Properties

Label 105.2.j.a.8.3
Level 105
Weight 2
Character 105.8
Analytic conductor 0.838
Analytic rank 0
Dimension 24
CM no
Inner twists 4

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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 8.3
Character \(\chi\) = 105.8
Dual form 105.2.j.a.92.3

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.24414 - 1.24414i) q^{2} +(1.66575 + 0.474620i) q^{3} +1.09578i q^{4} +(1.67522 + 1.48109i) q^{5} +(-1.48194 - 2.66293i) q^{6} +(0.707107 - 0.707107i) q^{7} +(-1.12498 + 1.12498i) q^{8} +(2.54947 + 1.58120i) q^{9} +O(q^{10})\) \(q+(-1.24414 - 1.24414i) q^{2} +(1.66575 + 0.474620i) 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} +(-0.520079 + 1.82530i) q^{12} +(-4.50889 - 4.50889i) q^{13} -1.75948 q^{14} +(2.08755 + 3.26223i) q^{15} +4.99083 q^{16} +(-2.13370 - 2.13370i) q^{17} +(-1.20467 - 5.13914i) 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} +(3.49632 + 3.84392i) q^{27} +(0.774834 + 0.774834i) q^{28} +2.97115 q^{29} +(1.46147 - 6.65589i) q^{30} -5.79770 q^{31} +(-3.95934 - 3.95934i) q^{32} +(0.736708 - 2.58559i) 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} +(-2.93087 - 0.835085i) q^{42} +(-2.09578 - 2.09578i) q^{43} +1.70088 q^{44} +(1.92903 + 6.42486i) q^{45} +9.35721 q^{46} +(-0.0358428 - 0.0358428i) q^{47} +(8.31349 + 2.36874i) 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} +(-1.99811 + 7.01270i) q^{57} +(-3.69653 - 3.69653i) q^{58} -4.93760 q^{59} +(-3.57468 + 2.28750i) q^{60} +3.31687 q^{61} +(7.21316 + 7.21316i) q^{62} +(2.92083 - 0.684672i) 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} +(-4.64692 + 1.08929i) q^{72} +(7.26776 + 7.26776i) q^{73} +3.06366 q^{74} +(-1.33455 + 8.55681i) q^{75} -4.61315 q^{76} +(-1.09758 - 1.09758i) q^{77} +(-5.32495 + 18.6887i) 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} +(4.94920 + 1.41016i) q^{87} +(1.74620 + 1.74620i) q^{88} -1.35643 q^{89} +(5.59346 - 10.3934i) q^{90} -6.37653 q^{91} +(-4.12069 - 4.12069i) q^{92} +(-9.65754 - 2.75170i) 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 0.113766 0.993508i \(-0.463709\pi\)
−0.993508 + 0.113766i \(0.963709\pi\)
\(3\) 1.66575 + 0.474620i 0.961723 + 0.274022i
\(4\) 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 \(-0.924817\pi\)
0.972236 0.234004i \(-0.0751828\pi\)
\(12\) −0.520079 + 1.82530i −0.150134 + 0.526919i
\(13\) −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
\(15\) 2.08755 + 3.26223i 0.539003 + 0.842304i
\(16\) 4.99083 1.24771
\(17\) −2.13370 2.13370i −0.517499 0.517499i 0.399315 0.916814i \(-0.369248\pi\)
−0.916814 + 0.399315i \(0.869248\pi\)
\(18\) −1.20467 5.13914i −0.283943 1.21131i
\(19\) 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 −0.980523 0.196404i \(-0.937074\pi\)
0.196404 + 0.980523i \(0.437074\pi\)
\(24\) −2.40787 + 1.34000i −0.491505 + 0.273526i
\(25\) 0.612732 + 4.96231i 0.122546 + 0.992463i
\(26\) 11.2194i 2.20030i
\(27\) 3.49632 + 3.84392i 0.672868 + 0.739763i
\(28\) 0.774834 + 0.774834i 0.146430 + 0.146430i
\(29\) 2.97115 0.551728 0.275864 0.961197i \(-0.411036\pi\)
0.275864 + 0.961197i \(0.411036\pi\)
\(30\) 1.46147 6.65589i 0.266826 1.21519i
\(31\) −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
\(33\) 0.736708 2.58559i 0.128244 0.450094i
\(34\) 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 \(-0.932774\pi\)
0.977781 0.209631i \(-0.0672261\pi\)
\(42\) −2.93087 0.835085i −0.452242 0.128856i
\(43\) −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
\(45\) 1.92903 + 6.42486i 0.287562 + 0.957762i
\(46\) 9.35721 1.37964
\(47\) −0.0358428 0.0358428i −0.00522821 0.00522821i 0.704488 0.709716i \(-0.251177\pi\)
−0.709716 + 0.704488i \(0.751177\pi\)
\(48\) 8.31349 + 2.36874i 1.19995 + 0.341899i
\(49\) 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 −0.346322 0.938116i \(-0.612569\pi\)
0.938116 + 0.346322i \(0.112569\pi\)
\(54\) 0.432457 9.13231i 0.0588500 1.24275i
\(55\) 2.29896 2.60029i 0.309992 0.350623i
\(56\) 1.59096i 0.212601i
\(57\) −1.99811 + 7.01270i −0.264657 + 0.928855i
\(58\) −3.69653 3.69653i −0.485378 0.485378i
\(59\) −4.93760 −0.642821 −0.321410 0.946940i \(-0.604157\pi\)
−0.321410 + 0.946940i \(0.604157\pi\)
\(60\) −3.57468 + 2.28750i −0.461490 + 0.295315i
\(61\) 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
\(63\) 2.92083 0.684672i 0.367989 0.0862606i
\(64\) 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 \(-0.889453\pi\)
0.940297 0.340356i \(-0.110547\pi\)
\(72\) −4.64692 + 1.08929i −0.547644 + 0.128374i
\(73\) 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
\(75\) −1.33455 + 8.55681i −0.154101 + 0.988055i
\(76\) −4.61315 −0.529165
\(77\) −1.09758 1.09758i −0.125080 0.125080i
\(78\) −5.32495 + 18.6887i −0.602931 + 2.11608i
\(79\) 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 \(0.646877\pi\)
−0.895417 + 0.445228i \(0.853123\pi\)
\(84\) 0.922931 + 1.65843i 0.100700 + 0.180950i
\(85\) −0.414214 6.73463i −0.0449278 0.730474i
\(86\) 5.21490i 0.562337i
\(87\) 4.94920 + 1.41016i 0.530610 + 0.151185i
\(88\) 1.74620 + 1.74620i 0.186145 + 0.186145i
\(89\) −1.35643 −0.143782 −0.0718908 0.997413i \(-0.522903\pi\)
−0.0718908 + 0.997413i \(0.522903\pi\)
\(90\) 5.59346 10.3934i 0.589602 1.09556i
\(91\) −6.37653 −0.668442
\(92\) −4.12069 4.12069i −0.429611 0.429611i
\(93\) −9.65754 2.75170i −1.00144 0.285338i
\(94\) 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 \(-0.782229\pi\)
0.774958 0.632012i \(-0.217771\pi\)
\(102\) −2.51988 + 8.84392i −0.249505 + 0.875679i
\(103\) −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
\(105\) 3.78286 + 0.830623i 0.369170 + 0.0810605i
\(106\) −10.7203 −1.04125
\(107\) 13.5523 + 13.5523i 1.31015 + 1.31015i 0.921302 + 0.388849i \(0.127127\pi\)
0.388849 + 0.921302i \(0.372873\pi\)
\(108\) −4.21209 + 3.83120i −0.405309 + 0.368658i
\(109\) 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 −0.000746132 1.00000i \(-0.500238\pi\)
1.00000 0.000746132i \(0.000237501\pi\)
\(114\) 11.2107 6.23886i 1.04998 0.584323i
\(115\) −11.8693 + 0.730023i −1.10682 + 0.0680750i
\(116\) 3.25572i 0.302286i
\(117\) −4.36583 18.6247i −0.403621 1.72186i
\(118\) 6.14308 + 6.14308i 0.565516 + 0.565516i
\(119\) −3.01751 −0.276615
\(120\) −6.01838 1.32149i −0.549401 0.120635i
\(121\) 8.59066 0.780969
\(122\) −4.12665 4.12665i −0.373610 0.373610i
\(123\) 1.27415 4.47185i 0.114887 0.403213i
\(124\) 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 \(0.00708365\pi\)
−0.999752 + 0.0222521i \(0.992916\pi\)
\(132\) 2.83324 + 0.807270i 0.246602 + 0.0702638i
\(133\) 2.97687 + 2.97687i 0.258127 + 0.258127i
\(134\) −4.25516 −0.367590
\(135\) 0.163918 + 11.6178i 0.0141078 + 0.999900i
\(136\) 4.80074 0.411660
\(137\) 2.61947 + 2.61947i 0.223797 + 0.223797i 0.810095 0.586298i \(-0.199415\pi\)
−0.586298 + 0.810095i \(0.699415\pi\)
\(138\) 15.5868 + 4.44112i 1.32684 + 0.378053i
\(139\) 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
\(147\) 0.474620 1.66575i 0.0391460 0.137389i
\(148\) −1.34916 1.34916i −0.110900 0.110900i
\(149\) 4.27965 0.350602 0.175301 0.984515i \(-0.443910\pi\)
0.175301 + 0.984515i \(0.443910\pi\)
\(150\) 12.3063 8.98552i 1.00480 0.733664i
\(151\) −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
\(153\) −2.06601 8.81363i −0.167027 0.712539i
\(154\) 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
\(162\) 5.05474 15.0069i 0.397138 1.17906i
\(163\) 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
\(165\) 5.06365 3.24031i 0.394205 0.252258i
\(166\) 30.3916 2.35884
\(167\) −13.8232 13.8232i −1.06967 1.06967i −0.997384 0.0722908i \(-0.976969\pi\)
−0.0722908 0.997384i \(-0.523031\pi\)
\(168\) −0.755101 + 2.65015i −0.0582573 + 0.204463i
\(169\) 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 −0.624179 0.781281i \(-0.714567\pi\)
0.781281 + 0.624179i \(0.214567\pi\)
\(174\) −4.40306 7.91195i −0.333795 0.599803i
\(175\) 3.94215 + 3.07562i 0.297999 + 0.232495i
\(176\) 7.74679i 0.583936i
\(177\) −8.22483 2.34348i −0.618216 0.176147i
\(178\) 1.68759 + 1.68759i 0.126491 + 0.126491i
\(179\) 11.9186 0.890841 0.445420 0.895322i \(-0.353054\pi\)
0.445420 + 0.895322i \(0.353054\pi\)
\(180\) −7.04024 + 2.11379i −0.524748 + 0.157553i
\(181\) −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
\(183\) 5.52508 + 1.57425i 0.408426 + 0.116372i
\(184\) 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 \(0.0642366\pi\)
−0.979706 + 0.200438i \(0.935763\pi\)
\(192\) 0.0615505 0.216021i 0.00444202 0.0155900i
\(193\) −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
\(195\) 5.29649 24.1215i 0.379289 1.72738i
\(196\) 1.09578 0.0782700
\(197\) 12.7155 + 12.7155i 0.905939 + 0.905939i 0.995942 0.0900024i \(-0.0286875\pi\)
−0.0900024 + 0.995942i \(0.528687\pi\)
\(198\) −7.97701 + 1.86989i −0.566901 + 0.132888i
\(199\) 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
\(207\) −15.5334 + 3.64119i −1.07965 + 0.253080i
\(208\) −22.5031 22.5031i −1.56031 1.56031i
\(209\) 6.53467 0.452013
\(210\) −3.67301 5.73983i −0.253462 0.396086i
\(211\) 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
\(213\) 2.72231 9.55439i 0.186530 0.654656i
\(214\) 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
\(222\) 5.10330 + 1.45407i 0.342511 + 0.0975910i
\(223\) 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
\(225\) −6.28427 + 13.6201i −0.418951 + 0.908009i
\(226\) −26.4311 −1.75817
\(227\) 15.7424 + 15.7424i 1.04486 + 1.04486i 0.998945 + 0.0459126i \(0.0146196\pi\)
0.0459126 + 0.998945i \(0.485380\pi\)
\(228\) −7.68438 2.18949i −0.508910 0.145003i
\(229\) 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 −0.159034 0.987273i \(-0.550838\pi\)
0.987273 + 0.159034i \(0.0508380\pi\)
\(234\) −17.7401 + 28.6035i −1.15971 + 1.86987i
\(235\) −0.00695813 0.113131i −0.000453898 0.00737986i
\(236\) 5.41052i 0.352195i
\(237\) −1.70568 + 5.98637i −0.110796 + 0.388856i
\(238\) 3.75421 + 3.75421i 0.243350 + 0.243350i
\(239\) −25.8260 −1.67054 −0.835271 0.549838i \(-0.814689\pi\)
−0.835271 + 0.549838i \(0.814689\pi\)
\(240\) 10.4186 + 16.2812i 0.672518 + 1.05095i
\(241\) −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
\(243\) 2.83578 + 15.3284i 0.181915 + 0.983314i
\(244\) 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 \(0.0703455\pi\)
−0.975679 + 0.219202i \(0.929655\pi\)
\(252\) 0.750250 + 3.20058i 0.0472613 + 0.201618i
\(253\) 5.83708 + 5.83708i 0.366974 + 0.366974i
\(254\) −25.2798 −1.58619
\(255\) 2.50641 11.4148i 0.156958 0.714825i
\(256\) 19.8460 1.24038
\(257\) 8.17057 + 8.17057i 0.509666 + 0.509666i 0.914424 0.404758i \(-0.132644\pi\)
−0.404758 + 0.914424i \(0.632644\pi\)
\(258\) −2.47509 + 8.68674i −0.154093 + 0.540813i
\(259\) 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 −0.703433 0.710762i \(-0.748350\pi\)
0.710762 + 0.703433i \(0.248350\pi\)
\(264\) 2.07996 + 3.73752i 0.128012 + 0.230028i
\(265\) 13.5984 0.836371i 0.835345 0.0513779i
\(266\) 7.40729i 0.454170i
\(267\) −2.25948 0.643790i −0.138278 0.0393993i
\(268\) 1.87387 + 1.87387i 0.114465 + 0.114465i
\(269\) 6.60330 0.402610 0.201305 0.979529i \(-0.435482\pi\)
0.201305 + 0.979529i \(0.435482\pi\)
\(270\) 14.2503 14.6581i 0.867243 0.892065i
\(271\) −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
\(273\) −10.6217 3.02643i −0.642856 0.183168i
\(274\) 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 \(-0.985687\pi\)
0.998989 0.0449495i \(-0.0143127\pi\)
\(282\) −0.0423300 + 0.148564i −0.00252071 + 0.00884685i
\(283\) 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
\(285\) −13.7337 + 8.78843i −0.813516 + 0.520582i
\(286\) 17.4148 1.02976
\(287\) −1.89828 1.89828i −0.112052 0.112052i
\(288\) −3.83372 16.3547i −0.225904 0.963712i
\(289\) 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 −0.772635 0.634850i \(-0.781062\pi\)
0.634850 + 0.772635i \(0.281062\pi\)
\(294\) −2.66293 + 1.48194i −0.155305 + 0.0864285i
\(295\) −8.27157 7.31304i −0.481590 0.425782i
\(296\) 2.77022i 0.161016i
\(297\) 5.96656 5.42702i 0.346215 0.314907i
\(298\) −5.32449 5.32449i −0.308439 0.308439i
\(299\) 33.9114 1.96115
\(300\) −9.37638 1.46238i −0.541346 0.0844303i
\(301\) −2.96388 −0.170835
\(302\) 6.48486 + 6.48486i 0.373162 + 0.373162i
\(303\) 6.02923 21.1606i 0.346370 1.21564i
\(304\) 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 \(-0.909294\pi\)
0.959673 0.281120i \(-0.0907059\pi\)
\(312\) 16.8987 + 4.81492i 0.956702 + 0.272591i
\(313\) −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
\(315\) 5.90709 + 3.17904i 0.332827 + 0.179118i
\(316\) −3.93800 −0.221530
\(317\) −14.9788 14.9788i −0.841296 0.841296i 0.147732 0.989027i \(-0.452803\pi\)
−0.989027 + 0.147732i \(0.952803\pi\)
\(318\) −17.8574 5.08809i −1.00140 0.285326i
\(319\) 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
\(327\) 2.29791 8.06487i 0.127075 0.445989i
\(328\) 3.02009 + 3.02009i 0.166757 + 0.166757i
\(329\) −0.0506894 −0.00279460
\(330\) −10.3313 2.26850i −0.568720 0.124877i
\(331\) −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
\(333\) −5.08582 + 1.19217i −0.278701 + 0.0653305i
\(334\) 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
\(342\) 21.6354 5.07157i 1.16991 0.274239i
\(343\) −0.707107 0.707107i −0.0381802 0.0381802i
\(344\) 4.71541 0.254238
\(345\) −20.1179 4.41738i −1.08311 0.237824i
\(346\) −5.14167 −0.276418
\(347\) −14.1837 14.1837i −0.761423 0.761423i 0.215157 0.976580i \(-0.430974\pi\)
−0.976580 + 0.215157i \(0.930974\pi\)
\(348\) −1.54523 + 5.42323i −0.0828330 + 0.290716i
\(349\) 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 \(0.525695\pi\)
−0.996744 + 0.0806368i \(0.974305\pi\)
\(354\) 7.31723 + 13.1485i 0.388906 + 0.698834i
\(355\) 8.49521 9.60869i 0.450879 0.509976i
\(356\) 1.48635i 0.0787765i
\(357\) −5.02643 1.43217i −0.266027 0.0757985i
\(358\) −14.8285 14.8285i −0.783710 0.783710i
\(359\) −18.8289 −0.993751 −0.496876 0.867822i \(-0.665519\pi\)
−0.496876 + 0.867822i \(0.665519\pi\)
\(360\) −9.39794 5.05772i −0.495315 0.266565i
\(361\) 1.27653 0.0671857
\(362\) 21.8900 + 21.8900i 1.15051 + 1.15051i
\(363\) 14.3099 + 4.07730i 0.751076 + 0.214003i
\(364\) 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
\(372\) 3.01526 10.5825i 0.156334 0.548679i
\(373\) 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
\(375\) −14.9091 + 12.3580i −0.769902 + 0.638162i
\(376\) 0.0806448 0.00415894
\(377\) −13.3966 13.3966i −0.689958 0.689958i
\(378\) −6.15172 6.76331i −0.316411 0.347867i
\(379\) 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 −0.999926 0.0121580i \(-0.996130\pi\)
0.0121580 + 0.999926i \(0.496130\pi\)
\(384\) −17.2943 + 9.62440i −0.882545 + 0.491143i
\(385\) −0.213071 3.46429i −0.0108591 0.176557i
\(386\) 34.5939i 1.76079i
\(387\) −2.02929 8.65698i −0.103154 0.440059i
\(388\) 12.0330 + 12.0330i 0.610882 + 0.610882i
\(389\) 30.7961 1.56142 0.780712 0.624891i \(-0.214856\pi\)
0.780712 + 0.624891i \(0.214856\pi\)
\(390\) −36.6002 + 23.4210i −1.85332 + 1.18597i
\(391\) 16.0476 0.811562
\(392\) 1.12498 + 1.12498i 0.0568200 + 0.0568200i
\(393\) −0.241759 + 0.848491i −0.0121951 + 0.0428007i
\(394\) 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 \(0.174835\pi\)
−0.852910 + 0.522058i \(0.825165\pi\)
\(402\) −7.08805 2.01958i −0.353520 0.100728i
\(403\) 26.1412 + 26.1412i 1.30218 + 1.30218i
\(404\) 13.9200 0.692547
\(405\) −5.24099 + 19.4302i −0.260427 + 0.965494i
\(406\) −5.22768 −0.259445
\(407\) 1.91113 + 1.91113i 0.0947311 + 0.0947311i
\(408\) 7.99685 + 2.27853i 0.395903 + 0.112804i
\(409\) 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
\(417\) −3.01563 + 10.5838i −0.147676 + 0.518293i
\(418\) −8.13006 8.13006i −0.397654 0.397654i
\(419\) −0.525515 −0.0256731 −0.0128365 0.999918i \(-0.504086\pi\)
−0.0128365 + 0.999918i \(0.504086\pi\)
\(420\) −0.910180 + 4.14519i −0.0444122 + 0.202264i
\(421\) −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
\(423\) −0.0347056 0.148055i −0.00168744 0.00719868i
\(424\) 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 \(-0.812993\pi\)
0.832329 0.554282i \(-0.187007\pi\)
\(432\) 17.4495 + 19.1843i 0.839542 + 0.923007i
\(433\) −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
\(435\) 6.20242 + 9.69255i 0.297383 + 0.464722i
\(436\) 5.30530 0.254078
\(437\) −15.8314 15.8314i −0.757321 0.757321i
\(438\) 8.58315 30.1239i 0.410119 1.43938i
\(439\) 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 −0.882032 0.471189i \(-0.843825\pi\)
0.471189 + 0.882032i \(0.343825\pi\)
\(444\) −1.60703 2.88771i −0.0762664 0.137045i
\(445\) −2.27232 2.00900i −0.107718 0.0952358i
\(446\) 21.9075i 1.03735i
\(447\) 7.12884 + 2.03121i 0.337183 + 0.0960727i
\(448\) −0.0917003 0.0917003i −0.00433243 0.00433243i
\(449\) −20.7599 −0.979723 −0.489861 0.871800i \(-0.662953\pi\)
−0.489861 + 0.871800i \(0.662953\pi\)
\(450\) 24.7639 9.12686i 1.16738 0.430244i
\(451\) −4.16702 −0.196217
\(452\) 11.6396 + 11.6396i 0.547481 + 0.547481i
\(453\) −8.68243 2.47387i −0.407936 0.116232i
\(454\) 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 \(-0.967594\pi\)
0.994822 0.101631i \(-0.0324061\pi\)
\(462\) −1.29622 + 4.54931i −0.0603058 + 0.211653i
\(463\) 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
\(465\) −12.1030 18.9134i −0.561263 0.877089i
\(466\) −31.4582 −1.45727
\(467\) −13.9629 13.9629i −0.646128 0.646128i 0.305927 0.952055i \(-0.401034\pi\)
−0.952055 + 0.305927i \(0.901034\pi\)
\(468\) 20.4086 4.78399i 0.943388 0.221140i
\(469\) 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
\(477\) 17.7963 4.17163i 0.814836 0.191006i
\(478\) 32.1312 + 32.1312i 1.46965 + 1.46965i
\(479\) 16.0067 0.731367 0.365683 0.930739i \(-0.380835\pi\)
0.365683 + 0.930739i \(0.380835\pi\)
\(480\) 4.65095 21.1816i 0.212286 0.966803i
\(481\) 11.1030 0.506252
\(482\) 13.0880 + 13.0880i 0.596140 + 0.596140i
\(483\) −2.52410 + 8.85874i −0.114851 + 0.403087i
\(484\) 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 \(0.235571\pi\)
−0.738423 + 0.674337i \(0.764429\pi\)
\(492\) 4.90016 + 1.39619i 0.220916 + 0.0629453i
\(493\) −6.33954 6.33954i −0.285519 0.285519i
\(494\) −47.2328 −2.12510
\(495\) 9.97271 2.99425i 0.448240 0.134581i
\(496\) −28.9353 −1.29923
\(497\) −4.05581 4.05581i −0.181928 0.181928i
\(498\) 50.6249 + 14.4244i 2.26855 + 0.646374i
\(499\) 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 \(-0.491695\pi\)
0.999660 0.0260875i \(-0.00830487\pi\)
\(504\) −2.51562 + 4.05611i −0.112055 + 0.180673i
\(505\) 18.8147 21.2808i 0.837245 0.946984i
\(506\) 14.5243i 0.645685i
\(507\) −13.1280 + 46.0749i −0.583036 + 2.04626i
\(508\) 11.1326 + 11.1326i 0.493929 + 0.493929i
\(509\) −25.8128 −1.14413 −0.572066 0.820208i \(-0.693858\pi\)
−0.572066 + 0.820208i \(0.693858\pi\)
\(510\) −17.3200 + 11.0833i −0.766943 + 0.490779i
\(511\) 10.2782 0.454679
\(512\) −8.53124 8.53124i −0.377031 0.377031i
\(513\) −16.1826 + 14.7193i −0.714480 + 0.649871i
\(514\) 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 \(-0.580948\pi\)
0.251572 0.967838i \(-0.419052\pi\)
\(522\) −3.57925 15.2691i −0.156659 0.668312i
\(523\) 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
\(525\) 5.10691 + 6.99425i 0.222884 + 0.305254i
\(526\) −0.295757 −0.0128956
\(527\) 12.3706 + 12.3706i 0.538870 + 0.538870i
\(528\) 3.67678 12.9042i 0.160011 0.561585i
\(529\) 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
\(537\) 19.8535 + 5.65682i 0.856743 + 0.244110i
\(538\) −8.21544 8.21544i −0.354193 0.354193i
\(539\) −1.55221 −0.0668583
\(540\) −12.7305 + 0.179618i −0.547836 + 0.00772954i
\(541\) 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
\(543\) −29.3080 8.35068i −1.25773 0.358362i
\(544\) 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
\(552\) 4.01574 14.0939i 0.170921 0.599876i
\(553\) 2.54119 + 2.54119i 0.108063 + 0.108063i
\(554\) 35.8116 1.52149
\(555\) −6.58683 1.44630i −0.279595 0.0613921i
\(556\) −6.96235 −0.295269
\(557\) 19.2396 + 19.2396i 0.815208 + 0.815208i 0.985409 0.170201i \(-0.0544418\pi\)
−0.170201 + 0.985409i \(0.554442\pi\)
\(558\) 6.98431 + 29.7952i 0.295669 + 1.26133i
\(559\) 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 −0.748702 0.662906i \(-0.769323\pi\)
0.662906 + 0.748702i \(0.269323\pi\)
\(564\) 0.0840650 0.0467828i 0.00353977 0.00196991i
\(565\) 33.5270 2.06208i 1.41049 0.0867523i
\(566\) 21.1284i 0.888092i
\(567\) 8.52917 + 2.87286i 0.358191 + 0.120649i
\(568\) 6.45262 + 6.45262i 0.270746 + 0.270746i
\(569\) −36.6125 −1.53487 −0.767437 0.641124i \(-0.778468\pi\)
−0.767437 + 0.641124i \(0.778468\pi\)
\(570\) 28.0208 + 6.15266i 1.17366 + 0.257707i
\(571\) −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
\(573\) −2.62950 + 9.22865i −0.109849 + 0.385533i
\(574\) 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
\(582\) −45.5156 12.9687i −1.88668 0.537569i
\(583\) −6.68741 6.68741i −0.276964 0.276964i
\(584\) −16.3521 −0.676657
\(585\) 20.2712 37.6667i 0.838111 1.55733i
\(586\) 5.86864 0.242431
\(587\) −4.70846 4.70846i −0.194339 0.194339i 0.603229 0.797568i \(-0.293880\pi\)
−0.797568 + 0.603229i \(0.793880\pi\)
\(588\) 1.82530 + 0.520079i 0.0752741 + 0.0214477i
\(589\) 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 −0.319651 0.947535i \(-0.603566\pi\)
0.947535 + 0.319651i \(0.103566\pi\)
\(594\) −14.1752 0.671263i −0.581617 0.0275422i
\(595\) −5.05500 4.46921i −0.207235 0.183220i
\(596\) 4.68955i 0.192092i
\(597\) 2.90224 10.1859i 0.118781 0.416880i
\(598\) −42.1906 42.1906i −1.72530 1.72530i
\(599\) 9.38844 0.383601 0.191801 0.981434i \(-0.438567\pi\)
0.191801 + 0.981434i \(0.438567\pi\)
\(600\) −8.12488 11.1276i −0.331697 0.454281i
\(601\) −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
\(603\) 7.06377 1.65582i 0.287659 0.0674303i
\(604\) 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
\(612\) 9.65780 2.26389i 0.390393 0.0915123i
\(613\) 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
\(615\) 8.75771 5.60420i 0.353145 0.225983i
\(616\) 2.46950 0.0994989
\(617\) 2.15297 + 2.15297i 0.0866754 + 0.0866754i 0.749115 0.662440i \(-0.230479\pi\)
−0.662440 + 0.749115i \(0.730479\pi\)
\(618\) −1.73367 + 6.08459i −0.0697384 + 0.244758i
\(619\) 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
\(627\) 10.8852 + 3.10148i 0.434711 + 0.123861i
\(628\) −4.77759 4.77759i −0.190646 0.190646i
\(629\) 5.25417 0.209498
\(630\) −3.39409 11.3044i −0.135224 0.450379i
\(631\) 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
\(633\) 20.8053 + 5.92801i 0.826937 + 0.235617i
\(634\) 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 \(0.100566\pi\)
−0.950506 + 0.310707i \(0.899434\pi\)
\(642\) 16.0051 56.1725i 0.631672 2.21695i
\(643\) −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
\(645\) 2.46187 11.2120i 0.0969359 0.441470i
\(646\) −22.3516 −0.879411
\(647\) 10.8002 + 10.8002i 0.424600 + 0.424600i 0.886784 0.462184i \(-0.152934\pi\)
−0.462184 + 0.886784i \(0.652934\pi\)
\(648\) −13.5696 4.57060i −0.533063 0.179550i
\(649\) 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 −0.535830 0.844326i \(-0.680001\pi\)
0.844326 + 0.535830i \(0.180001\pi\)
\(654\) −12.8928 + 7.17493i −0.504147 + 0.280562i
\(655\) −0.754429 + 0.853314i −0.0294780 + 0.0333417i
\(656\) 13.3983i 0.523115i
\(657\) 7.03717 + 30.0207i 0.274546 + 1.17122i
\(658\) 0.0630648 + 0.0630648i 0.00245852 + 0.00245852i
\(659\) 6.73141 0.262219 0.131109 0.991368i \(-0.458146\pi\)
0.131109 + 0.991368i \(0.458146\pi\)
\(660\) 3.55067 + 5.54865i 0.138209 + 0.215981i
\(661\) 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
\(663\) −9.13228 + 32.0512i −0.354668 + 1.24476i
\(664\) 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
\(672\) −9.32715 2.65756i −0.359802 0.102518i
\(673\) −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
\(675\) −16.9324 + 19.7052i −0.651729 + 0.758452i
\(676\) −30.3094 −1.16575
\(677\) −6.31136 6.31136i −0.242565 0.242565i 0.575345 0.817911i \(-0.304868\pi\)
−0.817911 + 0.575345i \(0.804868\pi\)
\(678\) −44.0277 12.5447i −1.69087 0.481777i
\(679\) 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 −0.165520 0.986206i \(-0.552930\pi\)
0.986206 + 0.165520i \(0.0529303\pi\)
\(684\) −11.7611 7.29431i −0.449697 0.278905i
\(685\) 0.508516 + 8.26788i 0.0194294 + 0.315899i
\(686\) 1.75948i 0.0671774i
\(687\) 3.92722 13.7832i 0.149833 0.525862i
\(688\) −10.4597 10.4597i −0.398771 0.398771i
\(689\) −38.8515 −1.48012
\(690\) 19.5336 + 30.5253i 0.743633 + 1.16208i
\(691\) 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
\(693\) −1.06275 4.53372i −0.0403706 0.172222i
\(694\) 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 \(-0.939335\pi\)
0.981894 0.189434i \(-0.0606652\pi\)
\(702\) −43.1264 + 39.2266i −1.62770 + 1.48051i
\(703\) −5.18340 5.18340i −0.195496 0.195496i
\(704\) −0.201296 −0.00758663
\(705\) 0.0421038 0.191751i 0.00158572 0.00722177i
\(706\) 50.3682 1.89563
\(707\) −8.98258 8.98258i −0.337825 0.337825i
\(708\) 2.56794 9.01260i 0.0965092 0.338714i
\(709\) 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
\(717\) −43.0197 12.2575i −1.60660 0.457765i
\(718\) 23.4258 + 23.4258i 0.874244 + 0.874244i
\(719\) −10.6931 −0.398786 −0.199393 0.979920i \(-0.563897\pi\)
−0.199393 + 0.979920i \(0.563897\pi\)
\(720\) 9.62744 + 32.0654i 0.358794 + 1.19501i
\(721\) −2.07604 −0.0773157
\(722\) −1.58818 1.58818i −0.0591060 0.0591060i
\(723\) −17.5232 4.99284i −0.651693 0.185686i
\(724\) 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
\(732\) −1.72503 + 6.05428i −0.0637590 + 0.223773i
\(733\) −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
\(735\) 3.26223 2.08755i 0.120329 0.0770005i
\(736\) 29.7782 1.09764
\(737\) −2.65439 2.65439i −0.0977759 0.0977759i
\(738\) −13.7964 + 3.23403i −0.507854 + 0.119046i
\(739\) 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 −0.621439 0.783463i \(-0.713451\pi\)
0.783463 + 0.621439i \(0.213451\pi\)
\(744\) 13.9601 7.76892i 0.511803 0.284822i
\(745\) 7.16936 + 6.33855i 0.262665 + 0.232227i
\(746\) 18.4118i 0.674105i
\(747\) −50.4514 + 11.8263i −1.84592 + 0.432703i
\(748\) −3.62917 3.62917i −0.132695 0.132695i
\(749\) 19.1658 0.700305
\(750\) 33.9241 + 3.17398i 1.23873 + 0.115897i
\(751\) −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
\(753\) −3.29654 + 11.5697i −0.120132 + 0.421624i
\(754\) 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 \(-0.614922\pi\)
0.353246 0.935531i \(-0.385078\pi\)
\(762\) −42.1099 11.9983i −1.52548 0.434652i
\(763\) −3.42351 3.42351i −0.123939 0.123939i
\(764\) −6.07087 −0.219636
\(765\) 9.59277 17.8247i 0.346828 0.644454i
\(766\) 48.1010 1.73796
\(767\) 22.2631 + 22.2631i 0.803873 + 0.803873i
\(768\) 33.0586 + 9.41932i 1.19290 + 0.339891i
\(769\) 15.3442i 0.553327i