Properties

Label 105.2.j.a.8.10
Level 105
Weight 2
Character 105.8
Analytic conductor 0.838
Analytic rank 0
Dimension 24
CM no
Inner twists 4

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) = \( 105 = 3 \cdot 5 \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 105.j (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(0.838429221223\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(12\) over \(\Q(i)\)
Coefficient ring index: multiple of None
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 8.10
Character \(\chi\) = 105.8
Dual form 105.2.j.a.92.10

$q$-expansion

\(f(q)\) \(=\) \(q+(1.24414 + 1.24414i) q^{2} +(0.474620 + 1.66575i) q^{3} +1.09578i q^{4} +(-1.67522 - 1.48109i) q^{5} +(-1.48194 + 2.66293i) q^{6} +(0.707107 - 0.707107i) q^{7} +(1.12498 - 1.12498i) q^{8} +(-2.54947 + 1.58120i) q^{9} +O(q^{10})\) \(q+(1.24414 + 1.24414i) q^{2} +(0.474620 + 1.66575i) q^{3} +1.09578i q^{4} +(-1.67522 - 1.48109i) q^{5} +(-1.48194 + 2.66293i) q^{6} +(0.707107 - 0.707107i) q^{7} +(1.12498 - 1.12498i) q^{8} +(-2.54947 + 1.58120i) q^{9} +(-0.241524 - 3.92690i) q^{10} +1.55221i q^{11} +(-1.82530 + 0.520079i) q^{12} +(-4.50889 - 4.50889i) q^{13} +1.75948 q^{14} +(1.67204 - 3.49346i) q^{15} +4.99083 q^{16} +(2.13370 + 2.13370i) q^{17} +(-5.13914 - 1.20467i) q^{18} +4.20993i q^{19} +(1.62295 - 1.83567i) q^{20} +(1.51347 + 0.842259i) q^{21} +(-1.93117 + 1.93117i) q^{22} +(3.76050 - 3.76050i) q^{23} +(2.40787 + 1.34000i) q^{24} +(0.612732 + 4.96231i) q^{25} -11.2194i q^{26} +(-3.84392 - 3.49632i) q^{27} +(0.774834 + 0.774834i) q^{28} -2.97115 q^{29} +(6.42662 - 2.26611i) q^{30} -5.79770 q^{31} +(3.95934 + 3.95934i) q^{32} +(-2.58559 + 0.736708i) q^{33} +5.30926i q^{34} +(-2.23185 + 0.137270i) q^{35} +(-1.73265 - 2.79366i) q^{36} +(-1.23123 + 1.23123i) q^{37} +(-5.23775 + 5.23775i) q^{38} +(5.37069 - 9.65070i) q^{39} +(-3.55078 + 0.218391i) q^{40} +2.68458i q^{41} +(0.835085 + 2.93087i) q^{42} +(-2.09578 - 2.09578i) q^{43} -1.70088 q^{44} +(6.61283 + 1.12714i) q^{45} +9.35721 q^{46} +(0.0358428 + 0.0358428i) q^{47} +(2.36874 + 8.31349i) q^{48} -1.00000i q^{49} +(-5.41150 + 6.93615i) q^{50} +(-2.54153 + 4.56692i) q^{51} +(4.94075 - 4.94075i) q^{52} +(-4.30833 + 4.30833i) q^{53} +(-0.432457 - 9.13231i) q^{54} +(2.29896 - 2.60029i) q^{55} -1.59096i q^{56} +(-7.01270 + 1.99811i) q^{57} +(-3.69653 - 3.69653i) q^{58} +4.93760 q^{59} +(3.82807 + 1.83219i) q^{60} +3.31687 q^{61} +(-7.21316 - 7.21316i) q^{62} +(-0.684672 + 2.92083i) q^{63} -0.129684i q^{64} +(0.875305 + 14.2315i) q^{65} +(-4.13342 - 2.30028i) q^{66} +(1.71008 - 1.71008i) q^{67} +(-2.33807 + 2.33807i) q^{68} +(8.04889 + 4.47927i) q^{69} +(-2.94752 - 2.60596i) q^{70} +5.73577i q^{71} +(-1.08929 + 4.64692i) q^{72} +(7.26776 + 7.26776i) q^{73} -3.06366 q^{74} +(-7.97518 + 3.37587i) q^{75} -4.61315 q^{76} +(1.09758 + 1.09758i) q^{77} +(18.6887 - 5.32495i) q^{78} +3.59379i q^{79} +(-8.36074 - 7.39187i) q^{80} +(3.99962 - 8.06245i) q^{81} +(-3.34000 + 3.34000i) q^{82} +(12.2139 - 12.2139i) q^{83} +(-0.922931 + 1.65843i) q^{84} +(-0.414214 - 6.73463i) q^{85} -5.21490i q^{86} +(-1.41016 - 4.94920i) q^{87} +(1.74620 + 1.74620i) q^{88} +1.35643 q^{89} +(6.82498 + 9.62963i) q^{90} -6.37653 q^{91} +(4.12069 + 4.12069i) q^{92} +(-2.75170 - 9.65754i) q^{93} +0.0891871i q^{94} +(6.23529 - 7.05256i) q^{95} +(-4.71611 + 8.47447i) q^{96} +(10.9812 - 10.9812i) q^{97} +(1.24414 - 1.24414i) q^{98} +(-2.45435 - 3.95731i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24q - 4q^{3} + O(q^{10}) \) \( 24q - 4q^{3} - 16q^{10} + 16q^{12} - 8q^{13} - 16q^{15} - 16q^{16} - 20q^{18} + 4q^{21} + 8q^{22} - 16q^{25} - 16q^{27} + 20q^{30} + 28q^{33} + 16q^{36} - 16q^{37} + 64q^{40} - 20q^{42} - 40q^{43} + 20q^{45} - 64q^{46} + 16q^{48} - 20q^{51} + 40q^{55} + 4q^{57} + 40q^{58} + 32q^{60} + 32q^{61} - 8q^{63} - 16q^{66} + 24q^{67} - 8q^{70} - 8q^{72} + 32q^{73} - 60q^{75} + 32q^{76} + 60q^{78} + 52q^{81} - 80q^{82} + 24q^{85} + 4q^{87} + 96q^{88} - 24q^{90} - 24q^{91} - 76q^{93} - 96q^{96} + 24q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/105\mathbb{Z}\right)^\times\).

\(n\) \(22\) \(31\) \(71\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(1\) \(-1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.24414 + 1.24414i 0.879741 + 0.879741i 0.993508 0.113766i \(-0.0362914\pi\)
−0.113766 + 0.993508i \(0.536291\pi\)
\(3\) 0.474620 + 1.66575i 0.274022 + 0.961723i
\(4\) 1.09578i 0.547890i
\(5\) −1.67522 1.48109i −0.749182 0.662365i
\(6\) −1.48194 + 2.66293i −0.605000 + 1.08714i
\(7\) 0.707107 0.707107i 0.267261 0.267261i
\(8\) 1.12498 1.12498i 0.397740 0.397740i
\(9\) −2.54947 + 1.58120i −0.849824 + 0.527067i
\(10\) −0.241524 3.92690i −0.0763766 1.24180i
\(11\) 1.55221i 0.468008i 0.972236 + 0.234004i \(0.0751828\pi\)
−0.972236 + 0.234004i \(0.924817\pi\)
\(12\) −1.82530 + 0.520079i −0.526919 + 0.150134i
\(13\) −4.50889 4.50889i −1.25054 1.25054i −0.955478 0.295062i \(-0.904660\pi\)
−0.295062 0.955478i \(-0.595340\pi\)
\(14\) 1.75948 0.470242
\(15\) 1.67204 3.49346i 0.431719 0.902008i
\(16\) 4.99083 1.24771
\(17\) 2.13370 + 2.13370i 0.517499 + 0.517499i 0.916814 0.399315i \(-0.130752\pi\)
−0.399315 + 0.916814i \(0.630752\pi\)
\(18\) −5.13914 1.20467i −1.21131 0.283943i
\(19\) 4.20993i 0.965823i 0.875669 + 0.482912i \(0.160421\pi\)
−0.875669 + 0.482912i \(0.839579\pi\)
\(20\) 1.62295 1.83567i 0.362903 0.410469i
\(21\) 1.51347 + 0.842259i 0.330267 + 0.183796i
\(22\) −1.93117 + 1.93117i −0.411726 + 0.411726i
\(23\) 3.76050 3.76050i 0.784119 0.784119i −0.196404 0.980523i \(-0.562926\pi\)
0.980523 + 0.196404i \(0.0629263\pi\)
\(24\) 2.40787 + 1.34000i 0.491505 + 0.273526i
\(25\) 0.612732 + 4.96231i 0.122546 + 0.992463i
\(26\) 11.2194i 2.20030i
\(27\) −3.84392 3.49632i −0.739763 0.672868i
\(28\) 0.774834 + 0.774834i 0.146430 + 0.146430i
\(29\) −2.97115 −0.551728 −0.275864 0.961197i \(-0.588964\pi\)
−0.275864 + 0.961197i \(0.588964\pi\)
\(30\) 6.42662 2.26611i 1.17334 0.413732i
\(31\) −5.79770 −1.04130 −0.520649 0.853771i \(-0.674310\pi\)
−0.520649 + 0.853771i \(0.674310\pi\)
\(32\) 3.95934 + 3.95934i 0.699919 + 0.699919i
\(33\) −2.58559 + 0.736708i −0.450094 + 0.128244i
\(34\) 5.30926i 0.910531i
\(35\) −2.23185 + 0.137270i −0.377252 + 0.0232029i
\(36\) −1.73265 2.79366i −0.288775 0.465610i
\(37\) −1.23123 + 1.23123i −0.202414 + 0.202414i −0.801033 0.598620i \(-0.795716\pi\)
0.598620 + 0.801033i \(0.295716\pi\)
\(38\) −5.23775 + 5.23775i −0.849675 + 0.849675i
\(39\) 5.37069 9.65070i 0.859998 1.54535i
\(40\) −3.55078 + 0.218391i −0.561428 + 0.0345306i
\(41\) 2.68458i 0.419261i 0.977781 + 0.209631i \(0.0672261\pi\)
−0.977781 + 0.209631i \(0.932774\pi\)
\(42\) 0.835085 + 2.93087i 0.128856 + 0.452242i
\(43\) −2.09578 2.09578i −0.319603 0.319603i 0.529011 0.848615i \(-0.322563\pi\)
−0.848615 + 0.529011i \(0.822563\pi\)
\(44\) −1.70088 −0.256417
\(45\) 6.61283 + 1.12714i 0.985783 + 0.168025i
\(46\) 9.35721 1.37964
\(47\) 0.0358428 + 0.0358428i 0.00522821 + 0.00522821i 0.709716 0.704488i \(-0.248823\pi\)
−0.704488 + 0.709716i \(0.748823\pi\)
\(48\) 2.36874 + 8.31349i 0.341899 + 1.19995i
\(49\) 1.00000i 0.142857i
\(50\) −5.41150 + 6.93615i −0.765302 + 0.980920i
\(51\) −2.54153 + 4.56692i −0.355885 + 0.639497i
\(52\) 4.94075 4.94075i 0.685158 0.685158i
\(53\) −4.30833 + 4.30833i −0.591794 + 0.591794i −0.938116 0.346322i \(-0.887431\pi\)
0.346322 + 0.938116i \(0.387431\pi\)
\(54\) −0.432457 9.13231i −0.0588500 1.24275i
\(55\) 2.29896 2.60029i 0.309992 0.350623i
\(56\) 1.59096i 0.212601i
\(57\) −7.01270 + 1.99811i −0.928855 + 0.264657i
\(58\) −3.69653 3.69653i −0.485378 0.485378i
\(59\) 4.93760 0.642821 0.321410 0.946940i \(-0.395843\pi\)
0.321410 + 0.946940i \(0.395843\pi\)
\(60\) 3.82807 + 1.83219i 0.494201 + 0.236535i
\(61\) 3.31687 0.424681 0.212341 0.977196i \(-0.431891\pi\)
0.212341 + 0.977196i \(0.431891\pi\)
\(62\) −7.21316 7.21316i −0.916073 0.916073i
\(63\) −0.684672 + 2.92083i −0.0862606 + 0.367989i
\(64\) 0.129684i 0.0162105i
\(65\) 0.875305 + 14.2315i 0.108568 + 1.76519i
\(66\) −4.13342 2.30028i −0.508788 0.283145i
\(67\) 1.71008 1.71008i 0.208919 0.208919i −0.594889 0.803808i \(-0.702804\pi\)
0.803808 + 0.594889i \(0.202804\pi\)
\(68\) −2.33807 + 2.33807i −0.283533 + 0.283533i
\(69\) 8.04889 + 4.47927i 0.968972 + 0.539240i
\(70\) −2.94752 2.60596i −0.352296 0.311471i
\(71\) 5.73577i 0.680711i 0.940297 + 0.340356i \(0.110547\pi\)
−0.940297 + 0.340356i \(0.889453\pi\)
\(72\) −1.08929 + 4.64692i −0.128374 + 0.547644i
\(73\) 7.26776 + 7.26776i 0.850627 + 0.850627i 0.990210 0.139583i \(-0.0445763\pi\)
−0.139583 + 0.990210i \(0.544576\pi\)
\(74\) −3.06366 −0.356143
\(75\) −7.97518 + 3.37587i −0.920894 + 0.389812i
\(76\) −4.61315 −0.529165
\(77\) 1.09758 + 1.09758i 0.125080 + 0.125080i
\(78\) 18.6887 5.32495i 2.11608 0.602931i
\(79\) 3.59379i 0.404333i 0.979351 + 0.202166i \(0.0647982\pi\)
−0.979351 + 0.202166i \(0.935202\pi\)
\(80\) −8.36074 7.39187i −0.934759 0.826437i
\(81\) 3.99962 8.06245i 0.444402 0.895828i
\(82\) −3.34000 + 3.34000i −0.368841 + 0.368841i
\(83\) 12.2139 12.2139i 1.34065 1.34065i 0.445228 0.895417i \(-0.353123\pi\)
0.895417 0.445228i \(-0.146877\pi\)
\(84\) −0.922931 + 1.65843i −0.100700 + 0.180950i
\(85\) −0.414214 6.73463i −0.0449278 0.730474i
\(86\) 5.21490i 0.562337i
\(87\) −1.41016 4.94920i −0.151185 0.530610i
\(88\) 1.74620 + 1.74620i 0.186145 + 0.186145i
\(89\) 1.35643 0.143782 0.0718908 0.997413i \(-0.477097\pi\)
0.0718908 + 0.997413i \(0.477097\pi\)
\(90\) 6.82498 + 9.62963i 0.719416 + 1.01505i
\(91\) −6.37653 −0.668442
\(92\) 4.12069 + 4.12069i 0.429611 + 0.429611i
\(93\) −2.75170 9.65754i −0.285338 1.00144i
\(94\) 0.0891871i 0.00919895i
\(95\) 6.23529 7.05256i 0.639727 0.723577i
\(96\) −4.71611 + 8.47447i −0.481336 + 0.864922i
\(97\) 10.9812 10.9812i 1.11497 1.11497i 0.122503 0.992468i \(-0.460908\pi\)
0.992468 0.122503i \(-0.0390922\pi\)
\(98\) 1.24414 1.24414i 0.125677 0.125677i
\(99\) −2.45435 3.95731i −0.246671 0.397724i
\(100\) −5.43760 + 0.671419i −0.543760 + 0.0671419i
\(101\) 12.7033i 1.26402i 0.774958 + 0.632012i \(0.217771\pi\)
−0.774958 + 0.632012i \(0.782229\pi\)
\(102\) −8.84392 + 2.51988i −0.875679 + 0.249505i
\(103\) −1.46798 1.46798i −0.144644 0.144644i 0.631076 0.775721i \(-0.282613\pi\)
−0.775721 + 0.631076i \(0.782613\pi\)
\(104\) −10.1448 −0.994779
\(105\) −1.28794 3.65256i −0.125690 0.356454i
\(106\) −10.7203 −1.04125
\(107\) −13.5523 13.5523i −1.31015 1.31015i −0.921302 0.388849i \(-0.872873\pi\)
−0.388849 0.921302i \(-0.627127\pi\)
\(108\) 3.83120 4.21209i 0.368658 0.405309i
\(109\) 4.84158i 0.463739i −0.972747 0.231869i \(-0.925516\pi\)
0.972747 0.231869i \(-0.0744842\pi\)
\(110\) 6.09536 0.374895i 0.581170 0.0357449i
\(111\) −2.63530 1.46656i −0.250132 0.139200i
\(112\) 3.52905 3.52905i 0.333464 0.333464i
\(113\) −10.6222 + 10.6222i −0.999254 + 0.999254i −1.00000 0.000746132i \(-0.999762\pi\)
0.000746132 1.00000i \(0.499762\pi\)
\(114\) −11.2107 6.23886i −1.04998 0.584323i
\(115\) −11.8693 + 0.730023i −1.10682 + 0.0680750i
\(116\) 3.25572i 0.302286i
\(117\) 18.6247 + 4.36583i 1.72186 + 0.403621i
\(118\) 6.14308 + 6.14308i 0.565516 + 0.565516i
\(119\) 3.01751 0.276615
\(120\) −2.04906 5.81108i −0.187053 0.530477i
\(121\) 8.59066 0.780969
\(122\) 4.12665 + 4.12665i 0.373610 + 0.373610i
\(123\) −4.47185 + 1.27415i −0.403213 + 0.114887i
\(124\) 6.35300i 0.570517i
\(125\) 6.32318 9.22049i 0.565563 0.824705i
\(126\) −4.48575 + 2.78209i −0.399623 + 0.247849i
\(127\) 10.1595 10.1595i 0.901511 0.901511i −0.0940560 0.995567i \(-0.529983\pi\)
0.995567 + 0.0940560i \(0.0299833\pi\)
\(128\) 8.08003 8.08003i 0.714180 0.714180i
\(129\) 2.49636 4.48575i 0.219792 0.394948i
\(130\) −16.6170 + 18.7950i −1.45740 + 1.64843i
\(131\) 0.509374i 0.0445042i −0.999752 0.0222521i \(-0.992916\pi\)
0.999752 0.0222521i \(-0.00708365\pi\)
\(132\) −0.807270 2.83324i −0.0702638 0.246602i
\(133\) 2.97687 + 2.97687i 0.258127 + 0.258127i
\(134\) 4.25516 0.367590
\(135\) 1.26104 + 11.5503i 0.108533 + 0.994093i
\(136\) 4.80074 0.411660
\(137\) −2.61947 2.61947i −0.223797 0.223797i 0.586298 0.810095i \(-0.300585\pi\)
−0.810095 + 0.586298i \(0.800585\pi\)
\(138\) 4.44112 + 15.5868i 0.378053 + 1.32684i
\(139\) 6.35379i 0.538921i 0.963011 + 0.269461i \(0.0868454\pi\)
−0.963011 + 0.269461i \(0.913155\pi\)
\(140\) −0.150418 2.44562i −0.0127126 0.206692i
\(141\) −0.0426936 + 0.0767170i −0.00359545 + 0.00646074i
\(142\) −7.13612 + 7.13612i −0.598850 + 0.598850i
\(143\) 6.99872 6.99872i 0.585262 0.585262i
\(144\) −12.7240 + 7.89149i −1.06033 + 0.657624i
\(145\) 4.97733 + 4.40054i 0.413344 + 0.365445i
\(146\) 18.0843i 1.49666i
\(147\) 1.66575 0.474620i 0.137389 0.0391460i
\(148\) −1.34916 1.34916i −0.110900 0.110900i
\(149\) −4.27965 −0.350602 −0.175301 0.984515i \(-0.556090\pi\)
−0.175301 + 0.984515i \(0.556090\pi\)
\(150\) −14.1223 5.72219i −1.15308 0.467215i
\(151\) −5.21232 −0.424172 −0.212086 0.977251i \(-0.568026\pi\)
−0.212086 + 0.977251i \(0.568026\pi\)
\(152\) 4.73607 + 4.73607i 0.384146 + 0.384146i
\(153\) −8.81363 2.06601i −0.712539 0.167027i
\(154\) 2.73108i 0.220077i
\(155\) 9.71243 + 8.58693i 0.780121 + 0.689719i
\(156\) 10.5750 + 5.88509i 0.846681 + 0.471185i
\(157\) −4.35999 + 4.35999i −0.347965 + 0.347965i −0.859351 0.511386i \(-0.829132\pi\)
0.511386 + 0.859351i \(0.329132\pi\)
\(158\) −4.47119 + 4.47119i −0.355708 + 0.355708i
\(159\) −9.22143 5.13179i −0.731307 0.406978i
\(160\) −0.768623 12.4969i −0.0607650 0.987968i
\(161\) 5.31816i 0.419129i
\(162\) 15.0069 5.05474i 1.17906 0.397138i
\(163\) 5.34339 + 5.34339i 0.418527 + 0.418527i 0.884696 0.466169i \(-0.154366\pi\)
−0.466169 + 0.884696i \(0.654366\pi\)
\(164\) −2.94171 −0.229709
\(165\) 5.42257 + 2.59535i 0.422147 + 0.202048i
\(166\) 30.3916 2.35884
\(167\) 13.8232 + 13.8232i 1.06967 + 1.06967i 0.997384 + 0.0722908i \(0.0230310\pi\)
0.0722908 + 0.997384i \(0.476969\pi\)
\(168\) 2.65015 0.755101i 0.204463 0.0582573i
\(169\) 27.6601i 2.12770i
\(170\) 7.86350 8.89418i 0.603103 0.682153i
\(171\) −6.65673 10.7331i −0.509053 0.820780i
\(172\) 2.29651 2.29651i 0.175108 0.175108i
\(173\) −2.06635 + 2.06635i −0.157102 + 0.157102i −0.781281 0.624179i \(-0.785433\pi\)
0.624179 + 0.781281i \(0.285433\pi\)
\(174\) 4.40306 7.91195i 0.333795 0.599803i
\(175\) 3.94215 + 3.07562i 0.297999 + 0.232495i
\(176\) 7.74679i 0.583936i
\(177\) 2.34348 + 8.22483i 0.176147 + 0.618216i
\(178\) 1.68759 + 1.68759i 0.126491 + 0.126491i
\(179\) −11.9186 −0.890841 −0.445420 0.895322i \(-0.646946\pi\)
−0.445420 + 0.895322i \(0.646946\pi\)
\(180\) −1.23510 + 7.24621i −0.0920591 + 0.540101i
\(181\) −17.5945 −1.30779 −0.653893 0.756587i \(-0.726865\pi\)
−0.653893 + 0.756587i \(0.726865\pi\)
\(182\) −7.93331 7.93331i −0.588056 0.588056i
\(183\) 1.57425 + 5.52508i 0.116372 + 0.408426i
\(184\) 8.46097i 0.623751i
\(185\) 3.88616 0.239018i 0.285716 0.0175730i
\(186\) 8.59184 15.4389i 0.629985 1.13203i
\(187\) −3.31195 + 3.31195i −0.242194 + 0.242194i
\(188\) −0.0392758 + 0.0392758i −0.00286449 + 0.00286449i
\(189\) −5.19034 + 0.245787i −0.377541 + 0.0178783i
\(190\) 16.5320 1.01680i 1.19936 0.0737663i
\(191\) 5.54023i 0.400877i −0.979706 0.200438i \(-0.935763\pi\)
0.979706 0.200438i \(-0.0642366\pi\)
\(192\) 0.216021 0.0615505i 0.0155900 0.00444202i
\(193\) −13.9027 13.9027i −1.00074 1.00074i −1.00000 0.000740397i \(-0.999764\pi\)
−0.000740397 1.00000i \(-0.500236\pi\)
\(194\) 27.3243 1.96177
\(195\) −23.2907 + 8.21257i −1.66788 + 0.588115i
\(196\) 1.09578 0.0782700
\(197\) −12.7155 12.7155i −0.905939 0.905939i 0.0900024 0.995942i \(-0.471313\pi\)
−0.995942 + 0.0900024i \(0.971313\pi\)
\(198\) 1.86989 7.97701i 0.132888 0.566901i
\(199\) 6.11487i 0.433472i −0.976230 0.216736i \(-0.930459\pi\)
0.976230 0.216736i \(-0.0695411\pi\)
\(200\) 6.27181 + 4.89318i 0.443484 + 0.346000i
\(201\) 3.66021 + 2.03693i 0.258171 + 0.143674i
\(202\) −15.8047 + 15.8047i −1.11201 + 1.11201i
\(203\) −2.10092 + 2.10092i −0.147455 + 0.147455i
\(204\) −5.00434 2.78495i −0.350374 0.194986i
\(205\) 3.97611 4.49727i 0.277704 0.314103i
\(206\) 3.65275i 0.254499i
\(207\) −3.64119 + 15.5334i −0.253080 + 1.07965i
\(208\) −22.5031 22.5031i −1.56031 1.56031i
\(209\) −6.53467 −0.452013
\(210\) 2.94193 6.14669i 0.203012 0.424162i
\(211\) 12.4900 0.859849 0.429924 0.902865i \(-0.358540\pi\)
0.429924 + 0.902865i \(0.358540\pi\)
\(212\) −4.72098 4.72098i −0.324238 0.324238i
\(213\) −9.55439 + 2.72231i −0.654656 + 0.186530i
\(214\) 33.7220i 2.30519i
\(215\) 0.406852 + 6.61494i 0.0277471 + 0.451135i
\(216\) −8.25761 + 0.391036i −0.561859 + 0.0266067i
\(217\) −4.09959 + 4.09959i −0.278298 + 0.278298i
\(218\) 6.02361 6.02361i 0.407970 0.407970i
\(219\) −8.65688 + 15.5557i −0.584978 + 1.05116i
\(220\) 2.84934 + 2.51916i 0.192103 + 0.169841i
\(221\) 19.2412i 1.29431i
\(222\) −1.45407 5.10330i −0.0975910 0.342511i
\(223\) 8.80424 + 8.80424i 0.589576 + 0.589576i 0.937516 0.347941i \(-0.113119\pi\)
−0.347941 + 0.937516i \(0.613119\pi\)
\(224\) 5.59935 0.374123
\(225\) −9.40855 11.6824i −0.627237 0.778829i
\(226\) −26.4311 −1.75817
\(227\) −15.7424 15.7424i −1.04486 1.04486i −0.998945 0.0459126i \(-0.985380\pi\)
−0.0459126 0.998945i \(-0.514620\pi\)
\(228\) −2.18949 7.68438i −0.145003 0.508910i
\(229\) 8.27446i 0.546791i −0.961902 0.273396i \(-0.911853\pi\)
0.961902 0.273396i \(-0.0881468\pi\)
\(230\) −15.6754 13.8589i −1.03360 0.913828i
\(231\) −1.30736 + 2.34922i −0.0860179 + 0.154567i
\(232\) −3.34247 + 3.34247i −0.219444 + 0.219444i
\(233\) −12.6425 + 12.6425i −0.828239 + 0.828239i −0.987273 0.159034i \(-0.949162\pi\)
0.159034 + 0.987273i \(0.449162\pi\)
\(234\) 17.7401 + 28.6035i 1.15971 + 1.86987i
\(235\) −0.00695813 0.113131i −0.000453898 0.00737986i
\(236\) 5.41052i 0.352195i
\(237\) −5.98637 + 1.70568i −0.388856 + 0.110796i
\(238\) 3.75421 + 3.75421i 0.243350 + 0.243350i
\(239\) 25.8260 1.67054 0.835271 0.549838i \(-0.185311\pi\)
0.835271 + 0.549838i \(0.185311\pi\)
\(240\) 8.34487 17.4353i 0.538659 1.12544i
\(241\) −10.5197 −0.677631 −0.338815 0.940853i \(-0.610026\pi\)
−0.338815 + 0.940853i \(0.610026\pi\)
\(242\) 10.6880 + 10.6880i 0.687051 + 0.687051i
\(243\) 15.3284 + 2.83578i 0.983314 + 0.181915i
\(244\) 3.63456i 0.232679i
\(245\) −1.48109 + 1.67522i −0.0946235 + 0.107026i
\(246\) −7.14885 3.97839i −0.455794 0.253653i
\(247\) 18.9821 18.9821i 1.20780 1.20780i
\(248\) −6.52229 + 6.52229i −0.414166 + 0.414166i
\(249\) 26.1422 + 14.5483i 1.65670 + 0.921964i
\(250\) 19.3385 3.60466i 1.22308 0.227979i
\(251\) 6.94563i 0.438405i −0.975679 0.219202i \(-0.929655\pi\)
0.975679 0.219202i \(-0.0703455\pi\)
\(252\) −3.20058 0.750250i −0.201618 0.0472613i
\(253\) 5.83708 + 5.83708i 0.366974 + 0.366974i
\(254\) 25.2798 1.58619
\(255\) 11.0216 3.88637i 0.690202 0.243374i
\(256\) 19.8460 1.24038
\(257\) −8.17057 8.17057i −0.509666 0.509666i 0.404758 0.914424i \(-0.367356\pi\)
−0.914424 + 0.404758i \(0.867356\pi\)
\(258\) 8.68674 2.47509i 0.540813 0.154093i
\(259\) 1.74123i 0.108195i
\(260\) −15.5945 + 0.959142i −0.967133 + 0.0594835i
\(261\) 7.57485 4.69797i 0.468872 0.290797i
\(262\) 0.633733 0.633733i 0.0391522 0.0391522i
\(263\) −0.118860 + 0.118860i −0.00732922 + 0.00732922i −0.710762 0.703433i \(-0.751650\pi\)
0.703433 + 0.710762i \(0.251650\pi\)
\(264\) −2.07996 + 3.73752i −0.128012 + 0.230028i
\(265\) 13.5984 0.836371i 0.835345 0.0513779i
\(266\) 7.40729i 0.454170i
\(267\) 0.643790 + 2.25948i 0.0393993 + 0.138278i
\(268\) 1.87387 + 1.87387i 0.114465 + 0.114465i
\(269\) −6.60330 −0.402610 −0.201305 0.979529i \(-0.564518\pi\)
−0.201305 + 0.979529i \(0.564518\pi\)
\(270\) −12.8013 + 15.9391i −0.779064 + 0.970025i
\(271\) −23.8292 −1.44752 −0.723759 0.690052i \(-0.757587\pi\)
−0.723759 + 0.690052i \(0.757587\pi\)
\(272\) 10.6489 + 10.6489i 0.645687 + 0.645687i
\(273\) −3.02643 10.6217i −0.183168 0.642856i
\(274\) 6.51800i 0.393767i
\(275\) −7.70253 + 0.951086i −0.464480 + 0.0573527i
\(276\) −4.90829 + 8.81981i −0.295444 + 0.530890i
\(277\) −14.3921 + 14.3921i −0.864736 + 0.864736i −0.991884 0.127147i \(-0.959418\pi\)
0.127147 + 0.991884i \(0.459418\pi\)
\(278\) −7.90501 + 7.90501i −0.474111 + 0.474111i
\(279\) 14.7811 9.16732i 0.884920 0.548833i
\(280\) −2.35636 + 2.66521i −0.140819 + 0.159277i
\(281\) 1.50698i 0.0898991i 0.998989 + 0.0449495i \(0.0143127\pi\)
−0.998989 + 0.0449495i \(0.985687\pi\)
\(282\) −0.148564 + 0.0423300i −0.00884685 + 0.00252071i
\(283\) 8.49114 + 8.49114i 0.504746 + 0.504746i 0.912909 0.408163i \(-0.133830\pi\)
−0.408163 + 0.912909i \(0.633830\pi\)
\(284\) −6.28515 −0.372955
\(285\) 14.7072 + 7.03917i 0.871180 + 0.416965i
\(286\) 17.4148 1.02976
\(287\) 1.89828 + 1.89828i 0.112052 + 0.112052i
\(288\) −16.3547 3.83372i −0.963712 0.225904i
\(289\) 7.89463i 0.464390i
\(290\) 0.717603 + 11.6674i 0.0421391 + 0.685133i
\(291\) 23.5039 + 13.0801i 1.37782 + 0.766768i
\(292\) −7.96387 + 7.96387i −0.466050 + 0.466050i
\(293\) 2.35851 2.35851i 0.137786 0.137786i −0.634850 0.772635i \(-0.718938\pi\)
0.772635 + 0.634850i \(0.218938\pi\)
\(294\) 2.66293 + 1.48194i 0.155305 + 0.0864285i
\(295\) −8.27157 7.31304i −0.481590 0.425782i
\(296\) 2.77022i 0.161016i
\(297\) 5.42702 5.96656i 0.314907 0.346215i
\(298\) −5.32449 5.32449i −0.308439 0.308439i
\(299\) −33.9114 −1.96115
\(300\) −3.69921 8.73904i −0.213574 0.504549i
\(301\) −2.96388 −0.170835
\(302\) −6.48486 6.48486i −0.373162 0.373162i
\(303\) −21.1606 + 6.02923i −1.21564 + 0.346370i
\(304\) 21.0110i 1.20506i
\(305\) −5.55649 4.91259i −0.318163 0.281294i
\(306\) −8.39500 13.5358i −0.479910 0.773791i
\(307\) −0.793602 + 0.793602i −0.0452933 + 0.0452933i −0.729391 0.684097i \(-0.760196\pi\)
0.684097 + 0.729391i \(0.260196\pi\)
\(308\) −1.20270 + 1.20270i −0.0685303 + 0.0685303i
\(309\) 1.74856 3.14203i 0.0994722 0.178744i
\(310\) 1.40028 + 22.7670i 0.0795308 + 1.29308i
\(311\) 9.91521i 0.562240i 0.959673 + 0.281120i \(0.0907059\pi\)
−0.959673 + 0.281120i \(0.909294\pi\)
\(312\) −4.81492 16.8987i −0.272591 0.956702i
\(313\) −9.95137 9.95137i −0.562484 0.562484i 0.367528 0.930012i \(-0.380204\pi\)
−0.930012 + 0.367528i \(0.880204\pi\)
\(314\) −10.8489 −0.612238
\(315\) 5.47299 3.87897i 0.308368 0.218555i
\(316\) −3.93800 −0.221530
\(317\) 14.9788 + 14.9788i 0.841296 + 0.841296i 0.989027 0.147732i \(-0.0471972\pi\)
−0.147732 + 0.989027i \(0.547197\pi\)
\(318\) −5.08809 17.8574i −0.285326 1.00140i
\(319\) 4.61183i 0.258213i
\(320\) −0.192074 + 0.217249i −0.0107372 + 0.0121446i
\(321\) 16.1426 29.0070i 0.900992 1.61901i
\(322\) 6.61654 6.61654i 0.368726 0.368726i
\(323\) −8.98273 + 8.98273i −0.499812 + 0.499812i
\(324\) 8.83467 + 4.38270i 0.490815 + 0.243483i
\(325\) 19.6118 25.1372i 1.08787 1.39436i
\(326\) 13.2959i 0.736391i
\(327\) 8.06487 2.29791i 0.445989 0.127075i
\(328\) 3.02009 + 3.02009i 0.166757 + 0.166757i
\(329\) 0.0506894 0.00279460
\(330\) 3.51746 + 9.97544i 0.193630 + 0.549130i
\(331\) −3.10247 −0.170527 −0.0852635 0.996358i \(-0.527173\pi\)
−0.0852635 + 0.996358i \(0.527173\pi\)
\(332\) 13.3837 + 13.3837i 0.734526 + 0.734526i
\(333\) 1.19217 5.08582i 0.0653305 0.278701i
\(334\) 34.3962i 1.88207i
\(335\) −5.39754 + 0.331976i −0.294899 + 0.0181378i
\(336\) 7.55348 + 4.20357i 0.412076 + 0.229323i
\(337\) −23.2030 + 23.2030i −1.26395 + 1.26395i −0.314784 + 0.949163i \(0.601932\pi\)
−0.949163 + 0.314784i \(0.898068\pi\)
\(338\) −34.4131 + 34.4131i −1.87183 + 1.87183i
\(339\) −22.7355 12.6525i −1.23482 0.687188i
\(340\) 7.37968 0.453887i 0.400219 0.0246155i
\(341\) 8.99922i 0.487335i
\(342\) 5.07157 21.6354i 0.274239 1.16991i
\(343\) −0.707107 0.707107i −0.0381802 0.0381802i
\(344\) −4.71541 −0.254238
\(345\) −6.84946 19.4249i −0.368762 1.04580i
\(346\) −5.14167 −0.276418
\(347\) 14.1837 + 14.1837i 0.761423 + 0.761423i 0.976580 0.215157i \(-0.0690262\pi\)
−0.215157 + 0.976580i \(0.569026\pi\)
\(348\) 5.42323 1.54523i 0.290716 0.0828330i
\(349\) 9.27152i 0.496293i 0.968723 + 0.248146i \(0.0798214\pi\)
−0.968723 + 0.248146i \(0.920179\pi\)
\(350\) 1.07809 + 8.73111i 0.0576264 + 0.466697i
\(351\) 1.56726 + 33.0963i 0.0836544 + 1.76655i
\(352\) −6.14571 + 6.14571i −0.327568 + 0.327568i
\(353\) 20.2421 20.2421i 1.07738 1.07738i 0.0806368 0.996744i \(-0.474305\pi\)
0.996744 0.0806368i \(-0.0256954\pi\)
\(354\) −7.31723 + 13.1485i −0.388906 + 0.698834i
\(355\) 8.49521 9.60869i 0.450879 0.509976i
\(356\) 1.48635i 0.0787765i
\(357\) 1.43217 + 5.02643i 0.0757985 + 0.266027i
\(358\) −14.8285 14.8285i −0.783710 0.783710i
\(359\) 18.8289 0.993751 0.496876 0.867822i \(-0.334481\pi\)
0.496876 + 0.867822i \(0.334481\pi\)
\(360\) 8.70730 6.17128i 0.458915 0.325255i
\(361\) 1.27653 0.0671857
\(362\) −21.8900 21.8900i −1.15051 1.15051i
\(363\) 4.07730 + 14.3099i 0.214003 + 0.751076i
\(364\) 6.98727i 0.366233i
\(365\) −1.41088 22.9393i −0.0738490 1.20070i
\(366\) −4.91540 + 8.83258i −0.256932 + 0.461686i
\(367\) 0.942012 0.942012i 0.0491726 0.0491726i −0.682093 0.731266i \(-0.738930\pi\)
0.731266 + 0.682093i \(0.238930\pi\)
\(368\) 18.7680 18.7680i 0.978351 0.978351i
\(369\) −4.24486 6.84426i −0.220978 0.356298i
\(370\) 5.13231 + 4.53756i 0.266816 + 0.235897i
\(371\) 6.09289i 0.316327i
\(372\) 10.5825 3.01526i 0.548679 0.156334i
\(373\) 7.39940 + 7.39940i 0.383127 + 0.383127i 0.872227 0.489101i \(-0.162675\pi\)
−0.489101 + 0.872227i \(0.662675\pi\)
\(374\) −8.24107 −0.426135
\(375\) 18.3602 + 6.15664i 0.948115 + 0.317928i
\(376\) 0.0806448 0.00415894
\(377\) 13.3966 + 13.3966i 0.689958 + 0.689958i
\(378\) −6.76331 6.15172i −0.347867 0.316411i
\(379\) 21.9486i 1.12743i −0.825971 0.563713i \(-0.809373\pi\)
0.825971 0.563713i \(-0.190627\pi\)
\(380\) 7.72805 + 6.83250i 0.396441 + 0.350500i
\(381\) 21.7452 + 12.1013i 1.11404 + 0.619970i
\(382\) 6.89283 6.89283i 0.352668 0.352668i
\(383\) 19.3310 19.3310i 0.987768 0.987768i −0.0121580 0.999926i \(-0.503870\pi\)
0.999926 + 0.0121580i \(0.00387012\pi\)
\(384\) 17.2943 + 9.62440i 0.882545 + 0.491143i
\(385\) −0.213071 3.46429i −0.0108591 0.176557i
\(386\) 34.5939i 1.76079i
\(387\) 8.65698 + 2.02929i 0.440059 + 0.103154i
\(388\) 12.0330 + 12.0330i 0.610882 + 0.610882i
\(389\) −30.7961 −1.56142 −0.780712 0.624891i \(-0.785144\pi\)
−0.780712 + 0.624891i \(0.785144\pi\)
\(390\) −39.1945 18.7593i −1.98469 0.949914i
\(391\) 16.0476 0.811562
\(392\) −1.12498 1.12498i −0.0568200 0.0568200i
\(393\) 0.848491 0.241759i 0.0428007 0.0121951i
\(394\) 31.6397i 1.59398i
\(395\) 5.32273 6.02039i 0.267816 0.302919i
\(396\) 4.33634 2.68943i 0.217909 0.135149i
\(397\) −20.8254 + 20.8254i −1.04520 + 1.04520i −0.0462702 + 0.998929i \(0.514734\pi\)
−0.998929 + 0.0462702i \(0.985266\pi\)
\(398\) 7.60777 7.60777i 0.381343 0.381343i
\(399\) −3.54585 + 6.37161i −0.177514 + 0.318979i
\(400\) 3.05804 + 24.7660i 0.152902 + 1.23830i
\(401\) 20.9084i 1.04412i −0.852910 0.522058i \(-0.825165\pi\)
0.852910 0.522058i \(-0.174835\pi\)
\(402\) 2.01958 + 7.08805i 0.100728 + 0.353520i
\(403\) 26.1412 + 26.1412i 1.30218 + 1.30218i
\(404\) −13.9200 −0.692547
\(405\) −18.6415 + 7.58258i −0.926302 + 0.376782i
\(406\) −5.22768 −0.259445
\(407\) −1.91113 1.91113i −0.0947311 0.0947311i
\(408\) 2.27853 + 7.99685i 0.112804 + 0.395903i
\(409\) 11.5773i 0.572460i −0.958161 0.286230i \(-0.907598\pi\)
0.958161 0.286230i \(-0.0924022\pi\)
\(410\) 10.5421 0.648391i 0.520637 0.0320217i
\(411\) 3.12014 5.60665i 0.153905 0.276556i
\(412\) 1.60858 1.60858i 0.0792493 0.0792493i
\(413\) 3.49141 3.49141i 0.171801 0.171801i
\(414\) −23.8559 + 14.7956i −1.17246 + 0.727165i
\(415\) −38.5508 + 2.37106i −1.89238 + 0.116391i
\(416\) 35.7044i 1.75055i
\(417\) −10.5838 + 3.01563i −0.518293 + 0.147676i
\(418\) −8.13006 8.13006i −0.397654 0.397654i
\(419\) 0.525515 0.0256731 0.0128365 0.999918i \(-0.495914\pi\)
0.0128365 + 0.999918i \(0.495914\pi\)
\(420\) 4.00241 1.41130i 0.195297 0.0688643i
\(421\) −15.5297 −0.756871 −0.378435 0.925628i \(-0.623538\pi\)
−0.378435 + 0.925628i \(0.623538\pi\)
\(422\) 15.5394 + 15.5394i 0.756445 + 0.756445i
\(423\) −0.148055 0.0347056i −0.00719868 0.00168744i
\(424\) 9.69354i 0.470760i
\(425\) −9.28071 + 11.8955i −0.450181 + 0.577016i
\(426\) −15.2740 8.50008i −0.740026 0.411830i
\(427\) 2.34538 2.34538i 0.113501 0.113501i
\(428\) 14.8503 14.8503i 0.717818 0.717818i
\(429\) 14.9799 + 8.33641i 0.723235 + 0.402486i
\(430\) −7.72374 + 8.73611i −0.372472 + 0.421292i
\(431\) 23.0144i 1.10856i 0.832329 + 0.554282i \(0.187007\pi\)
−0.832329 + 0.554282i \(0.812993\pi\)
\(432\) −19.1843 17.4495i −0.923007 0.839542i
\(433\) −15.4001 15.4001i −0.740081 0.740081i 0.232513 0.972593i \(-0.425305\pi\)
−0.972593 + 0.232513i \(0.925305\pi\)
\(434\) −10.2010 −0.489661
\(435\) −4.96788 + 10.3796i −0.238192 + 0.497663i
\(436\) 5.30530 0.254078
\(437\) 15.8314 + 15.8314i 0.757321 + 0.757321i
\(438\) −30.1239 + 8.58315i −1.43938 + 0.410119i
\(439\) 6.04288i 0.288411i 0.989548 + 0.144205i \(0.0460626\pi\)
−0.989548 + 0.144205i \(0.953937\pi\)
\(440\) −0.338988 5.51155i −0.0161606 0.262753i
\(441\) 1.58120 + 2.54947i 0.0752952 + 0.121403i
\(442\) 23.9388 23.9388i 1.13865 1.13865i
\(443\) 8.64725 8.64725i 0.410843 0.410843i −0.471189 0.882032i \(-0.656175\pi\)
0.882032 + 0.471189i \(0.156175\pi\)
\(444\) 1.60703 2.88771i 0.0762664 0.137045i
\(445\) −2.27232 2.00900i −0.107718 0.0952358i
\(446\) 21.9075i 1.03735i
\(447\) −2.03121 7.12884i −0.0960727 0.337183i
\(448\) −0.0917003 0.0917003i −0.00433243 0.00433243i
\(449\) 20.7599 0.979723 0.489861 0.871800i \(-0.337047\pi\)
0.489861 + 0.871800i \(0.337047\pi\)
\(450\) 2.82903 26.2402i 0.133362 1.23697i
\(451\) −4.16702 −0.196217
\(452\) −11.6396 11.6396i −0.547481 0.547481i
\(453\) −2.47387 8.68243i −0.116232 0.407936i
\(454\) 39.1715i 1.83841i
\(455\) 10.6821 + 9.44422i 0.500784 + 0.442752i
\(456\) −5.64130 + 10.1370i −0.264178 + 0.474707i
\(457\) 17.3075 17.3075i 0.809612 0.809612i −0.174963 0.984575i \(-0.555980\pi\)
0.984575 + 0.174963i \(0.0559805\pi\)
\(458\) 10.2946 10.2946i 0.481035 0.481035i
\(459\) −0.741664 15.6619i −0.0346179 0.731035i
\(460\) −0.799945 13.0062i −0.0372976 0.606416i
\(461\) 4.36421i 0.203262i 0.994822 + 0.101631i \(0.0324061\pi\)
−0.994822 + 0.101631i \(0.967594\pi\)
\(462\) −4.54931 + 1.29622i −0.211653 + 0.0603058i
\(463\) 2.04147 + 2.04147i 0.0948752 + 0.0948752i 0.752951 0.658076i \(-0.228630\pi\)
−0.658076 + 0.752951i \(0.728630\pi\)
\(464\) −14.8285 −0.688394
\(465\) −9.69400 + 20.2540i −0.449548 + 0.939259i
\(466\) −31.4582 −1.45727
\(467\) 13.9629 + 13.9629i 0.646128 + 0.646128i 0.952055 0.305927i \(-0.0989663\pi\)
−0.305927 + 0.952055i \(0.598966\pi\)
\(468\) −4.78399 + 20.4086i −0.221140 + 0.943388i
\(469\) 2.41842i 0.111672i
\(470\) 0.132094 0.149408i 0.00609306 0.00689169i
\(471\) −9.33200 5.19333i −0.429996 0.239296i
\(472\) 5.55469 5.55469i 0.255675 0.255675i
\(473\) 3.25308 3.25308i 0.149577 0.149577i
\(474\) −9.57001 5.32578i −0.439565 0.244621i
\(475\) −20.8910 + 2.57956i −0.958544 + 0.118358i
\(476\) 3.30653i 0.151555i
\(477\) 4.17163 17.7963i 0.191006 0.814836i
\(478\) 32.1312 + 32.1312i 1.46965 + 1.46965i
\(479\) −16.0067 −0.731367 −0.365683 0.930739i \(-0.619165\pi\)
−0.365683 + 0.930739i \(0.619165\pi\)
\(480\) 20.4520 7.21162i 0.933502 0.329164i
\(481\) 11.1030 0.506252
\(482\) −13.0880 13.0880i −0.596140 0.596140i
\(483\) 8.85874 2.52410i 0.403087 0.114851i
\(484\) 9.41347i 0.427885i
\(485\) −34.6601 + 2.13177i −1.57383 + 0.0967986i
\(486\) 15.5425 + 22.5988i 0.705024 + 1.02510i
\(487\) 20.6096 20.6096i 0.933908 0.933908i −0.0640391 0.997947i \(-0.520398\pi\)
0.997947 + 0.0640391i \(0.0203982\pi\)
\(488\) 3.73140 3.73140i 0.168913 0.168913i
\(489\) −6.36470 + 11.4369i −0.287822 + 0.517192i
\(490\) −3.92690 + 0.241524i −0.177399 + 0.0109109i
\(491\) 29.8846i 1.34867i −0.738423 0.674337i \(-0.764429\pi\)
0.738423 0.674337i \(-0.235571\pi\)
\(492\) −1.39619 4.90016i −0.0629453 0.220916i
\(493\) −6.33954 6.33954i −0.285519 0.285519i
\(494\) 47.2328 2.12510
\(495\) −1.74956 + 10.2645i −0.0786369 + 0.461354i
\(496\) −28.9353 −1.29923
\(497\) 4.05581 + 4.05581i 0.181928 + 0.181928i
\(498\) 14.4244 + 50.6249i 0.646374 + 2.26855i
\(499\) 0.940603i 0.0421072i 0.999778 + 0.0210536i \(0.00670206\pi\)
−0.999778 + 0.0210536i \(0.993298\pi\)
\(500\) 10.1036 + 6.92882i 0.451848 + 0.309866i
\(501\) −16.4653 + 29.5869i −0.735617 + 1.32185i
\(502\) 8.64136 8.64136i 0.385683 0.385683i
\(503\) −23.0051 + 23.0051i −1.02575 + 1.02575i −0.0260875 + 0.999660i \(0.508305\pi\)
−0.999660 + 0.0260875i \(0.991695\pi\)
\(504\) 2.51562 + 4.05611i 0.112055 + 0.180673i
\(505\) 18.8147 21.2808i 0.837245 0.946984i
\(506\) 14.5243i 0.645685i
\(507\) −46.0749 + 13.1280i −2.04626 + 0.583036i
\(508\) 11.1326 + 11.1326i 0.493929 + 0.493929i
\(509\) 25.8128 1.14413 0.572066 0.820208i \(-0.306142\pi\)
0.572066 + 0.820208i \(0.306142\pi\)
\(510\) 18.5477 + 8.87730i 0.821306 + 0.393094i
\(511\) 10.2782 0.454679
\(512\) 8.53124 + 8.53124i 0.377031 + 0.377031i
\(513\) 14.7193 16.1826i 0.649871 0.714480i
\(514\) 20.3307i 0.896749i
\(515\) 0.284978 + 4.63341i 0.0125576 + 0.204172i
\(516\) 4.91540 + 2.73546i 0.216388 + 0.120422i
\(517\) −0.0556354 + 0.0556354i −0.00244684 + 0.00244684i
\(518\) −2.16633 + 2.16633i −0.0951833 + 0.0951833i
\(519\) −4.42276 2.46130i −0.194138 0.108039i
\(520\) 16.9948 + 15.0254i 0.745270 + 0.658906i
\(521\) 44.1826i 1.93568i 0.251572 + 0.967838i \(0.419052\pi\)
−0.251572 + 0.967838i \(0.580948\pi\)
\(522\) 15.2691 + 3.57925i 0.668312 + 0.156659i
\(523\) 13.0685 + 13.0685i 0.571447 + 0.571447i 0.932533 0.361086i \(-0.117594\pi\)
−0.361086 + 0.932533i \(0.617594\pi\)
\(524\) 0.558162 0.0243834
\(525\) −3.25220 + 8.02641i −0.141938 + 0.350301i
\(526\) −0.295757 −0.0128956
\(527\) −12.3706 12.3706i −0.538870 0.538870i
\(528\) −12.9042 + 3.67678i −0.561585 + 0.160011i
\(529\) 5.28280i 0.229687i
\(530\) 17.9589 + 15.8778i 0.780087 + 0.689688i
\(531\) −12.5883 + 7.80733i −0.546285 + 0.338809i
\(532\) −3.26199 + 3.26199i −0.141425 + 0.141425i
\(533\) 12.1045 12.1045i 0.524303 0.524303i
\(534\) −2.01015 + 3.61208i −0.0869878 + 0.156310i
\(535\) 2.63089 + 42.7753i 0.113743 + 1.84934i
\(536\) 3.84760i 0.166191i
\(537\) −5.65682 19.8535i −0.244110 0.856743i
\(538\) −8.21544 8.21544i −0.354193 0.354193i
\(539\) 1.55221 0.0668583
\(540\) −12.6566 + 1.38182i −0.544654 + 0.0594640i
\(541\) 21.5590 0.926893 0.463446 0.886125i \(-0.346613\pi\)
0.463446 + 0.886125i \(0.346613\pi\)
\(542\) −29.6469 29.6469i −1.27344 1.27344i
\(543\) −8.35068 29.3080i −0.358362 1.25773i
\(544\) 16.8961i 0.724415i
\(545\) −7.17082 + 8.11071i −0.307164 + 0.347425i
\(546\) 9.44963 16.9802i 0.404407 0.726687i
\(547\) −29.6665 + 29.6665i −1.26845 + 1.26845i −0.321555 + 0.946891i \(0.604205\pi\)
−0.946891 + 0.321555i \(0.895795\pi\)
\(548\) 2.87037 2.87037i 0.122616 0.122616i
\(549\) −8.45626 + 5.24463i −0.360904 + 0.223835i
\(550\) −10.7663 8.39976i −0.459078 0.358167i
\(551\) 12.5083i 0.532872i
\(552\) 14.0939 4.01574i 0.599876 0.170921i
\(553\) 2.54119 + 2.54119i 0.108063 + 0.108063i
\(554\) −35.8116 −1.52149
\(555\) 2.24259 + 6.35994i 0.0951928 + 0.269965i
\(556\) −6.96235 −0.295269
\(557\) −19.2396 19.2396i −0.815208 0.815208i 0.170201 0.985409i \(-0.445558\pi\)
−0.985409 + 0.170201i \(0.945558\pi\)
\(558\) 29.7952 + 6.98431i 1.26133 + 0.295669i
\(559\) 18.8993i 0.799354i
\(560\) −11.1388 + 0.685090i −0.470699 + 0.0289504i
\(561\) −7.08880 3.94497i −0.299290 0.166557i
\(562\) −1.87490 + 1.87490i −0.0790880 + 0.0790880i
\(563\) 2.03574 2.03574i 0.0857962 0.0857962i −0.662906 0.748702i \(-0.730677\pi\)
0.748702 + 0.662906i \(0.230677\pi\)
\(564\) −0.0840650 0.0467828i −0.00353977 0.00196991i
\(565\) 33.5270 2.06208i 1.41049 0.0867523i
\(566\) 21.1284i 0.888092i
\(567\) −2.87286 8.52917i −0.120649 0.358191i
\(568\) 6.45262 + 6.45262i 0.270746 + 0.270746i
\(569\) 36.6125 1.53487 0.767437 0.641124i \(-0.221532\pi\)
0.767437 + 0.641124i \(0.221532\pi\)
\(570\) 9.54014 + 27.0556i 0.399592 + 1.13323i
\(571\) −9.88863 −0.413826 −0.206913 0.978359i \(-0.566342\pi\)
−0.206913 + 0.978359i \(0.566342\pi\)
\(572\) 7.66906 + 7.66906i 0.320659 + 0.320659i
\(573\) 9.22865 2.62950i 0.385533 0.109849i
\(574\) 4.72347i 0.197154i
\(575\) 20.9650 + 16.3566i 0.874300 + 0.682118i
\(576\) 0.205056 + 0.330625i 0.00854400 + 0.0137760i
\(577\) 3.44953 3.44953i 0.143606 0.143606i −0.631649 0.775255i \(-0.717622\pi\)
0.775255 + 0.631649i \(0.217622\pi\)
\(578\) 9.82204 9.82204i 0.408543 0.408543i
\(579\) 16.5600 29.7570i 0.688211 1.23666i
\(580\) −4.82202 + 5.45405i −0.200224 + 0.226467i
\(581\) 17.2730i 0.716605i
\(582\) 12.9687 + 45.5156i 0.537569 + 1.88668i
\(583\) −6.68741 6.68741i −0.276964 0.276964i
\(584\) 16.3521 0.676657
\(585\) −24.7343 34.8987i −1.02264 1.44288i
\(586\) 5.86864 0.242431
\(587\) 4.70846 + 4.70846i 0.194339 + 0.194339i 0.797568 0.603229i \(-0.206120\pi\)
−0.603229 + 0.797568i \(0.706120\pi\)
\(588\) 0.520079 + 1.82530i 0.0214477 + 0.0752741i
\(589\) 24.4079i 1.00571i
\(590\) −1.19255 19.3895i −0.0490965 0.798252i
\(591\) 15.1458 27.2158i 0.623016 1.11951i
\(592\) −6.14487 + 6.14487i −0.252553 + 0.252553i
\(593\) −15.2900 + 15.2900i −0.627884 + 0.627884i −0.947535 0.319651i \(-0.896434\pi\)
0.319651 + 0.947535i \(0.396434\pi\)
\(594\) 14.1752 0.671263i 0.581617 0.0275422i
\(595\) −5.05500 4.46921i −0.207235 0.183220i
\(596\) 4.68955i 0.192092i
\(597\) 10.1859 2.90224i 0.416880 0.118781i
\(598\) −42.1906 42.1906i −1.72530 1.72530i
\(599\) −9.38844 −0.383601 −0.191801 0.981434i \(-0.561433\pi\)
−0.191801 + 0.981434i \(0.561433\pi\)
\(600\) −5.17412 + 12.7697i −0.211233 + 0.521320i
\(601\) −4.87361 −0.198799 −0.0993993 0.995048i \(-0.531692\pi\)
−0.0993993 + 0.995048i \(0.531692\pi\)
\(602\) −3.68749 3.68749i −0.150291 0.150291i
\(603\) −1.65582 + 7.06377i −0.0674303 + 0.287659i
\(604\) 5.71155i 0.232400i
\(605\) −14.3912 12.7236i −0.585087 0.517286i
\(606\) −33.8280 18.8255i −1.37417 0.764734i
\(607\) −2.56287 + 2.56287i −0.104024 + 0.104024i −0.757203 0.653180i \(-0.773435\pi\)
0.653180 + 0.757203i \(0.273435\pi\)
\(608\) −16.6685 + 16.6685i −0.675998 + 0.675998i
\(609\) −4.49675 2.50247i −0.182217 0.101405i
\(610\) −0.801103 13.0250i −0.0324357 0.527367i
\(611\) 0.323222i 0.0130762i
\(612\) 2.26389 9.65780i 0.0915123 0.390393i
\(613\) 33.5166 + 33.5166i 1.35372 + 1.35372i 0.881457 + 0.472264i \(0.156563\pi\)
0.472264 + 0.881457i \(0.343437\pi\)
\(614\) −1.97471 −0.0796927
\(615\) 9.37848 + 4.48873i 0.378177 + 0.181003i
\(616\) 2.46950 0.0994989
\(617\) −2.15297 2.15297i −0.0866754 0.0866754i 0.662440 0.749115i \(-0.269521\pi\)
−0.749115 + 0.662440i \(0.769521\pi\)
\(618\) 6.08459 1.73367i 0.244758 0.0697384i
\(619\) 10.1941i 0.409737i −0.978789 0.204869i \(-0.934323\pi\)
0.978789 0.204869i \(-0.0656767\pi\)
\(620\) −9.40938 + 10.6427i −0.377890 + 0.427421i
\(621\) −27.6030 + 1.30713i −1.10767 + 0.0524534i
\(622\) −12.3359 + 12.3359i −0.494626 + 0.494626i
\(623\) 0.959142 0.959142i 0.0384272 0.0384272i
\(624\) 26.8042 48.1650i 1.07303 1.92814i
\(625\) −24.2491 + 6.08114i −0.969965 + 0.243245i
\(626\) 24.7618i 0.989682i
\(627\) −3.10148 10.8852i −0.123861 0.434711i
\(628\) −4.77759 4.77759i −0.190646 0.190646i
\(629\) −5.25417 −0.209498
\(630\) 11.6352 + 1.98319i 0.463556 + 0.0790122i
\(631\) 44.6402 1.77710 0.888550 0.458781i \(-0.151714\pi\)
0.888550 + 0.458781i \(0.151714\pi\)
\(632\) 4.04293 + 4.04293i 0.160819 + 0.160819i
\(633\) 5.92801 + 20.8053i 0.235617 + 0.826937i
\(634\) 37.2716i 1.48025i
\(635\) −32.0666 + 1.97226i −1.27252 + 0.0782666i
\(636\) 5.62332 10.1047i 0.222979 0.400676i
\(637\) −4.50889 + 4.50889i −0.178649 + 0.178649i
\(638\) 5.73777 5.73777i 0.227161 0.227161i
\(639\) −9.06940 14.6232i −0.358780 0.578485i
\(640\) −25.5031 + 1.56857i −1.00810 + 0.0620031i
\(641\) 15.7329i 0.621414i −0.950506 0.310707i \(-0.899434\pi\)
0.950506 0.310707i \(-0.100566\pi\)
\(642\) 56.1725 16.0051i 2.21695 0.631672i
\(643\) −11.7811 11.7811i −0.464600 0.464600i 0.435560 0.900160i \(-0.356551\pi\)
−0.900160 + 0.435560i \(0.856551\pi\)
\(644\) 5.82753 0.229637
\(645\) −10.8258 + 3.81730i −0.426264 + 0.150306i
\(646\) −22.3516 −0.879411
\(647\) −10.8002 10.8002i −0.424600 0.424600i 0.462184 0.886784i \(-0.347066\pi\)
−0.886784 + 0.462184i \(0.847066\pi\)
\(648\) −4.57060 13.5696i −0.179550 0.533063i
\(649\) 7.66417i 0.300845i
\(650\) 55.6741 6.87448i 2.18372 0.269639i
\(651\) −8.77466 4.88316i −0.343906 0.191386i
\(652\) −5.85518 + 5.85518i −0.229307 + 0.229307i
\(653\) −7.88328 + 7.88328i −0.308497 + 0.308497i −0.844326 0.535830i \(-0.819999\pi\)
0.535830 + 0.844326i \(0.319999\pi\)
\(654\) 12.8928 + 7.17493i 0.504147 + 0.280562i
\(655\) −0.754429 + 0.853314i −0.0294780 + 0.0333417i
\(656\) 13.3983i 0.523115i
\(657\) −30.0207 7.03717i −1.17122 0.274546i
\(658\) 0.0630648 + 0.0630648i 0.00245852 + 0.00245852i
\(659\) −6.73141 −0.262219 −0.131109 0.991368i \(-0.541854\pi\)
−0.131109 + 0.991368i \(0.541854\pi\)
\(660\) −2.84394 + 5.94195i −0.110700 + 0.231290i
\(661\) 4.43191 0.172381 0.0861906 0.996279i \(-0.472531\pi\)
0.0861906 + 0.996279i \(0.472531\pi\)
\(662\) −3.85991 3.85991i −0.150020 0.150020i
\(663\) 32.0512 9.13228i 1.24476 0.354668i
\(664\) 27.4807i 1.06646i
\(665\) −0.577896 9.39592i −0.0224099 0.364358i
\(666\) 7.81072 4.84426i 0.302659 0.187711i
\(667\) −11.1730 + 11.1730i −0.432621 + 0.432621i
\(668\) −15.1472 + 15.1472i −0.586064 + 0.586064i
\(669\) −10.4870 + 18.8444i −0.405452 + 0.728565i
\(670\) −7.12834 6.30229i −0.275392 0.243479i
\(671\) 5.14846i 0.198754i
\(672\) 2.65756 + 9.32715i 0.102518 + 0.359802i
\(673\) −3.35642 3.35642i −0.129381 0.129381i 0.639451 0.768832i \(-0.279162\pi\)
−0.768832 + 0.639451i \(0.779162\pi\)
\(674\) −57.7356 −2.22389
\(675\) 14.9946 21.2170i 0.577141 0.816644i
\(676\) −30.3094 −1.16575
\(677\) 6.31136 + 6.31136i 0.242565 + 0.242565i 0.817911 0.575345i \(-0.195132\pi\)
−0.575345 + 0.817911i \(0.695132\pi\)
\(678\) −12.5447 44.0277i −0.481777 1.69087i
\(679\) 15.5298i 0.595977i
\(680\) −8.04230 7.11034i −0.308408 0.272669i
\(681\) 18.7513 33.6946i 0.718551 1.29118i
\(682\) 11.1963 11.1963i 0.428729 0.428729i
\(683\) −21.4480 + 21.4480i −0.820686 + 0.820686i −0.986206 0.165520i \(-0.947070\pi\)
0.165520 + 0.986206i \(0.447070\pi\)
\(684\) 11.7611 7.29431i 0.449697 0.278905i
\(685\) 0.508516 + 8.26788i 0.0194294 + 0.315899i
\(686\) 1.75948i 0.0671774i
\(687\) 13.7832 3.92722i 0.525862 0.149833i
\(688\) −10.4597 10.4597i −0.398771 0.398771i
\(689\) 38.8515 1.48012
\(690\) 15.6456 32.6890i 0.595619 1.24445i
\(691\) 18.7943 0.714968 0.357484 0.933919i \(-0.383635\pi\)
0.357484 + 0.933919i \(0.383635\pi\)
\(692\) −2.26427 2.26427i −0.0860745 0.0860745i
\(693\) −4.53372 1.06275i −0.172222 0.0403706i
\(694\) 35.2932i 1.33971i
\(695\) 9.41054 10.6440i 0.356962 0.403750i
\(696\) −7.15414 3.98133i −0.271177 0.150912i
\(697\) −5.72810 + 5.72810i −0.216967 + 0.216967i
\(698\) −11.5351 + 11.5351i −0.436610 + 0.436610i
\(699\) −27.0597 15.0589i −1.02349 0.569581i
\(700\) −3.37020 + 4.31973i −0.127382 + 0.163271i
\(701\) 10.0310i 0.378867i 0.981894 + 0.189434i \(0.0606652\pi\)
−0.981894 + 0.189434i \(0.939335\pi\)
\(702\) −39.2266 + 43.1264i −1.48051 + 1.62770i
\(703\) −5.18340 5.18340i −0.195496 0.195496i
\(704\) 0.201296 0.00758663
\(705\) 0.185146 0.0652848i 0.00697301 0.00245877i
\(706\) 50.3682 1.89563
\(707\) 8.98258 + 8.98258i 0.337825 + 0.337825i
\(708\) −9.01260 + 2.56794i −0.338714 + 0.0965092i
\(709\) 48.4192i 1.81842i 0.416335 + 0.909211i \(0.363314\pi\)
−0.416335 + 0.909211i \(0.636686\pi\)
\(710\) 22.5238 1.38533i 0.845304 0.0519904i
\(711\) −5.68250 9.16227i −0.213110 0.343612i
\(712\) 1.52596 1.52596i 0.0571876 0.0571876i
\(713\) −21.8023 + 21.8023i −0.816502 + 0.816502i
\(714\) −4.47177 + 8.03542i −0.167352 + 0.300718i
\(715\) −22.0902 + 1.35865i −0.826125 + 0.0508108i
\(716\) 13.0602i 0.488083i
\(717\) 12.2575 + 43.0197i 0.457765 + 1.60660i
\(718\) 23.4258 + 23.4258i 0.874244 + 0.874244i
\(719\) 10.6931 0.398786 0.199393 0.979920i \(-0.436103\pi\)
0.199393 + 0.979920i \(0.436103\pi\)
\(720\) 33.0035 + 5.62538i 1.22997 + 0.209646i
\(721\) −2.07604 −0.0773157
\(722\) 1.58818 + 1.58818i 0.0591060 + 0.0591060i
\(723\) −4.99284 17.5232i −0.185686 0.651693i
\(724\) 19.2797i 0.716523i
\(725\) −1.82052 14.7438i −0.0676123 0.547569i
\(726\) −12.7308 + 22.8763i −0.472486 + 0.849020i
\(727\) 30.9245 30.9245i 1.14693 1.14693i 0.159773 0.987154i \(-0.448924\pi\)
0.987154 0.159773i \(-0.0510764\pi\)
\(728\) −7.17345 + 7.17345i −0.265866 + 0.265866i
\(729\) 2.55143 + 26.8792i 0.0944974 + 0.995525i
\(730\) 26.7845 30.2951i 0.991337 1.12127i
\(731\) 8.94354i 0.330789i
\(732\) −6.05428 + 1.72503i −0.223773 + 0.0637590i
\(733\) −23.0095 23.0095i −0.849876 0.849876i 0.140241 0.990117i \(-0.455212\pi\)
−0.990117 + 0.140241i \(0.955212\pi\)
\(734\) 2.34399 0.0865184
\(735\) −3.49346 1.67204i −0.128858 0.0616742i
\(736\) 29.7782 1.09764
\(737\) 2.65439 + 2.65439i 0.0977759 + 0.0977759i
\(738\) 3.23403 13.7964i 0.119046 0.507854i
\(739\) 31.0959i 1.14388i 0.820295 + 0.571941i \(0.193809\pi\)
−0.820295 + 0.571941i \(0.806191\pi\)
\(740\) 0.261911 + 4.25838i 0.00962805 + 0.156541i
\(741\) 40.6287 + 22.6102i 1.49253 + 0.830606i
\(742\) −7.58042 + 7.58042i −0.278286 + 0.278286i
\(743\) −4.41646 + 4.41646i −0.162024 + 0.162024i −0.783463 0.621439i \(-0.786549\pi\)
0.621439 + 0.783463i \(0.286549\pi\)
\(744\) −13.9601 7.76892i −0.511803 0.284822i
\(745\) 7.16936 + 6.33855i 0.262665 + 0.232227i
\(746\) 18.4118i 0.674105i
\(747\) −11.8263 + 50.4514i −0.432703 + 1.84592i
\(748\) −3.62917 3.62917i −0.132695 0.132695i
\(749\) −19.1658 −0.700305
\(750\) 15.1829 + 30.5024i 0.554402 + 1.11379i
\(751\) −20.7634 −0.757668 −0.378834 0.925465i \(-0.623675\pi\)
−0.378834 + 0.925465i \(0.623675\pi\)
\(752\) 0.178885 + 0.178885i 0.00652327 + 0.00652327i
\(753\) 11.5697 3.29654i 0.421624 0.120132i
\(754\) 33.3344i 1.21397i
\(755\) 8.73178 + 7.71992i 0.317782 + 0.280957i
\(756\) −0.269328 5.68747i −0.00979536 0.206851i
\(757\) 27.7515 27.7515i 1.00865 1.00865i 0.00868333 0.999962i \(-0.497236\pi\)
0.999962 0.00868333i \(-0.00276403\pi\)
\(758\) 27.3072 27.3072i 0.991843 0.991843i
\(759\) −6.95274 + 12.4935i −0.252369 + 0.453486i
\(760\) −0.919409 14.9485i −0.0333505 0.542240i
\(761\) 51.6155i 1.87106i 0.353246 + 0.935531i \(0.385078\pi\)
−0.353246 + 0.935531i \(0.614922\pi\)
\(762\) 11.9983 + 42.1099i 0.434652 + 1.52548i
\(763\) −3.42351 3.42351i −0.123939 0.123939i
\(764\) 6.07087 0.219636
\(765\) 11.7048 + 16.5148i 0.423189 + 0.597094i
\(766\) 48.1010 1.73796
\(767\) −22.2631 22.2631i −0.803873 0.803873i
\(768\) 9.41932 + 33.0586i 0.339891 + 1.19290i
\(769\) 15.3442i 0.553327i