Properties

Label 570.2.k.b.77.12
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 77.12
Character \(\chi\) \(=\) 570.77
Dual form 570.2.k.b.533.12

$q$-expansion

\(f(q)\) \(=\) \(q+(0.707107 - 0.707107i) q^{2} +(-0.581841 + 1.63140i) q^{3} -1.00000i q^{4} +(1.36872 - 1.76822i) q^{5} +(0.742149 + 1.56500i) q^{6} +(0.102829 + 0.102829i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-2.32292 - 1.89843i) q^{9} +O(q^{10})\) \(q+(0.707107 - 0.707107i) q^{2} +(-0.581841 + 1.63140i) 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} +(1.63140 + 0.581841i) q^{12} +(-0.754312 + 0.754312i) q^{13} +0.145422 q^{14} +(2.08830 + 3.26175i) q^{15} -1.00000 q^{16} +(2.33294 - 2.33294i) q^{17} +(-2.98495 + 0.300162i) 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} +(4.44866 - 2.68503i) q^{27} +(0.102829 - 0.102829i) q^{28} -2.40803 q^{29} +(3.78306 + 0.829756i) q^{30} +3.69470 q^{31} +(-0.707107 + 0.707107i) q^{32} +(9.99383 + 3.56432i) 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} +(-0.0846123 + 0.237241i) q^{42} +(-0.994803 + 0.994803i) q^{43} -6.12593 q^{44} +(-6.53627 + 1.50903i) q^{45} +8.78832 q^{46} +(4.88564 - 4.88564i) q^{47} +(0.581841 - 1.63140i) 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} +(1.63140 + 0.581841i) q^{57} +(-1.70274 + 1.70274i) q^{58} +7.12402 q^{59} +(3.26175 - 2.08830i) q^{60} -10.3444 q^{61} +(2.61255 - 2.61255i) q^{62} +(-0.0436501 - 0.434076i) 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} +(0.300162 + 2.98495i) q^{72} +(0.755853 - 0.755853i) q^{73} -5.17797 q^{74} +(8.62579 + 0.771844i) q^{75} -1.00000 q^{76} +(0.629921 - 0.629921i) q^{77} +(-1.74031 - 0.620684i) 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} +(1.40109 - 3.92846i) q^{87} +(-4.33169 + 4.33169i) q^{88} -2.30981 q^{89} +(-3.55480 + 5.68888i) q^{90} -0.155130 q^{91} +(6.21428 - 6.21428i) q^{92} +(-2.14973 + 6.02753i) 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
\(3\) −0.581841 + 1.63140i −0.335926 + 0.941888i
\(4\) 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 \(-0.625300\pi\)
0.383553 0.923519i \(-0.374700\pi\)
\(12\) 1.63140 + 0.581841i 0.470944 + 0.167963i
\(13\) −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
\(15\) 2.08830 + 3.26175i 0.539196 + 0.842180i
\(16\) −1.00000 −0.250000
\(17\) 2.33294 2.33294i 0.565820 0.565820i −0.365134 0.930955i \(-0.618977\pi\)
0.930955 + 0.365134i \(0.118977\pi\)
\(18\) −2.98495 + 0.300162i −0.703559 + 0.0707490i
\(19\) 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 \(0.118796\pi\)
0.364604 + 0.931163i \(0.381204\pi\)
\(24\) 1.56500 0.742149i 0.319454 0.151491i
\(25\) −1.25322 4.84040i −0.250644 0.968079i
\(26\) 1.06676i 0.209209i
\(27\) 4.44866 2.68503i 0.856146 0.516734i
\(28\) 0.102829 0.102829i 0.0194328 0.0194328i
\(29\) −2.40803 −0.447160 −0.223580 0.974686i \(-0.571774\pi\)
−0.223580 + 0.974686i \(0.571774\pi\)
\(30\) 3.78306 + 0.829756i 0.690688 + 0.151492i
\(31\) 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
\(33\) 9.99383 + 3.56432i 1.73970 + 0.620468i
\(34\) 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 \(0.297722\pi\)
−0.593561 + 0.804789i \(0.702278\pi\)
\(42\) −0.0846123 + 0.237241i −0.0130560 + 0.0366070i
\(43\) −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
\(45\) −6.53627 + 1.50903i −0.974370 + 0.224952i
\(46\) 8.78832 1.29577
\(47\) 4.88564 4.88564i 0.712645 0.712645i −0.254443 0.967088i \(-0.581892\pi\)
0.967088 + 0.254443i \(0.0818922\pi\)
\(48\) 0.581841 1.63140i 0.0839815 0.235472i
\(49\) 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 0.482443 0.875927i \(-0.339749\pi\)
−0.875927 + 0.482443i \(0.839749\pi\)
\(54\) 1.24708 5.04428i 0.169706 0.686440i
\(55\) −10.8320 8.38468i −1.46059 1.13059i
\(56\) 0.145422i 0.0194328i
\(57\) 1.63140 + 0.581841i 0.216084 + 0.0770667i
\(58\) −1.70274 + 1.70274i −0.223580 + 0.223580i
\(59\) 7.12402 0.927469 0.463734 0.885974i \(-0.346509\pi\)
0.463734 + 0.885974i \(0.346509\pi\)
\(60\) 3.26175 2.08830i 0.421090 0.269598i
\(61\) −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
\(63\) −0.0436501 0.434076i −0.00549940 0.0546884i
\(64\) 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 \(-0.994125\pi\)
0.999830 0.0184557i \(-0.00587497\pi\)
\(72\) 0.300162 + 2.98495i 0.0353745 + 0.351779i
\(73\) 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
\(75\) 8.62579 + 0.771844i 0.996020 + 0.0891248i
\(76\) −1.00000 −0.114708
\(77\) 0.629921 0.629921i 0.0717862 0.0717862i
\(78\) −1.74031 0.620684i −0.197051 0.0702786i
\(79\) 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 \(0.0848230\pi\)
0.263337 + 0.964704i \(0.415177\pi\)
\(84\) 0.107925 + 0.227584i 0.0117755 + 0.0248315i
\(85\) −0.932016 7.31829i −0.101091 0.793780i
\(86\) 1.40686i 0.151706i
\(87\) 1.40109 3.92846i 0.150213 0.421175i
\(88\) −4.33169 + 4.33169i −0.461759 + 0.461759i
\(89\) −2.30981 −0.244840 −0.122420 0.992478i \(-0.539065\pi\)
−0.122420 + 0.992478i \(0.539065\pi\)
\(90\) −3.55480 + 5.68888i −0.374709 + 0.599661i
\(91\) −0.155130 −0.0162620
\(92\) 6.21428 6.21428i 0.647883 0.647883i
\(93\) −2.14973 + 6.02753i −0.222917 + 0.625026i
\(94\) 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 \(0.125999\pi\)
−0.922674 + 0.385580i \(0.874001\pi\)
\(102\) 5.38243 + 1.91965i 0.532940 + 0.190074i
\(103\) −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
\(105\) −0.120664 + 0.550138i −0.0117756 + 0.0536880i
\(106\) −4.05117 −0.393484
\(107\) −10.9025 + 10.9025i −1.05399 + 1.05399i −0.0555308 + 0.998457i \(0.517685\pi\)
−0.998457 + 0.0555308i \(0.982315\pi\)
\(108\) −2.68503 4.44866i −0.258367 0.428073i
\(109\) 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 0.435348 0.900262i \(-0.356625\pi\)
−0.900262 + 0.435348i \(0.856625\pi\)
\(114\) 1.56500 0.742149i 0.146575 0.0695087i
\(115\) 19.4938 2.48262i 1.81781 0.231506i
\(116\) 2.40803i 0.223580i
\(117\) 3.18422 0.320201i 0.294381 0.0296026i
\(118\) 5.03744 5.03744i 0.463734 0.463734i
\(119\) 0.479786 0.0439819
\(120\) 0.829756 3.78306i 0.0757460 0.345344i
\(121\) −26.5270 −2.41155
\(122\) −7.31457 + 7.31457i −0.662230 + 0.662230i
\(123\) −16.8137 5.99664i −1.51604 0.540699i
\(124\) 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 \(-0.583635\pi\)
0.259735 0.965680i \(-0.416365\pi\)
\(132\) 3.56432 9.99383i 0.310234 0.869852i
\(133\) 0.102829 0.102829i 0.00891637 0.00891637i
\(134\) 6.18924 0.534669
\(135\) 1.34124 11.5413i 0.115436 0.993315i
\(136\) −3.29927 −0.282910
\(137\) 1.58617 1.58617i 0.135516 0.135516i −0.636095 0.771611i \(-0.719451\pi\)
0.771611 + 0.636095i \(0.219451\pi\)
\(138\) −5.11340 + 14.3373i −0.435282 + 1.22047i
\(139\) 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
\(147\) 11.3853 + 4.06058i 0.939043 + 0.334911i
\(148\) −3.66137 + 3.66137i −0.300963 + 0.300963i
\(149\) 9.86195 0.807922 0.403961 0.914776i \(-0.367633\pi\)
0.403961 + 0.914776i \(0.367633\pi\)
\(150\) 6.64513 5.55358i 0.542573 0.453448i
\(151\) −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
\(153\) −9.84815 + 0.990317i −0.796176 + 0.0800624i
\(154\) 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
\(162\) 7.50363 + 4.96945i 0.589541 + 0.390437i
\(163\) 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
\(165\) 19.9813 12.7928i 1.55554 0.995916i
\(166\) 15.8222 1.22804
\(167\) 14.9173 14.9173i 1.15434 1.15434i 0.168664 0.985674i \(-0.446055\pi\)
0.985674 0.168664i \(-0.0539453\pi\)
\(168\) 0.237241 + 0.0846123i 0.0183035 + 0.00652798i
\(169\) 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 0.902163 0.431395i \(-0.141978\pi\)
−0.431395 + 0.902163i \(0.641978\pi\)
\(174\) −1.78712 3.76856i −0.135481 0.285694i
\(175\) 0.368865 0.626598i 0.0278836 0.0473664i
\(176\) 6.12593i 0.461759i
\(177\) −4.14505 + 11.6221i −0.311561 + 0.873572i
\(178\) −1.63328 + 1.63328i −0.122420 + 0.122420i
\(179\) −8.96071 −0.669755 −0.334877 0.942262i \(-0.608695\pi\)
−0.334877 + 0.942262i \(0.608695\pi\)
\(180\) 1.50903 + 6.53627i 0.112476 + 0.487185i
\(181\) 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
\(183\) 6.01877 16.8758i 0.444920 1.24749i
\(184\) 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 \(0.187727\pi\)
−0.831073 + 0.556164i \(0.812273\pi\)
\(192\) −1.63140 0.581841i −0.117736 0.0419907i
\(193\) 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
\(195\) −4.03561 0.885149i −0.288996 0.0633868i
\(196\) −6.97885 −0.498489
\(197\) 3.02772 3.02772i 0.215716 0.215716i −0.590974 0.806690i \(-0.701257\pi\)
0.806690 + 0.590974i \(0.201257\pi\)
\(198\) 1.83877 + 18.2856i 0.130676 + 1.29950i
\(199\) 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
\(207\) −2.63792 26.2327i −0.183348 1.82330i
\(208\) 0.754312 0.754312i 0.0523021 0.0523021i
\(209\) −6.12593 −0.423740
\(210\) 0.303684 + 0.474329i 0.0209562 + 0.0327318i
\(211\) −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
\(213\) 0.507400 + 0.180965i 0.0347664 + 0.0123995i
\(214\) 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
\(222\) 3.01275 8.44733i 0.202203 0.566947i
\(223\) 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
\(225\) −6.27802 + 13.6230i −0.418535 + 0.908201i
\(226\) −6.98920 −0.464915
\(227\) 6.20188 6.20188i 0.411633 0.411633i −0.470674 0.882307i \(-0.655989\pi\)
0.882307 + 0.470674i \(0.155989\pi\)
\(228\) 0.581841 1.63140i 0.0385334 0.108042i
\(229\) 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 0.962358 0.271783i \(-0.0876134\pi\)
−0.271783 + 0.962358i \(0.587613\pi\)
\(234\) 2.02517 2.47800i 0.132389 0.161992i
\(235\) −1.95183 15.3260i −0.127323 0.999757i
\(236\) 7.12402i 0.463734i
\(237\) −23.3465 8.32658i −1.51652 0.540869i
\(238\) 0.339260 0.339260i 0.0219909 0.0219909i
\(239\) 6.27313 0.405775 0.202887 0.979202i \(-0.434967\pi\)
0.202887 + 0.979202i \(0.434967\pi\)
\(240\) −2.08830 3.26175i −0.134799 0.210545i
\(241\) 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
\(243\) −15.4312 2.20836i −0.989914 0.141666i
\(244\) 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 \(-0.679459\pi\)
0.534392 0.845237i \(-0.320541\pi\)
\(252\) −0.434076 + 0.0436501i −0.0273442 + 0.00274970i
\(253\) 38.0682 38.0682i 2.39333 2.39333i
\(254\) 12.4483 0.781074
\(255\) 12.4813 + 2.73759i 0.781611 + 0.171434i
\(256\) 1.00000 0.0625000
\(257\) 6.20250 6.20250i 0.386901 0.386901i −0.486679 0.873581i \(-0.661792\pi\)
0.873581 + 0.486679i \(0.161792\pi\)
\(258\) −2.29516 0.818571i −0.142890 0.0509620i
\(259\) 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 0.955442 0.295181i \(-0.0953798\pi\)
−0.295181 + 0.955442i \(0.595380\pi\)
\(264\) −4.54636 9.58706i −0.279809 0.590043i
\(265\) −8.98610 + 1.14442i −0.552012 + 0.0703011i
\(266\) 0.145422i 0.00891637i
\(267\) 1.34394 3.76823i 0.0822480 0.230612i
\(268\) 4.37645 4.37645i 0.267335 0.267335i
\(269\) 7.39882 0.451114 0.225557 0.974230i \(-0.427580\pi\)
0.225557 + 0.974230i \(0.427580\pi\)
\(270\) −7.21251 9.10932i −0.438939 0.554375i
\(271\) −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
\(273\) 0.0902608 0.253078i 0.00546283 0.0153170i
\(274\) 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 \(-0.978534\pi\)
0.997727 0.0673860i \(-0.0214659\pi\)
\(282\) 11.2719 + 4.02014i 0.671232 + 0.239396i
\(283\) −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
\(285\) 3.26175 2.08830i 0.193209 0.123700i
\(286\) 6.53489 0.386416
\(287\) −1.05979 + 1.05979i −0.0625572 + 0.0625572i
\(288\) 2.98495 0.300162i 0.175890 0.0176872i
\(289\) 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 0.665809 0.746122i \(-0.268087\pi\)
−0.746122 + 0.665809i \(0.768087\pi\)
\(294\) 10.9219 5.17935i 0.636977 0.302066i
\(295\) 9.75078 12.5969i 0.567712 0.733417i
\(296\) 5.17797i 0.300963i
\(297\) −16.4483 27.2522i −0.954427 1.58133i
\(298\) 6.97345 6.97345i 0.403961 0.403961i
\(299\) −9.37501 −0.542171
\(300\) 0.771844 8.62579i 0.0445624 0.498010i
\(301\) −0.204588 −0.0117923
\(302\) −5.58697 + 5.58697i −0.321494 + 0.321494i
\(303\) −12.6434 4.50930i −0.726346 0.259053i
\(304\) 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 \(0.0159087\pi\)
−0.998751 + 0.0499579i \(0.984091\pi\)
\(312\) −0.620684 + 1.74031i −0.0351393 + 0.0985256i
\(313\) −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
\(315\) −0.827287 0.516945i −0.0466123 0.0291265i
\(316\) 14.3107 0.805042
\(317\) −7.82453 + 7.82453i −0.439469 + 0.439469i −0.891833 0.452364i \(-0.850581\pi\)
0.452364 + 0.891833i \(0.350581\pi\)
\(318\) 2.35713 6.60907i 0.132182 0.370618i
\(319\) 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
\(327\) −1.56318 0.557509i −0.0864438 0.0308303i
\(328\) 7.28768 7.28768i 0.402395 0.402395i
\(329\) 1.00477 0.0553947
\(330\) 5.08303 23.1747i 0.279811 1.27573i
\(331\) −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
\(333\) 1.55423 + 15.4559i 0.0851713 + 0.846981i
\(334\) 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
\(342\) 0.300162 + 2.98495i 0.0162309 + 0.161407i
\(343\) 1.43743 1.43743i 0.0776137 0.0776137i
\(344\) 1.40686 0.0758530
\(345\) −7.29216 + 33.2467i −0.392597 + 1.78994i
\(346\) 8.75680 0.470769
\(347\) −7.91015 + 7.91015i −0.424639 + 0.424639i −0.886797 0.462158i \(-0.847075\pi\)
0.462158 + 0.886797i \(0.347075\pi\)
\(348\) −3.92846 1.40109i −0.210587 0.0751064i
\(349\) 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 0.799750 0.600333i \(-0.204965\pi\)
−0.600333 + 0.799750i \(0.704965\pi\)
\(354\) 5.28709 + 11.1491i 0.281006 + 0.592566i
\(355\) −0.549955 0.425701i −0.0291886 0.0225938i
\(356\) 2.30981i 0.122420i
\(357\) −0.279159 + 0.782721i −0.0147747 + 0.0414260i
\(358\) −6.33618 + 6.33618i −0.334877 + 0.334877i
\(359\) 17.1601 0.905676 0.452838 0.891593i \(-0.350412\pi\)
0.452838 + 0.891593i \(0.350412\pi\)
\(360\) 5.68888 + 3.55480i 0.299831 + 0.187354i
\(361\) −1.00000 −0.0526316
\(362\) 6.06928 6.06928i 0.318994 0.318994i
\(363\) 15.4345 43.2762i 0.810102 2.27141i
\(364\) 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
\(372\) 6.02753 + 2.14973i 0.312513 + 0.111458i
\(373\) −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
\(375\) 13.1711 14.1959i 0.680151 0.733072i
\(376\) −6.90934 −0.356322
\(377\) 1.81641 1.81641i 0.0935497 0.0935497i
\(378\) 0.646932 0.390461i 0.0332746 0.0200832i
\(379\) 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 0.795698 0.605693i \(-0.207104\pi\)
−0.605693 + 0.795698i \(0.707104\pi\)
\(384\) −1.56500 + 0.742149i −0.0798634 + 0.0378727i
\(385\) −0.251655 1.97603i −0.0128255 0.100708i
\(386\) 23.3968i 1.19087i
\(387\) 4.19941 0.422288i 0.213468 0.0214661i
\(388\) −0.595441 + 0.595441i −0.0302289 + 0.0302289i
\(389\) 27.6876 1.40382 0.701908 0.712268i \(-0.252332\pi\)
0.701908 + 0.712268i \(0.252332\pi\)
\(390\) −3.47950 + 2.22771i −0.176191 + 0.112804i
\(391\) 28.9951 1.46634
\(392\) −4.93479 + 4.93479i −0.249245 + 0.249245i
\(393\) 36.0628 + 12.8618i 1.81913 + 0.648794i
\(394\) 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 \(-0.743046\pi\)
0.691491 0.722385i \(-0.256954\pi\)
\(402\) −3.60115 + 10.0971i −0.179609 + 0.503599i
\(403\) −2.78696 + 2.78696i −0.138828 + 0.138828i
\(404\) 7.75006 0.385580
\(405\) 18.0480 + 8.90329i 0.896814 + 0.442408i
\(406\) −0.350180 −0.0173791
\(407\) −22.4293 + 22.4293i −1.11178 + 1.11178i
\(408\) 1.91965 5.38243i 0.0950369 0.266470i
\(409\) 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
\(417\) −18.2346 6.50340i −0.892953 0.318473i
\(418\) −4.33169 + 4.33169i −0.211870 + 0.211870i
\(419\) 6.96160 0.340096 0.170048 0.985436i \(-0.445608\pi\)
0.170048 + 0.985436i \(0.445608\pi\)
\(420\) 0.550138 + 0.120664i 0.0268440 + 0.00588782i
\(421\) −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
\(423\) −20.6240 + 2.07393i −1.00277 + 0.100838i
\(424\) 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 \(0.157160\pi\)
−0.880570 + 0.473917i \(0.842840\pi\)
\(432\) −4.44866 + 2.68503i −0.214036 + 0.129184i
\(433\) −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
\(435\) −5.02869 7.85439i −0.241107 0.376589i
\(436\) 0.958181 0.0458886
\(437\) 6.21428 6.21428i 0.297269 0.297269i
\(438\) 1.74386 + 0.621952i 0.0833250 + 0.0297180i
\(439\) 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 0.419746 0.907642i \(-0.362119\pi\)
−0.907642 + 0.419746i \(0.862119\pi\)
\(444\) −3.84282 8.10350i −0.182372 0.384575i
\(445\) −3.16148 + 4.08426i −0.149869 + 0.193613i
\(446\) 11.9755i 0.567057i
\(447\) −5.73809 + 16.0888i −0.271402 + 0.760973i
\(448\) −0.102829 + 0.102829i −0.00485820 + 0.00485820i
\(449\) −28.7172 −1.35525 −0.677623 0.735409i \(-0.736990\pi\)
−0.677623 + 0.735409i \(0.736990\pi\)
\(450\) 5.19369 + 14.0722i 0.244833 + 0.663368i
\(451\) 63.1359 2.97295
\(452\) −4.94211 + 4.94211i −0.232457 + 0.232457i
\(453\) 4.59722 12.8900i 0.215996 0.605623i
\(454\) 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 \(-0.687588\pi\)
0.555800 0.831316i \(-0.312412\pi\)
\(462\) 1.45332 + 0.518329i 0.0676146 + 0.0241148i
\(463\) −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
\(465\) 7.71564 + 12.0512i 0.357804 + 0.558861i
\(466\) 14.9075 0.690575
\(467\) 5.01672 5.01672i 0.232146 0.232146i −0.581442 0.813588i \(-0.697511\pi\)
0.813588 + 0.581442i \(0.197511\pi\)
\(468\) −0.320201 3.18422i −0.0148013 0.147190i
\(469\) 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
\(477\) 1.21601 + 12.0925i 0.0556772 + 0.553678i
\(478\) 4.43577 4.43577i 0.202887 0.202887i
\(479\) −6.25041 −0.285589 −0.142794 0.989752i \(-0.545609\pi\)
−0.142794 + 0.989752i \(0.545609\pi\)
\(480\) −3.78306 0.829756i −0.172672 0.0378730i
\(481\) 5.52364 0.251856
\(482\) 9.43457 9.43457i 0.429733 0.429733i
\(483\) −2.08495 0.743599i −0.0948683 0.0338349i
\(484\) 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 \(-0.925526\pi\)
0.972754 0.231838i \(-0.0744738\pi\)
\(492\) −5.99664 + 16.8137i −0.270350 + 0.758022i
\(493\) −5.61779 + 5.61779i −0.253012 + 0.253012i
\(494\) 1.06676 0.0479957
\(495\) 9.24420 + 40.0407i 0.415496 + 1.79970i
\(496\) −3.69470 −0.165897
\(497\) 0.0319819 0.0319819i 0.00143458 0.00143458i
\(498\) −9.20600 + 25.8123i −0.412531 + 1.15668i
\(499\) 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 0.161658 0.986847i \(-0.448316\pi\)
−0.986847 + 0.161658i \(0.948316\pi\)
\(504\) −0.276073 + 0.337803i −0.0122973 + 0.0150469i
\(505\) 13.7038 + 10.6077i 0.609812 + 0.472034i
\(506\) 53.8366i 2.39333i
\(507\) −19.3517 6.90181i −0.859439 0.306520i
\(508\) 8.80226 8.80226i 0.390537 0.390537i
\(509\) 40.9795 1.81638 0.908191 0.418555i \(-0.137463\pi\)
0.908191 + 0.418555i \(0.137463\pi\)
\(510\) 10.7614 6.88986i 0.476523 0.305088i
\(511\) 0.155447 0.00687656
\(512\) 0.707107 0.707107i 0.0312500 0.0312500i
\(513\) −2.68503 4.44866i −0.118547 0.196413i
\(514\) 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 \(-0.804954\pi\)
0.818066 0.575125i \(-0.195046\pi\)
\(522\) 7.18784 0.722800i 0.314603 0.0316361i
\(523\) 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
\(525\) 0.807611 + 0.966346i 0.0352470 + 0.0421748i
\(526\) 15.1429 0.660261
\(527\) 8.61951 8.61951i 0.375472 0.375472i
\(528\) −9.99383 3.56432i −0.434926 0.155117i
\(529\) 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
\(537\) 5.21371 14.6185i 0.224988 0.630834i
\(538\) 5.23176 5.23176i 0.225557 0.225557i
\(539\) −42.7520 −1.84146
\(540\) −11.5413 1.34124i −0.496657 0.0577180i
\(541\) 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
\(543\) −4.99409 + 14.0027i −0.214317 + 0.600914i
\(544\) 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
\(552\) 14.3373 + 5.11340i 0.610234 + 0.217641i
\(553\) −1.47155 + 1.47155i −0.0625768 + 0.0625768i
\(554\) 0.446483 0.0189693
\(555\) 4.29645 19.5885i 0.182374 0.831487i
\(556\) 11.1773 0.474022
\(557\) 17.1913 17.1913i 0.728419 0.728419i −0.241886 0.970305i \(-0.577766\pi\)
0.970305 + 0.241886i \(0.0777660\pi\)
\(558\) −11.0285 + 1.10901i −0.466873 + 0.0469482i
\(559\) 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 0.316777 0.948500i \(-0.397399\pi\)
−0.948500 + 0.316777i \(0.897399\pi\)
\(564\) 10.8131 5.12777i 0.455314 0.215918i
\(565\) −15.5031 + 1.97439i −0.652221 + 0.0830632i
\(566\) 24.5303i 1.03109i
\(567\) −0.722666 + 1.09119i −0.0303491 + 0.0458257i
\(568\) −0.219925 + 0.219925i −0.00922786 + 0.00922786i
\(569\) −35.8239 −1.50181 −0.750907 0.660408i \(-0.770383\pi\)
−0.750907 + 0.660408i \(0.770383\pi\)
\(570\) 0.829756 3.78306i 0.0347546 0.158455i
\(571\) −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
\(573\) −25.0790 8.94445i −1.04769 0.373660i
\(574\) 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
\(582\) 0.489957 1.37377i 0.0203094 0.0569446i
\(583\) −17.5484 + 17.5484i −0.726780 + 0.726780i
\(584\) −1.06894 −0.0442330
\(585\) 3.79211 6.06867i 0.156785 0.250908i
\(586\) −1.94418 −0.0803135
\(587\) −26.9429 + 26.9429i −1.11205 + 1.11205i −0.119179 + 0.992873i \(0.538026\pi\)
−0.992873 + 0.119179i \(0.961974\pi\)
\(588\) 4.06058 11.3853i 0.167456 0.469521i
\(589\) 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 0.990035 0.140822i \(-0.0449744\pi\)
−0.140822 + 0.990035i \(0.544974\pi\)
\(594\) −30.9009 7.63952i −1.26788 0.313453i
\(595\) 0.656692 0.848367i 0.0269217 0.0347797i
\(596\) 9.86195i 0.403961i
\(597\) 13.0791 + 4.66470i 0.535293 + 0.190913i
\(598\) −6.62914 + 6.62914i −0.271086 + 0.271086i
\(599\) 43.6578 1.78381 0.891904 0.452225i \(-0.149369\pi\)
0.891904 + 0.452225i \(0.149369\pi\)
\(600\) −5.55358 6.64513i −0.226724 0.271286i
\(601\) −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
\(603\) −1.85778 18.4746i −0.0756546 0.752342i
\(604\) 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
\(612\) 0.990317 + 9.84815i 0.0400312 + 0.398088i
\(613\) 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
\(615\) −33.6167 + 21.5227i −1.35555 + 0.867879i
\(616\) −0.890843 −0.0358931
\(617\) −26.0987 + 26.0987i −1.05069 + 1.05069i −0.0520498 + 0.998644i \(0.516575\pi\)
−0.998644 + 0.0520498i \(0.983425\pi\)
\(618\) −25.8702 9.22665i −1.04065 0.371150i
\(619\) 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
\(627\) 3.56432 9.99383i 0.142345 0.399115i
\(628\) 3.96376 3.96376i 0.158171 0.158171i
\(629\) −17.0835 −0.681164
\(630\) −0.950515 + 0.219445i −0.0378694 + 0.00874291i
\(631\) 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
\(633\) 2.62347 7.35584i 0.104274 0.292368i
\(634\) 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 \(0.0215904\pi\)
−0.997701 + 0.0677764i \(0.978410\pi\)
\(642\) −25.1537 8.97112i −0.992739 0.354062i
\(643\) 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
\(645\) −5.32224 1.16735i −0.209563 0.0459645i
\(646\) −3.29927 −0.129808
\(647\) −32.0282 + 32.0282i −1.25916 + 1.25916i −0.307662 + 0.951496i \(0.599547\pi\)
−0.951496 + 0.307662i \(0.900453\pi\)
\(648\) 4.96945 7.50363i 0.195219 0.294771i
\(649\) 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 0.134559 0.990906i \(-0.457038\pi\)
−0.990906 + 0.134559i \(0.957038\pi\)
\(654\) −1.49955 + 0.711114i −0.0586371 + 0.0278067i
\(655\) −39.0873 30.2561i −1.52727 1.18220i
\(656\) 10.3063i 0.402395i
\(657\) −3.19072 + 0.320855i −0.124482 + 0.0125177i
\(658\) 0.710478 0.710478i 0.0276973 0.0276973i
\(659\) 9.03239 0.351852 0.175926 0.984403i \(-0.443708\pi\)
0.175926 + 0.984403i \(0.443708\pi\)
\(660\) −12.7928 19.9813i −0.497958 0.777769i
\(661\) −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
\(663\) −5.74175 2.04780i −0.222991 0.0795301i
\(664\) 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
\(672\) 0.0846123 0.237241i 0.00326399 0.00915176i
\(673\) 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
\(675\) −18.5718 18.1684i −0.714827 0.699301i
\(676\) 11.8620 0.456232
\(677\) 0.194042 0.194042i 0.00745766 0.00745766i −0.703368 0.710826i \(-0.748321\pi\)
0.710826 + 0.703368i \(0.248321\pi\)
\(678\) 4.06660 11.4022i 0.156177 0.437898i
\(679\) 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 0.525495 0.850796i \(-0.323880\pi\)
−0.850796 + 0.525495i \(0.823880\pi\)
\(684\) 2.32292 + 1.89843i 0.0888192 + 0.0725882i
\(685\) −0.633682 4.97574i −0.0242117 0.190113i
\(686\) 2.03283i 0.0776137i
\(687\) 19.2695 + 6.87251i 0.735178 + 0.262202i
\(688\) 0.994803 0.994803i 0.0379265 0.0379265i
\(689\) 4.32162 0.164640
\(690\) 18.3526 + 28.6653i 0.698673 + 1.09127i
\(691\) −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
\(693\) −2.65912 + 0.267398i −0.101012 + 0.0101576i
\(694\) 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 \(-0.960129\pi\)
0.992165 0.124931i \(-0.0398711\pi\)
\(702\) 2.86428 + 4.74565i 0.108105 + 0.179113i
\(703\) −3.66137 + 3.66137i −0.138091 + 0.138091i
\(704\) 6.12593 0.230880
\(705\) 26.1384 + 5.73307i 0.984430 + 0.215920i
\(706\) 5.29865 0.199417
\(707\) −0.796928 + 0.796928i −0.0299716 + 0.0299716i
\(708\) 11.6221 + 4.14505i 0.436786 + 0.155780i
\(709\) 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
\(717\) −3.64996 + 10.2340i −0.136310 + 0.382195i
\(718\) 12.1340 12.1340i 0.452838 0.452838i
\(719\) −16.3498 −0.609746 −0.304873 0.952393i \(-0.598614\pi\)
−0.304873 + 0.952393i \(0.598614\pi\)
\(720\) 6.53627 1.50903i 0.243592 0.0562381i
\(721\) −2.30605 −0.0858819
\(722\) −0.707107 + 0.707107i −0.0263158 + 0.0263158i
\(723\) −7.76321 + 21.7669i −0.288717 + 0.809521i
\(724\) 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
\(732\) −16.8758 6.01877i −0.623747 0.222460i
\(733\) −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
\(735\) 22.7633 14.5739i 0.839636 0.537567i
\(736\) −8.78832 −0.323942
\(737\) 26.8099 26.8099i 0.987554 0.987554i
\(738\) −3.09357 30.7638i −0.113876 1.13243i
\(739\) 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 \(9.79262e-5\pi\)
0.000307644 1.00000i \(0.499902\pi\)
\(744\) 5.78220 2.74202i 0.211986 0.100527i
\(745\) 13.4982 17.4381i 0.494537 0.638883i
\(746\) 15.5260i 0.568446i
\(747\) −4.74923 47.2284i −0.173765 1.72800i
\(748\) −14.2914 + 14.2914i −0.522546 + 0.522546i
\(749\) −2.24219 −0.0819277
\(750\) −0.724644 19.3514i −0.0264603 0.706612i
\(751\) 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
\(753\) 43.6923 + 15.5829i 1.59224 + 0.567874i
\(754\) 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 \(-0.844688\pi\)
0.883307 0.468795i \(-0.155312\pi\)
\(762\) −7.24291 + 20.3081i −0.262383 + 0.735685i
\(763\) −0.0985285 + 0.0985285i −0.00356697 + 0.00356697i
\(764\) 15.3727 0.556164
\(765\) −11.7282 + 18.7692i −0.424036 + 0.678601i
\(766\) 5.25871 0.190005
\(767\) −5.37374 + 5.37374i −0.194034 + 0.194034i
\(768\) −0.581841 + 1.63140i −0.0209954 + 0.0588680i
\(769\) 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 0.424549 0.905405i \(-0.360433\pi\)
−0.905405 + 0.424549i \(0.860433\pi\)
\(774\) 2.67083 3.26804i 0.0960010 0.117467i
\(775\) −4.63027 17.8838i −0.166324 0.642406i
\(776\) 0.842081i 0.0302289i
\(777\) 1.22842 + 0.438119i 0.0440695 + 0.0157174i