Properties

Label 144.2.l.a.35.2
Level $144$
Weight $2$
Character 144.35
Analytic conductor $1.150$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 144 = 2^{4} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 144.l (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(1.14984578911\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(i)\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
Defining polynomial: \(x^{16} - 4 x^{14} + 6 x^{12} - 12 x^{10} + 33 x^{8} - 48 x^{6} + 96 x^{4} - 256 x^{2} + 256\)
Coefficient ring: \(\Z[a_1, \ldots, a_{17}]\)
Coefficient ring index: \( 2^{10} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 35.2
Root \(-1.36166 + 0.381939i\) of defining polynomial
Character \(\chi\) \(=\) 144.35
Dual form 144.2.l.a.107.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.12697 + 0.854358i) q^{2} +(0.540143 - 1.92568i) q^{4} +(0.763878 + 0.763878i) q^{5} +1.33620 q^{7} +(1.03649 + 2.63167i) q^{8} +O(q^{10})\) \(q+(-1.12697 + 0.854358i) q^{2} +(0.540143 - 1.92568i) q^{4} +(0.763878 + 0.763878i) q^{5} +1.33620 q^{7} +(1.03649 + 2.63167i) q^{8} +(-1.51350 - 0.208245i) q^{10} +(1.95945 - 1.95945i) q^{11} +(4.18757 + 4.18757i) q^{13} +(-1.50587 + 1.14160i) q^{14} +(-3.41649 - 2.08029i) q^{16} +4.03243i q^{17} +(-4.26785 + 4.26785i) q^{19} +(1.88359 - 1.05838i) q^{20} +(-0.534176 + 3.88231i) q^{22} -8.86408i q^{23} -3.83298i q^{25} +(-8.29696 - 1.14160i) q^{26} +(0.721742 - 2.57310i) q^{28} +(1.23934 - 1.23934i) q^{29} -2.87835i q^{31} +(5.62761 - 0.574478i) q^{32} +(-3.44514 - 4.54445i) q^{34} +(1.02070 + 1.02070i) q^{35} +(0.434870 - 0.434870i) q^{37} +(1.16348 - 8.45604i) q^{38} +(-1.21852 + 2.80203i) q^{40} -7.81179 q^{41} +(-5.49678 - 5.49678i) q^{43} +(-2.71489 - 4.83165i) q^{44} +(7.57310 + 9.98959i) q^{46} -3.20723 q^{47} -5.21456 q^{49} +(3.27474 + 4.31967i) q^{50} +(10.3258 - 5.80203i) q^{52} +(4.06777 + 4.06777i) q^{53} +2.99355 q^{55} +(1.38497 + 3.51645i) q^{56} +(-0.337865 + 2.45555i) q^{58} +(-4.71811 + 4.71811i) q^{59} +(3.26785 + 3.26785i) q^{61} +(2.45915 + 3.24383i) q^{62} +(-5.85136 + 5.45542i) q^{64} +6.39758i q^{65} +(-5.44348 + 5.44348i) q^{67} +(7.76518 + 2.17809i) q^{68} +(-2.02234 - 0.278258i) q^{70} +3.76718i q^{71} -10.5357i q^{73} +(-0.118553 + 0.861623i) q^{74} +(5.91327 + 10.5238i) q^{76} +(2.61822 - 2.61822i) q^{77} -11.1995i q^{79} +(-1.02070 - 4.19887i) q^{80} +(8.80369 - 6.67407i) q^{82} +(9.73306 + 9.73306i) q^{83} +(-3.08029 + 3.08029i) q^{85} +(10.8909 + 1.49851i) q^{86} +(7.18757 + 3.12566i) q^{88} -1.64130 q^{89} +(5.59544 + 5.59544i) q^{91} +(-17.0694 - 4.78787i) q^{92} +(3.61446 - 2.74012i) q^{94} -6.52023 q^{95} -5.70272 q^{97} +(5.87667 - 4.45510i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q + O(q^{10}) \) \( 16q - 8q^{10} - 16q^{16} + 16q^{19} - 40q^{22} - 24q^{28} + 24q^{34} + 72q^{40} - 32q^{43} + 40q^{46} + 16q^{49} + 24q^{52} - 64q^{55} + 24q^{58} - 32q^{61} - 48q^{64} - 16q^{67} - 72q^{70} + 80q^{82} - 32q^{85} + 48q^{88} + 48q^{91} + 72q^{94} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/144\mathbb{Z}\right)^\times\).

\(n\) \(37\) \(65\) \(127\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.12697 + 0.854358i −0.796891 + 0.604123i
\(3\) 0 0
\(4\) 0.540143 1.92568i 0.270072 0.962840i
\(5\) 0.763878 + 0.763878i 0.341617 + 0.341617i 0.856975 0.515358i \(-0.172341\pi\)
−0.515358 + 0.856975i \(0.672341\pi\)
\(6\) 0 0
\(7\) 1.33620 0.505038 0.252519 0.967592i \(-0.418741\pi\)
0.252519 + 0.967592i \(0.418741\pi\)
\(8\) 1.03649 + 2.63167i 0.366456 + 0.930435i
\(9\) 0 0
\(10\) −1.51350 0.208245i −0.478610 0.0658530i
\(11\) 1.95945 1.95945i 0.590795 0.590795i −0.347051 0.937846i \(-0.612817\pi\)
0.937846 + 0.347051i \(0.112817\pi\)
\(12\) 0 0
\(13\) 4.18757 + 4.18757i 1.16142 + 1.16142i 0.984165 + 0.177257i \(0.0567224\pi\)
0.177257 + 0.984165i \(0.443278\pi\)
\(14\) −1.50587 + 1.14160i −0.402460 + 0.305105i
\(15\) 0 0
\(16\) −3.41649 2.08029i −0.854123 0.520072i
\(17\) 4.03243i 0.978009i 0.872281 + 0.489004i \(0.162640\pi\)
−0.872281 + 0.489004i \(0.837360\pi\)
\(18\) 0 0
\(19\) −4.26785 + 4.26785i −0.979112 + 0.979112i −0.999786 0.0206739i \(-0.993419\pi\)
0.0206739 + 0.999786i \(0.493419\pi\)
\(20\) 1.88359 1.05838i 0.421183 0.236661i
\(21\) 0 0
\(22\) −0.534176 + 3.88231i −0.113887 + 0.827712i
\(23\) 8.86408i 1.84829i −0.382044 0.924144i \(-0.624780\pi\)
0.382044 0.924144i \(-0.375220\pi\)
\(24\) 0 0
\(25\) 3.83298i 0.766596i
\(26\) −8.29696 1.14160i −1.62717 0.223886i
\(27\) 0 0
\(28\) 0.721742 2.57310i 0.136396 0.486271i
\(29\) 1.23934 1.23934i 0.230140 0.230140i −0.582611 0.812751i \(-0.697969\pi\)
0.812751 + 0.582611i \(0.197969\pi\)
\(30\) 0 0
\(31\) 2.87835i 0.516968i −0.966016 0.258484i \(-0.916777\pi\)
0.966016 0.258484i \(-0.0832229\pi\)
\(32\) 5.62761 0.574478i 0.994830 0.101554i
\(33\) 0 0
\(34\) −3.44514 4.54445i −0.590837 0.779367i
\(35\) 1.02070 + 1.02070i 0.172529 + 0.172529i
\(36\) 0 0
\(37\) 0.434870 0.434870i 0.0714922 0.0714922i −0.670457 0.741949i \(-0.733902\pi\)
0.741949 + 0.670457i \(0.233902\pi\)
\(38\) 1.16348 8.45604i 0.188742 1.37175i
\(39\) 0 0
\(40\) −1.21852 + 2.80203i −0.192665 + 0.443040i
\(41\) −7.81179 −1.22000 −0.609998 0.792403i \(-0.708830\pi\)
−0.609998 + 0.792403i \(0.708830\pi\)
\(42\) 0 0
\(43\) −5.49678 5.49678i −0.838251 0.838251i 0.150378 0.988629i \(-0.451951\pi\)
−0.988629 + 0.150378i \(0.951951\pi\)
\(44\) −2.71489 4.83165i −0.409284 0.728398i
\(45\) 0 0
\(46\) 7.57310 + 9.98959i 1.11659 + 1.47289i
\(47\) −3.20723 −0.467822 −0.233911 0.972258i \(-0.575152\pi\)
−0.233911 + 0.972258i \(0.575152\pi\)
\(48\) 0 0
\(49\) −5.21456 −0.744937
\(50\) 3.27474 + 4.31967i 0.463118 + 0.610894i
\(51\) 0 0
\(52\) 10.3258 5.80203i 1.43193 0.804597i
\(53\) 4.06777 + 4.06777i 0.558751 + 0.558751i 0.928952 0.370201i \(-0.120711\pi\)
−0.370201 + 0.928952i \(0.620711\pi\)
\(54\) 0 0
\(55\) 2.99355 0.403651
\(56\) 1.38497 + 3.51645i 0.185074 + 0.469905i
\(57\) 0 0
\(58\) −0.337865 + 2.45555i −0.0443638 + 0.322430i
\(59\) −4.71811 + 4.71811i −0.614245 + 0.614245i −0.944049 0.329804i \(-0.893017\pi\)
0.329804 + 0.944049i \(0.393017\pi\)
\(60\) 0 0
\(61\) 3.26785 + 3.26785i 0.418406 + 0.418406i 0.884654 0.466248i \(-0.154395\pi\)
−0.466248 + 0.884654i \(0.654395\pi\)
\(62\) 2.45915 + 3.24383i 0.312312 + 0.411967i
\(63\) 0 0
\(64\) −5.85136 + 5.45542i −0.731420 + 0.681927i
\(65\) 6.39758i 0.793522i
\(66\) 0 0
\(67\) −5.44348 + 5.44348i −0.665027 + 0.665027i −0.956561 0.291533i \(-0.905835\pi\)
0.291533 + 0.956561i \(0.405835\pi\)
\(68\) 7.76518 + 2.17809i 0.941666 + 0.264132i
\(69\) 0 0
\(70\) −2.02234 0.278258i −0.241716 0.0332582i
\(71\) 3.76718i 0.447082i 0.974695 + 0.223541i \(0.0717616\pi\)
−0.974695 + 0.223541i \(0.928238\pi\)
\(72\) 0 0
\(73\) 10.5357i 1.23311i −0.787312 0.616555i \(-0.788528\pi\)
0.787312 0.616555i \(-0.211472\pi\)
\(74\) −0.118553 + 0.861623i −0.0137815 + 0.100162i
\(75\) 0 0
\(76\) 5.91327 + 10.5238i 0.678298 + 1.20716i
\(77\) 2.61822 2.61822i 0.298374 0.298374i
\(78\) 0 0
\(79\) 11.1995i 1.26004i −0.776578 0.630021i \(-0.783046\pi\)
0.776578 0.630021i \(-0.216954\pi\)
\(80\) −1.02070 4.19887i −0.114117 0.469447i
\(81\) 0 0
\(82\) 8.80369 6.67407i 0.972205 0.737028i
\(83\) 9.73306 + 9.73306i 1.06834 + 1.06834i 0.997487 + 0.0708558i \(0.0225730\pi\)
0.0708558 + 0.997487i \(0.477427\pi\)
\(84\) 0 0
\(85\) −3.08029 + 3.08029i −0.334104 + 0.334104i
\(86\) 10.8909 + 1.49851i 1.17440 + 0.161588i
\(87\) 0 0
\(88\) 7.18757 + 3.12566i 0.766197 + 0.333196i
\(89\) −1.64130 −0.173977 −0.0869886 0.996209i \(-0.527724\pi\)
−0.0869886 + 0.996209i \(0.527724\pi\)
\(90\) 0 0
\(91\) 5.59544 + 5.59544i 0.586562 + 0.586562i
\(92\) −17.0694 4.78787i −1.77961 0.499170i
\(93\) 0 0
\(94\) 3.61446 2.74012i 0.372803 0.282622i
\(95\) −6.52023 −0.668962
\(96\) 0 0
\(97\) −5.70272 −0.579024 −0.289512 0.957174i \(-0.593493\pi\)
−0.289512 + 0.957174i \(0.593493\pi\)
\(98\) 5.87667 4.45510i 0.593634 0.450033i
\(99\) 0 0
\(100\) −7.38110 2.07036i −0.738110 0.207036i
\(101\) −6.68599 6.68599i −0.665281 0.665281i 0.291339 0.956620i \(-0.405899\pi\)
−0.956620 + 0.291339i \(0.905899\pi\)
\(102\) 0 0
\(103\) 10.8784 1.07188 0.535938 0.844257i \(-0.319958\pi\)
0.535938 + 0.844257i \(0.319958\pi\)
\(104\) −6.67990 + 15.3607i −0.655018 + 1.50624i
\(105\) 0 0
\(106\) −8.05961 1.10894i −0.782818 0.107710i
\(107\) −1.31755 + 1.31755i −0.127372 + 0.127372i −0.767919 0.640547i \(-0.778708\pi\)
0.640547 + 0.767919i \(0.278708\pi\)
\(108\) 0 0
\(109\) −3.51516 3.51516i −0.336691 0.336691i 0.518429 0.855120i \(-0.326517\pi\)
−0.855120 + 0.518429i \(0.826517\pi\)
\(110\) −3.37366 + 2.55757i −0.321666 + 0.243855i
\(111\) 0 0
\(112\) −4.56513 2.77969i −0.431364 0.262656i
\(113\) 16.3139i 1.53469i −0.641236 0.767344i \(-0.721578\pi\)
0.641236 0.767344i \(-0.278422\pi\)
\(114\) 0 0
\(115\) 6.77107 6.77107i 0.631406 0.631406i
\(116\) −1.71716 3.05600i −0.159434 0.283742i
\(117\) 0 0
\(118\) 1.28623 9.34814i 0.118407 0.860566i
\(119\) 5.38815i 0.493931i
\(120\) 0 0
\(121\) 3.32115i 0.301922i
\(122\) −6.47470 0.890869i −0.586192 0.0806555i
\(123\) 0 0
\(124\) −5.54279 1.55472i −0.497757 0.139618i
\(125\) 6.74732 6.74732i 0.603499 0.603499i
\(126\) 0 0
\(127\) 20.7416i 1.84052i 0.391303 + 0.920262i \(0.372024\pi\)
−0.391303 + 0.920262i \(0.627976\pi\)
\(128\) 1.93345 11.1473i 0.170895 0.985289i
\(129\) 0 0
\(130\) −5.46582 7.20991i −0.479384 0.632351i
\(131\) −9.43621 9.43621i −0.824446 0.824446i 0.162296 0.986742i \(-0.448110\pi\)
−0.986742 + 0.162296i \(0.948110\pi\)
\(132\) 0 0
\(133\) −5.70272 + 5.70272i −0.494489 + 0.494489i
\(134\) 1.48398 10.7854i 0.128196 0.931713i
\(135\) 0 0
\(136\) −10.6120 + 4.17959i −0.909974 + 0.358397i
\(137\) 12.8211 1.09538 0.547692 0.836680i \(-0.315506\pi\)
0.547692 + 0.836680i \(0.315506\pi\)
\(138\) 0 0
\(139\) 1.44348 + 1.44348i 0.122435 + 0.122435i 0.765669 0.643235i \(-0.222408\pi\)
−0.643235 + 0.765669i \(0.722408\pi\)
\(140\) 2.51686 1.41421i 0.212713 0.119523i
\(141\) 0 0
\(142\) −3.21852 4.24551i −0.270092 0.356275i
\(143\) 16.4106 1.37232
\(144\) 0 0
\(145\) 1.89341 0.157239
\(146\) 9.00127 + 11.8735i 0.744950 + 0.982655i
\(147\) 0 0
\(148\) −0.602529 1.07231i −0.0495276 0.0881436i
\(149\) −6.42073 6.42073i −0.526007 0.526007i 0.393372 0.919379i \(-0.371308\pi\)
−0.919379 + 0.393372i \(0.871308\pi\)
\(150\) 0 0
\(151\) 0.205945 0.0167596 0.00837978 0.999965i \(-0.497333\pi\)
0.00837978 + 0.999965i \(0.497333\pi\)
\(152\) −15.6552 6.80797i −1.26980 0.552199i
\(153\) 0 0
\(154\) −0.713769 + 5.18757i −0.0575171 + 0.418026i
\(155\) 2.19871 2.19871i 0.176605 0.176605i
\(156\) 0 0
\(157\) −1.26785 1.26785i −0.101186 0.101186i 0.654702 0.755887i \(-0.272794\pi\)
−0.755887 + 0.654702i \(0.772794\pi\)
\(158\) 9.56839 + 12.6216i 0.761220 + 1.00412i
\(159\) 0 0
\(160\) 4.73764 + 3.85997i 0.374543 + 0.305158i
\(161\) 11.8442i 0.933456i
\(162\) 0 0
\(163\) 0.169186 0.169186i 0.0132517 0.0132517i −0.700450 0.713702i \(-0.747017\pi\)
0.713702 + 0.700450i \(0.247017\pi\)
\(164\) −4.21949 + 15.0430i −0.329486 + 1.17466i
\(165\) 0 0
\(166\) −19.2844 2.65339i −1.49676 0.205943i
\(167\) 10.4503i 0.808671i 0.914611 + 0.404335i \(0.132497\pi\)
−0.914611 + 0.404335i \(0.867503\pi\)
\(168\) 0 0
\(169\) 22.0714i 1.69780i
\(170\) 0.839735 6.10307i 0.0644048 0.468084i
\(171\) 0 0
\(172\) −13.5541 + 7.61599i −1.03349 + 0.580714i
\(173\) 0.974085 0.974085i 0.0740583 0.0740583i −0.669107 0.743166i \(-0.733323\pi\)
0.743166 + 0.669107i \(0.233323\pi\)
\(174\) 0 0
\(175\) 5.12165i 0.387160i
\(176\) −10.7706 + 2.61822i −0.811867 + 0.197356i
\(177\) 0 0
\(178\) 1.84970 1.40226i 0.138641 0.105104i
\(179\) 6.59560 + 6.59560i 0.492979 + 0.492979i 0.909243 0.416265i \(-0.136661\pi\)
−0.416265 + 0.909243i \(0.636661\pi\)
\(180\) 0 0
\(181\) 10.1876 10.1876i 0.757236 0.757236i −0.218583 0.975818i \(-0.570143\pi\)
0.975818 + 0.218583i \(0.0701433\pi\)
\(182\) −11.0864 1.52541i −0.821781 0.113071i
\(183\) 0 0
\(184\) 23.3273 9.18757i 1.71971 0.677316i
\(185\) 0.664376 0.0488459
\(186\) 0 0
\(187\) 7.90133 + 7.90133i 0.577803 + 0.577803i
\(188\) −1.73236 + 6.17609i −0.126345 + 0.450438i
\(189\) 0 0
\(190\) 7.34814 5.57062i 0.533090 0.404135i
\(191\) −14.2297 −1.02962 −0.514812 0.857303i \(-0.672138\pi\)
−0.514812 + 0.857303i \(0.672138\pi\)
\(192\) 0 0
\(193\) 6.53570 0.470450 0.235225 0.971941i \(-0.424417\pi\)
0.235225 + 0.971941i \(0.424417\pi\)
\(194\) 6.42682 4.87217i 0.461419 0.349801i
\(195\) 0 0
\(196\) −2.81661 + 10.0416i −0.201186 + 0.717255i
\(197\) 9.07713 + 9.07713i 0.646718 + 0.646718i 0.952198 0.305480i \(-0.0988169\pi\)
−0.305480 + 0.952198i \(0.598817\pi\)
\(198\) 0 0
\(199\) −10.0865 −0.715011 −0.357505 0.933911i \(-0.616373\pi\)
−0.357505 + 0.933911i \(0.616373\pi\)
\(200\) 10.0871 3.97286i 0.713268 0.280924i
\(201\) 0 0
\(202\) 13.2472 + 1.82271i 0.932068 + 0.128245i
\(203\) 1.65601 1.65601i 0.116229 0.116229i
\(204\) 0 0
\(205\) −5.96725 5.96725i −0.416771 0.416771i
\(206\) −12.2596 + 9.29401i −0.854169 + 0.647545i
\(207\) 0 0
\(208\) −5.59544 23.0181i −0.387974 1.59602i
\(209\) 16.7252i 1.15691i
\(210\) 0 0
\(211\) 17.9792 17.9792i 1.23774 1.23774i 0.276815 0.960923i \(-0.410721\pi\)
0.960923 0.276815i \(-0.0892789\pi\)
\(212\) 10.0304 5.63605i 0.688891 0.387085i
\(213\) 0 0
\(214\) 0.359185 2.61050i 0.0245534 0.178450i
\(215\) 8.39773i 0.572721i
\(216\) 0 0
\(217\) 3.84607i 0.261088i
\(218\) 6.96470 + 0.958288i 0.471709 + 0.0649035i
\(219\) 0 0
\(220\) 1.61695 5.76463i 0.109015 0.388651i
\(221\) −16.8861 + 16.8861i −1.13588 + 1.13588i
\(222\) 0 0
\(223\) 4.00861i 0.268437i 0.990952 + 0.134218i \(0.0428523\pi\)
−0.990952 + 0.134218i \(0.957148\pi\)
\(224\) 7.51963 0.767620i 0.502427 0.0512888i
\(225\) 0 0
\(226\) 13.9380 + 18.3854i 0.927139 + 1.22298i
\(227\) −13.7915 13.7915i −0.915373 0.915373i 0.0813152 0.996688i \(-0.474088\pi\)
−0.996688 + 0.0813152i \(0.974088\pi\)
\(228\) 0 0
\(229\) 3.47840 3.47840i 0.229859 0.229859i −0.582775 0.812634i \(-0.698033\pi\)
0.812634 + 0.582775i \(0.198033\pi\)
\(230\) −1.84590 + 13.4158i −0.121715 + 0.884609i
\(231\) 0 0
\(232\) 4.54611 + 1.97697i 0.298467 + 0.129794i
\(233\) 3.23973 0.212241 0.106121 0.994353i \(-0.466157\pi\)
0.106121 + 0.994353i \(0.466157\pi\)
\(234\) 0 0
\(235\) −2.44993 2.44993i −0.159816 0.159816i
\(236\) 6.53711 + 11.6340i 0.425530 + 0.757310i
\(237\) 0 0
\(238\) −4.60342 6.07231i −0.298395 0.393610i
\(239\) 24.2484 1.56850 0.784249 0.620446i \(-0.213048\pi\)
0.784249 + 0.620446i \(0.213048\pi\)
\(240\) 0 0
\(241\) 16.5596 1.06670 0.533348 0.845896i \(-0.320934\pi\)
0.533348 + 0.845896i \(0.320934\pi\)
\(242\) −2.83745 3.74285i −0.182398 0.240599i
\(243\) 0 0
\(244\) 8.05795 4.52773i 0.515857 0.289858i
\(245\) −3.98329 3.98329i −0.254483 0.254483i
\(246\) 0 0
\(247\) −35.7438 −2.27432
\(248\) 7.57487 2.98340i 0.481005 0.189446i
\(249\) 0 0
\(250\) −1.83943 + 13.3687i −0.116336 + 0.845510i
\(251\) −11.3957 + 11.3957i −0.719287 + 0.719287i −0.968459 0.249172i \(-0.919842\pi\)
0.249172 + 0.968459i \(0.419842\pi\)
\(252\) 0 0
\(253\) −17.3687 17.3687i −1.09196 1.09196i
\(254\) −17.7208 23.3753i −1.11190 1.46670i
\(255\) 0 0
\(256\) 7.34482 + 14.2146i 0.459051 + 0.888410i
\(257\) 3.54316i 0.221016i −0.993875 0.110508i \(-0.964752\pi\)
0.993875 0.110508i \(-0.0352478\pi\)
\(258\) 0 0
\(259\) 0.581076 0.581076i 0.0361063 0.0361063i
\(260\) 12.3197 + 3.45561i 0.764035 + 0.214308i
\(261\) 0 0
\(262\) 18.6963 + 2.57246i 1.15506 + 0.158927i
\(263\) 21.0534i 1.29821i 0.760701 + 0.649103i \(0.224855\pi\)
−0.760701 + 0.649103i \(0.775145\pi\)
\(264\) 0 0
\(265\) 6.21456i 0.381757i
\(266\) 1.55465 11.2990i 0.0953219 0.692786i
\(267\) 0 0
\(268\) 7.54215 + 13.4227i 0.460710 + 0.819920i
\(269\) −20.4077 + 20.4077i −1.24428 + 1.24428i −0.286072 + 0.958208i \(0.592350\pi\)
−0.958208 + 0.286072i \(0.907650\pi\)
\(270\) 0 0
\(271\) 5.06279i 0.307543i 0.988106 + 0.153771i \(0.0491419\pi\)
−0.988106 + 0.153771i \(0.950858\pi\)
\(272\) 8.38862 13.7768i 0.508635 0.835339i
\(273\) 0 0
\(274\) −14.4491 + 10.9539i −0.872902 + 0.661747i
\(275\) −7.51052 7.51052i −0.452901 0.452901i
\(276\) 0 0
\(277\) −5.86642 + 5.86642i −0.352479 + 0.352479i −0.861031 0.508552i \(-0.830181\pi\)
0.508552 + 0.861031i \(0.330181\pi\)
\(278\) −2.86002 0.393517i −0.171533 0.0236016i
\(279\) 0 0
\(280\) −1.62819 + 3.74408i −0.0973030 + 0.223752i
\(281\) 4.77316 0.284743 0.142371 0.989813i \(-0.454527\pi\)
0.142371 + 0.989813i \(0.454527\pi\)
\(282\) 0 0
\(283\) −10.0779 10.0779i −0.599066 0.599066i 0.340998 0.940064i \(-0.389235\pi\)
−0.940064 + 0.340998i \(0.889235\pi\)
\(284\) 7.25438 + 2.03481i 0.430468 + 0.120744i
\(285\) 0 0
\(286\) −18.4943 + 14.0205i −1.09359 + 0.829052i
\(287\) −10.4381 −0.616144
\(288\) 0 0
\(289\) 0.739481 0.0434989
\(290\) −2.13383 + 1.61765i −0.125303 + 0.0949919i
\(291\) 0 0
\(292\) −20.2884 5.69079i −1.18729 0.333028i
\(293\) 11.7829 + 11.7829i 0.688364 + 0.688364i 0.961870 0.273506i \(-0.0881834\pi\)
−0.273506 + 0.961870i \(0.588183\pi\)
\(294\) 0 0
\(295\) −7.20811 −0.419673
\(296\) 1.59517 + 0.693694i 0.0927177 + 0.0403202i
\(297\) 0 0
\(298\) 12.7216 + 1.75039i 0.736943 + 0.101398i
\(299\) 37.1189 37.1189i 2.14664 2.14664i
\(300\) 0 0
\(301\) −7.34482 7.34482i −0.423348 0.423348i
\(302\) −0.232095 + 0.175951i −0.0133555 + 0.0101248i
\(303\) 0 0
\(304\) 23.4594 5.70272i 1.34549 0.327074i
\(305\) 4.99248i 0.285869i
\(306\) 0 0
\(307\) −4.31322 + 4.31322i −0.246169 + 0.246169i −0.819396 0.573228i \(-0.805691\pi\)
0.573228 + 0.819396i \(0.305691\pi\)
\(308\) −3.62764 6.45607i −0.206704 0.367869i
\(309\) 0 0
\(310\) −0.599404 + 4.35638i −0.0340438 + 0.247426i
\(311\) 27.4434i 1.55617i −0.628156 0.778087i \(-0.716190\pi\)
0.628156 0.778087i \(-0.283810\pi\)
\(312\) 0 0
\(313\) 18.8568i 1.06585i 0.846162 + 0.532926i \(0.178908\pi\)
−0.846162 + 0.532926i \(0.821092\pi\)
\(314\) 2.51204 + 0.345637i 0.141762 + 0.0195054i
\(315\) 0 0
\(316\) −21.5667 6.04933i −1.21322 0.340302i
\(317\) −0.154552 + 0.154552i −0.00868053 + 0.00868053i −0.711434 0.702753i \(-0.751954\pi\)
0.702753 + 0.711434i \(0.251954\pi\)
\(318\) 0 0
\(319\) 4.85685i 0.271931i
\(320\) −8.63700 0.302453i −0.482823 0.0169076i
\(321\) 0 0
\(322\) 10.1192 + 13.3481i 0.563922 + 0.743863i
\(323\) −17.2098 17.2098i −0.957580 0.957580i
\(324\) 0 0
\(325\) 16.0509 16.0509i 0.890342 0.890342i
\(326\) −0.0461227 + 0.335213i −0.00255450 + 0.0185657i
\(327\) 0 0
\(328\) −8.09687 20.5580i −0.447075 1.13513i
\(329\) −4.28551 −0.236268
\(330\) 0 0
\(331\) −16.3132 16.3132i −0.896656 0.896656i 0.0984829 0.995139i \(-0.468601\pi\)
−0.995139 + 0.0984829i \(0.968601\pi\)
\(332\) 24.0000 13.4855i 1.31717 0.740114i
\(333\) 0 0
\(334\) −8.92833 11.7773i −0.488536 0.644423i
\(335\) −8.31631 −0.454369
\(336\) 0 0
\(337\) 1.89341 0.103141 0.0515704 0.998669i \(-0.483577\pi\)
0.0515704 + 0.998669i \(0.483577\pi\)
\(338\) −18.8569 24.8739i −1.02568 1.35296i
\(339\) 0 0
\(340\) 4.26785 + 7.59544i 0.231457 + 0.411921i
\(341\) −5.63998 5.63998i −0.305422 0.305422i
\(342\) 0 0
\(343\) −16.3211 −0.881259
\(344\) 8.76832 20.1631i 0.472756 1.08712i
\(345\) 0 0
\(346\) −0.265551 + 1.92999i −0.0142761 + 0.103757i
\(347\) −19.7630 + 19.7630i −1.06093 + 1.06093i −0.0629131 + 0.998019i \(0.520039\pi\)
−0.998019 + 0.0629131i \(0.979961\pi\)
\(348\) 0 0
\(349\) 18.1008 + 18.1008i 0.968915 + 0.968915i 0.999531 0.0306158i \(-0.00974685\pi\)
−0.0306158 + 0.999531i \(0.509747\pi\)
\(350\) 4.37572 + 5.77197i 0.233892 + 0.308525i
\(351\) 0 0
\(352\) 9.90133 12.1527i 0.527743 0.647738i
\(353\) 19.3695i 1.03093i 0.856910 + 0.515466i \(0.172381\pi\)
−0.856910 + 0.515466i \(0.827619\pi\)
\(354\) 0 0
\(355\) −2.87766 + 2.87766i −0.152730 + 0.152730i
\(356\) −0.886536 + 3.16061i −0.0469863 + 0.167512i
\(357\) 0 0
\(358\) −13.0681 1.79807i −0.690670 0.0950308i
\(359\) 7.09236i 0.374321i 0.982329 + 0.187160i \(0.0599284\pi\)
−0.982329 + 0.187160i \(0.940072\pi\)
\(360\) 0 0
\(361\) 17.4291i 0.917322i
\(362\) −2.77729 + 20.1850i −0.145971 + 1.06090i
\(363\) 0 0
\(364\) 13.7974 7.75270i 0.723179 0.406352i
\(365\) 8.04799 8.04799i 0.421251 0.421251i
\(366\) 0 0
\(367\) 1.65735i 0.0865130i 0.999064 + 0.0432565i \(0.0137733\pi\)
−0.999064 + 0.0432565i \(0.986227\pi\)
\(368\) −18.4398 + 30.2840i −0.961242 + 1.57867i
\(369\) 0 0
\(370\) −0.748734 + 0.567615i −0.0389248 + 0.0295089i
\(371\) 5.43537 + 5.43537i 0.282190 + 0.282190i
\(372\) 0 0
\(373\) −3.48241 + 3.48241i −0.180312 + 0.180312i −0.791492 0.611180i \(-0.790695\pi\)
0.611180 + 0.791492i \(0.290695\pi\)
\(374\) −15.6552 2.15403i −0.809510 0.111382i
\(375\) 0 0
\(376\) −3.32427 8.44036i −0.171436 0.435278i
\(377\) 10.3797 0.534579
\(378\) 0 0
\(379\) 19.1548 + 19.1548i 0.983917 + 0.983917i 0.999873 0.0159558i \(-0.00507910\pi\)
−0.0159558 + 0.999873i \(0.505079\pi\)
\(380\) −3.52186 + 12.5559i −0.180668 + 0.644103i
\(381\) 0 0
\(382\) 16.0365 12.1573i 0.820498 0.622019i
\(383\) 15.2907 0.781319 0.390660 0.920535i \(-0.372247\pi\)
0.390660 + 0.920535i \(0.372247\pi\)
\(384\) 0 0
\(385\) 4.00000 0.203859
\(386\) −7.36557 + 5.58383i −0.374898 + 0.284210i
\(387\) 0 0
\(388\) −3.08029 + 10.9816i −0.156378 + 0.557507i
\(389\) −22.7144 22.7144i −1.15166 1.15166i −0.986219 0.165445i \(-0.947094\pi\)
−0.165445 0.986219i \(1.44709\pi\)
\(390\) 0 0
\(391\) 35.7438 1.80764
\(392\) −5.40486 13.7230i −0.272987 0.693116i
\(393\) 0 0
\(394\) −17.9848 2.47457i −0.906062 0.124667i
\(395\) 8.55505 8.55505i 0.430451 0.430451i
\(396\) 0 0
\(397\) 7.45854 + 7.45854i 0.374334 + 0.374334i 0.869053 0.494719i \(-0.164729\pi\)
−0.494719 + 0.869053i \(0.664729\pi\)
\(398\) 11.3672 8.61746i 0.569786 0.431954i
\(399\) 0 0
\(400\) −7.97370 + 13.0953i −0.398685 + 0.654767i
\(401\) 11.5911i 0.578834i −0.957203 0.289417i \(-0.906539\pi\)
0.957203 0.289417i \(-0.0934615\pi\)
\(402\) 0 0
\(403\) 12.0533 12.0533i 0.600417 0.600417i
\(404\) −16.4865 + 9.26369i −0.820233 + 0.460886i
\(405\) 0 0
\(406\) −0.451456 + 3.28112i −0.0224054 + 0.162839i
\(407\) 1.70421i 0.0844745i
\(408\) 0 0
\(409\) 12.4659i 0.616398i 0.951322 + 0.308199i \(0.0997262\pi\)
−0.951322 + 0.308199i \(0.900274\pi\)
\(410\) 11.8231 + 1.62677i 0.583902 + 0.0803404i
\(411\) 0 0
\(412\) 5.87587 20.9482i 0.289483 1.03205i
\(413\) −6.30435 + 6.30435i −0.310217 + 0.310217i
\(414\) 0 0
\(415\) 14.8697i 0.729927i
\(416\) 25.9716 + 21.1603i 1.27336 + 1.03747i
\(417\) 0 0
\(418\) −14.2894 18.8489i −0.698915 0.921931i
\(419\) 14.4096 + 14.4096i 0.703953 + 0.703953i 0.965257 0.261304i \(-0.0841525\pi\)
−0.261304 + 0.965257i \(0.584152\pi\)
\(420\) 0 0
\(421\) −5.83630 + 5.83630i −0.284444 + 0.284444i −0.834878 0.550434i \(-0.814462\pi\)
0.550434 + 0.834878i \(0.314462\pi\)
\(422\) −4.90141 + 35.6228i −0.238597 + 1.73409i
\(423\) 0 0
\(424\) −6.48880 + 14.9212i −0.315124 + 0.724640i
\(425\) 15.4562 0.749738
\(426\) 0 0
\(427\) 4.36652 + 4.36652i 0.211311 + 0.211311i
\(428\) 1.82551 + 3.24884i 0.0882395 + 0.157039i
\(429\) 0 0
\(430\) 7.17467 + 9.46403i 0.345993 + 0.456396i
\(431\) 18.4510 0.888755 0.444377 0.895840i \(-0.353425\pi\)
0.444377 + 0.895840i \(0.353425\pi\)
\(432\) 0 0
\(433\) 6.58166 0.316295 0.158147 0.987416i \(-0.449448\pi\)
0.158147 + 0.987416i \(0.449448\pi\)
\(434\) 3.28592 + 4.33442i 0.157729 + 0.208059i
\(435\) 0 0
\(436\) −8.66776 + 4.87038i −0.415110 + 0.233249i
\(437\) 37.8306 + 37.8306i 1.80968 + 1.80968i
\(438\) 0 0
\(439\) 3.68747 0.175993 0.0879966 0.996121i \(-0.471954\pi\)
0.0879966 + 0.996121i \(0.471954\pi\)
\(440\) 3.10280 + 7.87804i 0.147920 + 0.375571i
\(441\) 0 0
\(442\) 4.60342 33.4569i 0.218962 1.59138i
\(443\) −3.31861 + 3.31861i −0.157672 + 0.157672i −0.781534 0.623862i \(-0.785563\pi\)
0.623862 + 0.781534i \(0.285563\pi\)
\(444\) 0 0
\(445\) −1.25375 1.25375i −0.0594335 0.0594335i
\(446\) −3.42479 4.51760i −0.162169 0.213915i
\(447\) 0 0
\(448\) −7.81861 + 7.28955i −0.369395 + 0.344399i
\(449\) 20.3555i 0.960635i −0.877095 0.480318i \(-0.840521\pi\)
0.877095 0.480318i \(-0.159479\pi\)
\(450\) 0 0
\(451\) −15.3068 + 15.3068i −0.720768 + 0.720768i
\(452\) −31.4155 8.81187i −1.47766 0.414475i
\(453\) 0 0
\(454\) 27.3255 + 3.75978i 1.28245 + 0.176455i
\(455\) 8.54847i 0.400758i
\(456\) 0 0
\(457\) 10.0239i 0.468897i −0.972129 0.234448i \(-0.924672\pi\)
0.972129 0.234448i \(-0.0753284\pi\)
\(458\) −0.948267 + 6.89186i −0.0443096 + 0.322036i
\(459\) 0 0
\(460\) −9.38158 16.6963i −0.437418 0.778468i
\(461\) 16.4043 16.4043i 0.764026 0.764026i −0.213021 0.977048i \(-0.568330\pi\)
0.977048 + 0.213021i \(0.0683304\pi\)
\(462\) 0 0
\(463\) 0.997833i 0.0463732i −0.999731 0.0231866i \(-0.992619\pi\)
0.999731 0.0231866i \(-0.00738119\pi\)
\(464\) −6.81239 + 1.65601i −0.316257 + 0.0768786i
\(465\) 0 0
\(466\) −3.65109 + 2.76789i −0.169133 + 0.128220i
\(467\) 9.73306 + 9.73306i 0.450392 + 0.450392i 0.895485 0.445092i \(-0.146829\pi\)
−0.445092 + 0.895485i \(0.646829\pi\)
\(468\) 0 0
\(469\) −7.27361 + 7.27361i −0.335864 + 0.335864i
\(470\) 4.85413 + 0.667890i 0.223904 + 0.0308075i
\(471\) 0 0
\(472\) −17.3068 7.52620i −0.796609 0.346422i
\(473\) −21.5413 −0.990469
\(474\) 0 0
\(475\) 16.3586 + 16.3586i 0.750584 + 0.750584i
\(476\) 10.3759 + 2.91038i 0.475577 + 0.133397i
\(477\) 0 0
\(478\) −27.3273 + 20.7168i −1.24992 + 0.947565i
\(479\) −37.0669 −1.69363 −0.846816 0.531886i \(-0.821483\pi\)
−0.846816 + 0.531886i \(0.821483\pi\)
\(480\) 0 0
\(481\) 3.64210 0.166065
\(482\) −18.6622 + 14.1478i −0.850041 + 0.644415i
\(483\) 0 0
\(484\) 6.39546 + 1.79389i 0.290703 + 0.0815406i
\(485\) −4.35618 4.35618i −0.197804 0.197804i
\(486\) 0 0
\(487\) 33.1866 1.50383 0.751914 0.659261i \(-0.229131\pi\)
0.751914 + 0.659261i \(0.229131\pi\)
\(488\) −5.21280 + 11.9870i −0.235972 + 0.542627i
\(489\) 0 0
\(490\) 7.89221 + 1.08591i 0.356534 + 0.0490563i
\(491\) −10.2580 + 10.2580i −0.462936 + 0.462936i −0.899617 0.436681i \(-0.856154\pi\)
0.436681 + 0.899617i \(0.356154\pi\)
\(492\) 0 0
\(493\) 4.99757 + 4.99757i 0.225079 + 0.225079i
\(494\) 40.2824 30.5380i 1.81239 1.37397i
\(495\) 0 0
\(496\) −5.98780 + 9.83387i −0.268860 + 0.441554i
\(497\) 5.03372i 0.225793i
\(498\) 0 0
\(499\) 4.19733 4.19733i 0.187898 0.187898i −0.606889 0.794787i \(-0.707583\pi\)
0.794787 + 0.606889i \(0.207583\pi\)
\(500\) −9.34866 16.6377i −0.418085 0.744060i
\(501\) 0 0
\(502\) 3.10664 22.5786i 0.138656 1.00773i
\(503\) 21.0655i 0.939266i −0.882862 0.469633i \(-0.844386\pi\)
0.882862 0.469633i \(-0.155614\pi\)
\(504\) 0 0
\(505\) 10.2146i 0.454542i
\(506\) 34.4131 + 4.73498i 1.52985 + 0.210496i
\(507\) 0 0
\(508\) 39.9418 + 11.2035i 1.77213 + 0.497073i
\(509\) 22.6424 22.6424i 1.00361 1.00361i 0.00361481 0.999993i \(-0.498849\pi\)
0.999993 0.00361481i \(-0.00115063\pi\)
\(510\) 0 0
\(511\) 14.0779i 0.622768i
\(512\) −20.4218 9.74434i −0.902522 0.430643i
\(513\) 0 0
\(514\) 3.02713 + 3.99305i 0.133521 + 0.176126i
\(515\) 8.30973 + 8.30973i 0.366171 + 0.366171i
\(516\) 0 0
\(517\) −6.28439 + 6.28439i −0.276387 + 0.276387i
\(518\) −0.158411 + 1.15130i −0.00696016 + 0.0505854i
\(519\) 0 0
\(520\) −16.8363 + 6.63105i −0.738321 + 0.290791i
\(521\) −38.3351 −1.67949 −0.839746 0.542980i \(-0.817296\pi\)
−0.839746 + 0.542980i \(0.817296\pi\)
\(522\) 0 0
\(523\) −5.39811 5.39811i −0.236043 0.236043i 0.579166 0.815209i \(-0.303378\pi\)
−0.815209 + 0.579166i \(0.803378\pi\)
\(524\) −23.2680 + 13.0742i −1.01647 + 0.571150i
\(525\) 0 0
\(526\) −17.9871 23.7266i −0.784275 1.03453i
\(527\) 11.6068 0.505599
\(528\) 0 0
\(529\) −55.5719 −2.41617
\(530\) −5.30946 7.00365i −0.230628 0.304219i
\(531\) 0 0
\(532\) 7.90133 + 14.0619i 0.342566 + 0.609661i
\(533\) −32.7124 32.7124i −1.41693 1.41693i
\(534\) 0 0
\(535\) −2.01289 −0.0870249
\(536\) −19.9676 8.68331i −0.862468 0.375062i
\(537\) 0 0
\(538\) 5.56347 40.4345i 0.239858 1.74325i
\(539\) −10.2176 + 10.2176i −0.440105 + 0.440105i
\(540\) 0 0
\(541\) 5.51516 + 5.51516i 0.237115 + 0.237115i 0.815654 0.578539i \(-0.196377\pi\)
−0.578539 + 0.815654i \(0.696377\pi\)
\(542\) −4.32544 5.70564i −0.185794 0.245078i
\(543\) 0 0
\(544\) 2.31654 + 22.6930i 0.0993210 + 0.972952i
\(545\) 5.37030i 0.230038i
\(546\) 0 0
\(547\) −23.2535 + 23.2535i −0.994247 + 0.994247i −0.999984 0.00573636i \(-0.998174\pi\)
0.00573636 + 0.999984i \(0.498174\pi\)
\(548\) 6.92525 24.6894i 0.295832 1.05468i
\(549\) 0 0
\(550\) 14.8808 + 2.04749i 0.634521 + 0.0873052i
\(551\) 10.5787i 0.450666i
\(552\) 0 0
\(553\) 14.9648i 0.636369i
\(554\) 1.59928 11.6233i 0.0679469 0.493828i
\(555\) 0 0
\(556\) 3.55938 2.00000i 0.150951 0.0848189i
\(557\) 26.9066 26.9066i 1.14007 1.14007i 0.151635 0.988437i \(-0.451546\pi\)
0.988437 0.151635i \(-0.0484537\pi\)
\(558\) 0 0
\(559\) 46.0362i 1.94712i
\(560\) −1.36386 5.61054i −0.0576336 0.237089i
\(561\) 0 0
\(562\) −5.37922 + 4.07799i −0.226909 + 0.172019i
\(563\) 21.4144 + 21.4144i 0.902508 + 0.902508i 0.995653 0.0931446i \(-0.0296919\pi\)
−0.0931446 + 0.995653i \(0.529692\pi\)
\(564\) 0 0
\(565\) 12.4619 12.4619i 0.524275 0.524275i
\(566\) 19.9676 + 2.74738i 0.839300 + 0.115481i
\(567\) 0 0
\(568\) −9.91396 + 3.90465i −0.415980 + 0.163836i
\(569\) −1.54807 −0.0648986 −0.0324493 0.999473i \(-0.510331\pi\)
−0.0324493 + 0.999473i \(0.510331\pi\)
\(570\) 0 0
\(571\) −12.3384 12.3384i −0.516345 0.516345i 0.400119 0.916463i \(-0.368969\pi\)
−0.916463 + 0.400119i \(0.868969\pi\)
\(572\) 8.86408 31.6016i 0.370626 1.32133i
\(573\) 0 0
\(574\) 11.7635 8.91792i 0.491000 0.372227i
\(575\) −33.9759 −1.41689
\(576\) 0 0
\(577\) −24.9648 −1.03930 −0.519650 0.854380i \(-0.673937\pi\)
−0.519650 + 0.854380i \(0.673937\pi\)
\(578\) −0.833376 + 0.631782i −0.0346639 + 0.0262787i
\(579\) 0 0
\(580\) 1.02271 3.64611i 0.0424659 0.151396i
\(581\) 13.0054 + 13.0054i 0.539553 + 0.539553i
\(582\) 0 0
\(583\) 15.9411 0.660215
\(584\) 27.7265 10.9202i 1.14733 0.451881i
\(585\) 0 0
\(586\) −23.3458 3.21221i −0.964408 0.132695i
\(587\) −3.99426 + 3.99426i −0.164861 + 0.164861i −0.784716 0.619855i \(-0.787191\pi\)
0.619855 + 0.784716i \(0.287191\pi\)
\(588\) 0 0
\(589\) 12.2844 + 12.2844i 0.506169 + 0.506169i
\(590\) 8.12336 6.15831i 0.334433 0.253534i
\(591\) 0 0
\(592\) −2.39038 + 0.581076i −0.0982442 + 0.0238821i
\(593\) 21.0442i 0.864183i −0.901830 0.432092i \(-0.857776\pi\)
0.901830 0.432092i \(-0.142224\pi\)
\(594\) 0 0
\(595\) −4.11589 + 4.11589i −0.168735 + 0.168735i
\(596\) −15.8324 + 8.89616i −0.648520 + 0.364401i
\(597\) 0 0
\(598\) −10.1192 + 73.5449i −0.413805 + 3.00748i
\(599\) 12.7718i 0.521840i 0.965360 + 0.260920i \(0.0840259\pi\)
−0.965360 + 0.260920i \(0.915974\pi\)
\(600\) 0 0
\(601\) 44.2967i 1.80690i −0.428691 0.903451i \(-0.641025\pi\)
0.428691 0.903451i \(-0.358975\pi\)
\(602\) 14.5525 + 2.00232i 0.593117 + 0.0816083i
\(603\) 0 0
\(604\) 0.111240 0.396584i 0.00452628 0.0161368i
\(605\) −2.53695 + 2.53695i −0.103142 + 0.103142i
\(606\) 0 0
\(607\) 26.8784i 1.09096i 0.838124 + 0.545479i \(0.183652\pi\)
−0.838124 + 0.545479i \(0.816348\pi\)
\(608\) −21.5660 + 26.4696i −0.874617 + 1.07348i
\(609\) 0 0
\(610\) −4.26537 5.62640i −0.172700 0.227806i
\(611\) −13.4305 13.4305i −0.543339 0.543339i
\(612\) 0 0
\(613\) −27.6602 + 27.6602i −1.11719 + 1.11719i −0.125033 + 0.992153i \(0.539904\pi\)
−0.992153 + 0.125033i \(0.960096\pi\)
\(614\) 1.17585 8.54593i 0.0474536 0.344886i
\(615\) 0 0
\(616\) 9.60406 + 4.17652i 0.386958 + 0.168277i
\(617\) 19.6148 0.789661 0.394831 0.918754i \(-0.370803\pi\)
0.394831 + 0.918754i \(0.370803\pi\)
\(618\) 0 0
\(619\) −11.7854 11.7854i −0.473697 0.473697i 0.429412 0.903109i \(-0.358721\pi\)
−0.903109 + 0.429412i \(0.858721\pi\)
\(620\) −3.04640 5.42163i −0.122346 0.217738i
\(621\) 0 0
\(622\) 23.4465 + 30.9281i 0.940120 + 1.24010i
\(623\) −2.19311 −0.0878651
\(624\) 0 0
\(625\) −8.85665 −0.354266
\(626\) −16.1105 21.2512i −0.643905 0.849368i
\(627\) 0 0
\(628\) −3.12630 + 1.75666i −0.124753 + 0.0700982i
\(629\) 1.75359 + 1.75359i 0.0699200 + 0.0699200i
\(630\) 0 0
\(631\) 18.8195 0.749193 0.374596 0.927188i \(-0.377781\pi\)
0.374596 + 0.927188i \(0.377781\pi\)
\(632\) 29.4734 11.6082i 1.17239 0.461750i
\(633\) 0 0
\(634\) 0.0421335 0.306220i 0.00167333 0.0121615i
\(635\) −15.8441 + 15.8441i −0.628753 + 0.628753i
\(636\) 0 0
\(637\) −21.8363 21.8363i −0.865186 0.865186i
\(638\) 4.14949 + 5.47354i 0.164280 + 0.216700i
\(639\) 0 0
\(640\) 9.99208 7.03823i 0.394972 0.278211i
\(641\) 17.9718i 0.709845i 0.934896 + 0.354923i \(0.115493\pi\)
−0.934896 + 0.354923i \(0.884507\pi\)
\(642\) 0 0
\(643\) −9.92589 + 9.92589i −0.391439 + 0.391439i −0.875200 0.483761i \(-0.839270\pi\)
0.483761 + 0.875200i \(0.339270\pi\)
\(644\) −22.8082 6.39758i −0.898769 0.252100i
\(645\) 0 0
\(646\) 34.0984 + 4.69168i 1.34158 + 0.184591i
\(647\) 13.6801i 0.537820i −0.963165 0.268910i \(-0.913337\pi\)
0.963165 0.268910i \(-0.0866635\pi\)
\(648\) 0 0
\(649\) 18.4897i 0.725786i
\(650\) −4.37572 + 31.8021i −0.171630 + 1.24738i
\(651\) 0 0
\(652\) −0.234413 0.417182i −0.00918033 0.0163381i
\(653\) −31.1940 + 31.1940i −1.22071 + 1.22071i −0.253336 + 0.967378i \(0.581528\pi\)
−0.967378 + 0.253336i \(0.918472\pi\)
\(654\) 0 0
\(655\) 14.4162i 0.563288i
\(656\) 26.6889 + 16.2508i 1.04203 + 0.634486i
\(657\) 0 0
\(658\) 4.82966 3.66136i 0.188280 0.142735i
\(659\) 27.2397 + 27.2397i 1.06111 + 1.06111i 0.998007 + 0.0631026i \(0.0200995\pi\)
0.0631026 + 0.998007i \(0.479900\pi\)
\(660\) 0 0
\(661\) −12.0770 + 12.0770i −0.469740 + 0.469740i −0.901830 0.432091i \(-0.857776\pi\)
0.432091 + 0.901830i \(0.357776\pi\)
\(662\) 32.3219 + 4.44725i 1.25623 + 0.172847i
\(663\) 0 0
\(664\) −15.5259 + 35.7025i −0.602523 + 1.38552i
\(665\) −8.71237 −0.337851
\(666\) 0 0
\(667\) −10.9856 10.9856i −0.425365 0.425365i
\(668\) 20.1240 + 5.64467i 0.778621 + 0.218399i
\(669\) 0 0
\(670\) 9.37227 7.10511i 0.362082 0.274494i
\(671\) 12.8064 0.494384
\(672\) 0 0
\(673\) 11.0108 0.424434 0.212217 0.977223i \(-0.431932\pi\)
0.212217 + 0.977223i \(0.431932\pi\)
\(674\) −2.13383 + 1.61765i −0.0821920 + 0.0623097i
\(675\) 0 0
\(676\) 42.5025 + 11.9217i 1.63471 + 0.458528i
\(677\) −5.26708 5.26708i −0.202430 0.202430i 0.598610 0.801040i \(-0.295720\pi\)
−0.801040 + 0.598610i \(0.795720\pi\)
\(678\) 0 0
\(679\) −7.62000 −0.292429
\(680\) −11.2990 4.91360i −0.433297 0.188428i
\(681\) 0 0
\(682\) 11.1747 + 1.53755i 0.427900 + 0.0588758i
\(683\) −16.0080 + 16.0080i −0.612528 + 0.612528i −0.943604 0.331076i \(-0.892588\pi\)
0.331076 + 0.943604i \(0.392588\pi\)
\(684\) 0 0
\(685\) 9.79379 + 9.79379i 0.374201 + 0.374201i
\(686\) 18.3935 13.9441i 0.702268 0.532389i
\(687\) 0 0
\(688\) 7.34482 + 30.2146i 0.280019 + 1.15192i
\(689\) 34.0681i 1.29789i
\(690\) 0 0
\(691\) 7.63348 7.63348i 0.290391 0.290391i −0.546843 0.837235i \(-0.684171\pi\)
0.837235 + 0.546843i \(0.184171\pi\)
\(692\) −1.34963 2.40192i −0.0513053 0.0913074i
\(693\) 0 0
\(694\) 5.38770 39.1570i 0.204514 1.48638i
\(695\) 2.20529i 0.0836514i
\(696\) 0 0
\(697\) 31.5005i 1.19317i
\(698\) −35.8638 4.93458i −1.35746 0.186777i
\(699\) 0 0
\(700\) −9.86265 2.76642i −0.372773 0.104561i
\(701\) 18.3494 18.3494i 0.693049 0.693049i −0.269853 0.962902i \(-0.586975\pi\)
0.962902 + 0.269853i \(0.0869750\pi\)
\(702\) 0 0
\(703\) 3.71192i 0.139998i
\(704\) −0.775831 + 22.1550i −0.0292402 + 0.834999i
\(705\) 0 0
\(706\) −16.5485 21.8289i −0.622810 0.821541i
\(707\) −8.93385 8.93385i −0.335992 0.335992i
\(708\) 0 0
\(709\) 19.8774 19.8774i 0.746511 0.746511i −0.227311 0.973822i \(-0.572993\pi\)
0.973822 + 0.227311i \(0.0729934\pi\)
\(710\) 0.784497 5.70161i 0.0294416 0.213977i
\(711\) 0 0
\(712\) −1.70119 4.31935i −0.0637550 0.161875i
\(713\) −25.5140 −0.955505
\(714\) 0 0
\(715\) 12.5357 + 12.5357i 0.468809 + 0.468809i
\(716\) 16.2636 9.13845i 0.607799 0.341520i
\(717\) 0 0
\(718\) −6.05942 7.99291i −0.226136 0.298293i
\(719\) 16.1176 0.601083 0.300542 0.953769i \(-0.402833\pi\)
0.300542 + 0.953769i \(0.402833\pi\)
\(720\) 0 0
\(721\) 14.5357 0.541338
\(722\) 14.8907 + 19.6422i 0.554175 + 0.731006i
\(723\) 0 0
\(724\) −14.1153 25.1207i −0.524589 0.933605i
\(725\) −4.75038 4.75038i −0.176425 0.176425i
\(726\) 0 0
\(727\) 16.4536 0.610229 0.305115 0.952316i \(-0.401305\pi\)
0.305115 + 0.952316i \(0.401305\pi\)
\(728\) −8.92571 + 20.5250i −0.330809 + 0.760707i
\(729\) 0 0
\(730\) −2.19401 + 15.9457i −0.0812040 + 0.590179i
\(731\) 22.1654 22.1654i 0.819816 0.819816i
\(732\) 0 0
\(733\) 24.5995 + 24.5995i 0.908602 + 0.908602i 0.996159 0.0875578i \(-0.0279063\pi\)
−0.0875578 + 0.996159i \(0.527906\pi\)
\(734\) −1.41597 1.86779i −0.0522644 0.0689414i
\(735\) 0 0
\(736\) −5.09222 49.8836i −0.187702 1.83873i
\(737\) 21.3324i 0.785790i
\(738\) 0 0
\(739\) 3.06707 3.06707i 0.112824 0.112824i −0.648441 0.761265i \(-0.724579\pi\)
0.761265 + 0.648441i \(0.224579\pi\)
\(740\) 0.358858 1.27937i 0.0131919 0.0470308i
\(741\) 0 0
\(742\) −10.7693 1.48177i −0.395353 0.0543975i
\(743\) 1.16681i 0.0428061i −0.999771 0.0214031i \(-0.993187\pi\)
0.999771 0.0214031i \(-0.00681333\pi\)
\(744\) 0 0
\(745\) 9.80931i 0.359385i
\(746\) 0.949361 6.89981i 0.0347586 0.252620i
\(747\) 0 0
\(748\) 19.4833 10.9476i 0.712380 0.400284i
\(749\) −1.76051 + 1.76051i −0.0643278 + 0.0643278i
\(750\) 0 0
\(751\) 2.12809i 0.0776552i −0.999246 0.0388276i \(-0.987638\pi\)
0.999246 0.0388276i \(-0.0123623\pi\)
\(752\) 10.9575 + 6.67195i 0.399577 + 0.243301i
\(753\) 0 0
\(754\) −11.6976 + 8.86795i −0.426002 + 0.322952i
\(755\) 0.157317 + 0.157317i 0.00572534 + 0.00572534i
\(756\) 0 0
\(757\) 19.1573 19.1573i 0.696282 0.696282i −0.267324 0.963607i \(-0.586140\pi\)
0.963607 + 0.267324i \(0.0861395\pi\)
\(758\) −37.9521 5.22191i −1.37848 0.189668i
\(759\) 0 0
\(760\) −6.75818 17.1591i −0.245145 0.622426i
\(761\) 10.2848 0.372824 0.186412 0.982472i \(-0.440314\pi\)
0.186412 + 0.982472i \(0.440314\pi\)
\(762\) 0 0
\(763\) −4.69697 4.69697i −0.170042 0.170042i
\(764\) −7.68607 + 27.4018i −0.278072 + 0.991363i
\(765\) 0 0
\(766\) −17.2322 + 13.0638i −0.622626 + 0.472013i
\(767\) −39.5147 −1.42679
\(768\) 0 0
\(769\) −15.2860 −0.551226 −0.275613 0.961269i \(-0.588881\pi\)
−0.275613 + 0.961269i \(0.588881\pi\)
\(770\) −4.50790 + 3.41743i −0.162453 + 0.123156i
\(771\) 0 0
\(772\) 3.53022 12.5857i 0.127055 0.452968i
\(773\) 23.6903 + 23.6903i 0.852081 + 0.852081i 0.990389 0.138308i \(-0.0441664\pi\)
−0.138308 + 0.990389i \(0.544166\pi\)
\(774\) 0 0
\(775\) −11.0327 −0.396305
\(776\) −5.91084 15.0077i −0.212187 0.538744i
\(777\) 0 0
\(778\) 45.0047 + 6.19230i 1.61350 + 0.222005i
\(779\) 33.3396 33.3396i 1.19451 1.19451i
\(780\) 0 0
\(781\) 7.38158 + 7.38158i 0.264134 + 0.264134i
\(782\) −40.2824 + 30.5380i −1.44049 + 1.09204i
\(783\) 0 0
\(784\) 17.8155 + 10.8478i 0.636267 + 0.387420i
\(785\) 1.93697i 0.0691333i
\(786\) 0 0
\(787\) −29.3220 + 29.3220i −1.04522 + 1.04522i −0.0462895 + 0.998928i \(0.514740\pi\)
−0.998928 + 0.0462895i \(0.985260\pi\)
\(788\) 22.3826 12.5767i 0.797347 0.448026i
\(789\) 0 0
\(790\) −2.33224 +