Properties

Label 585.2.bs.a.289.4
Level $585$
Weight $2$
Character 585.289
Analytic conductor $4.671$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 585 = 3^{2} \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 585.bs (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(4.67124851824\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
Defining polynomial: \( x^{12} - 8x^{10} + 54x^{8} - 78x^{6} + 92x^{4} - 10x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 65)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 289.4
Root \(0.286513 + 0.165418i\) of defining polynomial
Character \(\chi\) \(=\) 585.289
Dual form 585.2.bs.a.334.4

$q$-expansion

\(f(q)\) \(=\) \(q+(0.286513 - 0.165418i) q^{2} +(-0.945274 + 1.63726i) q^{4} +(2.12291 + 0.702335i) q^{5} +(2.90420 + 1.67674i) q^{7} +1.28714i q^{8} +O(q^{10})\) \(q+(0.286513 - 0.165418i) q^{2} +(-0.945274 + 1.63726i) q^{4} +(2.12291 + 0.702335i) q^{5} +(2.90420 + 1.67674i) q^{7} +1.28714i q^{8} +(0.724419 - 0.149939i) q^{10} +(-1.62291 - 2.81095i) q^{11} +(-1.21648 + 3.39414i) q^{13} +1.10945 q^{14} +(-1.67763 - 2.90574i) q^{16} +(1.68772 + 0.974404i) q^{17} +(-0.622905 + 1.07890i) q^{19} +(-3.15663 + 2.81185i) q^{20} +(-0.929966 - 0.536916i) q^{22} +(-2.33117 + 1.34590i) q^{23} +(4.01345 + 2.98198i) q^{25} +(0.212916 + 1.17369i) q^{26} +(-5.49052 + 3.16995i) q^{28} +(-1.50000 - 2.59808i) q^{29} +3.78109 q^{31} +(-3.19071 - 1.84216i) q^{32} +0.644737 q^{34} +(4.98770 + 5.59927i) q^{35} +(-1.68772 + 0.974404i) q^{37} +0.412160i q^{38} +(-0.904000 + 2.73247i) q^{40} +(1.39055 + 2.40850i) q^{41} +(7.56654 + 4.36854i) q^{43} +6.13636 q^{44} +(-0.445274 + 0.771236i) q^{46} -6.86960i q^{47} +(2.12291 + 3.67698i) q^{49} +(1.64318 + 0.190477i) q^{50} +(-4.40719 - 5.20008i) q^{52} +12.8336i q^{53} +(-1.47104 - 7.10721i) q^{55} +(-2.15819 + 3.73809i) q^{56} +(-0.859539 - 0.496255i) q^{58} +(1.26764 - 2.19562i) q^{59} +(3.74581 - 6.48793i) q^{61} +(1.08333 - 0.625462i) q^{62} +5.49162 q^{64} +(-4.96629 + 6.35106i) q^{65} +(3.47722 - 2.00758i) q^{67} +(-3.19071 + 1.84216i) q^{68} +(2.35526 + 0.779207i) q^{70} +(2.62291 - 4.54300i) q^{71} -5.46493i q^{73} +(-0.322368 + 0.558359i) q^{74} +(-1.17763 - 2.03972i) q^{76} -10.8848i q^{77} -13.7811 q^{79} +(-1.52065 - 7.34688i) q^{80} +(0.796819 + 0.460044i) q^{82} -8.61955i q^{83} +(2.89851 + 3.25391i) q^{85} +2.89055 q^{86} +(3.61808 - 2.08890i) q^{88} +(-5.15819 - 8.93425i) q^{89} +(-9.22398 + 7.81753i) q^{91} -5.08898i q^{92} +(-1.13636 - 1.96823i) q^{94} +(-2.08012 + 1.85292i) q^{95} +(-4.56055 - 2.63304i) q^{97} +(1.21648 + 0.702335i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q + 4 q^{4} + 6 q^{5}+O(q^{10}) \) Copy content Toggle raw display \( 12 q + 4 q^{4} + 6 q^{5} + 7 q^{10} + 44 q^{14} - 16 q^{16} + 12 q^{19} + q^{20} - 2 q^{25} - 24 q^{26} - 18 q^{29} - 16 q^{31} + 16 q^{34} - 10 q^{35} + 70 q^{40} - 14 q^{41} + 4 q^{44} + 10 q^{46} + 6 q^{49} + 31 q^{50} - 26 q^{55} + 16 q^{56} + 4 q^{59} + 6 q^{61} - 12 q^{64} - 23 q^{65} + 20 q^{70} + 12 q^{71} - 8 q^{74} - 10 q^{76} - 104 q^{79} - 33 q^{80} + 21 q^{85} + 4 q^{86} - 20 q^{89} - 44 q^{91} + 56 q^{94} - 20 q^{95}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/585\mathbb{Z}\right)^\times\).

\(n\) \(326\) \(352\) \(496\)
\(\chi(n)\) \(1\) \(-1\) \(e\left(\frac{1}{3}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.286513 0.165418i 0.202595 0.116968i −0.395270 0.918565i \(-0.629349\pi\)
0.597865 + 0.801597i \(0.296016\pi\)
\(3\) 0 0
\(4\) −0.945274 + 1.63726i −0.472637 + 0.818631i
\(5\) 2.12291 + 0.702335i 0.949392 + 0.314094i
\(6\) 0 0
\(7\) 2.90420 + 1.67674i 1.09768 + 0.633748i 0.935611 0.353031i \(-0.114849\pi\)
0.162072 + 0.986779i \(0.448182\pi\)
\(8\) 1.28714i 0.455071i
\(9\) 0 0
\(10\) 0.724419 0.149939i 0.229081 0.0474150i
\(11\) −1.62291 2.81095i −0.489324 0.847535i 0.510600 0.859818i \(-0.329423\pi\)
−0.999925 + 0.0122837i \(0.996090\pi\)
\(12\) 0 0
\(13\) −1.21648 + 3.39414i −0.337391 + 0.941365i
\(14\) 1.10945 0.296514
\(15\) 0 0
\(16\) −1.67763 2.90574i −0.419408 0.726436i
\(17\) 1.68772 + 0.974404i 0.409332 + 0.236328i 0.690503 0.723330i \(-0.257389\pi\)
−0.281171 + 0.959658i \(0.590723\pi\)
\(18\) 0 0
\(19\) −0.622905 + 1.07890i −0.142904 + 0.247517i −0.928589 0.371110i \(-0.878977\pi\)
0.785685 + 0.618627i \(0.212311\pi\)
\(20\) −3.15663 + 2.81185i −0.705844 + 0.628750i
\(21\) 0 0
\(22\) −0.929966 0.536916i −0.198269 0.114471i
\(23\) −2.33117 + 1.34590i −0.486083 + 0.280640i −0.722948 0.690903i \(-0.757213\pi\)
0.236865 + 0.971543i \(0.423880\pi\)
\(24\) 0 0
\(25\) 4.01345 + 2.98198i 0.802690 + 0.596396i
\(26\) 0.212916 + 1.17369i 0.0417562 + 0.230180i
\(27\) 0 0
\(28\) −5.49052 + 3.16995i −1.03761 + 0.599065i
\(29\) −1.50000 2.59808i −0.278543 0.482451i 0.692480 0.721437i \(-0.256518\pi\)
−0.971023 + 0.238987i \(0.923185\pi\)
\(30\) 0 0
\(31\) 3.78109 0.679105 0.339552 0.940587i \(-0.389724\pi\)
0.339552 + 0.940587i \(0.389724\pi\)
\(32\) −3.19071 1.84216i −0.564043 0.325650i
\(33\) 0 0
\(34\) 0.644737 0.110571
\(35\) 4.98770 + 5.59927i 0.843076 + 0.946450i
\(36\) 0 0
\(37\) −1.68772 + 0.974404i −0.277459 + 0.160191i −0.632273 0.774746i \(-0.717878\pi\)
0.354813 + 0.934937i \(0.384544\pi\)
\(38\) 0.412160i 0.0668611i
\(39\) 0 0
\(40\) −0.904000 + 2.73247i −0.142935 + 0.432041i
\(41\) 1.39055 + 2.40850i 0.217167 + 0.376144i 0.953941 0.299995i \(-0.0969851\pi\)
−0.736774 + 0.676139i \(0.763652\pi\)
\(42\) 0 0
\(43\) 7.56654 + 4.36854i 1.15389 + 0.666197i 0.949831 0.312763i \(-0.101255\pi\)
0.204055 + 0.978959i \(0.434588\pi\)
\(44\) 6.13636 0.925091
\(45\) 0 0
\(46\) −0.445274 + 0.771236i −0.0656520 + 0.113713i
\(47\) 6.86960i 1.00203i −0.865437 0.501017i \(-0.832959\pi\)
0.865437 0.501017i \(-0.167041\pi\)
\(48\) 0 0
\(49\) 2.12291 + 3.67698i 0.303272 + 0.525283i
\(50\) 1.64318 + 0.190477i 0.232381 + 0.0269375i
\(51\) 0 0
\(52\) −4.40719 5.20008i −0.611167 0.721122i
\(53\) 12.8336i 1.76282i 0.472347 + 0.881412i \(0.343407\pi\)
−0.472347 + 0.881412i \(0.656593\pi\)
\(54\) 0 0
\(55\) −1.47104 7.10721i −0.198355 0.958336i
\(56\) −2.15819 + 3.73809i −0.288400 + 0.499524i
\(57\) 0 0
\(58\) −0.859539 0.496255i −0.112863 0.0651614i
\(59\) 1.26764 2.19562i 0.165033 0.285845i −0.771634 0.636067i \(-0.780560\pi\)
0.936667 + 0.350221i \(0.113894\pi\)
\(60\) 0 0
\(61\) 3.74581 6.48793i 0.479602 0.830695i −0.520124 0.854090i \(-0.674114\pi\)
0.999726 + 0.0233957i \(0.00744777\pi\)
\(62\) 1.08333 0.625462i 0.137583 0.0794338i
\(63\) 0 0
\(64\) 5.49162 0.686453
\(65\) −4.96629 + 6.35106i −0.615993 + 0.787752i
\(66\) 0 0
\(67\) 3.47722 2.00758i 0.424810 0.245264i −0.272323 0.962206i \(-0.587792\pi\)
0.697133 + 0.716942i \(0.254459\pi\)
\(68\) −3.19071 + 1.84216i −0.386930 + 0.223394i
\(69\) 0 0
\(70\) 2.35526 + 0.779207i 0.281508 + 0.0931331i
\(71\) 2.62291 4.54300i 0.311282 0.539155i −0.667359 0.744737i \(-0.732575\pi\)
0.978640 + 0.205581i \(0.0659084\pi\)
\(72\) 0 0
\(73\) 5.46493i 0.639622i −0.947481 0.319811i \(-0.896381\pi\)
0.947481 0.319811i \(-0.103619\pi\)
\(74\) −0.322368 + 0.558359i −0.0374746 + 0.0649079i
\(75\) 0 0
\(76\) −1.17763 2.03972i −0.135084 0.233972i
\(77\) 10.8848i 1.24043i
\(78\) 0 0
\(79\) −13.7811 −1.55049 −0.775247 0.631658i \(-0.782375\pi\)
−0.775247 + 0.631658i \(0.782375\pi\)
\(80\) −1.52065 7.34688i −0.170014 0.821406i
\(81\) 0 0
\(82\) 0.796819 + 0.460044i 0.0879940 + 0.0508033i
\(83\) 8.61955i 0.946119i −0.881031 0.473059i \(-0.843150\pi\)
0.881031 0.473059i \(-0.156850\pi\)
\(84\) 0 0
\(85\) 2.89851 + 3.25391i 0.314387 + 0.352936i
\(86\) 2.89055 0.311696
\(87\) 0 0
\(88\) 3.61808 2.08890i 0.385688 0.222677i
\(89\) −5.15819 8.93425i −0.546767 0.947028i −0.998493 0.0548717i \(-0.982525\pi\)
0.451726 0.892156i \(-0.350808\pi\)
\(90\) 0 0
\(91\) −9.22398 + 7.81753i −0.966936 + 0.819500i
\(92\) 5.08898i 0.530563i
\(93\) 0 0
\(94\) −1.13636 1.96823i −0.117206 0.203007i
\(95\) −2.08012 + 1.85292i −0.213416 + 0.190106i
\(96\) 0 0
\(97\) −4.56055 2.63304i −0.463054 0.267344i 0.250273 0.968175i \(-0.419479\pi\)
−0.713328 + 0.700831i \(0.752813\pi\)
\(98\) 1.21648 + 0.702335i 0.122883 + 0.0709465i
\(99\) 0 0
\(100\) −8.67609 + 3.75229i −0.867609 + 0.375229i
\(101\) 2.85526 + 4.94546i 0.284109 + 0.492092i 0.972393 0.233350i \(-0.0749688\pi\)
−0.688283 + 0.725442i \(0.741635\pi\)
\(102\) 0 0
\(103\) 7.36863i 0.726052i −0.931779 0.363026i \(-0.881744\pi\)
0.931779 0.363026i \(-0.118256\pi\)
\(104\) −4.36872 1.56577i −0.428388 0.153537i
\(105\) 0 0
\(106\) 2.12291 + 3.67698i 0.206195 + 0.357140i
\(107\) 7.42568 4.28722i 0.717868 0.414461i −0.0960996 0.995372i \(-0.530637\pi\)
0.813967 + 0.580911i \(0.197303\pi\)
\(108\) 0 0
\(109\) 8.49162 0.813350 0.406675 0.913573i \(-0.366688\pi\)
0.406675 + 0.913573i \(0.366688\pi\)
\(110\) −1.59714 1.79297i −0.152281 0.170953i
\(111\) 0 0
\(112\) 11.2518i 1.06320i
\(113\) −6.35006 3.66621i −0.597363 0.344888i 0.170640 0.985333i \(-0.445416\pi\)
−0.768004 + 0.640446i \(0.778750\pi\)
\(114\) 0 0
\(115\) −5.89413 + 1.21996i −0.549630 + 0.113762i
\(116\) 5.67164 0.526599
\(117\) 0 0
\(118\) 0.838765i 0.0772145i
\(119\) 3.26764 + 5.65972i 0.299544 + 0.518826i
\(120\) 0 0
\(121\) 0.232358 0.402456i 0.0211234 0.0365869i
\(122\) 2.47850i 0.224393i
\(123\) 0 0
\(124\) −3.57417 + 6.19064i −0.320970 + 0.555936i
\(125\) 6.42583 + 9.14925i 0.574744 + 0.818333i
\(126\) 0 0
\(127\) 7.93599 4.58185i 0.704205 0.406573i −0.104707 0.994503i \(-0.533390\pi\)
0.808912 + 0.587930i \(0.200057\pi\)
\(128\) 7.95484 4.59273i 0.703115 0.405944i
\(129\) 0 0
\(130\) −0.372325 + 2.64118i −0.0326551 + 0.231646i
\(131\) −10.0000 −0.873704 −0.436852 0.899533i \(-0.643907\pi\)
−0.436852 + 0.899533i \(0.643907\pi\)
\(132\) 0 0
\(133\) −3.61808 + 2.08890i −0.313727 + 0.181130i
\(134\) 0.664179 1.15039i 0.0573763 0.0993787i
\(135\) 0 0
\(136\) −1.25419 + 2.17232i −0.107546 + 0.186275i
\(137\) −14.5914 8.42435i −1.24663 0.719741i −0.276193 0.961102i \(-0.589073\pi\)
−0.970435 + 0.241361i \(0.922406\pi\)
\(138\) 0 0
\(139\) −0.513452 + 0.889325i −0.0435505 + 0.0754316i −0.886979 0.461810i \(-0.847200\pi\)
0.843429 + 0.537241i \(0.180534\pi\)
\(140\) −13.8822 + 2.87333i −1.17326 + 0.242841i
\(141\) 0 0
\(142\) 1.73551i 0.145640i
\(143\) 11.5150 2.08890i 0.962933 0.174682i
\(144\) 0 0
\(145\) −1.35964 6.56897i −0.112912 0.545523i
\(146\) −0.904000 1.56577i −0.0748155 0.129584i
\(147\) 0 0
\(148\) 3.68431i 0.302849i
\(149\) −7.92583 + 13.7279i −0.649309 + 1.12464i 0.333979 + 0.942581i \(0.391609\pi\)
−0.983288 + 0.182056i \(0.941725\pi\)
\(150\) 0 0
\(151\) 14.5454 1.18369 0.591845 0.806052i \(-0.298400\pi\)
0.591845 + 0.806052i \(0.298400\pi\)
\(152\) −1.38869 0.801763i −0.112638 0.0650316i
\(153\) 0 0
\(154\) −1.80054 3.11862i −0.145091 0.251306i
\(155\) 8.02690 + 2.65559i 0.644736 + 0.213302i
\(156\) 0 0
\(157\) 10.9210i 0.871588i −0.900047 0.435794i \(-0.856468\pi\)
0.900047 0.435794i \(-0.143532\pi\)
\(158\) −3.94846 + 2.27964i −0.314123 + 0.181359i
\(159\) 0 0
\(160\) −5.47976 6.15167i −0.433213 0.486332i
\(161\) −9.02690 −0.711420
\(162\) 0 0
\(163\) 3.61808 + 2.08890i 0.283390 + 0.163615i 0.634957 0.772547i \(-0.281018\pi\)
−0.351567 + 0.936163i \(0.614351\pi\)
\(164\) −5.25779 −0.410564
\(165\) 0 0
\(166\) −1.42583 2.46961i −0.110666 0.191679i
\(167\) −2.90420 + 1.67674i −0.224733 + 0.129750i −0.608140 0.793830i \(-0.708084\pi\)
0.383407 + 0.923580i \(0.374751\pi\)
\(168\) 0 0
\(169\) −10.0404 8.25780i −0.772335 0.635215i
\(170\) 1.36872 + 0.452821i 0.104976 + 0.0347298i
\(171\) 0 0
\(172\) −14.3049 + 8.25894i −1.09074 + 0.629738i
\(173\) 7.56654 + 4.36854i 0.575273 + 0.332134i 0.759253 0.650796i \(-0.225565\pi\)
−0.183979 + 0.982930i \(0.558898\pi\)
\(174\) 0 0
\(175\) 6.65585 + 15.3898i 0.503135 + 1.16336i
\(176\) −5.44527 + 9.43149i −0.410453 + 0.710925i
\(177\) 0 0
\(178\) −2.95577 1.70652i −0.221545 0.127909i
\(179\) 9.00507 + 15.5972i 0.673071 + 1.16579i 0.977029 + 0.213107i \(0.0683584\pi\)
−0.303958 + 0.952685i \(0.598308\pi\)
\(180\) 0 0
\(181\) 1.04366 0.0775749 0.0387875 0.999247i \(-0.487650\pi\)
0.0387875 + 0.999247i \(0.487650\pi\)
\(182\) −1.34963 + 3.76564i −0.100041 + 0.279128i
\(183\) 0 0
\(184\) −1.73236 3.00053i −0.127711 0.221202i
\(185\) −4.26722 + 0.883225i −0.313732 + 0.0649360i
\(186\) 0 0
\(187\) 6.32546i 0.462564i
\(188\) 11.2473 + 6.49365i 0.820296 + 0.473598i
\(189\) 0 0
\(190\) −0.289474 + 0.874976i −0.0210006 + 0.0634774i
\(191\) 12.7593 22.0997i 0.923228 1.59908i 0.128841 0.991665i \(-0.458874\pi\)
0.794387 0.607412i \(-0.207792\pi\)
\(192\) 0 0
\(193\) −17.1652 + 9.91035i −1.23558 + 0.713362i −0.968188 0.250225i \(-0.919495\pi\)
−0.267392 + 0.963588i \(0.586162\pi\)
\(194\) −1.74221 −0.125083
\(195\) 0 0
\(196\) −8.02690 −0.573350
\(197\) 18.7512 10.8260i 1.33596 0.771319i 0.349758 0.936840i \(-0.386264\pi\)
0.986206 + 0.165521i \(0.0529304\pi\)
\(198\) 0 0
\(199\) 9.11453 15.7868i 0.646112 1.11910i −0.337932 0.941171i \(-0.609727\pi\)
0.984044 0.177928i \(-0.0569393\pi\)
\(200\) −3.83821 + 5.16586i −0.271402 + 0.365281i
\(201\) 0 0
\(202\) 1.63614 + 0.944625i 0.115118 + 0.0664636i
\(203\) 10.0604i 0.706104i
\(204\) 0 0
\(205\) 1.26043 + 6.08964i 0.0880321 + 0.425319i
\(206\) −1.21891 2.11121i −0.0849252 0.147095i
\(207\) 0 0
\(208\) 11.9033 2.15934i 0.825345 0.149723i
\(209\) 4.04366 0.279706
\(210\) 0 0
\(211\) −9.64981 16.7140i −0.664320 1.15064i −0.979469 0.201594i \(-0.935388\pi\)
0.315149 0.949042i \(-0.397946\pi\)
\(212\) −21.0119 12.1312i −1.44310 0.833176i
\(213\) 0 0
\(214\) 1.41837 2.45669i 0.0969577 0.167936i
\(215\) 12.9949 + 14.5882i 0.886242 + 0.994910i
\(216\) 0 0
\(217\) 10.9810 + 6.33991i 0.745442 + 0.430381i
\(218\) 2.43296 1.40467i 0.164781 0.0951362i
\(219\) 0 0
\(220\) 13.0269 + 4.30978i 0.878274 + 0.290565i
\(221\) −5.36034 + 4.54300i −0.360575 + 0.305596i
\(222\) 0 0
\(223\) 10.7134 6.18537i 0.717421 0.414203i −0.0963818 0.995344i \(-0.530727\pi\)
0.813803 + 0.581141i \(0.197394\pi\)
\(224\) −6.17763 10.7000i −0.412760 0.714922i
\(225\) 0 0
\(226\) −2.42583 −0.161364
\(227\) 5.33715 + 3.08141i 0.354239 + 0.204520i 0.666551 0.745460i \(-0.267770\pi\)
−0.312311 + 0.949980i \(0.601103\pi\)
\(228\) 0 0
\(229\) 26.9832 1.78310 0.891551 0.452920i \(-0.149618\pi\)
0.891551 + 0.452920i \(0.149618\pi\)
\(230\) −1.48694 + 1.32453i −0.0980459 + 0.0873370i
\(231\) 0 0
\(232\) 3.34408 1.93070i 0.219549 0.126757i
\(233\) 0.824319i 0.0540029i −0.999635 0.0270015i \(-0.991404\pi\)
0.999635 0.0270015i \(-0.00859588\pi\)
\(234\) 0 0
\(235\) 4.82476 14.5835i 0.314733 0.951323i
\(236\) 2.39654 + 4.15092i 0.156001 + 0.270202i
\(237\) 0 0
\(238\) 1.87244 + 1.08106i 0.121372 + 0.0700744i
\(239\) 4.00000 0.258738 0.129369 0.991596i \(-0.458705\pi\)
0.129369 + 0.991596i \(0.458705\pi\)
\(240\) 0 0
\(241\) −11.3469 + 19.6534i −0.730917 + 1.26599i 0.225575 + 0.974226i \(0.427574\pi\)
−0.956492 + 0.291760i \(0.905759\pi\)
\(242\) 0.153745i 0.00988310i
\(243\) 0 0
\(244\) 7.08163 + 12.2657i 0.453355 + 0.785234i
\(245\) 1.92426 + 9.29687i 0.122936 + 0.593955i
\(246\) 0 0
\(247\) −2.90420 3.42669i −0.184790 0.218035i
\(248\) 4.86678i 0.309041i
\(249\) 0 0
\(250\) 3.35454 + 1.55843i 0.212159 + 0.0985635i
\(251\) 9.51345 16.4778i 0.600484 1.04007i −0.392264 0.919853i \(-0.628308\pi\)
0.992748 0.120216i \(-0.0383586\pi\)
\(252\) 0 0
\(253\) 7.56654 + 4.36854i 0.475704 + 0.274648i
\(254\) 1.51584 2.62552i 0.0951124 0.164739i
\(255\) 0 0
\(256\) −3.97218 + 6.88001i −0.248261 + 0.430001i
\(257\) −1.82857 + 1.05573i −0.114063 + 0.0658544i −0.555946 0.831218i \(-0.687644\pi\)
0.441883 + 0.897073i \(0.354311\pi\)
\(258\) 0 0
\(259\) −6.53528 −0.406083
\(260\) −5.70384 14.1346i −0.353737 0.876591i
\(261\) 0 0
\(262\) −2.86513 + 1.65418i −0.177008 + 0.102196i
\(263\) −25.9092 + 14.9587i −1.59763 + 0.922391i −0.605685 + 0.795704i \(0.707101\pi\)
−0.991943 + 0.126687i \(0.959566\pi\)
\(264\) 0 0
\(265\) −9.01345 + 27.2444i −0.553692 + 1.67361i
\(266\) −0.691084 + 1.19699i −0.0423731 + 0.0733923i
\(267\) 0 0
\(268\) 7.59083i 0.463684i
\(269\) −9.29455 + 16.0986i −0.566699 + 0.981551i 0.430191 + 0.902738i \(0.358446\pi\)
−0.996889 + 0.0788127i \(0.974887\pi\)
\(270\) 0 0
\(271\) −2.91238 5.04439i −0.176914 0.306425i 0.763908 0.645326i \(-0.223278\pi\)
−0.940822 + 0.338901i \(0.889945\pi\)
\(272\) 6.53876i 0.396471i
\(273\) 0 0
\(274\) −5.57417 −0.336748
\(275\) 1.86875 16.1211i 0.112690 0.972139i
\(276\) 0 0
\(277\) −11.7263 6.77017i −0.704564 0.406780i 0.104481 0.994527i \(-0.466682\pi\)
−0.809045 + 0.587747i \(0.800015\pi\)
\(278\) 0.339738i 0.0203761i
\(279\) 0 0
\(280\) −7.20702 + 6.41985i −0.430702 + 0.383659i
\(281\) 0.464716 0.0277226 0.0138613 0.999904i \(-0.495588\pi\)
0.0138613 + 0.999904i \(0.495588\pi\)
\(282\) 0 0
\(283\) −8.71259 + 5.03022i −0.517910 + 0.299015i −0.736079 0.676896i \(-0.763325\pi\)
0.218169 + 0.975911i \(0.429991\pi\)
\(284\) 4.95873 + 8.58877i 0.294246 + 0.509649i
\(285\) 0 0
\(286\) 2.95365 2.50329i 0.174653 0.148022i
\(287\) 9.32634i 0.550516i
\(288\) 0 0
\(289\) −6.60107 11.4334i −0.388298 0.672553i
\(290\) −1.47618 1.65719i −0.0866844 0.0973133i
\(291\) 0 0
\(292\) 8.94752 + 5.16586i 0.523614 + 0.302309i
\(293\) −11.6481 6.72506i −0.680492 0.392882i 0.119548 0.992828i \(-0.461855\pi\)
−0.800040 + 0.599946i \(0.795189\pi\)
\(294\) 0 0
\(295\) 4.23314 3.77079i 0.246463 0.219544i
\(296\) −1.25419 2.17232i −0.0728983 0.126264i
\(297\) 0 0
\(298\) 5.24431i 0.303795i
\(299\) −1.73236 9.54958i −0.100185 0.552266i
\(300\) 0 0
\(301\) 14.6498 + 25.3742i 0.844401 + 1.46255i
\(302\) 4.16745 2.40608i 0.239810 0.138454i
\(303\) 0 0
\(304\) 4.18002 0.239741
\(305\) 12.5087 11.1425i 0.716246 0.638015i
\(306\) 0 0
\(307\) 24.6077i 1.40444i 0.711961 + 0.702219i \(0.247807\pi\)
−0.711961 + 0.702219i \(0.752193\pi\)
\(308\) 17.8212 + 10.2891i 1.01546 + 0.586274i
\(309\) 0 0
\(310\) 2.73909 0.566935i 0.155570 0.0321997i
\(311\) −2.43781 −0.138236 −0.0691178 0.997609i \(-0.522018\pi\)
−0.0691178 + 0.997609i \(0.522018\pi\)
\(312\) 0 0
\(313\) 19.2965i 1.09071i 0.838207 + 0.545353i \(0.183604\pi\)
−0.838207 + 0.545353i \(0.816396\pi\)
\(314\) −1.80653 3.12900i −0.101948 0.176579i
\(315\) 0 0
\(316\) 13.0269 22.5633i 0.732821 1.26928i
\(317\) 28.8217i 1.61879i 0.587265 + 0.809395i \(0.300205\pi\)
−0.587265 + 0.809395i \(0.699795\pi\)
\(318\) 0 0
\(319\) −4.86872 + 8.43286i −0.272596 + 0.472150i
\(320\) 11.6582 + 3.85695i 0.651713 + 0.215610i
\(321\) 0 0
\(322\) −2.58632 + 1.49321i −0.144130 + 0.0832136i
\(323\) −2.10258 + 1.21392i −0.116990 + 0.0675445i
\(324\) 0 0
\(325\) −15.0035 + 9.99470i −0.832246 + 0.554406i
\(326\) 1.38217 0.0765512
\(327\) 0 0
\(328\) −3.10006 + 1.78982i −0.171172 + 0.0988264i
\(329\) 11.5185 19.9507i 0.635037 1.09992i
\(330\) 0 0
\(331\) 1.48655 2.57478i 0.0817081 0.141522i −0.822276 0.569089i \(-0.807296\pi\)
0.903984 + 0.427567i \(0.140629\pi\)
\(332\) 14.1125 + 8.14783i 0.774522 + 0.447171i
\(333\) 0 0
\(334\) −0.554726 + 0.960814i −0.0303533 + 0.0525734i
\(335\) 8.79180 1.81972i 0.480347 0.0994218i
\(336\) 0 0
\(337\) 1.90370i 0.103701i 0.998655 + 0.0518505i \(0.0165119\pi\)
−0.998655 + 0.0518505i \(0.983488\pi\)
\(338\) −4.24268 0.705107i −0.230771 0.0383528i
\(339\) 0 0
\(340\) −8.06738 + 1.66978i −0.437515 + 0.0905565i
\(341\) −6.13636 10.6285i −0.332302 0.575565i
\(342\) 0 0
\(343\) 9.23611i 0.498703i
\(344\) −5.62291 + 9.73916i −0.303167 + 0.525100i
\(345\) 0 0
\(346\) 2.89055 0.155397
\(347\) −10.9420 6.31735i −0.587396 0.339133i 0.176671 0.984270i \(-0.443467\pi\)
−0.764067 + 0.645137i \(0.776800\pi\)
\(348\) 0 0
\(349\) 4.48655 + 7.77093i 0.240159 + 0.415968i 0.960760 0.277383i \(-0.0894670\pi\)
−0.720600 + 0.693351i \(0.756134\pi\)
\(350\) 4.45274 + 3.30837i 0.238009 + 0.176840i
\(351\) 0 0
\(352\) 11.9586i 0.637395i
\(353\) −29.6618 + 17.1252i −1.57874 + 0.911484i −0.583701 + 0.811969i \(0.698396\pi\)
−0.995036 + 0.0995150i \(0.968271\pi\)
\(354\) 0 0
\(355\) 8.75889 7.80221i 0.464874 0.414098i
\(356\) 19.5036 1.03369
\(357\) 0 0
\(358\) 5.16014 + 2.97921i 0.272722 + 0.157456i
\(359\) 22.4043 1.18245 0.591227 0.806505i \(-0.298644\pi\)
0.591227 + 0.806505i \(0.298644\pi\)
\(360\) 0 0
\(361\) 8.72398 + 15.1104i 0.459157 + 0.795283i
\(362\) 0.299023 0.172641i 0.0157163 0.00907381i
\(363\) 0 0
\(364\) −4.08016 22.4918i −0.213858 1.17889i
\(365\) 3.83821 11.6015i 0.200901 0.607252i
\(366\) 0 0
\(367\) −11.4273 + 6.59753i −0.596498 + 0.344388i −0.767663 0.640854i \(-0.778580\pi\)
0.171165 + 0.985242i \(0.445247\pi\)
\(368\) 7.82169 + 4.51586i 0.407734 + 0.235405i
\(369\) 0 0
\(370\) −1.07651 + 0.958932i −0.0559652 + 0.0498525i
\(371\) −21.5185 + 37.2712i −1.11719 + 1.93502i
\(372\) 0 0
\(373\) −13.2168 7.63070i −0.684338 0.395103i 0.117149 0.993114i \(-0.462624\pi\)
−0.801488 + 0.598012i \(0.795958\pi\)
\(374\) −1.04635 1.81233i −0.0541053 0.0937131i
\(375\) 0 0
\(376\) 8.84210 0.455997
\(377\) 10.6430 1.93070i 0.548140 0.0994362i
\(378\) 0 0
\(379\) 9.11453 + 15.7868i 0.468182 + 0.810915i 0.999339 0.0363588i \(-0.0115759\pi\)
−0.531157 + 0.847273i \(0.678243\pi\)
\(380\) −1.06744 5.15722i −0.0547583 0.264560i
\(381\) 0 0
\(382\) 8.44246i 0.431954i
\(383\) −1.24784 0.720440i −0.0637616 0.0368128i 0.467780 0.883845i \(-0.345054\pi\)
−0.531542 + 0.847032i \(0.678387\pi\)
\(384\) 0 0
\(385\) 7.64474 23.1073i 0.389612 1.17766i
\(386\) −3.27870 + 5.67888i −0.166882 + 0.289048i
\(387\) 0 0
\(388\) 8.62194 4.97788i 0.437713 0.252714i
\(389\) −18.7912 −0.952754 −0.476377 0.879241i \(-0.658050\pi\)
−0.476377 + 0.879241i \(0.658050\pi\)
\(390\) 0 0
\(391\) −5.24581 −0.265292
\(392\) −4.73277 + 2.73247i −0.239041 + 0.138010i
\(393\) 0 0
\(394\) 3.58163 6.20357i 0.180440 0.312531i
\(395\) −29.2560 9.67894i −1.47203 0.487000i
\(396\) 0 0
\(397\) 14.8027 + 8.54634i 0.742926 + 0.428928i 0.823132 0.567850i \(-0.192225\pi\)
−0.0802063 + 0.996778i \(0.525558\pi\)
\(398\) 6.03084i 0.302298i
\(399\) 0 0
\(400\) 1.93177 16.6647i 0.0965886 0.833236i
\(401\) 11.1011 + 19.2276i 0.554361 + 0.960182i 0.997953 + 0.0639527i \(0.0203707\pi\)
−0.443592 + 0.896229i \(0.646296\pi\)
\(402\) 0 0
\(403\) −4.59962 + 12.8336i −0.229124 + 0.639285i
\(404\) −10.7960 −0.537122
\(405\) 0 0
\(406\) −1.66418 2.88244i −0.0825918 0.143053i
\(407\) 5.47801 + 3.16273i 0.271535 + 0.156771i
\(408\) 0 0
\(409\) −4.81638 + 8.34221i −0.238155 + 0.412496i −0.960185 0.279366i \(-0.909876\pi\)
0.722030 + 0.691862i \(0.243209\pi\)
\(410\) 1.36847 + 1.53626i 0.0675838 + 0.0758706i
\(411\) 0 0
\(412\) 12.0644 + 6.96537i 0.594369 + 0.343159i
\(413\) 7.36296 4.25101i 0.362308 0.209178i
\(414\) 0 0
\(415\) 6.05381 18.2985i 0.297170 0.898238i
\(416\) 10.1340 8.58877i 0.496859 0.421099i
\(417\) 0 0
\(418\) 1.15856 0.668896i 0.0566671 0.0327168i
\(419\) 0.978168 + 1.69424i 0.0477866 + 0.0827689i 0.888929 0.458044i \(-0.151450\pi\)
−0.841143 + 0.540813i \(0.818117\pi\)
\(420\) 0 0
\(421\) −12.0807 −0.588778 −0.294389 0.955686i \(-0.595116\pi\)
−0.294389 + 0.955686i \(0.595116\pi\)
\(422\) −5.52959 3.19251i −0.269176 0.155409i
\(423\) 0 0
\(424\) −16.5185 −0.802210
\(425\) 3.86792 + 8.94346i 0.187622 + 0.433822i
\(426\) 0 0
\(427\) 21.7571 12.5615i 1.05290 0.607893i
\(428\) 16.2104i 0.783558i
\(429\) 0 0
\(430\) 6.13636 + 2.03013i 0.295921 + 0.0979016i
\(431\) 12.2945 + 21.2948i 0.592207 + 1.02573i 0.993934 + 0.109974i \(0.0350767\pi\)
−0.401727 + 0.915759i \(0.631590\pi\)
\(432\) 0 0
\(433\) −31.2400 18.0364i −1.50130 0.866775i −0.999999 0.00150085i \(-0.999522\pi\)
−0.501299 0.865274i \(-0.667144\pi\)
\(434\) 4.19495 0.201364
\(435\) 0 0
\(436\) −8.02690 + 13.9030i −0.384419 + 0.665833i
\(437\) 3.35348i 0.160419i
\(438\) 0 0
\(439\) 1.26764 + 2.19562i 0.0605013 + 0.104791i 0.894690 0.446688i \(-0.147397\pi\)
−0.834188 + 0.551480i \(0.814063\pi\)
\(440\) 9.14794 1.89343i 0.436111 0.0902658i
\(441\) 0 0
\(442\) −0.784309 + 2.18833i −0.0373058 + 0.104088i
\(443\) 19.3579i 0.919721i −0.887991 0.459860i \(-0.847899\pi\)
0.887991 0.459860i \(-0.152101\pi\)
\(444\) 0 0
\(445\) −4.67552 22.5893i −0.221641 1.07084i
\(446\) 2.04635 3.54438i 0.0968973 0.167831i
\(447\) 0 0
\(448\) 15.9487 + 9.20801i 0.753507 + 0.435038i
\(449\) 12.4040 21.4844i 0.585381 1.01391i −0.409447 0.912334i \(-0.634278\pi\)
0.994828 0.101576i \(-0.0323884\pi\)
\(450\) 0 0
\(451\) 4.51345 7.81753i 0.212530 0.368113i
\(452\) 12.0051 6.93114i 0.564672 0.326013i
\(453\) 0 0
\(454\) 2.03888 0.0956896
\(455\) −25.0722 + 10.1176i −1.17540 + 0.474318i
\(456\) 0 0
\(457\) 6.55363 3.78374i 0.306566 0.176996i −0.338823 0.940850i \(-0.610029\pi\)
0.645389 + 0.763854i \(0.276695\pi\)
\(458\) 7.73105 4.46352i 0.361248 0.208567i
\(459\) 0 0
\(460\) 3.57417 10.8034i 0.166646 0.503712i
\(461\) −6.17164 + 10.6896i −0.287442 + 0.497864i −0.973198 0.229967i \(-0.926138\pi\)
0.685756 + 0.727831i \(0.259472\pi\)
\(462\) 0 0
\(463\) 22.8578i 1.06229i −0.847281 0.531146i \(-0.821762\pi\)
0.847281 0.531146i \(-0.178238\pi\)
\(464\) −5.03289 + 8.71723i −0.233646 + 0.404687i
\(465\) 0 0
\(466\) −0.136357 0.236178i −0.00631664 0.0109407i
\(467\) 15.2976i 0.707889i 0.935266 + 0.353945i \(0.115160\pi\)
−0.935266 + 0.353945i \(0.884840\pi\)
\(468\) 0 0
\(469\) 13.4647 0.621743
\(470\) −1.03002 4.97647i −0.0475115 0.229547i
\(471\) 0 0
\(472\) 2.82606 + 1.63163i 0.130080 + 0.0751017i
\(473\) 28.3589i 1.30394i
\(474\) 0 0
\(475\) −5.71727 + 2.47264i −0.262326 + 0.113452i
\(476\) −12.3553 −0.566303
\(477\) 0 0
\(478\) 1.14605 0.661673i 0.0524192 0.0302642i
\(479\) −12.1414 21.0296i −0.554756 0.960866i −0.997922 0.0644264i \(-0.979478\pi\)
0.443166 0.896439i \(-0.353855\pi\)
\(480\) 0 0
\(481\) −1.25419 6.91369i −0.0571861 0.315237i
\(482\) 7.50793i 0.341977i
\(483\) 0 0
\(484\) 0.439284 + 0.760862i 0.0199674 + 0.0345846i
\(485\) −7.83235 8.79272i −0.355649 0.399257i
\(486\) 0 0
\(487\) −31.9462 18.4441i −1.44762 0.835783i −0.449280 0.893391i \(-0.648319\pi\)
−0.998339 + 0.0576081i \(0.981653\pi\)
\(488\) 8.35085 + 4.82136i 0.378025 + 0.218253i
\(489\) 0 0
\(490\) 2.08920 + 2.34537i 0.0943803 + 0.105953i
\(491\) −17.6767 30.6170i −0.797739 1.38172i −0.921085 0.389361i \(-0.872696\pi\)
0.123346 0.992364i \(-0.460637\pi\)
\(492\) 0 0
\(493\) 5.84642i 0.263310i
\(494\) −1.39893 0.501383i −0.0629407 0.0225583i
\(495\) 0 0
\(496\) −6.34328 10.9869i −0.284822 0.493326i
\(497\) 15.2349 8.79585i 0.683377 0.394548i
\(498\) 0 0
\(499\) −16.2189 −0.726058 −0.363029 0.931778i \(-0.618257\pi\)
−0.363029 + 0.931778i \(0.618257\pi\)
\(500\) −21.0539 + 1.87223i −0.941558 + 0.0837286i
\(501\) 0 0
\(502\) 6.29480i 0.280950i
\(503\) −17.5270 10.1192i −0.781489 0.451193i 0.0554688 0.998460i \(-0.482335\pi\)
−0.836958 + 0.547268i \(0.815668\pi\)
\(504\) 0 0
\(505\) 2.58808 + 12.5041i 0.115168 + 0.556425i
\(506\) 2.89055 0.128500
\(507\) 0 0
\(508\) 17.3244i 0.768646i
\(509\) 10.0185 + 17.3526i 0.444063 + 0.769140i 0.997986 0.0634276i \(-0.0202032\pi\)
−0.553923 + 0.832568i \(0.686870\pi\)
\(510\) 0 0
\(511\) 9.16326 15.8712i 0.405359 0.702102i
\(512\) 20.9992i 0.928042i
\(513\) 0 0
\(514\) −0.349273 + 0.604959i −0.0154058 + 0.0266836i
\(515\) 5.17524 15.6429i 0.228048 0.689308i
\(516\) 0 0
\(517\) −19.3101 + 11.1487i −0.849259 + 0.490320i
\(518\) −1.87244 + 1.08106i −0.0822704 + 0.0474988i
\(519\) 0 0
\(520\) −8.17467 6.39229i −0.358483 0.280320i
\(521\) −16.0269 −0.702151 −0.351076 0.936347i \(-0.614184\pi\)
−0.351076 + 0.936347i \(0.614184\pi\)
\(522\) 0 0
\(523\) 10.1654 5.86898i 0.444501 0.256633i −0.261004 0.965338i \(-0.584054\pi\)
0.705505 + 0.708705i \(0.250720\pi\)
\(524\) 9.45274 16.3726i 0.412945 0.715241i
\(525\) 0 0
\(526\) −4.94887 + 8.57170i −0.215781 + 0.373744i
\(527\) 6.38142 + 3.68431i 0.277979 + 0.160491i
\(528\) 0 0
\(529\) −7.87709 + 13.6435i −0.342482 + 0.593197i
\(530\) 1.92426 + 9.29687i 0.0835844 + 0.403830i
\(531\) 0 0
\(532\) 7.89832i 0.342436i
\(533\) −9.86635 + 1.78982i −0.427359 + 0.0775258i
\(534\) 0 0
\(535\) 18.7751 3.88605i 0.811718 0.168008i
\(536\) 2.58402 + 4.47565i 0.111613 + 0.193319i
\(537\) 0 0
\(538\) 6.14995i 0.265143i
\(539\) 6.89055 11.9348i 0.296797 0.514067i
\(540\) 0 0
\(541\) −21.8080 −0.937599 −0.468800 0.883305i \(-0.655313\pi\)
−0.468800 + 0.883305i \(0.655313\pi\)
\(542\) −1.66887 0.963521i −0.0716840 0.0413868i
\(543\) 0 0
\(544\) −3.59001 6.21808i −0.153920 0.266598i
\(545\) 18.0269 + 5.96396i 0.772188 + 0.255468i
\(546\) 0 0
\(547\) 6.30924i 0.269764i −0.990862 0.134882i \(-0.956935\pi\)
0.990862 0.134882i \(-0.0430655\pi\)
\(548\) 27.5858 15.9266i 1.17840 0.680352i
\(549\) 0 0
\(550\) −2.13130 4.92803i −0.0908790 0.210132i
\(551\) 3.73743 0.159220
\(552\) 0 0
\(553\) −40.0230 23.1073i −1.70195 0.982622i
\(554\) −4.47964 −0.190322
\(555\) 0 0
\(556\) −0.970706 1.68131i −0.0411671 0.0713035i
\(557\) −31.0364 + 17.9189i −1.31506 + 0.759247i −0.982929 0.183987i \(-0.941099\pi\)
−0.332126 + 0.943235i \(0.607766\pi\)
\(558\) 0 0
\(559\) −24.0320 + 20.3676i −1.01644 + 0.861459i
\(560\) 7.90253 23.8865i 0.333943 1.00939i
\(561\) 0 0
\(562\) 0.133147 0.0768725i 0.00561647 0.00324267i
\(563\) −4.33196 2.50106i −0.182570 0.105407i 0.405929 0.913904i \(-0.366948\pi\)
−0.588500 + 0.808497i \(0.700281\pi\)
\(564\) 0 0
\(565\) −10.9057 12.2429i −0.458805 0.515062i
\(566\) −1.66418 + 2.88244i −0.0699507 + 0.121158i
\(567\) 0 0
\(568\) 5.84746 + 3.37603i 0.245354 + 0.141655i
\(569\) 6.58402 + 11.4039i 0.276017 + 0.478075i 0.970391 0.241539i \(-0.0776522\pi\)
−0.694375 + 0.719614i \(0.744319\pi\)
\(570\) 0 0
\(571\) 19.8349 0.830065 0.415032 0.909807i \(-0.363770\pi\)
0.415032 + 0.909807i \(0.363770\pi\)
\(572\) −7.46475 + 20.8276i −0.312117 + 0.870848i
\(573\) 0 0
\(574\) 1.54275 + 2.67212i 0.0643930 + 0.111532i
\(575\) −13.3695 1.54979i −0.557547 0.0646307i
\(576\) 0 0
\(577\) 10.9210i 0.454646i 0.973819 + 0.227323i \(0.0729972\pi\)
−0.973819 + 0.227323i \(0.927003\pi\)
\(578\) −3.78258 2.18388i −0.157335 0.0908373i
\(579\) 0 0
\(580\) 12.0404 + 3.98339i 0.499949 + 0.165401i
\(581\) 14.4527 25.0329i 0.599601 1.03854i
\(582\) 0 0
\(583\) 36.0745 20.8276i 1.49406 0.862593i
\(584\) 7.03411 0.291073
\(585\) 0 0
\(586\) −4.44979 −0.183819
\(587\) −35.0303 + 20.2247i −1.44585 + 0.834764i −0.998231 0.0594576i \(-0.981063\pi\)
−0.447624 + 0.894222i \(0.647730\pi\)
\(588\) 0 0
\(589\) −2.35526 + 4.07944i −0.0970469 + 0.168090i
\(590\) 0.589093 1.78062i 0.0242526 0.0733069i
\(591\) 0 0
\(592\) 5.66274 + 3.26938i 0.232737 + 0.134371i
\(593\) 1.47709i 0.0606569i 0.999540 + 0.0303284i \(0.00965532\pi\)
−0.999540 + 0.0303284i \(0.990345\pi\)
\(594\) 0 0
\(595\) 2.96188 + 14.3100i 0.121425 + 0.586654i
\(596\) −14.9842 25.9533i −0.613775 1.06309i
\(597\) 0 0
\(598\) −2.07602 2.44951i −0.0848947 0.100168i
\(599\) 2.27271 0.0928606 0.0464303 0.998922i \(-0.485215\pi\)
0.0464303 + 0.998922i \(0.485215\pi\)
\(600\) 0 0
\(601\) −3.70215 6.41231i −0.151014 0.261563i 0.780587 0.625048i \(-0.214920\pi\)
−0.931600 + 0.363484i \(0.881587\pi\)
\(602\) 8.39472 + 4.84669i 0.342143 + 0.197536i
\(603\) 0 0
\(604\) −13.7494 + 23.8147i −0.559456 + 0.969005i
\(605\) 0.775932 0.691182i 0.0315461 0.0281006i
\(606\) 0 0
\(607\) 9.26059 + 5.34661i 0.375876 + 0.217012i 0.676022 0.736881i \(-0.263702\pi\)
−0.300146 + 0.953893i \(0.597036\pi\)
\(608\) 3.97502 2.29498i 0.161208 0.0930736i
\(609\) 0 0
\(610\) 1.74074 5.26162i 0.0704804 0.213037i
\(611\) 23.3164 + 8.35673i 0.943280 + 0.338077i
\(612\) 0 0
\(613\) −5.26673 + 3.04075i −0.212721 + 0.122815i −0.602575 0.798062i \(-0.705859\pi\)
0.389854 + 0.920877i \(0.372525\pi\)
\(614\) 4.07057 + 7.05043i 0.164275 + 0.284532i
\(615\) 0 0
\(616\) 14.0101 0.564485
\(617\) 27.5732 + 15.9194i 1.11006 + 0.640892i 0.938844 0.344342i \(-0.111898\pi\)
0.171213 + 0.985234i \(0.445231\pi\)
\(618\) 0 0
\(619\) 26.4043 1.06128 0.530639 0.847598i \(-0.321952\pi\)
0.530639 + 0.847598i \(0.321952\pi\)
\(620\) −11.9355 + 10.6319i −0.479342 + 0.426987i
\(621\) 0 0
\(622\) −0.698464 + 0.403259i −0.0280059 + 0.0161692i
\(623\) 34.5957i 1.38605i
\(624\) 0 0
\(625\) 7.21560 + 23.9361i 0.288624 + 0.957443i
\(626\) 3.19200 + 5.52871i 0.127578 + 0.220972i
\(627\) 0 0
\(628\) 17.8805 + 10.3233i 0.713509 + 0.411944i
\(629\) −3.79785 −0.151430
\(630\) 0 0
\(631\) −17.5840 + 30.4564i −0.700009 + 1.21245i 0.268454 + 0.963293i \(0.413487\pi\)
−0.968463 + 0.249158i \(0.919846\pi\)
\(632\) 17.7381i 0.705585i
\(633\) 0 0
\(634\) 4.76764 + 8.25780i 0.189347 + 0.327959i
\(635\) 20.0653 4.15310i 0.796269 0.164811i
\(636\) 0 0
\(637\) −15.0626 + 2.73247i −0.596804 + 0.108264i
\(638\) 3.22150i 0.127540i
\(639\) 0 0
\(640\) 20.1130 4.16297i 0.795036 0.164556i
\(641\) 2.76257 4.78491i 0.109115 0.188993i −0.806297 0.591511i \(-0.798532\pi\)
0.915412 + 0.402518i \(0.131865\pi\)
\(642\) 0 0
\(643\) −27.8472 16.0776i −1.09819 0.634039i −0.162444 0.986718i \(-0.551938\pi\)
−0.935744 + 0.352679i \(0.885271\pi\)
\(644\) 8.53289 14.7794i 0.336243 0.582390i
\(645\) 0 0
\(646\) −0.401610 + 0.695609i −0.0158011 + 0.0273684i
\(647\) 11.9376 6.89216i 0.469314 0.270959i −0.246638 0.969108i \(-0.579326\pi\)
0.715953 + 0.698149i \(0.245993\pi\)
\(648\) 0 0
\(649\) −8.22905 −0.323019
\(650\) −2.64540 + 5.34547i −0.103761 + 0.209667i
\(651\) 0 0
\(652\) −6.84015 + 3.94916i −0.267881 + 0.154661i
\(653\) 7.36296 4.25101i 0.288135 0.166355i −0.348965 0.937136i \(-0.613467\pi\)
0.637100 + 0.770781i \(0.280134\pi\)
\(654\) 0 0
\(655\) −21.2291 7.02335i −0.829488 0.274425i
\(656\) 4.66565 8.08115i 0.182163 0.315516i
\(657\) 0 0
\(658\) 7.62150i 0.297117i
\(659\) −2.02183 + 3.50192i −0.0787594 + 0.136415i −0.902715 0.430239i \(-0.858429\pi\)
0.823956 + 0.566654i \(0.191763\pi\)
\(660\) 0 0
\(661\) −15.6364 27.0830i −0.608184 1.05341i −0.991540 0.129805i \(-0.958565\pi\)
0.383356 0.923601i \(-0.374768\pi\)
\(662\) 0.983609i 0.0382290i
\(663\) 0 0
\(664\) 11.0945 0.430551
\(665\) −9.14794 + 1.89343i −0.354742 + 0.0734241i
\(666\) 0 0
\(667\) 6.99351 + 4.03771i 0.270790 + 0.156341i
\(668\) 6.33991i 0.245298i
\(669\) 0 0
\(670\) 2.21795 1.97570i 0.0856869 0.0763278i
\(671\) −24.3164 −0.938723
\(672\) 0 0
\(673\) 27.7768 16.0370i 1.07072 0.618179i 0.142340 0.989818i \(-0.454537\pi\)
0.928377 + 0.371639i \(0.121204\pi\)
\(674\) 0.314906 + 0.545433i 0.0121297 + 0.0210093i
\(675\) 0 0
\(676\) 23.0111 8.63282i 0.885041 0.332031i
\(677\) 14.2382i 0.547220i −0.961841 0.273610i \(-0.911782\pi\)
0.961841 0.273610i \(-0.0882177\pi\)
\(678\) 0 0
\(679\) −8.82983 15.2937i −0.338858 0.586919i
\(680\) −4.18822 + 3.73077i −0.160611 + 0.143068i
\(681\) 0 0
\(682\) −3.51629 2.03013i −0.134646 0.0777377i
\(683\) 22.3302 + 12.8923i 0.854440 + 0.493311i 0.862146 0.506659i \(-0.169120\pi\)
−0.00770647 + 0.999970i \(0.502453\pi\)
\(684\) 0 0
\(685\) −25.0595 28.1322i −0.957473 1.07487i
\(686\) −1.52782 2.64626i −0.0583325 0.101035i
\(687\) 0 0
\(688\) 29.3152i 1.11763i
\(689\) −43.5589 15.6118i −1.65946 0.594761i
\(690\) 0 0
\(691\) 0.0218318 + 0.0378138i 0.000830522 + 0.00143851i 0.866440 0.499281i \(-0.166402\pi\)
−0.865610 + 0.500719i \(0.833069\pi\)
\(692\) −14.3049 + 8.25894i −0.543791 + 0.313958i
\(693\) 0 0
\(694\) −4.18002 −0.158671
\(695\) −1.71461 + 1.52734i −0.0650390 + 0.0579352i
\(696\) 0 0
\(697\) 5.41982i 0.205290i
\(698\) 2.57091 + 1.48431i 0.0973103 + 0.0561821i
\(699\) 0 0
\(700\) −31.4887 3.65016i −1.19016 0.137963i
\(701\) 14.5454 0.549373 0.274687 0.961534i \(-0.411426\pi\)
0.274687 + 0.961534i \(0.411426\pi\)
\(702\) 0 0
\(703\) 2.42785i 0.0915679i
\(704\) −8.91238 15.4367i −0.335898 0.581792i
\(705\) 0 0
\(706\) −5.66565 + 9.81320i −0.213230 + 0.369325i
\(707\) 19.1501i 0.720214i
\(708\) 0 0
\(709\) 9.81638 17.0025i 0.368662 0.638541i −0.620695 0.784052i \(-0.713149\pi\)
0.989357 + 0.145511i \(0.0464827\pi\)
\(710\) 1.21891 3.68431i 0.0457447 0.138270i
\(711\) 0 0
\(712\) 11.4996 6.63929i 0.430965 0.248818i
\(713\) −8.81438 + 5.08898i −0.330101 + 0.190584i
\(714\) 0 0
\(715\) 25.9124 + 3.65285i 0.969067 + 0.136609i
\(716\) −34.0490 −1.27247
\(717\) 0 0
\(718\) 6.41912 3.70608i 0.239559 0.138310i
\(719\) −23.7156 + 41.0766i −0.884443 + 1.53190i −0.0380914 + 0.999274i \(0.512128\pi\)
−0.846351 + 0.532625i \(0.821206\pi\)
\(720\) 0 0
\(721\) 12.3553 21.3999i 0.460134 0.796976i
\(722\) 4.99906 + 2.88621i 0.186046 + 0.107414i
\(723\) 0 0
\(724\) −0.986548 + 1.70875i −0.0366648 + 0.0635052i
\(725\) 1.72723 14.9002i 0.0641477 0.553380i
\(726\) 0 0
\(727\) 34.0951i 1.26452i 0.774757 + 0.632259i \(0.217872\pi\)
−0.774757 + 0.632259i \(0.782128\pi\)
\(728\) −10.0622 11.8725i −0.372931 0.440024i
\(729\) 0 0
\(730\) −0.819409 3.95890i −0.0303277 0.146525i
\(731\) 8.51345 + 14.7457i 0.314881 + 0.545391i
\(732\) 0 0
\(733\) 14.3920i 0.531580i 0.964031 + 0.265790i \(0.0856327\pi\)
−0.964031 + 0.265790i \(0.914367\pi\)
\(734\) −2.18270 + 3.78055i −0.0805651 + 0.139543i
\(735\) 0 0
\(736\) 9.91745 0.365562
\(737\) −11.2864 6.51621i −0.415740 0.240028i
\(738\) 0 0
\(739\) −17.2240 29.8328i −0.633594 1.09742i −0.986811 0.161876i \(-0.948246\pi\)
0.353217 0.935541i \(-0.385088\pi\)
\(740\) 2.58762 7.82145i 0.0951228 0.287522i
\(741\) 0 0
\(742\) 14.2382i 0.522702i
\(743\) 35.2589 20.3567i 1.29352 0.746816i 0.314246 0.949342i \(-0.398248\pi\)
0.979277 + 0.202526i \(0.0649150\pi\)
\(744\) 0 0
\(745\) −26.4674 + 23.5765i −0.969690 + 0.863777i
\(746\) −5.04903 −0.184858
\(747\) 0 0
\(748\) 10.3564 + 5.97929i 0.378669 + 0.218625i
\(749\) 28.7542 1.05066
\(750\) 0 0
\(751\) −16.2509 28.1474i −0.593003 1.02711i −0.993825 0.110956i \(-0.964609\pi\)
0.400822 0.916156i \(-0.368725\pi\)
\(752\) −19.9613 + 11.5247i −0.727914 + 0.420261i
\(753\) 0 0
\(754\) 2.72997 2.31371i 0.0994196 0.0842603i
\(755\) 30.8786 + 10.2158i 1.12379 + 0.371790i
\(756\) 0 0
\(757\) −11.2864 + 6.51621i −0.410211 + 0.236836i −0.690881 0.722969i \(-0.742777\pi\)
0.280669 + 0.959805i \(0.409444\pi\)
\(758\) 5.22286 + 3.01542i 0.189703 + 0.109525i
\(759\) 0 0
\(760\) −2.38496 2.67739i −0.0865116 0.0971193i
\(761\) −1.99493 + 3.45532i −0.0723161 + 0.125255i −0.899916 0.436063i \(-0.856372\pi\)
0.827600 + 0.561318i \(0.189706\pi\)
\(762\) 0 0
\(763\) 24.6613 + 14.2382i 0.892800 + 0.515458i
\(764\) 24.1220 + 41.7805i 0.872703 + 1.51157i
\(765\) 0 0
\(766\) −0.476696 −0.0172237
\(767\) 5.91018 + 6.97348i 0.213404 + 0.251798i
\(768\) 0 0
\(769\) 3.33343 + 5.77367i 0.120207 + 0.208204i 0.919849 0.392272i \(-0.128311\pi\)
−0.799642 + 0.600476i \(0.794978\pi\)
\(770\) −1.63205 7.88512i −0.0588151 0.284160i
\(771\) 0 0
\(772\) 37.4720i 1.34865i
\(773\) −41.8593 24.1675i −1.50557 0.869244i −0.999979 0.00647254i \(-0.997940\pi\)
−0.505595 0.862771i \(-0.668727\pi\)
\(774\) 0 0
\(775\) 15.1752 + 11.2751i 0.545111 + 0.405015i
\(776\) 3.38907 5.87005i 0.121661 0.210723i
\(777\) 0 0
\(778\) −5.38393 + 3.10841i −0.193023 + 0.111442i
\(779\) −3.46472 −0.124136
\(780\) 0 0
\(781\) −17.0269 −0.609271
\(782\) −1.50299 + 0.867753i −0.0537469 + 0.0310308i
\(783\) 0 0
\(784\) 7.12291 12.3372i 0.254389 0.440615i
\(785\) 7.67017 23.1842i 0.273760 0.827478i
\(786\) 0