263241 + 0.000109038i
\(540\) 0 0
\(541\) −357.866 148.233i −0.661490 0.273998i 0.0265752 0.999647i \(-0.491540\pi\)
−0.688066 + 0.725649i \(0.741540\pi\)
\(542\) −376.739 498.972i −0.695091 0.920613i
\(543\) 0 0
\(544\) 912.826 84.1940i 1.67799 0.154768i
\(545\) 48.3271 0.0886735
\(546\) 0 0
\(547\) 187.175 451.879i 0.342184 0.826105i −0.655311 0.755360i \(-0.727462\pi\)
0.997494 0.0707454i \(-0.0225378\pi\)
\(548\) −8.20852 + 4.57029i −0.0149791 + 0.00833994i
\(549\) 0 0
\(550\) −124.437 479.301i −0.226249 0.871456i
\(551\) −124.611 124.611i −0.226155 0.226155i
\(552\) 0 0
\(553\) −248.351 248.351i −0.449097 0.449097i
\(554\) 372.199 + 218.770i 0.671839 + 0.394892i
\(555\) 0 0
\(556\) −785.995 + 91.0524i −1.41366 + 0.163763i
\(557\) −307.716 + 742.891i −0.552452 + 1.33374i 0.363181 + 0.931719i \(0.381691\pi\)
−0.915632 + 0.402017i \(0.868309\pi\)
\(558\) 0 0
\(559\) −116.510 −0.208426
\(560\) −152.773 + 109.842i −0.272808 + 0.196146i
\(561\) 0 0
\(562\) 665.863 + 92.9417i 1.18481 + 0.165377i
\(563\) −706.303 292.560i −1.25454 0.519646i −0.346307 0.938121i \(-0.612565\pi\)
−0.908228 + 0.418476i \(0.862565\pi\)
\(564\) 0 0
\(565\) −186.656 + 77.3156i −0.330365 + 0.136842i
\(566\) −109.626 64.4360i −0.193686 0.113844i
\(567\) 0 0
\(568\) 55.8475 + 24.6761i 0.0983231 + 0.0434439i
\(569\) 552.550 552.550i 0.971089 0.971089i −0.0285048 0.999594i \(-0.509075\pi\)
0.999594 + 0.0285048i \(0.00907459\pi\)
\(570\) 0 0
\(571\) −476.739 + 197.472i −0.834919 + 0.345835i −0.758848 0.651268i \(-0.774237\pi\)
−0.0760707 + 0.997102i \(0.524237\pi\)
\(572\) −53.7854 + 188.914i −0.0940304 + 0.330269i
\(573\) 0 0
\(574\) −225.292 + 170.103i −0.392495 + 0.296346i
\(575\) 763.214i 1.32733i
\(576\) 0 0
\(577\) −188.090 −0.325980 −0.162990 0.986628i \(-0.552114\pi\)
−0.162990 + 0.986628i \(0.552114\pi\)
\(578\) 640.703 + 848.578i 1.10848 + 1.46813i
\(579\) 0 0
\(580\) 59.9650 + 17.0725i 0.103388 + 0.0294354i
\(581\) −292.326 705.737i −0.503143 1.21469i
\(582\) 0 0
\(583\) 396.316 + 396.316i 0.679787 + 0.679787i
\(584\) −262.885 116.155i −0.450146 0.198896i
\(585\) 0 0
\(586\) −125.954 + 214.289i −0.214939 + 0.365681i
\(587\) −229.302 553.585i −0.390634 0.943075i −0.989802 0.142451i \(-0.954502\pi\)
0.599167 0.800624i \(-0.295498\pi\)
\(588\) 0 0
\(589\) −41.6642 + 100.586i −0.0707372 + 0.170775i
\(590\) 13.8917 99.5246i 0.0235453 0.168686i
\(591\) 0 0
\(592\) −176.298 + 1078.45i −0.297800 + 1.82170i
\(593\) 378.708i 0.638630i 0.947649 + 0.319315i \(0.103453\pi\)
−0.947649 + 0.319315i \(0.896547\pi\)
\(594\) 0 0
\(595\) −311.246 128.922i −0.523102 0.216676i
\(596\) 8.03146 + 69.3302i 0.0134756 + 0.116326i
\(597\) 0 0
\(598\) −153.404 + 260.990i −0.256528 + 0.436438i
\(599\) −745.316 + 745.316i −1.24427 + 1.24427i −0.286055 + 0.958213i \(0.592344\pi\)
−0.958213 + 0.286055i \(0.907656\pi\)
\(600\) 0 0
\(601\) 130.996 130.996i 0.217963 0.217963i −0.589676 0.807640i \(-0.700745\pi\)
0.807640 + 0.589676i \(0.200745\pi\)
\(602\) 358.983 93.1999i 0.596316 0.154817i
\(603\) 0 0
\(604\) −350.425 629.386i −0.580174 1.04203i
\(605\) −5.63517 2.33416i −0.00931433 0.00385812i
\(606\) 0 0
\(607\) 732.344i 1.20650i 0.797553 + 0.603249i \(0.206127\pi\)
−0.797553 + 0.603249i \(0.793873\pi\)
\(608\) −180.018 + 580.458i −0.296082 + 0.954701i
\(609\) 0 0
\(610\) 221.713 167.400i 0.363464 0.274427i
\(611\) −97.5969 + 235.620i −0.159733 + 0.385630i
\(612\) 0 0
\(613\) 208.204 + 502.648i 0.339647 + 0.819981i 0.997749 + 0.0670521i \(0.0213594\pi\)
−0.658102 + 0.752928i \(0.728641\pi\)
\(614\) −221.543 853.328i −0.360819 1.38979i
\(615\) 0 0
\(616\) 14.6018 625.092i 0.0237043 1.01476i
\(617\) −209.834 209.834i −0.340087 0.340087i 0.516313 0.856400i \(-0.327304\pi\)
−0.856400 + 0.516313i \(0.827304\pi\)
\(618\) 0 0
\(619\) 175.433 + 423.533i 0.283414 + 0.684222i 0.999911 0.0133688i \(-0.00425556\pi\)
−0.716497 + 0.697590i \(0.754256\pi\)
\(620\) −4.43252 38.2629i −0.00714922 0.0617144i
\(621\) 0 0
\(622\) 418.672 + 58.4386i 0.673106 + 0.0939527i
\(623\) 105.213 0.168881
\(624\) 0 0
\(625\) 421.338i 0.674141i
\(626\) −827.642 115.523i −1.32211 0.184541i
\(627\) 0 0
\(628\) 635.249 801.712i 1.01154 1.27661i
\(629\) −1807.59 + 748.727i −2.87375 + 1.19035i
\(630\) 0 0
\(631\) 232.756 232.756i 0.368868 0.368868i −0.498196 0.867064i \(-0.666004\pi\)
0.867064 + 0.498196i \(0.166004\pi\)
\(632\) 374.274 144.885i 0.592206 0.229248i
\(633\) 0 0
\(634\) −121.230 466.947i −0.191214 0.736509i
\(635\) −198.707 + 82.3071i −0.312924 + 0.129617i
\(636\) 0 0
\(637\) 0.0559042 + 0.0231563i 8.77618e−5 + 3.63521e-5i
\(638\) −165.346 + 124.842i −0.259163 + 0.195676i
\(639\) 0 0
\(640\) −44.2541 210.408i −0.0691470 0.328762i
\(641\) 123.632 0.192873 0.0964366 0.995339i \(-0.469256\pi\)
0.0964366 + 0.995339i \(0.469256\pi\)
\(642\) 0 0
\(643\) −351.513 + 848.628i −0.546677 + 1.31979i 0.373260 + 0.927727i \(0.378240\pi\)
−0.919936 + 0.392068i \(0.871760\pi\)
\(644\) 263.883 926.854i 0.409756 1.43921i
\(645\) 0 0
\(646\) −1053.19 + 273.431i −1.63032 + 0.423268i
\(647\) 191.561 + 191.561i 0.296076 + 0.296076i 0.839475 0.543399i \(-0.182863\pi\)
−0.543399 + 0.839475i \(0.682863\pi\)
\(648\) 0 0
\(649\) 236.122 + 236.122i 0.363825 + 0.363825i
\(650\) −98.8664 + 168.204i −0.152102 + 0.258775i
\(651\) 0 0
\(652\) 312.089 + 247.289i 0.478664 + 0.379277i
\(653\) 89.1964 215.339i 0.136595 0.329769i −0.840750 0.541424i \(-0.817885\pi\)
0.977344 + 0.211655i \(0.0678853\pi\)
\(654\) 0 0
\(655\) −88.3853 −0.134939
\(656\) −73.7479 314.037i −0.112421 0.478714i
\(657\) 0 0
\(658\) 112.229 804.045i 0.170561 1.22195i
\(659\) 911.099 + 377.389i 1.38255 + 0.572670i 0.945161 0.326604i \(-0.105904\pi\)
0.437386 + 0.899274i \(0.355904\pi\)
\(660\) 0 0
\(661\) −496.993 + 205.861i −0.751880 + 0.311439i −0.725509 0.688213i \(-0.758395\pi\)
−0.0263718 + 0.999652i \(0.508395\pi\)
\(662\) −531.310 + 903.930i −0.802582 + 1.36545i
\(663\) 0 0
\(664\) 872.650 + 20.3847i 1.31423 + 0.0306998i
\(665\) 157.928 157.928i 0.237485 0.237485i
\(666\) 0 0
\(667\) −295.014 + 122.199i −0.442300 + 0.183207i
\(668\) 1106.27 615.941i 1.65609 0.922068i
\(669\) 0 0
\(670\) 191.467 + 253.588i 0.285772 + 0.378490i
\(671\) 923.172i 1.37582i
\(672\) 0 0
\(673\) 374.150 0.555944 0.277972 0.960589i \(-0.410338\pi\)
0.277972 + 0.960589i \(0.410338\pi\)
\(674\) 395.984 298.980i 0.587514 0.443591i
\(675\) 0 0
\(676\) −523.008 + 291.197i −0.773680 + 0.430764i
\(677\) −12.3571 29.8326i −0.0182527 0.0440659i 0.914490 0.404608i \(-0.132592\pi\)
−0.932743 + 0.360542i \(0.882592\pi\)
\(678\) 0 0
\(679\) 70.8184 + 70.8184i 0.104298 + 0.104298i
\(680\) 278.493 265.779i 0.409548 0.390851i
\(681\) 0 0
\(682\) 110.348 + 64.8603i 0.161801 + 0.0951030i
\(683\) −22.0894 53.3285i −0.0323417 0.0780799i 0.906883 0.421382i \(-0.138455\pi\)
−0.939225 + 0.343302i \(0.888455\pi\)
\(684\) 0 0
\(685\) −1.50984 + 3.64508i −0.00220415 + 0.00532128i
\(686\) 679.318 + 94.8198i 0.990260 + 0.138221i
\(687\) 0 0
\(688\) −68.3737 + 418.256i −0.0993803 + 0.607930i
\(689\) 220.830i 0.320508i
\(690\) 0 0
\(691\) −622.510 257.852i −0.900883 0.373158i −0.116323 0.993211i \(-0.537111\pi\)
−0.784560 + 0.620053i \(0.787111\pi\)
\(692\) −108.676 86.1111i −0.157046 0.124438i
\(693\) 0 0
\(694\) −189.356 111.299i −0.272848 0.160374i
\(695\) −234.958 + 234.958i −0.338069 + 0.338069i
\(696\) 0 0
\(697\) 408.394 408.394i 0.585932 0.585932i
\(698\) −266.499 1026.49i −0.381803 1.47061i
\(699\) 0 0
\(700\) 170.069 597.343i 0.242955 0.853347i
\(701\) 34.0835 + 14.1179i 0.0486213 + 0.0201396i 0.406862 0.913490i \(-0.366623\pi\)
−0.358240 + 0.933629i \(0.616623\pi\)
\(702\) 0 0
\(703\) 1297.09i 1.84507i
\(704\) 646.611 + 303.946i 0.918482 + 0.431741i
\(705\) 0 0
\(706\) −223.706 296.286i −0.316863 0.419669i
\(707\) −361.698 + 873.215i −0.511595 + 1.23510i
\(708\) 0 0
\(709\) 285.114 + 688.325i 0.402135 + 0.970840i 0.987147 + 0.159815i \(0.0510898\pi\)
−0.585012 + 0.811025i \(0.698910\pi\)
\(710\) 24.8174 6.44316i 0.0349541 0.00907487i
\(711\) 0 0
\(712\) −48.5900 + 109.970i −0.0682444 + 0.154452i
\(713\) 139.497 + 139.497i 0.195647 + 0.195647i
\(714\) 0 0
\(715\) 31.5660 + 76.2071i 0.0441483 + 0.106583i
\(716\) −37.1878 + 46.9327i −0.0519383 + 0.0655484i
\(717\) 0 0
\(718\) −87.1339 + 624.254i −0.121356 + 0.869435i
\(719\) 478.037 0.664863 0.332432 0.943127i \(-0.392131\pi\)
0.332432 + 0.943127i \(0.392131\pi\)
\(720\) 0 0
\(721\) 48.2761i 0.0669571i
\(722\) −0.0879139 + 0.629843i −0.000121764 + 0.000872358i
\(723\) 0 0
\(724\) 76.5249 + 660.588i 0.105697 + 0.912415i
\(725\) −190.132 + 78.7553i −0.262251 + 0.108628i
\(726\) 0 0
\(727\) −408.395 + 408.395i −0.561753 + 0.561753i −0.929805 0.368052i \(-0.880025\pi\)
0.368052 + 0.929805i \(0.380025\pi\)
\(728\) −178.221 + 170.085i −0.244809 + 0.233633i
\(729\) 0 0
\(730\) −116.820 + 30.3292i −0.160028 + 0.0415468i
\(731\) −701.038 + 290.379i −0.959012 + 0.397236i
\(732\) 0 0
\(733\) 747.573 + 309.655i 1.01988 + 0.422449i 0.829050 0.559174i \(-0.188882\pi\)
0.190831 + 0.981623i \(0.438882\pi\)
\(734\) −642.060 850.376i −0.874741 1.15855i
\(735\) 0 0
\(736\) 846.892 + 703.860i 1.15067 + 0.956331i
\(737\) −1055.89 −1.43269
\(738\) 0 0
\(739\) −348.876 + 842.261i −0.472092 + 1.13973i 0.491145 + 0.871078i \(0.336579\pi\)
−0.963237 + 0.268653i \(0.913421\pi\)
\(740\) 223.234 + 400.943i 0.301668 + 0.541815i
\(741\) 0 0
\(742\) 176.648 + 680.405i 0.238071 + 0.916988i
\(743\) 345.072 + 345.072i 0.464430 + 0.464430i 0.900104 0.435674i \(-0.143490\pi\)
−0.435674 + 0.900104i \(0.643490\pi\)
\(744\) 0 0
\(745\) 20.7250 + 20.7250i 0.0278187 + 0.0278187i
\(746\) 518.132 + 304.546i 0.694547 + 0.408239i
\(747\) 0 0
\(748\) 147.207 + 1270.74i 0.196801 + 1.69885i
\(749\) 31.8967 77.0054i 0.0425857 0.102811i
\(750\) 0 0
\(751\) 642.659 0.855737 0.427869 0.903841i \(-0.359265\pi\)
0.427869 + 0.903841i \(0.359265\pi\)
\(752\) 788.568 + 488.632i 1.04863 + 0.649777i
\(753\) 0 0
\(754\) 80.8474 + 11.2847i 0.107225 + 0.0149665i
\(755\) −279.485 115.767i −0.370179 0.153333i
\(756\) 0 0
\(757\) 241.802 100.158i 0.319422 0.132309i −0.217211 0.976125i \(-0.569696\pi\)
0.536633 + 0.843816i \(0.319696\pi\)
\(758\) −571.723 336.046i −0.754252 0.443332i
\(759\) 0 0
\(760\) 92.1330 + 238.003i 0.121228 + 0.313162i
\(761\) 253.025 253.025i 0.332490 0.332490i −0.521042 0.853531i \(-0.674456\pi\)
0.853531 + 0.521042i \(0.174456\pi\)
\(762\) 0 0
\(763\) −186.086 + 77.0793i −0.243887 + 0.101021i
\(764\) −7.69944 2.19210i −0.0100778 0.00286923i
\(765\) 0 0
\(766\) 260.707 196.842i 0.340349 0.256974i
\(767\) 131.569i 0.171537i
\(768\) 0 0
\(769\) −1066.22 −1.38650 −0.693248 0.720699i \(-0.743821\pi\)
−0.693248 + 0.720699i \(0.743821\pi\)
\(770\) −158.219 209.553i −0.205479 0.272147i
\(771\) 0 0
\(772\) 117.747 413.571i 0.152522 0.535714i
\(773\) 497.702 + 1201.56i 0.643857 + 1.55441i 0.821435 + 0.570302i \(0.193174\pi\)
−0.177578 + 0.984107i \(0.556826\pi\)
\(774\) 0 0
\(775\) 89.9033 + 89.9033i 0.116004 + 0.116004i
\(776\) −106.726 + 41.3146i −0.137534 + 0.0532404i
\(777\) 0 0
\(778\) 71.6934 121.974i 0.0921509 0.156779i
\(779\) 146.527 + 353.749i 0.188097 + 0.454106i
\(780\) 0 0
\(781\) −32.6056 + 78.7170i −0.0417486 + 0.100790i
\(782\) −272.559 + 1952.70i −0.348541 + 2.49705i
\(783\) 0 0
\(784\) 0.115935 0.187099i 0.000147876 0.000238647i
\(785\) 429.553i 0.547201i
\(786\) 0 0
\(787\) 307.578 + 127.403i 0.390823 + 0.161884i 0.569437 0.822035i \(-0.307161\pi\)
−0.178614 + 0.983919i \(0.557161\pi\)