Properties

Label 570.2.k.b.77.2
Level $570$
Weight $2$
Character 570.77
Analytic conductor $4.551$
Analytic rank $0$
Dimension $36$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 570.k (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(4.55147291521\)
Analytic rank: \(0\)
Dimension: \(36\)
Relative dimension: \(18\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 77.2
Character \(\chi\) \(=\) 570.77
Dual form 570.2.k.b.533.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.707107 + 0.707107i) q^{2} +(-1.63140 + 0.581841i) q^{3} -1.00000i q^{4} +(-1.36872 + 1.76822i) q^{5} +(0.742149 - 1.56500i) q^{6} +(0.102829 + 0.102829i) q^{7} +(0.707107 + 0.707107i) q^{8} +(2.32292 - 1.89843i) q^{9} +O(q^{10})\) \(q+(-0.707107 + 0.707107i) q^{2} +(-1.63140 + 0.581841i) q^{3} -1.00000i q^{4} +(-1.36872 + 1.76822i) q^{5} +(0.742149 - 1.56500i) q^{6} +(0.102829 + 0.102829i) q^{7} +(0.707107 + 0.707107i) q^{8} +(2.32292 - 1.89843i) q^{9} +(-0.282491 - 2.21815i) q^{10} +6.12593i q^{11} +(0.581841 + 1.63140i) q^{12} +(-0.754312 + 0.754312i) q^{13} -0.145422 q^{14} +(1.20410 - 3.68105i) q^{15} -1.00000 q^{16} +(-2.33294 + 2.33294i) q^{17} +(-0.300162 + 2.98495i) q^{18} -1.00000i q^{19} +(1.76822 + 1.36872i) q^{20} +(-0.227584 - 0.107925i) q^{21} +(-4.33169 - 4.33169i) q^{22} +(-6.21428 - 6.21428i) q^{23} +(-1.56500 - 0.742149i) q^{24} +(-1.25322 - 4.84040i) q^{25} -1.06676i q^{26} +(-2.68503 + 4.44866i) q^{27} +(0.102829 - 0.102829i) q^{28} +2.40803 q^{29} +(1.75147 + 3.45433i) q^{30} +3.69470 q^{31} +(0.707107 - 0.707107i) q^{32} +(-3.56432 - 9.99383i) q^{33} -3.29927i q^{34} +(-0.322567 + 0.0410804i) q^{35} +(-1.89843 - 2.32292i) q^{36} +(-3.66137 - 3.66137i) q^{37} +(0.707107 + 0.707107i) q^{38} +(0.791694 - 1.66947i) q^{39} +(-2.21815 + 0.282491i) q^{40} -10.3063i q^{41} +(0.237241 - 0.0846123i) q^{42} +(-0.994803 + 0.994803i) q^{43} +6.12593 q^{44} +(0.177416 + 6.70586i) q^{45} +8.78832 q^{46} +(-4.88564 + 4.88564i) q^{47} +(1.63140 - 0.581841i) q^{48} -6.97885i q^{49} +(4.30884 + 2.53652i) q^{50} +(2.44855 - 5.16335i) q^{51} +(0.754312 + 0.754312i) q^{52} +(2.86461 + 2.86461i) q^{53} +(-1.24708 - 5.04428i) q^{54} +(-10.8320 - 8.38468i) q^{55} +0.145422i q^{56} +(0.581841 + 1.63140i) q^{57} +(-1.70274 + 1.70274i) q^{58} -7.12402 q^{59} +(-3.68105 - 1.20410i) q^{60} -10.3444 q^{61} +(-2.61255 + 2.61255i) q^{62} +(0.434076 + 0.0436501i) q^{63} +1.00000i q^{64} +(-0.301350 - 2.36623i) q^{65} +(9.58706 + 4.54636i) q^{66} +(4.37645 + 4.37645i) q^{67} +(2.33294 + 2.33294i) q^{68} +(13.7537 + 6.52225i) q^{69} +(0.199041 - 0.257138i) q^{70} +0.311021i q^{71} +(2.98495 + 0.300162i) q^{72} +(0.755853 - 0.755853i) q^{73} +5.17797 q^{74} +(4.86084 + 7.16744i) q^{75} -1.00000 q^{76} +(-0.629921 + 0.629921i) q^{77} +(0.620684 + 1.74031i) q^{78} +14.3107i q^{79} +(1.36872 - 1.76822i) q^{80} +(1.79194 - 8.81981i) q^{81} +(7.28768 + 7.28768i) q^{82} +(-11.1880 - 11.1880i) q^{83} +(-0.107925 + 0.227584i) q^{84} +(-0.932016 - 7.31829i) q^{85} -1.40686i q^{86} +(-3.92846 + 1.40109i) q^{87} +(-4.33169 + 4.33169i) q^{88} +2.30981 q^{89} +(-4.86721 - 4.61631i) q^{90} -0.155130 q^{91} +(-6.21428 + 6.21428i) q^{92} +(-6.02753 + 2.14973i) q^{93} -6.90934i q^{94} +(1.76822 + 1.36872i) q^{95} +(-0.742149 + 1.56500i) q^{96} +(-0.595441 - 0.595441i) q^{97} +(4.93479 + 4.93479i) q^{98} +(11.6296 + 14.2301i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 36q + 4q^{3} + 4q^{6} + 20q^{7} + O(q^{10}) \) \( 36q + 4q^{3} + 4q^{6} + 20q^{7} - 4q^{10} - 4q^{12} + 8q^{13} + 4q^{15} - 36q^{16} + 16q^{21} - 4q^{22} + 16q^{25} - 44q^{27} + 20q^{28} + 32q^{30} - 24q^{31} - 4q^{33} + 4q^{36} - 8q^{40} + 12q^{42} - 8q^{43} + 28q^{45} - 16q^{46} - 4q^{48} + 40q^{51} - 8q^{52} - 36q^{55} - 4q^{57} + 44q^{58} + 16q^{60} - 120q^{61} - 12q^{63} + 80q^{67} - 36q^{70} + 44q^{73} + 4q^{75} - 36q^{76} - 64q^{78} + 36q^{81} + 8q^{82} - 24q^{85} - 28q^{87} - 4q^{88} + 44q^{90} - 72q^{93} - 4q^{96} + 92q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/570\mathbb{Z}\right)^\times\).

\(n\) \(191\) \(211\) \(457\)
\(\chi(n)\) \(-1\) \(1\) \(e\left(\frac{1}{4}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.707107 + 0.707107i −0.500000 + 0.500000i
\(3\) −1.63140 + 0.581841i −0.941888 + 0.335926i
\(4\) 1.00000i 0.500000i
\(5\) −1.36872 + 1.76822i −0.612110 + 0.790773i
\(6\) 0.742149 1.56500i 0.302981 0.638907i
\(7\) 0.102829 + 0.102829i 0.0388656 + 0.0388656i 0.726272 0.687407i \(-0.241251\pi\)
−0.687407 + 0.726272i \(0.741251\pi\)
\(8\) 0.707107 + 0.707107i 0.250000 + 0.250000i
\(9\) 2.32292 1.89843i 0.774307 0.632810i
\(10\) −0.282491 2.21815i −0.0893316 0.701441i
\(11\) 6.12593i 1.84704i 0.383553 + 0.923519i \(0.374700\pi\)
−0.383553 + 0.923519i \(0.625300\pi\)
\(12\) 0.581841 + 1.63140i 0.167963 + 0.470944i
\(13\) −0.754312 + 0.754312i −0.209209 + 0.209209i −0.803931 0.594722i \(-0.797262\pi\)
0.594722 + 0.803931i \(0.297262\pi\)
\(14\) −0.145422 −0.0388656
\(15\) 1.20410 3.68105i 0.310898 0.950443i
\(16\) −1.00000 −0.250000
\(17\) −2.33294 + 2.33294i −0.565820 + 0.565820i −0.930955 0.365134i \(-0.881023\pi\)
0.365134 + 0.930955i \(0.381023\pi\)
\(18\) −0.300162 + 2.98495i −0.0707490 + 0.703559i
\(19\) 1.00000i 0.229416i
\(20\) 1.76822 + 1.36872i 0.395386 + 0.306055i
\(21\) −0.227584 0.107925i −0.0496630 0.0235511i
\(22\) −4.33169 4.33169i −0.923519 0.923519i
\(23\) −6.21428 6.21428i −1.29577 1.29577i −0.931163 0.364604i \(-0.881204\pi\)
−0.364604 0.931163i \(-0.618796\pi\)
\(24\) −1.56500 0.742149i −0.319454 0.151491i
\(25\) −1.25322 4.84040i −0.250644 0.968079i
\(26\) 1.06676i 0.209209i
\(27\) −2.68503 + 4.44866i −0.516734 + 0.856146i
\(28\) 0.102829 0.102829i 0.0194328 0.0194328i
\(29\) 2.40803 0.447160 0.223580 0.974686i \(-0.428226\pi\)
0.223580 + 0.974686i \(0.428226\pi\)
\(30\) 1.75147 + 3.45433i 0.319773 + 0.630671i
\(31\) 3.69470 0.663588 0.331794 0.943352i \(-0.392346\pi\)
0.331794 + 0.943352i \(0.392346\pi\)
\(32\) 0.707107 0.707107i 0.125000 0.125000i
\(33\) −3.56432 9.99383i −0.620468 1.73970i
\(34\) 3.29927i 0.565820i
\(35\) −0.322567 + 0.0410804i −0.0545238 + 0.00694385i
\(36\) −1.89843 2.32292i −0.316405 0.387154i
\(37\) −3.66137 3.66137i −0.601926 0.601926i 0.338897 0.940823i \(-0.389946\pi\)
−0.940823 + 0.338897i \(0.889946\pi\)
\(38\) 0.707107 + 0.707107i 0.114708 + 0.114708i
\(39\) 0.791694 1.66947i 0.126773 0.267330i
\(40\) −2.21815 + 0.282491i −0.350721 + 0.0446658i
\(41\) 10.3063i 1.60958i −0.593561 0.804789i \(-0.702278\pi\)
0.593561 0.804789i \(-0.297722\pi\)
\(42\) 0.237241 0.0846123i 0.0366070 0.0130560i
\(43\) −0.994803 + 0.994803i −0.151706 + 0.151706i −0.778880 0.627174i \(-0.784212\pi\)
0.627174 + 0.778880i \(0.284212\pi\)
\(44\) 6.12593 0.923519
\(45\) 0.177416 + 6.70586i 0.0264475 + 0.999650i
\(46\) 8.78832 1.29577
\(47\) −4.88564 + 4.88564i −0.712645 + 0.712645i −0.967088 0.254443i \(-0.918108\pi\)
0.254443 + 0.967088i \(0.418108\pi\)
\(48\) 1.63140 0.581841i 0.235472 0.0839815i
\(49\) 6.97885i 0.996979i
\(50\) 4.30884 + 2.53652i 0.609361 + 0.358718i
\(51\) 2.44855 5.16335i 0.342866 0.723014i
\(52\) 0.754312 + 0.754312i 0.104604 + 0.104604i
\(53\) 2.86461 + 2.86461i 0.393484 + 0.393484i 0.875927 0.482443i \(-0.160251\pi\)
−0.482443 + 0.875927i \(0.660251\pi\)
\(54\) −1.24708 5.04428i −0.169706 0.686440i
\(55\) −10.8320 8.38468i −1.46059 1.13059i
\(56\) 0.145422i 0.0194328i
\(57\) 0.581841 + 1.63140i 0.0770667 + 0.216084i
\(58\) −1.70274 + 1.70274i −0.223580 + 0.223580i
\(59\) −7.12402 −0.927469 −0.463734 0.885974i \(-0.653491\pi\)
−0.463734 + 0.885974i \(0.653491\pi\)
\(60\) −3.68105 1.20410i −0.475222 0.155449i
\(61\) −10.3444 −1.32446 −0.662230 0.749301i \(-0.730390\pi\)
−0.662230 + 0.749301i \(0.730390\pi\)
\(62\) −2.61255 + 2.61255i −0.331794 + 0.331794i
\(63\) 0.434076 + 0.0436501i 0.0546884 + 0.00549940i
\(64\) 1.00000i 0.125000i
\(65\) −0.301350 2.36623i −0.0373779 0.293495i
\(66\) 9.58706 + 4.54636i 1.18009 + 0.559618i
\(67\) 4.37645 + 4.37645i 0.534669 + 0.534669i 0.921958 0.387289i \(-0.126589\pi\)
−0.387289 + 0.921958i \(0.626589\pi\)
\(68\) 2.33294 + 2.33294i 0.282910 + 0.282910i
\(69\) 13.7537 + 6.52225i 1.65575 + 0.785186i
\(70\) 0.199041 0.257138i 0.0237900 0.0307338i
\(71\) 0.311021i 0.0369114i 0.999830 + 0.0184557i \(0.00587497\pi\)
−0.999830 + 0.0184557i \(0.994125\pi\)
\(72\) 2.98495 + 0.300162i 0.351779 + 0.0353745i
\(73\) 0.755853 0.755853i 0.0884659 0.0884659i −0.661489 0.749955i \(-0.730075\pi\)
0.749955 + 0.661489i \(0.230075\pi\)
\(74\) 5.17797 0.601926
\(75\) 4.86084 + 7.16744i 0.561281 + 0.827625i
\(76\) −1.00000 −0.114708
\(77\) −0.629921 + 0.629921i −0.0717862 + 0.0717862i
\(78\) 0.620684 + 1.74031i 0.0702786 + 0.197051i
\(79\) 14.3107i 1.61008i 0.593218 + 0.805042i \(0.297857\pi\)
−0.593218 + 0.805042i \(0.702143\pi\)
\(80\) 1.36872 1.76822i 0.153027 0.197693i
\(81\) 1.79194 8.81981i 0.199104 0.979978i
\(82\) 7.28768 + 7.28768i 0.804789 + 0.804789i
\(83\) −11.1880 11.1880i −1.22804 1.22804i −0.964704 0.263337i \(-0.915177\pi\)
−0.263337 0.964704i \(-0.584823\pi\)
\(84\) −0.107925 + 0.227584i −0.0117755 + 0.0248315i
\(85\) −0.932016 7.31829i −0.101091 0.793780i
\(86\) 1.40686i 0.151706i
\(87\) −3.92846 + 1.40109i −0.421175 + 0.150213i
\(88\) −4.33169 + 4.33169i −0.461759 + 0.461759i
\(89\) 2.30981 0.244840 0.122420 0.992478i \(-0.460935\pi\)
0.122420 + 0.992478i \(0.460935\pi\)
\(90\) −4.86721 4.61631i −0.513049 0.486601i
\(91\) −0.155130 −0.0162620
\(92\) −6.21428 + 6.21428i −0.647883 + 0.647883i
\(93\) −6.02753 + 2.14973i −0.625026 + 0.222917i
\(94\) 6.90934i 0.712645i
\(95\) 1.76822 + 1.36872i 0.181416 + 0.140428i
\(96\) −0.742149 + 1.56500i −0.0757453 + 0.159727i
\(97\) −0.595441 0.595441i −0.0604579 0.0604579i 0.676231 0.736689i \(-0.263612\pi\)
−0.736689 + 0.676231i \(0.763612\pi\)
\(98\) 4.93479 + 4.93479i 0.498489 + 0.498489i
\(99\) 11.6296 + 14.2301i 1.16882 + 1.43018i
\(100\) −4.84040 + 1.25322i −0.484040 + 0.125322i
\(101\) 7.75006i 0.771160i −0.922674 0.385580i \(-0.874001\pi\)
0.922674 0.385580i \(-0.125999\pi\)
\(102\) 1.91965 + 5.38243i 0.190074 + 0.532940i
\(103\) −11.2131 + 11.2131i −1.10486 + 1.10486i −0.111042 + 0.993816i \(0.535419\pi\)
−0.993816 + 0.111042i \(0.964581\pi\)
\(104\) −1.06676 −0.104604
\(105\) 0.502334 0.254701i 0.0490227 0.0248563i
\(106\) −4.05117 −0.393484
\(107\) 10.9025 10.9025i 1.05399 1.05399i 0.0555308 0.998457i \(-0.482315\pi\)
0.998457 0.0555308i \(-0.0176851\pi\)
\(108\) 4.44866 + 2.68503i 0.428073 + 0.258367i
\(109\) 0.958181i 0.0917771i 0.998947 + 0.0458886i \(0.0146119\pi\)
−0.998947 + 0.0458886i \(0.985388\pi\)
\(110\) 13.5882 1.73052i 1.29559 0.164999i
\(111\) 8.10350 + 3.84282i 0.769150 + 0.364745i
\(112\) −0.102829 0.102829i −0.00971639 0.00971639i
\(113\) 4.94211 + 4.94211i 0.464915 + 0.464915i 0.900262 0.435348i \(-0.143375\pi\)
−0.435348 + 0.900262i \(0.643375\pi\)
\(114\) −1.56500 0.742149i −0.146575 0.0695087i
\(115\) 19.4938 2.48262i 1.81781 0.231506i
\(116\) 2.40803i 0.223580i
\(117\) −0.320201 + 3.18422i −0.0296026 + 0.294381i
\(118\) 5.03744 5.03744i 0.463734 0.463734i
\(119\) −0.479786 −0.0439819
\(120\) 3.45433 1.75147i 0.315335 0.159886i
\(121\) −26.5270 −2.41155
\(122\) 7.31457 7.31457i 0.662230 0.662230i
\(123\) 5.99664 + 16.8137i 0.540699 + 1.51604i
\(124\) 3.69470i 0.331794i
\(125\) 10.2742 + 4.40918i 0.918952 + 0.394369i
\(126\) −0.337803 + 0.276073i −0.0300939 + 0.0245945i
\(127\) 8.80226 + 8.80226i 0.781074 + 0.781074i 0.980012 0.198938i \(-0.0637492\pi\)
−0.198938 + 0.980012i \(0.563749\pi\)
\(128\) −0.707107 0.707107i −0.0625000 0.0625000i
\(129\) 1.04410 2.20174i 0.0919281 0.193852i
\(130\) 1.88627 + 1.46009i 0.165436 + 0.128059i
\(131\) 22.1054i 1.93136i 0.259735 + 0.965680i \(0.416365\pi\)
−0.259735 + 0.965680i \(0.583635\pi\)
\(132\) −9.99383 + 3.56432i −0.869852 + 0.310234i
\(133\) 0.102829 0.102829i 0.00891637 0.00891637i
\(134\) −6.18924 −0.534669
\(135\) −4.19118 10.8367i −0.360719 0.932674i
\(136\) −3.29927 −0.282910
\(137\) −1.58617 + 1.58617i −0.135516 + 0.135516i −0.771611 0.636095i \(-0.780549\pi\)
0.636095 + 0.771611i \(0.280549\pi\)
\(138\) −14.3373 + 5.11340i −1.22047 + 0.435282i
\(139\) 11.1773i 0.948045i 0.880513 + 0.474022i \(0.157198\pi\)
−0.880513 + 0.474022i \(0.842802\pi\)
\(140\) 0.0410804 + 0.322567i 0.00347192 + 0.0272619i
\(141\) 5.12777 10.8131i 0.431836 0.910627i
\(142\) −0.219925 0.219925i −0.0184557 0.0184557i
\(143\) −4.62086 4.62086i −0.386416 0.386416i
\(144\) −2.32292 + 1.89843i −0.193577 + 0.158202i
\(145\) −3.29592 + 4.25793i −0.273711 + 0.353602i
\(146\) 1.06894i 0.0884659i
\(147\) 4.06058 + 11.3853i 0.334911 + 0.939043i
\(148\) −3.66137 + 3.66137i −0.300963 + 0.300963i
\(149\) −9.86195 −0.807922 −0.403961 0.914776i \(-0.632367\pi\)
−0.403961 + 0.914776i \(0.632367\pi\)
\(150\) −8.50528 1.63102i −0.694453 0.133172i
\(151\) −7.90117 −0.642988 −0.321494 0.946912i \(-0.604185\pi\)
−0.321494 + 0.946912i \(0.604185\pi\)
\(152\) 0.707107 0.707107i 0.0573539 0.0573539i
\(153\) −0.990317 + 9.84815i −0.0800624 + 0.796176i
\(154\) 0.890843i 0.0717862i
\(155\) −5.05701 + 6.53306i −0.406189 + 0.524748i
\(156\) −1.66947 0.791694i −0.133665 0.0633863i
\(157\) 3.96376 + 3.96376i 0.316342 + 0.316342i 0.847360 0.531018i \(-0.178190\pi\)
−0.531018 + 0.847360i \(0.678190\pi\)
\(158\) −10.1192 10.1192i −0.805042 0.805042i
\(159\) −6.34006 3.00657i −0.502800 0.238437i
\(160\) 0.282491 + 2.21815i 0.0223329 + 0.175360i
\(161\) 1.27801i 0.100721i
\(162\) 4.96945 + 7.50363i 0.390437 + 0.589541i
\(163\) 6.35109 6.35109i 0.497456 0.497456i −0.413189 0.910645i \(-0.635585\pi\)
0.910645 + 0.413189i \(0.135585\pi\)
\(164\) −10.3063 −0.804789
\(165\) 22.5499 + 7.37625i 1.75550 + 0.574240i
\(166\) 15.8222 1.22804
\(167\) −14.9173 + 14.9173i −1.15434 + 1.15434i −0.168664 + 0.985674i \(0.553945\pi\)
−0.985674 + 0.168664i \(0.946055\pi\)
\(168\) −0.0846123 0.237241i −0.00652798 0.0183035i
\(169\) 11.8620i 0.912464i
\(170\) 5.83385 + 4.51578i 0.447435 + 0.346344i
\(171\) −1.89843 2.32292i −0.145176 0.177638i
\(172\) 0.994803 + 0.994803i 0.0758530 + 0.0758530i
\(173\) −6.19199 6.19199i −0.470769 0.470769i 0.431395 0.902163i \(-0.358022\pi\)
−0.902163 + 0.431395i \(0.858022\pi\)
\(174\) 1.78712 3.76856i 0.135481 0.285694i
\(175\) 0.368865 0.626598i 0.0278836 0.0473664i
\(176\) 6.12593i 0.461759i
\(177\) 11.6221 4.14505i 0.873572 0.311561i
\(178\) −1.63328 + 1.63328i −0.122420 + 0.122420i
\(179\) 8.96071 0.669755 0.334877 0.942262i \(-0.391305\pi\)
0.334877 + 0.942262i \(0.391305\pi\)
\(180\) 6.70586 0.177416i 0.499825 0.0132238i
\(181\) 8.58326 0.637989 0.318994 0.947757i \(-0.396655\pi\)
0.318994 + 0.947757i \(0.396655\pi\)
\(182\) 0.109693 0.109693i 0.00813101 0.00813101i
\(183\) 16.8758 6.01877i 1.24749 0.444920i
\(184\) 8.78832i 0.647883i
\(185\) 11.4855 1.46273i 0.844432 0.107542i
\(186\) 2.74202 5.78220i 0.201055 0.423971i
\(187\) −14.2914 14.2914i −1.04509 1.04509i
\(188\) 4.88564 + 4.88564i 0.356322 + 0.356322i
\(189\) −0.733548 + 0.181352i −0.0533578 + 0.0131914i
\(190\) −2.21815 + 0.282491i −0.160922 + 0.0204941i
\(191\) 15.3727i 1.11233i −0.831073 0.556164i \(-0.812273\pi\)
0.831073 0.556164i \(-0.187727\pi\)
\(192\) −0.581841 1.63140i −0.0419907 0.117736i
\(193\) 16.5440 16.5440i 1.19087 1.19087i 0.214042 0.976824i \(-0.431337\pi\)
0.976824 0.214042i \(-0.0686629\pi\)
\(194\) 0.842081 0.0604579
\(195\) 1.86839 + 3.68493i 0.133798 + 0.263883i
\(196\) −6.97885 −0.498489
\(197\) −3.02772 + 3.02772i −0.215716 + 0.215716i −0.806690 0.590974i \(-0.798743\pi\)
0.590974 + 0.806690i \(0.298743\pi\)
\(198\) −18.2856 1.83877i −1.29950 0.130676i
\(199\) 8.01713i 0.568319i −0.958777 0.284160i \(-0.908285\pi\)
0.958777 0.284160i \(-0.0917146\pi\)
\(200\) 2.53652 4.30884i 0.179359 0.304681i
\(201\) −9.68614 4.59334i −0.683208 0.323989i
\(202\) 5.48012 + 5.48012i 0.385580 + 0.385580i
\(203\) 0.247615 + 0.247615i 0.0173791 + 0.0173791i
\(204\) −5.16335 2.44855i −0.361507 0.171433i
\(205\) 18.2239 + 14.1065i 1.27281 + 0.985238i
\(206\) 15.8577i 1.10486i
\(207\) −26.2327 2.63792i −1.82330 0.183348i
\(208\) 0.754312 0.754312i 0.0523021 0.0523021i
\(209\) 6.12593 0.423740
\(210\) −0.175103 + 0.535304i −0.0120832 + 0.0369395i
\(211\) −4.50891 −0.310406 −0.155203 0.987883i \(-0.549603\pi\)
−0.155203 + 0.987883i \(0.549603\pi\)
\(212\) 2.86461 2.86461i 0.196742 0.196742i
\(213\) −0.180965 0.507400i −0.0123995 0.0347664i
\(214\) 15.4185i 1.05399i
\(215\) −0.397427 3.12064i −0.0271043 0.212826i
\(216\) −5.04428 + 1.24708i −0.343220 + 0.0848530i
\(217\) 0.379921 + 0.379921i 0.0257907 + 0.0257907i
\(218\) −0.677536 0.677536i −0.0458886 0.0458886i
\(219\) −0.793312 + 1.67288i −0.0536070 + 0.113043i
\(220\) −8.38468 + 10.8320i −0.565295 + 0.730294i
\(221\) 3.51953i 0.236749i
\(222\) −8.44733 + 3.01275i −0.566947 + 0.202203i
\(223\) 8.46796 8.46796i 0.567057 0.567057i −0.364246 0.931303i \(-0.618673\pi\)
0.931303 + 0.364246i \(0.118673\pi\)
\(224\) 0.145422 0.00971639
\(225\) −12.1003 8.86472i −0.806685 0.590982i
\(226\) −6.98920 −0.464915
\(227\) −6.20188 + 6.20188i −0.411633 + 0.411633i −0.882307 0.470674i \(-0.844011\pi\)
0.470674 + 0.882307i \(0.344011\pi\)
\(228\) 1.63140 0.581841i 0.108042 0.0385334i
\(229\) 11.8117i 0.780536i −0.920701 0.390268i \(-0.872382\pi\)
0.920701 0.390268i \(-0.127618\pi\)
\(230\) −12.0287 + 15.5397i −0.793151 + 1.02466i
\(231\) 0.661138 1.39417i 0.0434997 0.0917294i
\(232\) 1.70274 + 1.70274i 0.111790 + 0.111790i
\(233\) −10.5412 10.5412i −0.690575 0.690575i 0.271783 0.962358i \(-0.412387\pi\)
−0.962358 + 0.271783i \(0.912387\pi\)
\(234\) −2.02517 2.47800i −0.132389 0.161992i
\(235\) −1.95183 15.3260i −0.127323 0.999757i
\(236\) 7.12402i 0.463734i
\(237\) −8.32658 23.3465i −0.540869 1.51652i
\(238\) 0.339260 0.339260i 0.0219909 0.0219909i
\(239\) −6.27313 −0.405775 −0.202887 0.979202i \(-0.565033\pi\)
−0.202887 + 0.979202i \(0.565033\pi\)
\(240\) −1.20410 + 3.68105i −0.0777245 + 0.237611i
\(241\) 13.3425 0.859466 0.429733 0.902956i \(-0.358608\pi\)
0.429733 + 0.902956i \(0.358608\pi\)
\(242\) 18.7574 18.7574i 1.20577 1.20577i
\(243\) 2.20836 + 15.4312i 0.141666 + 0.989914i
\(244\) 10.3444i 0.662230i
\(245\) 12.3402 + 9.55209i 0.788384 + 0.610260i
\(246\) −16.1294 7.64884i −1.02837 0.487672i
\(247\) 0.754312 + 0.754312i 0.0479957 + 0.0479957i
\(248\) 2.61255 + 2.61255i 0.165897 + 0.165897i
\(249\) 24.7617 + 11.7424i 1.56921 + 0.744146i
\(250\) −10.3827 + 4.14720i −0.656661 + 0.262292i
\(251\) 26.7821i 1.69047i 0.534392 + 0.845237i \(0.320541\pi\)
−0.534392 + 0.845237i \(0.679459\pi\)
\(252\) 0.0436501 0.434076i 0.00274970 0.0273442i
\(253\) 38.0682 38.0682i 2.39333 2.39333i
\(254\) −12.4483 −0.781074
\(255\) 5.77857 + 11.3968i 0.361868 + 0.713693i
\(256\) 1.00000 0.0625000
\(257\) −6.20250 + 6.20250i −0.386901 + 0.386901i −0.873581 0.486679i \(-0.838208\pi\)
0.486679 + 0.873581i \(0.338208\pi\)
\(258\) 0.818571 + 2.29516i 0.0509620 + 0.142890i
\(259\) 0.752988i 0.0467884i
\(260\) −2.36623 + 0.301350i −0.146748 + 0.0186889i
\(261\) 5.59367 4.57148i 0.346239 0.282967i
\(262\) −15.6309 15.6309i −0.965680 0.965680i
\(263\) −10.7076 10.7076i −0.660261 0.660261i 0.295181 0.955442i \(-0.404620\pi\)
−0.955442 + 0.295181i \(0.904620\pi\)
\(264\) 4.54636 9.58706i 0.279809 0.590043i
\(265\) −8.98610 + 1.14442i −0.552012 + 0.0703011i
\(266\) 0.145422i 0.00891637i
\(267\) −3.76823 + 1.34394i −0.230612 + 0.0822480i
\(268\) 4.37645 4.37645i 0.267335 0.267335i
\(269\) −7.39882 −0.451114 −0.225557 0.974230i \(-0.572420\pi\)
−0.225557 + 0.974230i \(0.572420\pi\)
\(270\) 10.6263 + 4.69909i 0.646697 + 0.285978i
\(271\) −32.2520 −1.95917 −0.979585 0.201030i \(-0.935571\pi\)
−0.979585 + 0.201030i \(0.935571\pi\)
\(272\) 2.33294 2.33294i 0.141455 0.141455i
\(273\) 0.253078 0.0902608i 0.0153170 0.00546283i
\(274\) 2.24319i 0.135516i
\(275\) 29.6519 7.67712i 1.78808 0.462948i
\(276\) 6.52225 13.7537i 0.392593 0.827875i
\(277\) 0.315711 + 0.315711i 0.0189693 + 0.0189693i 0.716528 0.697559i \(-0.245730\pi\)
−0.697559 + 0.716528i \(0.745730\pi\)
\(278\) −7.90353 7.90353i −0.474022 0.474022i
\(279\) 8.58251 7.01413i 0.513821 0.419925i
\(280\) −0.257138 0.199041i −0.0153669 0.0118950i
\(281\) 2.25919i 0.134772i 0.997727 + 0.0673860i \(0.0214659\pi\)
−0.997727 + 0.0673860i \(0.978534\pi\)
\(282\) 4.02014 + 11.2719i 0.239396 + 0.671232i
\(283\) −17.3455 + 17.3455i −1.03109 + 1.03109i −0.0315844 + 0.999501i \(0.510055\pi\)
−0.999501 + 0.0315844i \(0.989945\pi\)
\(284\) 0.311021 0.0184557
\(285\) −3.68105 1.20410i −0.218047 0.0713249i
\(286\) 6.53489 0.386416
\(287\) 1.05979 1.05979i 0.0625572 0.0625572i
\(288\) 0.300162 2.98495i 0.0176872 0.175890i
\(289\) 6.11480i 0.359694i
\(290\) −0.680248 5.34138i −0.0399455 0.313657i
\(291\) 1.31785 + 0.624950i 0.0772539 + 0.0366352i
\(292\) −0.755853 0.755853i −0.0442330 0.0442330i
\(293\) 1.37475 + 1.37475i 0.0803135 + 0.0803135i 0.746122 0.665809i \(-0.231913\pi\)
−0.665809 + 0.746122i \(0.731913\pi\)
\(294\) −10.9219 5.17935i −0.636977 0.302066i
\(295\) 9.75078 12.5969i 0.567712 0.733417i
\(296\) 5.17797i 0.300963i
\(297\) −27.2522 16.4483i −1.58133 0.954427i
\(298\) 6.97345 6.97345i 0.403961 0.403961i
\(299\) 9.37501 0.542171
\(300\) 7.16744 4.86084i 0.413813 0.280641i
\(301\) −0.204588 −0.0117923
\(302\) 5.58697 5.58697i 0.321494 0.321494i
\(303\) 4.50930 + 12.6434i 0.259053 + 0.726346i
\(304\) 1.00000i 0.0573539i
\(305\) 14.1585 18.2911i 0.810715 1.04735i
\(306\) −6.26343 7.66395i −0.358057 0.438119i
\(307\) 2.48065 + 2.48065i 0.141578 + 0.141578i 0.774343 0.632765i \(-0.218080\pi\)
−0.632765 + 0.774343i \(0.718080\pi\)
\(308\) 0.629921 + 0.629921i 0.0358931 + 0.0358931i
\(309\) 11.7688 24.8172i 0.669502 1.41180i
\(310\) −1.04372 8.19542i −0.0592794 0.465468i
\(311\) 1.76203i 0.0999158i −0.998751 0.0499579i \(-0.984091\pi\)
0.998751 0.0499579i \(-0.0159087\pi\)
\(312\) 1.74031 0.620684i 0.0985256 0.0351393i
\(313\) −9.58013 + 9.58013i −0.541501 + 0.541501i −0.923969 0.382468i \(-0.875074\pi\)
0.382468 + 0.923969i \(0.375074\pi\)
\(314\) −5.60560 −0.316342
\(315\) −0.671311 + 0.707798i −0.0378241 + 0.0398799i
\(316\) 14.3107 0.805042
\(317\) 7.82453 7.82453i 0.439469 0.439469i −0.452364 0.891833i \(-0.649419\pi\)
0.891833 + 0.452364i \(0.149419\pi\)
\(318\) 6.60907 2.35713i 0.370618 0.132182i
\(319\) 14.7514i 0.825922i
\(320\) −1.76822 1.36872i −0.0988466 0.0765137i
\(321\) −11.4428 + 24.1299i −0.638677 + 1.34680i
\(322\) 0.903691 + 0.903691i 0.0503607 + 0.0503607i
\(323\) 2.33294 + 2.33294i 0.129808 + 0.129808i
\(324\) −8.81981 1.79194i −0.489989 0.0995521i
\(325\) 4.59649 + 2.70585i 0.254967 + 0.150094i
\(326\) 8.98180i 0.497456i
\(327\) −0.557509 1.56318i −0.0308303 0.0864438i
\(328\) 7.28768 7.28768i 0.402395 0.402395i
\(329\) −1.00477 −0.0553947
\(330\) −21.1610 + 10.7294i −1.16487 + 0.590632i
\(331\) −10.1328 −0.556947 −0.278473 0.960444i \(-0.589828\pi\)
−0.278473 + 0.960444i \(0.589828\pi\)
\(332\) −11.1880 + 11.1880i −0.614020 + 0.614020i
\(333\) −15.4559 1.55423i −0.846981 0.0851713i
\(334\) 21.0963i 1.15434i
\(335\) −13.7287 + 1.74841i −0.750078 + 0.0955257i
\(336\) 0.227584 + 0.107925i 0.0124157 + 0.00588777i
\(337\) 8.59971 + 8.59971i 0.468456 + 0.468456i 0.901414 0.432958i \(-0.142530\pi\)
−0.432958 + 0.901414i \(0.642530\pi\)
\(338\) −8.38772 8.38772i −0.456232 0.456232i
\(339\) −10.9381 5.18703i −0.594075 0.281721i
\(340\) −7.31829 + 0.932016i −0.396890 + 0.0505457i
\(341\) 22.6335i 1.22567i
\(342\) 2.98495 + 0.300162i 0.161407 + 0.0162309i
\(343\) 1.43743 1.43743i 0.0776137 0.0776137i
\(344\) −1.40686 −0.0758530
\(345\) −30.3577 + 15.3925i −1.63440 + 0.828702i
\(346\) 8.75680 0.470769
\(347\) 7.91015 7.91015i 0.424639 0.424639i −0.462158 0.886797i \(-0.652925\pi\)
0.886797 + 0.462158i \(0.152925\pi\)
\(348\) 1.40109 + 3.92846i 0.0751064 + 0.210587i
\(349\) 18.5835i 0.994752i 0.867535 + 0.497376i \(0.165703\pi\)
−0.867535 + 0.497376i \(0.834297\pi\)
\(350\) 0.182245 + 0.703899i 0.00974140 + 0.0376250i
\(351\) −1.33033 5.38103i −0.0710079 0.287218i
\(352\) 4.33169 + 4.33169i 0.230880 + 0.230880i
\(353\) −3.74671 3.74671i −0.199417 0.199417i 0.600333 0.799750i \(-0.295035\pi\)
−0.799750 + 0.600333i \(0.795035\pi\)
\(354\) −5.28709 + 11.1491i −0.281006 + 0.592566i
\(355\) −0.549955 0.425701i −0.0291886 0.0225938i
\(356\) 2.30981i 0.122420i
\(357\) 0.782721 0.279159i 0.0414260 0.0147747i
\(358\) −6.33618 + 6.33618i −0.334877 + 0.334877i
\(359\) −17.1601 −0.905676 −0.452838 0.891593i \(-0.649588\pi\)
−0.452838 + 0.891593i \(0.649588\pi\)
\(360\) −4.61631 + 4.86721i −0.243301 + 0.256524i
\(361\) −1.00000 −0.0526316
\(362\) −6.06928 + 6.06928i −0.318994 + 0.318994i
\(363\) 43.2762 15.4345i 2.27141 0.810102i
\(364\) 0.155130i 0.00813101i
\(365\) 0.301966 + 2.37107i 0.0158056 + 0.124107i
\(366\) −7.67706 + 16.1889i −0.401286 + 0.846207i
\(367\) 24.6532 + 24.6532i 1.28689 + 1.28689i 0.936668 + 0.350218i \(0.113892\pi\)
0.350218 + 0.936668i \(0.386108\pi\)
\(368\) 6.21428 + 6.21428i 0.323942 + 0.323942i
\(369\) −19.5658 23.9408i −1.01856 1.24631i
\(370\) −7.08718 + 9.15579i −0.368445 + 0.475987i
\(371\) 0.589127i 0.0305860i
\(372\) 2.14973 + 6.02753i 0.111458 + 0.312513i
\(373\) −10.9785 + 10.9785i −0.568446 + 0.568446i −0.931693 0.363247i \(-0.881668\pi\)
0.363247 + 0.931693i \(0.381668\pi\)
\(374\) 20.2111 1.04509
\(375\) −19.3268 1.21517i −0.998029 0.0627514i
\(376\) −6.90934 −0.356322
\(377\) −1.81641 + 1.81641i −0.0935497 + 0.0935497i
\(378\) 0.390461 0.646932i 0.0200832 0.0332746i
\(379\) 31.8871i 1.63793i −0.573843 0.818966i \(-0.694548\pi\)
0.573843 0.818966i \(-0.305452\pi\)
\(380\) 1.36872 1.76822i 0.0702138 0.0907079i
\(381\) −19.4815 9.23848i −0.998068 0.473302i
\(382\) 10.8701 + 10.8701i 0.556164 + 0.556164i
\(383\) −3.71847 3.71847i −0.190005 0.190005i 0.605693 0.795698i \(-0.292896\pi\)
−0.795698 + 0.605693i \(0.792896\pi\)
\(384\) 1.56500 + 0.742149i 0.0798634 + 0.0378727i
\(385\) −0.251655 1.97603i −0.0128255 0.100708i
\(386\) 23.3968i 1.19087i
\(387\) −0.422288 + 4.19941i −0.0214661 + 0.213468i
\(388\) −0.595441 + 0.595441i −0.0302289 + 0.0302289i
\(389\) −27.6876 −1.40382 −0.701908 0.712268i \(-0.747668\pi\)
−0.701908 + 0.712268i \(0.747668\pi\)
\(390\) −3.92679 1.28449i −0.198841 0.0650425i
\(391\) 28.9951 1.46634
\(392\) 4.93479 4.93479i 0.249245 0.249245i
\(393\) −12.8618 36.0628i −0.648794 1.81913i
\(394\) 4.28184i 0.215716i
\(395\) −25.3046 19.5874i −1.27321 0.985548i
\(396\) 14.2301 11.6296i 0.715088 0.584412i
\(397\) −0.647982 0.647982i −0.0325213 0.0325213i 0.690659 0.723180i \(-0.257321\pi\)
−0.723180 + 0.690659i \(0.757321\pi\)
\(398\) 5.66897 + 5.66897i 0.284160 + 0.284160i
\(399\) −0.107925 + 0.227584i −0.00540299 + 0.0113935i
\(400\) 1.25322 + 4.84040i 0.0626609 + 0.242020i
\(401\) 28.9315i 1.44477i 0.691491 + 0.722385i \(0.256954\pi\)
−0.691491 + 0.722385i \(0.743046\pi\)
\(402\) 10.0971 3.60115i 0.503599 0.179609i
\(403\) −2.78696 + 2.78696i −0.138828 + 0.138828i
\(404\) −7.75006 −0.385580
\(405\) 13.1427 + 15.2404i 0.653067 + 0.757300i
\(406\) −0.350180 −0.0173791
\(407\) 22.4293 22.4293i 1.11178 1.11178i
\(408\) 5.38243 1.91965i 0.266470 0.0950369i
\(409\) 15.5261i 0.767717i −0.923392 0.383859i \(-0.874595\pi\)
0.923392 0.383859i \(-0.125405\pi\)
\(410\) −22.8610 + 2.91145i −1.12902 + 0.143786i
\(411\) 1.66478 3.51058i 0.0821176 0.173164i
\(412\) 11.2131 + 11.2131i 0.552429 + 0.552429i
\(413\) −0.732553 0.732553i −0.0360466 0.0360466i
\(414\) 20.4146 16.6840i 1.00332 0.819974i
\(415\) 35.0960 4.46963i 1.72280 0.219406i
\(416\) 1.06676i 0.0523021i
\(417\) −6.50340 18.2346i −0.318473 0.892953i
\(418\) −4.33169 + 4.33169i −0.211870 + 0.211870i
\(419\) −6.96160 −0.340096 −0.170048 0.985436i \(-0.554392\pi\)
−0.170048 + 0.985436i \(0.554392\pi\)
\(420\) −0.254701 0.502334i −0.0124281 0.0245114i
\(421\) −29.4232 −1.43400 −0.717000 0.697073i \(-0.754485\pi\)
−0.717000 + 0.697073i \(0.754485\pi\)
\(422\) 3.18828 3.18828i 0.155203 0.155203i
\(423\) −2.07393 + 20.6240i −0.100838 + 1.00277i
\(424\) 4.05117i 0.196742i
\(425\) 14.2160 + 8.36867i 0.689578 + 0.405940i
\(426\) 0.486747 + 0.230824i 0.0235830 + 0.0111835i
\(427\) −1.06370 1.06370i −0.0514759 0.0514759i
\(428\) −10.9025 10.9025i −0.526994 0.526994i
\(429\) 10.2271 + 4.84986i 0.493768 + 0.234154i
\(430\) 2.48765 + 1.92560i 0.119965 + 0.0928607i
\(431\) 19.6775i 0.947834i −0.880570 0.473917i \(-0.842840\pi\)
0.880570 0.473917i \(-0.157160\pi\)
\(432\) 2.68503 4.44866i 0.129184 0.214036i
\(433\) −22.2656 + 22.2656i −1.07002 + 1.07002i −0.0726615 + 0.997357i \(0.523149\pi\)
−0.997357 + 0.0726615i \(0.976851\pi\)
\(434\) −0.537290 −0.0257907
\(435\) 2.89952 8.86409i 0.139021 0.425000i
\(436\) 0.958181 0.0458886
\(437\) −6.21428 + 6.21428i −0.297269 + 0.297269i
\(438\) −0.621952 1.74386i −0.0297180 0.0833250i
\(439\) 1.96512i 0.0937899i 0.998900 + 0.0468950i \(0.0149326\pi\)
−0.998900 + 0.0468950i \(0.985067\pi\)
\(440\) −1.73052 13.5882i −0.0824994 0.647794i
\(441\) −13.2489 16.2113i −0.630898 0.771968i
\(442\) 2.48868 + 2.48868i 0.118374 + 0.118374i
\(443\) 10.2690 + 10.2690i 0.487896 + 0.487896i 0.907642 0.419746i \(-0.137881\pi\)
−0.419746 + 0.907642i \(0.637881\pi\)
\(444\) 3.84282 8.10350i 0.182372 0.384575i
\(445\) −3.16148 + 4.08426i −0.149869 + 0.193613i
\(446\) 11.9755i 0.567057i
\(447\) 16.0888 5.73809i 0.760973 0.271402i
\(448\) −0.102829 + 0.102829i −0.00485820 + 0.00485820i
\(449\) 28.7172 1.35525 0.677623 0.735409i \(-0.263010\pi\)
0.677623 + 0.735409i \(0.263010\pi\)
\(450\) 14.8245 2.28788i 0.698833 0.107852i
\(451\) 63.1359 2.97295
\(452\) 4.94211 4.94211i 0.232457 0.232457i
\(453\) 12.8900 4.59722i 0.605623 0.215996i
\(454\) 8.77078i 0.411633i
\(455\) 0.212329 0.274304i 0.00995414 0.0128596i
\(456\) −0.742149 + 1.56500i −0.0347543 + 0.0732877i
\(457\) 13.0668 + 13.0668i 0.611239 + 0.611239i 0.943269 0.332030i \(-0.107733\pi\)
−0.332030 + 0.943269i \(0.607733\pi\)
\(458\) 8.35210 + 8.35210i 0.390268 + 0.390268i
\(459\) −4.11445 16.6425i −0.192046 0.776804i
\(460\) −2.48262 19.4938i −0.115753 0.908904i
\(461\) 35.6982i 1.66263i 0.555800 + 0.831316i \(0.312412\pi\)
−0.555800 + 0.831316i \(0.687588\pi\)
\(462\) 0.518329 + 1.45332i 0.0241148 + 0.0676146i
\(463\) −18.7714 + 18.7714i −0.872381 + 0.872381i −0.992731 0.120350i \(-0.961598\pi\)
0.120350 + 0.992731i \(0.461598\pi\)
\(464\) −2.40803 −0.111790
\(465\) 4.44880 13.6004i 0.206308 0.630703i
\(466\) 14.9075 0.690575
\(467\) −5.01672 + 5.01672i −0.232146 + 0.232146i −0.813588 0.581442i \(-0.802489\pi\)
0.581442 + 0.813588i \(0.302489\pi\)
\(468\) 3.18422 + 0.320201i 0.147190 + 0.0148013i
\(469\) 0.900050i 0.0415604i
\(470\) 12.2173 + 9.45695i 0.563540 + 0.436217i
\(471\) −8.77274 4.16019i −0.404227 0.191692i
\(472\) −5.03744 5.03744i −0.231867 0.231867i
\(473\) −6.09409 6.09409i −0.280207 0.280207i
\(474\) 22.3963 + 10.6207i 1.02869 + 0.487825i
\(475\) −4.84040 + 1.25322i −0.222093 + 0.0575016i
\(476\) 0.479786i 0.0219909i
\(477\) 12.0925 + 1.21601i 0.553678 + 0.0556772i
\(478\) 4.43577 4.43577i 0.202887 0.202887i
\(479\) 6.25041 0.285589 0.142794 0.989752i \(-0.454391\pi\)
0.142794 + 0.989752i \(0.454391\pi\)
\(480\) −1.75147 3.45433i −0.0799432 0.157668i
\(481\) 5.52364 0.251856
\(482\) −9.43457 + 9.43457i −0.429733 + 0.429733i
\(483\) 0.743599 + 2.08495i 0.0338349 + 0.0948683i
\(484\) 26.5270i 1.20577i
\(485\) 1.86786 0.237880i 0.0848153 0.0108016i
\(486\) −12.4731 9.34999i −0.565790 0.424124i
\(487\) −11.4086 11.4086i −0.516973 0.516973i 0.399681 0.916654i \(-0.369121\pi\)
−0.916654 + 0.399681i \(0.869121\pi\)
\(488\) −7.31457 7.31457i −0.331115 0.331115i
\(489\) −6.66584 + 14.0565i −0.301439 + 0.635656i
\(490\) −15.4802 + 1.97147i −0.699322 + 0.0890617i
\(491\) 10.2744i 0.463675i 0.972754 + 0.231838i \(0.0744738\pi\)
−0.972754 + 0.231838i \(0.925526\pi\)
\(492\) 16.8137 5.99664i 0.758022 0.270350i
\(493\) −5.61779 + 5.61779i −0.253012 + 0.253012i
\(494\) −1.06676 −0.0479957
\(495\) −41.0796 + 1.08684i −1.84639 + 0.0488496i
\(496\) −3.69470 −0.165897
\(497\) −0.0319819 + 0.0319819i −0.00143458 + 0.00143458i
\(498\) −25.8123 + 9.20600i −1.15668 + 0.412531i
\(499\) 26.3326i 1.17881i 0.807839 + 0.589404i \(0.200637\pi\)
−0.807839 + 0.589404i \(0.799363\pi\)
\(500\) 4.40918 10.2742i 0.197184 0.459476i
\(501\) 15.6566 33.0156i 0.699485 1.47503i
\(502\) −18.9378 18.9378i −0.845237 0.845237i
\(503\) 18.5070 + 18.5070i 0.825188 + 0.825188i 0.986847 0.161658i \(-0.0516843\pi\)
−0.161658 + 0.986847i \(0.551684\pi\)
\(504\) 0.276073 + 0.337803i 0.0122973 + 0.0150469i
\(505\) 13.7038 + 10.6077i 0.609812 + 0.472034i
\(506\) 53.8366i 2.39333i
\(507\) −6.90181 19.3517i −0.306520 0.859439i
\(508\) 8.80226 8.80226i 0.390537 0.390537i
\(509\) −40.9795 −1.81638 −0.908191 0.418555i \(-0.862537\pi\)
−0.908191 + 0.418555i \(0.862537\pi\)
\(510\) −12.1448 3.97266i −0.537780 0.175912i
\(511\) 0.155447 0.00687656
\(512\) −0.707107 + 0.707107i −0.0312500 + 0.0312500i
\(513\) 4.44866 + 2.68503i 0.196413 + 0.118547i
\(514\) 8.77166i 0.386901i
\(515\) −4.47966 35.1748i −0.197397 1.54999i
\(516\) −2.20174 1.04410i −0.0969261 0.0459641i
\(517\) −29.9291 29.9291i −1.31628 1.31628i
\(518\) 0.532443 + 0.532443i 0.0233942 + 0.0233942i
\(519\) 13.7044 + 6.49886i 0.601555 + 0.285268i
\(520\) 1.46009 1.88627i 0.0640293 0.0827182i
\(521\) 26.2549i 1.15025i 0.818066 + 0.575125i \(0.195046\pi\)
−0.818066 + 0.575125i \(0.804954\pi\)
\(522\) −0.722800 + 7.18784i −0.0316361 + 0.314603i
\(523\) 12.9426 12.9426i 0.565942 0.565942i −0.365047 0.930989i \(-0.618947\pi\)
0.930989 + 0.365047i \(0.118947\pi\)
\(524\) 22.1054 0.965680
\(525\) −0.237185 + 1.23685i −0.0103516 + 0.0539806i
\(526\) 15.1429 0.660261
\(527\) −8.61951 + 8.61951i −0.375472 + 0.375472i
\(528\) 3.56432 + 9.99383i 0.155117 + 0.434926i
\(529\) 54.2345i 2.35802i
\(530\) 5.54491 7.16336i 0.240855 0.311156i
\(531\) −16.5485 + 13.5244i −0.718146 + 0.586911i
\(532\) −0.102829 0.102829i −0.00445819 0.00445819i
\(533\) 7.77419 + 7.77419i 0.336738 + 0.336738i
\(534\) 1.71423 3.61485i 0.0741818 0.156430i
\(535\) 4.35560 + 34.2006i 0.188309 + 1.47862i
\(536\) 6.18924i 0.267335i
\(537\) −14.6185 + 5.21371i −0.630834 + 0.224988i
\(538\) 5.23176 5.23176i 0.225557 0.225557i
\(539\) 42.7520 1.84146
\(540\) −10.8367 + 4.19118i −0.466337 + 0.180360i
\(541\) 17.1469 0.737202 0.368601 0.929588i \(-0.379837\pi\)
0.368601 + 0.929588i \(0.379837\pi\)
\(542\) 22.8056 22.8056i 0.979585 0.979585i
\(543\) −14.0027 + 4.99409i −0.600914 + 0.214317i
\(544\) 3.29927i 0.141455i
\(545\) −1.69428 1.31148i −0.0725749 0.0561777i
\(546\) −0.115129 + 0.242778i −0.00492709 + 0.0103899i
\(547\) 0.690907 + 0.690907i 0.0295410 + 0.0295410i 0.721723 0.692182i \(-0.243350\pi\)
−0.692182 + 0.721723i \(0.743350\pi\)
\(548\) 1.58617 + 1.58617i 0.0677580 + 0.0677580i
\(549\) −24.0292 + 19.6380i −1.02554 + 0.838131i
\(550\) −15.5385 + 26.3956i −0.662566 + 1.12551i
\(551\) 2.40803i 0.102586i
\(552\) 5.11340 + 14.3373i 0.217641 + 0.610234i
\(553\) −1.47155 + 1.47155i −0.0625768 + 0.0625768i
\(554\) −0.446483 −0.0189693
\(555\) −17.8864 + 9.06904i −0.759234 + 0.384959i
\(556\) 11.1773 0.474022
\(557\) −17.1913 + 17.1913i −0.728419 + 0.728419i −0.970305 0.241886i \(-0.922234\pi\)
0.241886 + 0.970305i \(0.422234\pi\)
\(558\) −1.10901 + 11.0285i −0.0469482 + 0.466873i
\(559\) 1.50078i 0.0634764i
\(560\) 0.322567 0.0410804i 0.0136310 0.00173596i
\(561\) 31.6303 + 14.9997i 1.33543 + 0.633286i
\(562\) −1.59749 1.59749i −0.0673860 0.0673860i
\(563\) 14.9893 + 14.9893i 0.631723 + 0.631723i 0.948500 0.316777i \(-0.102601\pi\)
−0.316777 + 0.948500i \(0.602601\pi\)
\(564\) −10.8131 5.12777i −0.455314 0.215918i
\(565\) −15.5031 + 1.97439i −0.652221 + 0.0830632i
\(566\) 24.5303i 1.03109i
\(567\) 1.09119 0.722666i 0.0458257 0.0303491i
\(568\) −0.219925 + 0.219925i −0.00922786 + 0.00922786i
\(569\) 35.8239 1.50181 0.750907 0.660408i \(-0.229617\pi\)
0.750907 + 0.660408i \(0.229617\pi\)
\(570\) 3.45433 1.75147i 0.144686 0.0733609i
\(571\) −5.53111 −0.231470 −0.115735 0.993280i \(-0.536922\pi\)
−0.115735 + 0.993280i \(0.536922\pi\)
\(572\) −4.62086 + 4.62086i −0.193208 + 0.193208i
\(573\) 8.94445 + 25.0790i 0.373660 + 1.04769i
\(574\) 1.49876i 0.0625572i
\(575\) −22.2917 + 37.8674i −0.929630 + 1.57918i
\(576\) 1.89843 + 2.32292i 0.0791012 + 0.0967884i
\(577\) 7.04676 + 7.04676i 0.293360 + 0.293360i 0.838406 0.545046i \(-0.183488\pi\)
−0.545046 + 0.838406i \(0.683488\pi\)
\(578\) −4.32382 4.32382i −0.179847 0.179847i
\(579\) −17.3639 + 36.6159i −0.721620 + 1.52171i
\(580\) 4.25793 + 3.29592i 0.176801 + 0.136856i
\(581\) 2.30089i 0.0954570i
\(582\) −1.37377 + 0.489957i −0.0569446 + 0.0203094i
\(583\) −17.5484 + 17.5484i −0.726780 + 0.726780i
\(584\) 1.06894 0.0442330
\(585\) −5.19214 4.92448i −0.214668 0.203602i
\(586\) −1.94418 −0.0803135
\(587\) 26.9429 26.9429i 1.11205 1.11205i 0.119179 0.992873i \(-0.461974\pi\)
0.992873 0.119179i \(-0.0380262\pi\)
\(588\) 11.3853 4.06058i 0.469521 0.167456i
\(589\) 3.69470i 0.152238i
\(590\) 2.01247 + 15.8022i 0.0828523 + 0.650565i
\(591\) 3.17776 6.70106i 0.130716 0.275645i
\(592\) 3.66137 + 3.66137i 0.150482 + 0.150482i
\(593\) −20.6797 20.6797i −0.849213 0.849213i 0.140822 0.990035i \(-0.455026\pi\)
−0.990035 + 0.140822i \(0.955026\pi\)
\(594\) 30.9009 7.63952i 1.26788 0.313453i
\(595\) 0.656692 0.848367i 0.0269217 0.0347797i
\(596\) 9.86195i 0.403961i
\(597\) 4.66470 + 13.0791i 0.190913 + 0.535293i
\(598\) −6.62914 + 6.62914i −0.271086 + 0.271086i
\(599\) −43.6578 −1.78381 −0.891904 0.452225i \(-0.850631\pi\)
−0.891904 + 0.452225i \(0.850631\pi\)
\(600\) −1.63102 + 8.50528i −0.0665860 + 0.347227i
\(601\) −34.9857 −1.42710 −0.713548 0.700606i \(-0.752913\pi\)
−0.713548 + 0.700606i \(0.752913\pi\)
\(602\) 0.144666 0.144666i 0.00589614 0.00589614i
\(603\) 18.4746 + 1.85778i 0.752342 + 0.0756546i
\(604\) 7.90117i 0.321494i
\(605\) 36.3080 46.9057i 1.47613 1.90699i
\(606\) −12.1288 5.75170i −0.492699 0.233647i
\(607\) 17.1411 + 17.1411i 0.695736 + 0.695736i 0.963488 0.267752i \(-0.0862806\pi\)
−0.267752 + 0.963488i \(0.586281\pi\)
\(608\) −0.707107 0.707107i −0.0286770 0.0286770i
\(609\) −0.548030 0.259886i −0.0222073 0.0105311i
\(610\) 2.92219 + 22.9454i 0.118316 + 0.929031i
\(611\) 7.37060i 0.298183i
\(612\) 9.84815 + 0.990317i 0.398088 + 0.0400312i
\(613\) 11.6759 11.6759i 0.471584 0.471584i −0.430843 0.902427i \(-0.641784\pi\)
0.902427 + 0.430843i \(0.141784\pi\)
\(614\) −3.50817 −0.141578
\(615\) −37.9381 12.4099i −1.52981 0.500414i
\(616\) −0.890843 −0.0358931
\(617\) 26.0987 26.0987i 1.05069 1.05069i 0.0520498 0.998644i \(-0.483425\pi\)
0.998644 0.0520498i \(-0.0165754\pi\)
\(618\) 9.22665 + 25.8702i 0.371150 + 1.04065i
\(619\) 23.5922i 0.948249i −0.880458 0.474124i \(-0.842765\pi\)
0.880458 0.474124i \(-0.157235\pi\)
\(620\) 6.53306 + 5.05701i 0.262374 + 0.203094i
\(621\) 44.3308 10.9597i 1.77893 0.439799i
\(622\) 1.24595 + 1.24595i 0.0499579 + 0.0499579i
\(623\) 0.237515 + 0.237515i 0.00951583 + 0.00951583i
\(624\) −0.791694 + 1.66947i −0.0316931 + 0.0668324i
\(625\) −21.8589 + 12.1321i −0.874356 + 0.485286i
\(626\) 13.5483i 0.541501i
\(627\) −9.99383 + 3.56432i −0.399115 + 0.142345i
\(628\) 3.96376 3.96376i 0.158171 0.158171i
\(629\) 17.0835 0.681164
\(630\) −0.0258001 0.975177i −0.00102790 0.0388520i
\(631\) 33.3627 1.32815 0.664075 0.747666i \(-0.268826\pi\)
0.664075 + 0.747666i \(0.268826\pi\)
\(632\) −10.1192 + 10.1192i −0.402521 + 0.402521i
\(633\) 7.35584 2.62347i 0.292368 0.104274i
\(634\) 11.0656i 0.439469i
\(635\) −27.6122 + 3.51653i −1.09576 + 0.139549i
\(636\) −3.00657 + 6.34006i −0.119218 + 0.251400i
\(637\) 5.26423 + 5.26423i 0.208577 + 0.208577i
\(638\) −10.4308 10.4308i −0.412961 0.412961i
\(639\) 0.590452 + 0.722478i 0.0233579 + 0.0285808i
\(640\) 2.21815 0.282491i 0.0876802 0.0111665i
\(641\) 3.43192i 0.135553i −0.997701 0.0677764i \(-0.978410\pi\)
0.997701 0.0677764i \(-0.0215904\pi\)
\(642\) −8.97112 25.1537i −0.354062 0.992739i
\(643\) 14.6003 14.6003i 0.575778 0.575778i −0.357959 0.933737i \(-0.616527\pi\)
0.933737 + 0.357959i \(0.116527\pi\)
\(644\) −1.27801 −0.0503607
\(645\) 2.46408 + 4.85976i 0.0970229 + 0.191353i
\(646\) −3.29927 −0.129808
\(647\) 32.0282 32.0282i 1.25916 1.25916i 0.307662 0.951496i \(-0.400453\pi\)
0.951496 0.307662i \(-0.0995466\pi\)
\(648\) 7.50363 4.96945i 0.294771 0.195219i
\(649\) 43.6413i 1.71307i
\(650\) −5.16354 + 1.33688i −0.202531 + 0.0524368i
\(651\) −0.840857 0.398749i −0.0329558 0.0156282i
\(652\) −6.35109 6.35109i −0.248728 0.248728i
\(653\) 21.8830 + 21.8830i 0.856346 + 0.856346i 0.990906 0.134559i \(-0.0429619\pi\)
−0.134559 + 0.990906i \(0.542962\pi\)
\(654\) 1.49955 + 0.711114i 0.0586371 + 0.0278067i
\(655\) −39.0873 30.2561i −1.52727 1.18220i
\(656\) 10.3063i 0.402395i
\(657\) 0.320855 3.19072i 0.0125177 0.124482i
\(658\) 0.710478 0.710478i 0.0276973 0.0276973i
\(659\) −9.03239 −0.351852 −0.175926 0.984403i \(-0.556292\pi\)
−0.175926 + 0.984403i \(0.556292\pi\)
\(660\) 7.37625 22.5499i 0.287120 0.877752i
\(661\) −29.1658 −1.13442 −0.567210 0.823573i \(-0.691977\pi\)
−0.567210 + 0.823573i \(0.691977\pi\)
\(662\) 7.16494 7.16494i 0.278473 0.278473i
\(663\) 2.04780 + 5.74175i 0.0795301 + 0.222991i
\(664\) 15.8222i 0.614020i
\(665\) 0.0410804 + 0.322567i 0.00159303 + 0.0125086i
\(666\) 12.0280 9.83000i 0.466076 0.380905i
\(667\) −14.9642 14.9642i −0.579415 0.579415i
\(668\) 14.9173 + 14.9173i 0.577169 + 0.577169i
\(669\) −8.88761 + 18.7416i −0.343615 + 0.724593i
\(670\) 8.47133 10.9440i 0.327276 0.422802i
\(671\) 63.3688i 2.44633i
\(672\) −0.237241 + 0.0846123i −0.00915176 + 0.00326399i
\(673\) 13.7053 13.7053i 0.528300 0.528300i −0.391765 0.920065i \(-0.628135\pi\)
0.920065 + 0.391765i \(0.128135\pi\)
\(674\) −12.1618 −0.468456
\(675\) 24.8982 + 7.42146i 0.958333 + 0.285652i
\(676\) 11.8620 0.456232
\(677\) −0.194042 + 0.194042i −0.00745766 + 0.00745766i −0.710826 0.703368i \(-0.751679\pi\)
0.703368 + 0.710826i \(0.251679\pi\)
\(678\) 11.4022 4.06660i 0.437898 0.156177i
\(679\) 0.122457i 0.00469946i
\(680\) 4.51578 5.83385i 0.173172 0.223718i
\(681\) 6.50923 13.7262i 0.249434 0.525991i
\(682\) −16.0043 16.0043i −0.612836 0.612836i
\(683\) 8.50150 + 8.50150i 0.325301 + 0.325301i 0.850796 0.525495i \(-0.176120\pi\)
−0.525495 + 0.850796i \(0.676120\pi\)
\(684\) −2.32292 + 1.89843i −0.0888192 + 0.0725882i
\(685\) −0.633682 4.97574i −0.0242117 0.190113i
\(686\) 2.03283i 0.0776137i
\(687\) 6.87251 + 19.2695i 0.262202 + 0.735178i
\(688\) 0.994803 0.994803i 0.0379265 0.0379265i
\(689\) −4.32162 −0.164640
\(690\) 10.5820 32.3503i 0.402851 1.23155i
\(691\) −34.6840 −1.31944 −0.659721 0.751511i \(-0.729325\pi\)
−0.659721 + 0.751511i \(0.729325\pi\)
\(692\) −6.19199 + 6.19199i −0.235384 + 0.235384i
\(693\) −0.267398 + 2.65912i −0.0101576 + 0.101012i
\(694\) 11.1866i 0.424639i
\(695\) −19.7639 15.2986i −0.749688 0.580307i
\(696\) −3.76856 1.78712i −0.142847 0.0677406i
\(697\) 24.0440 + 24.0440i 0.910732 + 0.910732i
\(698\) −13.1405 13.1405i −0.497376 0.497376i
\(699\) 23.3301 + 11.0636i 0.882427 + 0.418462i
\(700\) −0.626598 0.368865i −0.0236832 0.0139418i
\(701\) 6.61547i 0.249863i 0.992165 + 0.124931i \(0.0398711\pi\)
−0.992165 + 0.124931i \(0.960129\pi\)
\(702\) 4.74565 + 2.86428i 0.179113 + 0.108105i
\(703\) −3.66137 + 3.66137i −0.138091 + 0.138091i
\(704\) −6.12593 −0.230880
\(705\) 12.1015 + 23.8671i 0.455769 + 0.898888i
\(706\) 5.29865 0.199417
\(707\) 0.796928 0.796928i 0.0299716 0.0299716i
\(708\) −4.14505 11.6221i −0.155780 0.436786i
\(709\) 17.2370i 0.647351i −0.946168 0.323675i \(-0.895081\pi\)
0.946168 0.323675i \(-0.104919\pi\)
\(710\) 0.689892 0.0878608i 0.0258912 0.00329736i
\(711\) 27.1679 + 33.2427i 1.01888 + 1.24670i
\(712\) 1.63328 + 1.63328i 0.0612099 + 0.0612099i
\(713\) −22.9599 22.9599i −0.859856 0.859856i
\(714\) −0.356073 + 0.750863i −0.0133257 + 0.0281003i
\(715\) 14.4954 1.84605i 0.542096 0.0690383i
\(716\) 8.96071i 0.334877i
\(717\) 10.2340 3.64996i 0.382195 0.136310i
\(718\) 12.1340 12.1340i 0.452838 0.452838i
\(719\) 16.3498 0.609746 0.304873 0.952393i \(-0.401386\pi\)
0.304873 + 0.952393i \(0.401386\pi\)
\(720\) −0.177416 6.70586i −0.00661189 0.249913i
\(721\) −2.30605 −0.0858819
\(722\) 0.707107 0.707107i 0.0263158 0.0263158i
\(723\) −21.7669 + 7.76321i −0.809521 + 0.288717i
\(724\) 8.58326i 0.318994i
\(725\) −3.01779 11.6558i −0.112078 0.432887i
\(726\) −19.6870 + 41.5147i −0.730654 + 1.54076i
\(727\) −33.8444 33.8444i −1.25522 1.25522i −0.953349 0.301871i \(-0.902389\pi\)
−0.301871 0.953349i \(-0.597611\pi\)
\(728\) −0.109693 0.109693i −0.00406550 0.00406550i
\(729\) −12.5812 23.8896i −0.465972 0.884800i
\(730\) −1.89012 1.46308i −0.0699565 0.0541509i
\(731\) 4.64163i 0.171677i
\(732\) −6.01877 16.8758i −0.222460 0.623747i
\(733\) −8.42136 + 8.42136i −0.311050 + 0.311050i −0.845316 0.534266i \(-0.820588\pi\)
0.534266 + 0.845316i \(0.320588\pi\)
\(734\) −34.8649 −1.28689
\(735\) −25.6895 8.40325i −0.947572 0.309959i
\(736\) −8.78832 −0.323942
\(737\) −26.8099 + 26.8099i −0.987554 + 0.987554i
\(738\) 30.7638 + 3.09357i 1.13243 + 0.113876i
\(739\) 18.4254i 0.677788i 0.940825 + 0.338894i \(0.110053\pi\)
−0.940825 + 0.338894i \(0.889947\pi\)
\(740\) −1.46273 11.4855i −0.0537710 0.422216i
\(741\) −1.66947 0.791694i −0.0613296 0.0290836i
\(742\) −0.416576 0.416576i −0.0152930 0.0152930i
\(743\) −27.2664 27.2664i −1.00031 1.00031i −1.00000 0.000307644i \(-0.999902\pi\)
−0.000307644 1.00000i \(-0.500098\pi\)
\(744\) −5.78220 2.74202i −0.211986 0.100527i
\(745\) 13.4982 17.4381i 0.494537 0.638883i
\(746\) 15.5260i 0.568446i
\(747\) −47.2284 4.74923i −1.72800 0.173765i
\(748\) −14.2914 + 14.2914i −0.522546 + 0.522546i
\(749\) 2.24219 0.0819277
\(750\) 14.5253 12.8068i 0.530390 0.467639i
\(751\) 29.9776 1.09390 0.546949 0.837166i \(-0.315789\pi\)
0.546949 + 0.837166i \(0.315789\pi\)
\(752\) 4.88564 4.88564i 0.178161 0.178161i
\(753\) −15.5829 43.6923i −0.567874 1.59224i
\(754\) 2.56879i 0.0935497i
\(755\) 10.8145 13.9710i 0.393579 0.508458i
\(756\) 0.181352 + 0.733548i 0.00659572 + 0.0266789i
\(757\) 14.2204 + 14.2204i 0.516851 + 0.516851i 0.916617 0.399766i \(-0.130909\pi\)
−0.399766 + 0.916617i \(0.630909\pi\)
\(758\) 22.5476 + 22.5476i 0.818966 + 0.818966i
\(759\) −39.9548 + 84.2541i −1.45027 + 3.05823i
\(760\) 0.282491 + 2.21815i 0.0102470 + 0.0804608i
\(761\) 25.8646i 0.937590i 0.883307 + 0.468795i \(0.155312\pi\)
−0.883307 + 0.468795i \(0.844688\pi\)
\(762\) 20.3081 7.24291i 0.735685 0.262383i
\(763\) −0.0985285 + 0.0985285i −0.00356697 + 0.00356697i
\(764\) −15.3727 −0.556164
\(765\) −16.0582 15.2304i −0.580587 0.550658i
\(766\) 5.25871 0.190005
\(767\) 5.37374 5.37374i 0.194034 0.194034i
\(768\) −1.63140 + 0.581841i −0.0588680 + 0.0209954i
\(769\) 3.81692i 0.137642i −0.997629 0.0688208i \(-0.978076\pi\)
0.997629 0.0688208i \(-0.0219237\pi\)
\(770\) 1.57521 + 1.21931i 0.0567666 + 0.0439410i
\(771\) 6.50988 13.7276i 0.234448 0.494388i
\(772\) −16.5440 16.5440i −0.595433 0.595433i
\(773\) 13.3692 + 13.3692i 0.480857 + 0.480857i 0.905405 0.424549i \(-0.139567\pi\)
−0.424549 + 0.905405i \(0.639567\pi\)
\(774\) −2.67083 3.26804i −0.0960010 0.117467i
\(775\) −4.63027 17.8838i −0.166324 0.642406i
\(776\) 0.842081i 0.0302289i
\(777\) 0.438119 + 1.22842i 0.0157174 + 0.0440695i