Properties

Label 1110.2.u.e.401.6
Level $1110$
Weight $2$
Character 1110.401
Analytic conductor $8.863$
Analytic rank $0$
Dimension $40$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1110.u (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(8.86339462436\)
Analytic rank: \(0\)
Dimension: \(40\)
Relative dimension: \(20\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 401.6
Character \(\chi\) \(=\) 1110.401
Dual form 1110.2.u.e.191.6

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.707107 + 0.707107i) q^{2} +(-0.912132 - 1.47242i) q^{3} -1.00000i q^{4} +(-0.707107 - 0.707107i) q^{5} +(1.68613 + 0.396182i) q^{6} +0.363832 q^{7} +(0.707107 + 0.707107i) q^{8} +(-1.33603 + 2.68608i) q^{9} +O(q^{10})\) \(q+(-0.707107 + 0.707107i) q^{2} +(-0.912132 - 1.47242i) q^{3} -1.00000i q^{4} +(-0.707107 - 0.707107i) q^{5} +(1.68613 + 0.396182i) q^{6} +0.363832 q^{7} +(0.707107 + 0.707107i) q^{8} +(-1.33603 + 2.68608i) q^{9} +1.00000 q^{10} +1.23669 q^{11} +(-1.47242 + 0.912132i) q^{12} +(2.54719 - 2.54719i) q^{13} +(-0.257268 + 0.257268i) q^{14} +(-0.396182 + 1.68613i) q^{15} -1.00000 q^{16} +(2.79453 + 2.79453i) q^{17} +(-0.954629 - 2.84406i) q^{18} +(1.40229 - 1.40229i) q^{19} +(-0.707107 + 0.707107i) q^{20} +(-0.331863 - 0.535713i) q^{21} +(-0.874474 + 0.874474i) q^{22} +(0.456993 + 0.456993i) q^{23} +(0.396182 - 1.68613i) q^{24} +1.00000i q^{25} +3.60228i q^{26} +(5.17367 - 0.482863i) q^{27} -0.363832i q^{28} +(-1.61230 + 1.61230i) q^{29} +(-0.912132 - 1.47242i) q^{30} +(0.163461 + 0.163461i) q^{31} +(0.707107 - 0.707107i) q^{32} +(-1.12803 - 1.82093i) q^{33} -3.95206 q^{34} +(-0.257268 - 0.257268i) q^{35} +(2.68608 + 1.33603i) q^{36} +(5.07126 - 3.35892i) q^{37} +1.98313i q^{38} +(-6.07391 - 1.42716i) q^{39} -1.00000i q^{40} -0.545166 q^{41} +(0.613469 + 0.144144i) q^{42} +(4.75447 - 4.75447i) q^{43} -1.23669i q^{44} +(2.84406 - 0.954629i) q^{45} -0.646286 q^{46} +1.60456i q^{47} +(0.912132 + 1.47242i) q^{48} -6.86763 q^{49} +(-0.707107 - 0.707107i) q^{50} +(1.56574 - 6.66370i) q^{51} +(-2.54719 - 2.54719i) q^{52} -8.02046i q^{53} +(-3.31690 + 3.99977i) q^{54} +(-0.874474 - 0.874474i) q^{55} +(0.257268 + 0.257268i) q^{56} +(-3.34382 - 0.785681i) q^{57} -2.28014i q^{58} +(-6.45749 - 6.45749i) q^{59} +(1.68613 + 0.396182i) q^{60} +(2.60993 + 2.60993i) q^{61} -0.231169 q^{62} +(-0.486091 + 0.977282i) q^{63} +1.00000i q^{64} -3.60228 q^{65} +(2.08523 + 0.489956i) q^{66} -4.94984i q^{67} +(2.79453 - 2.79453i) q^{68} +(0.256047 - 1.08972i) q^{69} +0.363832 q^{70} -14.8100i q^{71} +(-2.84406 + 0.954629i) q^{72} -1.60743i q^{73} +(-1.21080 + 5.96104i) q^{74} +(1.47242 - 0.912132i) q^{75} +(-1.40229 - 1.40229i) q^{76} +0.449949 q^{77} +(5.30406 - 3.28575i) q^{78} +(2.32156 - 2.32156i) q^{79} +(0.707107 + 0.707107i) q^{80} +(-5.43004 - 7.17737i) q^{81} +(0.385490 - 0.385490i) q^{82} -8.43976i q^{83} +(-0.535713 + 0.331863i) q^{84} -3.95206i q^{85} +6.72384i q^{86} +(3.84461 + 0.903350i) q^{87} +(0.874474 + 0.874474i) q^{88} +(-0.550261 + 0.550261i) q^{89} +(-1.33603 + 2.68608i) q^{90} +(0.926751 - 0.926751i) q^{91} +(0.456993 - 0.456993i) q^{92} +(0.0915850 - 0.389781i) q^{93} +(-1.13460 - 1.13460i) q^{94} -1.98313 q^{95} +(-1.68613 - 0.396182i) q^{96} +(-0.870659 + 0.870659i) q^{97} +(4.85614 - 4.85614i) q^{98} +(-1.65226 + 3.32185i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 40q - 24q^{7} - 8q^{9} + O(q^{10}) \) \( 40q - 24q^{7} - 8q^{9} + 40q^{10} - 8q^{12} - 16q^{13} - 40q^{16} + 8q^{18} + 16q^{19} - 24q^{31} + 24q^{33} - 8q^{34} + 16q^{39} - 20q^{42} - 32q^{43} - 8q^{45} + 72q^{46} + 96q^{49} + 20q^{51} + 16q^{52} + 24q^{54} - 16q^{57} + 40q^{61} - 24q^{63} - 44q^{66} - 24q^{70} + 8q^{72} + 8q^{75} - 16q^{76} + 48q^{79} + 24q^{81} - 56q^{82} - 8q^{84} + 12q^{87} - 8q^{90} - 64q^{91} + 12q^{93} + 24q^{94} + 8q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times\).

\(n\) \(371\) \(631\) \(667\)
\(\chi(n)\) \(-1\) \(e\left(\frac{1}{4}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.707107 + 0.707107i −0.500000 + 0.500000i
\(3\) −0.912132 1.47242i −0.526620 0.850101i
\(4\) 1.00000i 0.500000i
\(5\) −0.707107 0.707107i −0.316228 0.316228i
\(6\) 1.68613 + 0.396182i 0.688360 + 0.161741i
\(7\) 0.363832 0.137516 0.0687578 0.997633i \(-0.478096\pi\)
0.0687578 + 0.997633i \(0.478096\pi\)
\(8\) 0.707107 + 0.707107i 0.250000 + 0.250000i
\(9\) −1.33603 + 2.68608i −0.445344 + 0.895360i
\(10\) 1.00000 0.316228
\(11\) 1.23669 0.372877 0.186438 0.982467i \(-0.440306\pi\)
0.186438 + 0.982467i \(0.440306\pi\)
\(12\) −1.47242 + 0.912132i −0.425051 + 0.263310i
\(13\) 2.54719 2.54719i 0.706464 0.706464i −0.259326 0.965790i \(-0.583500\pi\)
0.965790 + 0.259326i \(0.0835002\pi\)
\(14\) −0.257268 + 0.257268i −0.0687578 + 0.0687578i
\(15\) −0.396182 + 1.68613i −0.102294 + 0.435357i
\(16\) −1.00000 −0.250000
\(17\) 2.79453 + 2.79453i 0.677773 + 0.677773i 0.959496 0.281723i \(-0.0909058\pi\)
−0.281723 + 0.959496i \(0.590906\pi\)
\(18\) −0.954629 2.84406i −0.225008 0.670352i
\(19\) 1.40229 1.40229i 0.321706 0.321706i −0.527715 0.849421i \(-0.676951\pi\)
0.849421 + 0.527715i \(0.176951\pi\)
\(20\) −0.707107 + 0.707107i −0.158114 + 0.158114i
\(21\) −0.331863 0.535713i −0.0724184 0.116902i
\(22\) −0.874474 + 0.874474i −0.186438 + 0.186438i
\(23\) 0.456993 + 0.456993i 0.0952897 + 0.0952897i 0.753145 0.657855i \(-0.228536\pi\)
−0.657855 + 0.753145i \(0.728536\pi\)
\(24\) 0.396182 1.68613i 0.0808704 0.344180i
\(25\) 1.00000i 0.200000i
\(26\) 3.60228i 0.706464i
\(27\) 5.17367 0.482863i 0.995673 0.0929270i
\(28\) 0.363832i 0.0687578i
\(29\) −1.61230 + 1.61230i −0.299397 + 0.299397i −0.840778 0.541381i \(-0.817902\pi\)
0.541381 + 0.840778i \(0.317902\pi\)
\(30\) −0.912132 1.47242i −0.166532 0.268826i
\(31\) 0.163461 + 0.163461i 0.0293585 + 0.0293585i 0.721634 0.692275i \(-0.243392\pi\)
−0.692275 + 0.721634i \(0.743392\pi\)
\(32\) 0.707107 0.707107i 0.125000 0.125000i
\(33\) −1.12803 1.82093i −0.196364 0.316983i
\(34\) −3.95206 −0.677773
\(35\) −0.257268 0.257268i −0.0434863 0.0434863i
\(36\) 2.68608 + 1.33603i 0.447680 + 0.222672i
\(37\) 5.07126 3.35892i 0.833709 0.552204i
\(38\) 1.98313i 0.321706i
\(39\) −6.07391 1.42716i −0.972604 0.228528i
\(40\) 1.00000i 0.158114i
\(41\) −0.545166 −0.0851406 −0.0425703 0.999093i \(-0.513555\pi\)
−0.0425703 + 0.999093i \(0.513555\pi\)
\(42\) 0.613469 + 0.144144i 0.0946603 + 0.0222419i
\(43\) 4.75447 4.75447i 0.725050 0.725050i −0.244579 0.969629i \(-0.578650\pi\)
0.969629 + 0.244579i \(0.0786498\pi\)
\(44\) 1.23669i 0.186438i
\(45\) 2.84406 0.954629i 0.423968 0.142308i
\(46\) −0.646286 −0.0952897
\(47\) 1.60456i 0.234049i 0.993129 + 0.117025i \(0.0373357\pi\)
−0.993129 + 0.117025i \(0.962664\pi\)
\(48\) 0.912132 + 1.47242i 0.131655 + 0.212525i
\(49\) −6.86763 −0.981089
\(50\) −0.707107 0.707107i −0.100000 0.100000i
\(51\) 1.56574 6.66370i 0.219247 0.933105i
\(52\) −2.54719 2.54719i −0.353232 0.353232i
\(53\) 8.02046i 1.10169i −0.834606 0.550847i \(-0.814305\pi\)
0.834606 0.550847i \(-0.185695\pi\)
\(54\) −3.31690 + 3.99977i −0.451373 + 0.544300i
\(55\) −0.874474 0.874474i −0.117914 0.117914i
\(56\) 0.257268 + 0.257268i 0.0343789 + 0.0343789i
\(57\) −3.34382 0.785681i −0.442900 0.104066i
\(58\) 2.28014i 0.299397i
\(59\) −6.45749 6.45749i −0.840694 0.840694i 0.148255 0.988949i \(-0.452634\pi\)
−0.988949 + 0.148255i \(0.952634\pi\)
\(60\) 1.68613 + 0.396182i 0.217679 + 0.0511469i
\(61\) 2.60993 + 2.60993i 0.334167 + 0.334167i 0.854167 0.520000i \(-0.174068\pi\)
−0.520000 + 0.854167i \(0.674068\pi\)
\(62\) −0.231169 −0.0293585
\(63\) −0.486091 + 0.977282i −0.0612417 + 0.123126i
\(64\) 1.00000i 0.125000i
\(65\) −3.60228 −0.446807
\(66\) 2.08523 + 0.489956i 0.256674 + 0.0603094i
\(67\) 4.94984i 0.604719i −0.953194 0.302359i \(-0.902226\pi\)
0.953194 0.302359i \(-0.0977743\pi\)
\(68\) 2.79453 2.79453i 0.338887 0.338887i
\(69\) 0.256047 1.08972i 0.0308244 0.131187i
\(70\) 0.363832 0.0434863
\(71\) 14.8100i 1.75762i −0.477174 0.878809i \(-0.658339\pi\)
0.477174 0.878809i \(-0.341661\pi\)
\(72\) −2.84406 + 0.954629i −0.335176 + 0.112504i
\(73\) 1.60743i 0.188135i −0.995566 0.0940675i \(-0.970013\pi\)
0.995566 0.0940675i \(-0.0299869\pi\)
\(74\) −1.21080 + 5.96104i −0.140753 + 0.692956i
\(75\) 1.47242 0.912132i 0.170020 0.105324i
\(76\) −1.40229 1.40229i −0.160853 0.160853i
\(77\) 0.449949 0.0512764
\(78\) 5.30406 3.28575i 0.600566 0.372038i
\(79\) 2.32156 2.32156i 0.261196 0.261196i −0.564344 0.825540i \(-0.690871\pi\)
0.825540 + 0.564344i \(0.190871\pi\)
\(80\) 0.707107 + 0.707107i 0.0790569 + 0.0790569i
\(81\) −5.43004 7.17737i −0.603338 0.797485i
\(82\) 0.385490 0.385490i 0.0425703 0.0425703i
\(83\) 8.43976i 0.926384i −0.886258 0.463192i \(-0.846704\pi\)
0.886258 0.463192i \(-0.153296\pi\)
\(84\) −0.535713 + 0.331863i −0.0584511 + 0.0362092i
\(85\) 3.95206i 0.428662i
\(86\) 6.72384i 0.725050i
\(87\) 3.84461 + 0.903350i 0.412186 + 0.0968493i
\(88\) 0.874474 + 0.874474i 0.0932192 + 0.0932192i
\(89\) −0.550261 + 0.550261i −0.0583276 + 0.0583276i −0.735669 0.677341i \(-0.763132\pi\)
0.677341 + 0.735669i \(0.263132\pi\)
\(90\) −1.33603 + 2.68608i −0.140830 + 0.283138i
\(91\) 0.926751 0.926751i 0.0971499 0.0971499i
\(92\) 0.456993 0.456993i 0.0476448 0.0476448i
\(93\) 0.0915850 0.389781i 0.00949692 0.0404184i
\(94\) −1.13460 1.13460i −0.117025 0.117025i
\(95\) −1.98313 −0.203465
\(96\) −1.68613 0.396182i −0.172090 0.0404352i
\(97\) −0.870659 + 0.870659i −0.0884021 + 0.0884021i −0.749925 0.661523i \(-0.769910\pi\)
0.661523 + 0.749925i \(0.269910\pi\)
\(98\) 4.85614 4.85614i 0.490545 0.490545i
\(99\) −1.65226 + 3.32185i −0.166058 + 0.333859i
\(100\) 1.00000 0.100000
\(101\) 0.868845 0.0864533 0.0432267 0.999065i \(-0.486236\pi\)
0.0432267 + 0.999065i \(0.486236\pi\)
\(102\) 3.60480 + 5.81909i 0.356929 + 0.576176i
\(103\) 7.68967 + 7.68967i 0.757686 + 0.757686i 0.975901 0.218215i \(-0.0700234\pi\)
−0.218215 + 0.975901i \(0.570023\pi\)
\(104\) 3.60228 0.353232
\(105\) −0.144144 + 0.613469i −0.0140670 + 0.0598684i
\(106\) 5.67132 + 5.67132i 0.550847 + 0.550847i
\(107\) 8.05854i 0.779048i −0.921016 0.389524i \(-0.872639\pi\)
0.921016 0.389524i \(-0.127361\pi\)
\(108\) −0.482863 5.17367i −0.0464635 0.497836i
\(109\) 0.884855 0.884855i 0.0847537 0.0847537i −0.663459 0.748213i \(-0.730912\pi\)
0.748213 + 0.663459i \(0.230912\pi\)
\(110\) 1.23669 0.117914
\(111\) −9.57139 4.40323i −0.908477 0.417936i
\(112\) −0.363832 −0.0343789
\(113\) 7.40005 7.40005i 0.696138 0.696138i −0.267437 0.963575i \(-0.586177\pi\)
0.963575 + 0.267437i \(0.0861769\pi\)
\(114\) 2.92000 1.80888i 0.273483 0.169417i
\(115\) 0.646286i 0.0602665i
\(116\) 1.61230 + 1.61230i 0.149698 + 0.149698i
\(117\) 3.43884 + 10.2451i 0.317920 + 0.947159i
\(118\) 9.13227 0.840694
\(119\) 1.01674 + 1.01674i 0.0932044 + 0.0932044i
\(120\) −1.47242 + 0.912132i −0.134413 + 0.0832659i
\(121\) −9.47059 −0.860963
\(122\) −3.69100 −0.334167
\(123\) 0.497263 + 0.802712i 0.0448367 + 0.0723781i
\(124\) 0.163461 0.163461i 0.0146792 0.0146792i
\(125\) 0.707107 0.707107i 0.0632456 0.0632456i
\(126\) −0.347325 1.03476i −0.0309421 0.0921839i
\(127\) 18.9130 1.67825 0.839127 0.543936i \(-0.183067\pi\)
0.839127 + 0.543936i \(0.183067\pi\)
\(128\) −0.707107 0.707107i −0.0625000 0.0625000i
\(129\) −11.3373 2.66386i −0.998191 0.234540i
\(130\) 2.54719 2.54719i 0.223404 0.223404i
\(131\) 1.74566 1.74566i 0.152519 0.152519i −0.626723 0.779242i \(-0.715604\pi\)
0.779242 + 0.626723i \(0.215604\pi\)
\(132\) −1.82093 + 1.12803i −0.158491 + 0.0981821i
\(133\) 0.510197 0.510197i 0.0442397 0.0442397i
\(134\) 3.50006 + 3.50006i 0.302359 + 0.302359i
\(135\) −3.99977 3.31690i −0.344246 0.285473i
\(136\) 3.95206i 0.338887i
\(137\) 8.31134i 0.710085i 0.934850 + 0.355043i \(0.115534\pi\)
−0.934850 + 0.355043i \(0.884466\pi\)
\(138\) 0.589498 + 0.951603i 0.0501814 + 0.0810058i
\(139\) 2.62959i 0.223039i −0.993762 0.111520i \(-0.964428\pi\)
0.993762 0.111520i \(-0.0355718\pi\)
\(140\) −0.257268 + 0.257268i −0.0217431 + 0.0217431i
\(141\) 2.36259 1.46357i 0.198966 0.123255i
\(142\) 10.4722 + 10.4722i 0.878809 + 0.878809i
\(143\) 3.15010 3.15010i 0.263424 0.263424i
\(144\) 1.33603 2.68608i 0.111336 0.223840i
\(145\) 2.28014 0.189355
\(146\) 1.13662 + 1.13662i 0.0940675 + 0.0940675i
\(147\) 6.26418 + 10.1120i 0.516661 + 0.834025i
\(148\) −3.35892 5.07126i −0.276102 0.416855i
\(149\) 10.2673i 0.841131i 0.907262 + 0.420566i \(0.138168\pi\)
−0.907262 + 0.420566i \(0.861832\pi\)
\(150\) −0.396182 + 1.68613i −0.0323481 + 0.137672i
\(151\) 5.53248i 0.450226i 0.974333 + 0.225113i \(0.0722752\pi\)
−0.974333 + 0.225113i \(0.927725\pi\)
\(152\) 1.98313 0.160853
\(153\) −11.2399 + 3.77275i −0.908693 + 0.305009i
\(154\) −0.318162 + 0.318162i −0.0256382 + 0.0256382i
\(155\) 0.231169i 0.0185679i
\(156\) −1.42716 + 6.07391i −0.114264 + 0.486302i
\(157\) 7.35707 0.587158 0.293579 0.955935i \(-0.405154\pi\)
0.293579 + 0.955935i \(0.405154\pi\)
\(158\) 3.28319i 0.261196i
\(159\) −11.8095 + 7.31572i −0.936552 + 0.580174i
\(160\) −1.00000 −0.0790569
\(161\) 0.166269 + 0.166269i 0.0131038 + 0.0131038i
\(162\) 8.91479 + 1.23555i 0.700412 + 0.0970736i
\(163\) 8.15725 + 8.15725i 0.638925 + 0.638925i 0.950290 0.311365i \(-0.100786\pi\)
−0.311365 + 0.950290i \(0.600786\pi\)
\(164\) 0.545166i 0.0425703i
\(165\) −0.489956 + 2.08523i −0.0381430 + 0.162335i
\(166\) 5.96781 + 5.96781i 0.463192 + 0.463192i
\(167\) −7.06777 7.06777i −0.546921 0.546921i 0.378628 0.925549i \(-0.376396\pi\)
−0.925549 + 0.378628i \(0.876396\pi\)
\(168\) 0.144144 0.613469i 0.0111209 0.0473302i
\(169\) 0.0236067i 0.00181590i
\(170\) 2.79453 + 2.79453i 0.214331 + 0.214331i
\(171\) 1.89315 + 5.64015i 0.144773 + 0.431313i
\(172\) −4.75447 4.75447i −0.362525 0.362525i
\(173\) −6.52900 −0.496391 −0.248195 0.968710i \(-0.579837\pi\)
−0.248195 + 0.968710i \(0.579837\pi\)
\(174\) −3.35732 + 2.07979i −0.254517 + 0.157668i
\(175\) 0.363832i 0.0275031i
\(176\) −1.23669 −0.0932192
\(177\) −3.61804 + 15.3982i −0.271949 + 1.15740i
\(178\) 0.778187i 0.0583276i
\(179\) −5.04499 + 5.04499i −0.377080 + 0.377080i −0.870048 0.492968i \(-0.835912\pi\)
0.492968 + 0.870048i \(0.335912\pi\)
\(180\) −0.954629 2.84406i −0.0711538 0.211984i
\(181\) 1.67529 0.124523 0.0622617 0.998060i \(-0.480169\pi\)
0.0622617 + 0.998060i \(0.480169\pi\)
\(182\) 1.31062i 0.0971499i
\(183\) 1.46231 6.22350i 0.108097 0.460055i
\(184\) 0.646286i 0.0476448i
\(185\) −5.96104 1.21080i −0.438264 0.0890199i
\(186\) 0.210857 + 0.340377i 0.0154608 + 0.0249577i
\(187\) 3.45598 + 3.45598i 0.252726 + 0.252726i
\(188\) 1.60456 0.117025
\(189\) 1.88235 0.175681i 0.136921 0.0127789i
\(190\) 1.40229 1.40229i 0.101732 0.101732i
\(191\) −6.28026 6.28026i −0.454424 0.454424i 0.442396 0.896820i \(-0.354129\pi\)
−0.896820 + 0.442396i \(0.854129\pi\)
\(192\) 1.47242 0.912132i 0.106263 0.0658275i
\(193\) 4.14557 4.14557i 0.298405 0.298405i −0.541984 0.840389i \(-0.682327\pi\)
0.840389 + 0.541984i \(0.182327\pi\)
\(194\) 1.23130i 0.0884021i
\(195\) 3.28575 + 5.30406i 0.235298 + 0.379831i
\(196\) 6.86763i 0.490545i
\(197\) 17.9073i 1.27584i 0.770102 + 0.637921i \(0.220205\pi\)
−0.770102 + 0.637921i \(0.779795\pi\)
\(198\) −1.18058 3.51723i −0.0839003 0.249959i
\(199\) −16.9444 16.9444i −1.20116 1.20116i −0.973815 0.227343i \(-0.926996\pi\)
−0.227343 0.973815i \(-0.573004\pi\)
\(200\) −0.707107 + 0.707107i −0.0500000 + 0.0500000i
\(201\) −7.28823 + 4.51490i −0.514072 + 0.318457i
\(202\) −0.614366 + 0.614366i −0.0432267 + 0.0432267i
\(203\) −0.586607 + 0.586607i −0.0411717 + 0.0411717i
\(204\) −6.66370 1.56574i −0.466552 0.109624i
\(205\) 0.385490 + 0.385490i 0.0269238 + 0.0269238i
\(206\) −10.8748 −0.757686
\(207\) −1.83808 + 0.616963i −0.127755 + 0.0428819i
\(208\) −2.54719 + 2.54719i −0.176616 + 0.176616i
\(209\) 1.73420 1.73420i 0.119957 0.119957i
\(210\) −0.331863 0.535713i −0.0229007 0.0369677i
\(211\) 21.7223 1.49543 0.747714 0.664021i \(-0.231152\pi\)
0.747714 + 0.664021i \(0.231152\pi\)
\(212\) −8.02046 −0.550847
\(213\) −21.8064 + 13.5086i −1.49415 + 0.925596i
\(214\) 5.69825 + 5.69825i 0.389524 + 0.389524i
\(215\) −6.72384 −0.458562
\(216\) 3.99977 + 3.31690i 0.272150 + 0.225686i
\(217\) 0.0594724 + 0.0594724i 0.00403725 + 0.00403725i
\(218\) 1.25137i 0.0847537i
\(219\) −2.36680 + 1.46618i −0.159934 + 0.0990755i
\(220\) −0.874474 + 0.874474i −0.0589570 + 0.0589570i
\(221\) 14.2364 0.957646
\(222\) 9.88155 3.65445i 0.663206 0.245270i
\(223\) 7.24611 0.485235 0.242618 0.970122i \(-0.421994\pi\)
0.242618 + 0.970122i \(0.421994\pi\)
\(224\) 0.257268 0.257268i 0.0171895 0.0171895i
\(225\) −2.68608 1.33603i −0.179072 0.0890687i
\(226\) 10.4652i 0.696138i
\(227\) −7.21839 7.21839i −0.479102 0.479102i 0.425743 0.904844i \(-0.360013\pi\)
−0.904844 + 0.425743i \(0.860013\pi\)
\(228\) −0.785681 + 3.34382i −0.0520330 + 0.221450i
\(229\) −15.0972 −0.997648 −0.498824 0.866703i \(-0.666235\pi\)
−0.498824 + 0.866703i \(0.666235\pi\)
\(230\) 0.456993 + 0.456993i 0.0301332 + 0.0301332i
\(231\) −0.410412 0.662512i −0.0270032 0.0435901i
\(232\) −2.28014 −0.149698
\(233\) −1.67396 −0.109665 −0.0548324 0.998496i \(-0.517462\pi\)
−0.0548324 + 0.998496i \(0.517462\pi\)
\(234\) −9.67600 4.81275i −0.632540 0.314619i
\(235\) 1.13460 1.13460i 0.0740129 0.0740129i
\(236\) −6.45749 + 6.45749i −0.420347 + 0.420347i
\(237\) −5.53589 1.30074i −0.359595 0.0844922i
\(238\) −1.43789 −0.0932044
\(239\) 8.93980 + 8.93980i 0.578268 + 0.578268i 0.934426 0.356158i \(-0.115914\pi\)
−0.356158 + 0.934426i \(0.615914\pi\)
\(240\) 0.396182 1.68613i 0.0255735 0.108839i
\(241\) −1.90045 + 1.90045i −0.122419 + 0.122419i −0.765662 0.643243i \(-0.777588\pi\)
0.643243 + 0.765662i \(0.277588\pi\)
\(242\) 6.69672 6.69672i 0.430481 0.430481i
\(243\) −5.61517 + 14.5420i −0.360213 + 0.932870i
\(244\) 2.60993 2.60993i 0.167084 0.167084i
\(245\) 4.85614 + 4.85614i 0.310248 + 0.310248i
\(246\) −0.919221 0.215985i −0.0586074 0.0137707i
\(247\) 7.14379i 0.454548i
\(248\) 0.231169i 0.0146792i
\(249\) −12.4269 + 7.69817i −0.787520 + 0.487852i
\(250\) 1.00000i 0.0632456i
\(251\) 7.01214 7.01214i 0.442602 0.442602i −0.450283 0.892886i \(-0.648677\pi\)
0.892886 + 0.450283i \(0.148677\pi\)
\(252\) 0.977282 + 0.486091i 0.0615630 + 0.0306209i
\(253\) 0.565160 + 0.565160i 0.0355313 + 0.0355313i
\(254\) −13.3735 + 13.3735i −0.839127 + 0.839127i
\(255\) −5.81909 + 3.60480i −0.364406 + 0.225742i
\(256\) 1.00000 0.0625000
\(257\) −14.2100 14.2100i −0.886395 0.886395i 0.107779 0.994175i \(-0.465626\pi\)
−0.994175 + 0.107779i \(0.965626\pi\)
\(258\) 9.90030 6.13303i 0.616366 0.381826i
\(259\) 1.84509 1.22208i 0.114648 0.0759367i
\(260\) 3.60228i 0.223404i
\(261\) −2.17668 6.48485i −0.134733 0.401402i
\(262\) 2.46874i 0.152519i
\(263\) 19.1855 1.18303 0.591514 0.806295i \(-0.298530\pi\)
0.591514 + 0.806295i \(0.298530\pi\)
\(264\) 0.489956 2.08523i 0.0301547 0.128337i
\(265\) −5.67132 + 5.67132i −0.348386 + 0.348386i
\(266\) 0.721527i 0.0442397i
\(267\) 1.31213 + 0.308304i 0.0803008 + 0.0188679i
\(268\) −4.94984 −0.302359
\(269\) 28.0625i 1.71100i 0.517804 + 0.855499i \(0.326750\pi\)
−0.517804 + 0.855499i \(0.673250\pi\)
\(270\) 5.17367 0.482863i 0.314859 0.0293861i
\(271\) 16.3324 0.992121 0.496060 0.868288i \(-0.334779\pi\)
0.496060 + 0.868288i \(0.334779\pi\)
\(272\) −2.79453 2.79453i −0.169443 0.169443i
\(273\) −2.20988 0.519246i −0.133748 0.0314262i
\(274\) −5.87700 5.87700i −0.355043 0.355043i
\(275\) 1.23669i 0.0745754i
\(276\) −1.08972 0.256047i −0.0655936 0.0154122i
\(277\) −3.32318 3.32318i −0.199670 0.199670i 0.600188 0.799859i \(-0.295092\pi\)
−0.799859 + 0.600188i \(0.795092\pi\)
\(278\) 1.85940 + 1.85940i 0.111520 + 0.111520i
\(279\) −0.657458 + 0.220680i −0.0393610 + 0.0132118i
\(280\) 0.363832i 0.0217431i
\(281\) 2.25670 + 2.25670i 0.134624 + 0.134624i 0.771207 0.636584i \(-0.219653\pi\)
−0.636584 + 0.771207i \(0.719653\pi\)
\(282\) −0.635699 + 2.70550i −0.0378553 + 0.161110i
\(283\) 13.9425 + 13.9425i 0.828796 + 0.828796i 0.987350 0.158554i \(-0.0506833\pi\)
−0.158554 + 0.987350i \(0.550683\pi\)
\(284\) −14.8100 −0.878809
\(285\) 1.80888 + 2.92000i 0.107149 + 0.172966i
\(286\) 4.45491i 0.263424i
\(287\) −0.198349 −0.0117082
\(288\) 0.954629 + 2.84406i 0.0562520 + 0.167588i
\(289\) 1.38119i 0.0812466i
\(290\) −1.61230 + 1.61230i −0.0946776 + 0.0946776i
\(291\) 2.07613 + 0.487818i 0.121705 + 0.0285964i
\(292\) −1.60743 −0.0940675
\(293\) 17.4323i 1.01841i −0.860646 0.509203i \(-0.829940\pi\)
0.860646 0.509203i \(-0.170060\pi\)
\(294\) −11.5797 2.72083i −0.675343 0.158682i
\(295\) 9.13227i 0.531702i
\(296\) 5.96104 + 1.21080i 0.346478 + 0.0703764i
\(297\) 6.39824 0.597153i 0.371263 0.0346503i
\(298\) −7.26009 7.26009i −0.420566 0.420566i
\(299\) 2.32810 0.134638
\(300\) −0.912132 1.47242i −0.0526620 0.0850101i
\(301\) 1.72983 1.72983i 0.0997057 0.0997057i
\(302\) −3.91205 3.91205i −0.225113 0.225113i
\(303\) −0.792501 1.27930i −0.0455280 0.0734941i
\(304\) −1.40229 + 1.40229i −0.0804266 + 0.0804266i
\(305\) 3.69100i 0.211346i
\(306\) 5.28008 10.6156i 0.301842 0.606851i
\(307\) 5.19902i 0.296724i −0.988933 0.148362i \(-0.952600\pi\)
0.988933 0.148362i \(-0.0474001\pi\)
\(308\) 0.449949i 0.0256382i
\(309\) 4.30842 18.3364i 0.245097 1.04312i
\(310\) 0.163461 + 0.163461i 0.00928397 + 0.00928397i
\(311\) 3.82476 3.82476i 0.216882 0.216882i −0.590301 0.807183i \(-0.700991\pi\)
0.807183 + 0.590301i \(0.200991\pi\)
\(312\) −3.28575 5.30406i −0.186019 0.300283i
\(313\) −23.6109 + 23.6109i −1.33457 + 1.33457i −0.433331 + 0.901235i \(0.642662\pi\)
−0.901235 + 0.433331i \(0.857338\pi\)
\(314\) −5.20223 + 5.20223i −0.293579 + 0.293579i
\(315\) 1.03476 0.347325i 0.0583022 0.0195695i
\(316\) −2.32156 2.32156i −0.130598 0.130598i
\(317\) −14.6490 −0.822767 −0.411384 0.911462i \(-0.634954\pi\)
−0.411384 + 0.911462i \(0.634954\pi\)
\(318\) 3.17756 13.5235i 0.178189 0.758363i
\(319\) −1.99392 + 1.99392i −0.111638 + 0.111638i
\(320\) 0.707107 0.707107i 0.0395285 0.0395285i
\(321\) −11.8655 + 7.35045i −0.662270 + 0.410262i
\(322\) −0.235140 −0.0131038
\(323\) 7.83746 0.436088
\(324\) −7.17737 + 5.43004i −0.398743 + 0.301669i
\(325\) 2.54719 + 2.54719i 0.141293 + 0.141293i
\(326\) −11.5361 −0.638925
\(327\) −2.10998 0.495772i −0.116682 0.0274163i
\(328\) −0.385490 0.385490i −0.0212851 0.0212851i
\(329\) 0.583791i 0.0321855i
\(330\) −1.12803 1.82093i −0.0620958 0.100239i
\(331\) −2.77763 + 2.77763i −0.152672 + 0.152672i −0.779310 0.626638i \(-0.784430\pi\)
0.626638 + 0.779310i \(0.284430\pi\)
\(332\) −8.43976 −0.463192
\(333\) 2.24698 + 18.1094i 0.123134 + 0.992390i
\(334\) 9.99534 0.546921
\(335\) −3.50006 + 3.50006i −0.191229 + 0.191229i
\(336\) 0.331863 + 0.535713i 0.0181046 + 0.0292256i
\(337\) 11.7097i 0.637870i −0.947777 0.318935i \(-0.896675\pi\)
0.947777 0.318935i \(-0.103325\pi\)
\(338\) −0.0166925 0.0166925i −0.000907951 0.000907951i
\(339\) −17.6458 4.14614i −0.958387 0.225188i
\(340\) −3.95206 −0.214331
\(341\) 0.202151 + 0.202151i 0.0109471 + 0.0109471i
\(342\) −5.32685 2.64952i −0.288043 0.143270i
\(343\) −5.04549 −0.272431
\(344\) 6.72384 0.362525
\(345\) −0.951603 + 0.589498i −0.0512326 + 0.0317375i
\(346\) 4.61670 4.61670i 0.248195 0.248195i
\(347\) 19.9380 19.9380i 1.07033 1.07033i 0.0729969 0.997332i \(-0.476744\pi\)
0.997332 0.0729969i \(-0.0232563\pi\)
\(348\) 0.903350 3.84461i 0.0484246 0.206093i
\(349\) −20.6832 −1.10715 −0.553574 0.832800i \(-0.686736\pi\)
−0.553574 + 0.832800i \(0.686736\pi\)
\(350\) −0.257268 0.257268i −0.0137516 0.0137516i
\(351\) 11.9484 14.4083i 0.637758 0.769057i
\(352\) 0.874474 0.874474i 0.0466096 0.0466096i
\(353\) −5.36743 + 5.36743i −0.285680 + 0.285680i −0.835369 0.549690i \(-0.814746\pi\)
0.549690 + 0.835369i \(0.314746\pi\)
\(354\) −8.32984 13.4465i −0.442726 0.714675i
\(355\) −10.4722 + 10.4722i −0.555808 + 0.555808i
\(356\) 0.550261 + 0.550261i 0.0291638 + 0.0291638i
\(357\) 0.569666 2.42447i 0.0301499 0.128316i
\(358\) 7.13469i 0.377080i
\(359\) 15.5141i 0.818802i 0.912355 + 0.409401i \(0.134262\pi\)
−0.912355 + 0.409401i \(0.865738\pi\)
\(360\) 2.68608 + 1.33603i 0.141569 + 0.0704150i
\(361\) 15.0672i 0.793010i
\(362\) −1.18461 + 1.18461i −0.0622617 + 0.0622617i
\(363\) 8.63843 + 13.9447i 0.453400 + 0.731905i
\(364\) −0.926751 0.926751i −0.0485750 0.0485750i
\(365\) −1.13662 + 1.13662i −0.0594935 + 0.0594935i
\(366\) 3.36667 + 5.43469i 0.175979 + 0.284076i
\(367\) −23.5145 −1.22745 −0.613724 0.789521i \(-0.710329\pi\)
−0.613724 + 0.789521i \(0.710329\pi\)
\(368\) −0.456993 0.456993i −0.0238224 0.0238224i
\(369\) 0.728358 1.46436i 0.0379168 0.0762315i
\(370\) 5.07126 3.35892i 0.263642 0.174622i
\(371\) 2.91810i 0.151500i
\(372\) −0.389781 0.0915850i −0.0202092 0.00474846i
\(373\) 37.4002i 1.93651i 0.249963 + 0.968255i \(0.419581\pi\)
−0.249963 + 0.968255i \(0.580419\pi\)
\(374\) −4.88749 −0.252726
\(375\) −1.68613 0.396182i −0.0870715 0.0204588i
\(376\) −1.13460 + 1.13460i −0.0585124 + 0.0585124i
\(377\) 8.21369i 0.423026i
\(378\) −1.20680 + 1.45525i −0.0620709 + 0.0748498i
\(379\) 30.3654 1.55977 0.779883 0.625925i \(-0.215279\pi\)
0.779883 + 0.625925i \(0.215279\pi\)
\(380\) 1.98313i 0.101732i
\(381\) −17.2511 27.8478i −0.883801 1.42668i
\(382\) 8.88163 0.454424
\(383\) −3.46804 3.46804i −0.177209 0.177209i 0.612929 0.790138i \(-0.289991\pi\)
−0.790138 + 0.612929i \(0.789991\pi\)
\(384\) −0.396182 + 1.68613i −0.0202176 + 0.0860450i
\(385\) −0.318162 0.318162i −0.0162150 0.0162150i
\(386\) 5.86272i 0.298405i
\(387\) 6.41877 + 19.1230i 0.326284 + 0.972077i
\(388\) 0.870659 + 0.870659i 0.0442010 + 0.0442010i
\(389\) 7.62835 + 7.62835i 0.386772 + 0.386772i 0.873535 0.486762i \(-0.161822\pi\)
−0.486762 + 0.873535i \(0.661822\pi\)
\(390\) −6.07391 1.42716i −0.307564 0.0722669i
\(391\) 2.55416i 0.129170i
\(392\) −4.85614 4.85614i −0.245272 0.245272i
\(393\) −4.16262 0.978070i −0.209976 0.0493371i
\(394\) −12.6624 12.6624i −0.637921 0.637921i
\(395\) −3.28319 −0.165195
\(396\) 3.32185 + 1.65226i 0.166929 + 0.0830291i
\(397\) 15.6581i 0.785860i −0.919568 0.392930i \(-0.871461\pi\)
0.919568 0.392930i \(-0.128539\pi\)
\(398\) 23.9630 1.20116
\(399\) −1.21659 0.285856i −0.0609057 0.0143107i
\(400\) 1.00000i 0.0500000i
\(401\) −12.5130 + 12.5130i −0.624871 + 0.624871i −0.946773 0.321902i \(-0.895678\pi\)
0.321902 + 0.946773i \(0.395678\pi\)
\(402\) 1.96104 8.34608i 0.0978077 0.416264i
\(403\) 0.832734 0.0414814
\(404\) 0.868845i 0.0432267i
\(405\) −1.23555 + 8.91479i −0.0613947 + 0.442979i
\(406\) 0.829588i 0.0411717i
\(407\) 6.27158 4.15396i 0.310871 0.205904i
\(408\) 5.81909 3.60480i 0.288088 0.178464i
\(409\) −10.4273 10.4273i −0.515599 0.515599i 0.400638 0.916236i \(-0.368789\pi\)
−0.916236 + 0.400638i \(0.868789\pi\)
\(410\) −0.545166 −0.0269238
\(411\) 12.2378 7.58103i 0.603644 0.373945i
\(412\) 7.68967 7.68967i 0.378843 0.378843i
\(413\) −2.34944 2.34944i −0.115609 0.115609i
\(414\) 0.863458 1.73598i 0.0424366 0.0853185i
\(415\) −5.96781 + 5.96781i −0.292948 + 0.292948i
\(416\) 3.60228i 0.176616i
\(417\) −3.87186 + 2.39854i −0.189606 + 0.117457i
\(418\) 2.45252i 0.119957i
\(419\) 7.73667i 0.377961i 0.981981 + 0.188980i \(0.0605183\pi\)
−0.981981 + 0.188980i \(0.939482\pi\)
\(420\) 0.613469 + 0.144144i 0.0299342 + 0.00703350i
\(421\) −7.36859 7.36859i −0.359123 0.359123i 0.504366 0.863490i \(-0.331726\pi\)
−0.863490 + 0.504366i \(0.831726\pi\)
\(422\) −15.3600 + 15.3600i −0.747714 + 0.747714i
\(423\) −4.30998 2.14374i −0.209558 0.104232i
\(424\) 5.67132 5.67132i 0.275424 0.275424i
\(425\) −2.79453 + 2.79453i −0.135555 + 0.135555i
\(426\) 5.86744 24.9715i 0.284278 1.20987i
\(427\) 0.949576 + 0.949576i 0.0459532 + 0.0459532i
\(428\) −8.05854 −0.389524
\(429\) −7.51156 1.76496i −0.362662 0.0852128i
\(430\) 4.75447 4.75447i 0.229281 0.229281i
\(431\) 21.5577 21.5577i 1.03840 1.03840i 0.0391638 0.999233i \(-0.487531\pi\)
0.999233 0.0391638i \(-0.0124694\pi\)
\(432\) −5.17367 + 0.482863i −0.248918 + 0.0232317i
\(433\) 35.8755 1.72407 0.862034 0.506851i \(-0.169190\pi\)
0.862034 + 0.506851i \(0.169190\pi\)
\(434\) −0.0841067 −0.00403725
\(435\) −2.07979 3.35732i −0.0997181 0.160971i
\(436\) −0.884855 0.884855i −0.0423769 0.0423769i
\(437\) 1.28167 0.0613106
\(438\) 0.636833 2.71033i 0.0304291 0.129505i
\(439\) 13.1830 + 13.1830i 0.629190 + 0.629190i 0.947864 0.318674i \(-0.103238\pi\)
−0.318674 + 0.947864i \(0.603238\pi\)
\(440\) 1.23669i 0.0589570i
\(441\) 9.17536 18.4470i 0.436922 0.878428i
\(442\) −10.0667 + 10.0667i −0.478823 + 0.478823i
\(443\) 39.5691 1.87999 0.939993 0.341193i \(-0.110831\pi\)
0.939993 + 0.341193i \(0.110831\pi\)
\(444\) −4.40323 + 9.57139i −0.208968 + 0.454238i
\(445\) 0.778187 0.0368896
\(446\) −5.12377 + 5.12377i −0.242618 + 0.242618i
\(447\) 15.1178 9.36514i 0.715046 0.442956i
\(448\) 0.363832i 0.0171895i
\(449\) 12.2930 + 12.2930i 0.580144 + 0.580144i 0.934943 0.354799i \(-0.115451\pi\)
−0.354799 + 0.934943i \(0.615451\pi\)
\(450\) 2.84406 0.954629i 0.134070 0.0450016i
\(451\) −0.674202 −0.0317470
\(452\) −7.40005 7.40005i −0.348069 0.348069i
\(453\) 8.14612 5.04635i 0.382738 0.237098i
\(454\) 10.2083 0.479102
\(455\) −1.31062 −0.0614430
\(456\) −1.80888 2.92000i −0.0847084 0.136741i
\(457\) 16.2368 16.2368i 0.759525 0.759525i −0.216711 0.976236i \(-0.569533\pi\)
0.976236 + 0.216711i \(0.0695328\pi\)
\(458\) 10.6753 10.6753i 0.498824 0.498824i
\(459\) 15.8074 + 13.1086i 0.737824 + 0.611857i
\(460\) −0.646286 −0.0301332
\(461\) 24.0001 + 24.0001i 1.11780 + 1.11780i 0.992064 + 0.125733i \(0.0401282\pi\)
0.125733 + 0.992064i \(0.459872\pi\)
\(462\) 0.758672 + 0.178262i 0.0352966 + 0.00829348i
\(463\) −9.18675 + 9.18675i −0.426945 + 0.426945i −0.887586 0.460642i \(-0.847619\pi\)
0.460642 + 0.887586i \(0.347619\pi\)
\(464\) 1.61230 1.61230i 0.0748492 0.0748492i
\(465\) −0.340377 + 0.210857i −0.0157846 + 0.00977824i
\(466\) 1.18367 1.18367i 0.0548324 0.0548324i
\(467\) −19.8576 19.8576i −0.918901 0.918901i 0.0780485 0.996950i \(-0.475131\pi\)
−0.996950 + 0.0780485i \(0.975131\pi\)
\(468\) 10.2451 3.43884i 0.473580 0.158960i
\(469\) 1.80091i 0.0831583i
\(470\) 1.60456i 0.0740129i
\(471\) −6.71061 10.8327i −0.309209 0.499143i
\(472\) 9.13227i 0.420347i
\(473\) 5.87982 5.87982i 0.270354 0.270354i
\(474\) 4.83423 2.99470i 0.222043 0.137551i
\(475\) 1.40229 + 1.40229i 0.0643413 + 0.0643413i
\(476\) 1.01674 1.01674i 0.0466022 0.0466022i
\(477\) 21.5436 + 10.7156i 0.986413 + 0.490633i
\(478\) −12.6428 −0.578268
\(479\) −11.7978 11.7978i −0.539054 0.539054i 0.384197 0.923251i \(-0.374478\pi\)
−0.923251 + 0.384197i \(0.874478\pi\)
\(480\) 0.912132 + 1.47242i 0.0416329 + 0.0672064i
\(481\) 4.36164 21.4733i 0.198874 0.979098i
\(482\) 2.68764i 0.122419i
\(483\) 0.0931582 0.396476i 0.00423884 0.0180403i
\(484\) 9.47059i 0.430481i
\(485\) 1.23130 0.0559104
\(486\) −6.31222 14.2533i −0.286328 0.646542i
\(487\) −25.1254 + 25.1254i −1.13854 + 1.13854i −0.149830 + 0.988712i \(0.547873\pi\)
−0.988712 + 0.149830i \(0.952127\pi\)
\(488\) 3.69100i 0.167084i
\(489\) 4.57039 19.4514i 0.206680 0.879621i
\(490\) −6.86763 −0.310248
\(491\) 4.62838i 0.208876i 0.994531 + 0.104438i \(0.0333044\pi\)
−0.994531 + 0.104438i \(0.966696\pi\)
\(492\) 0.802712 0.497263i 0.0361891 0.0224184i
\(493\) −9.01125 −0.405846
\(494\) 5.05142 + 5.05142i 0.227274 + 0.227274i
\(495\) 3.51723 1.18058i 0.158088 0.0530632i
\(496\) −0.163461 0.163461i −0.00733962 0.00733962i
\(497\) 5.38834i 0.241700i
\(498\) 3.34368 14.2305i 0.149834 0.637686i
\(499\) −5.53591 5.53591i −0.247822 0.247822i 0.572255 0.820076i \(-0.306069\pi\)
−0.820076 + 0.572255i \(0.806069\pi\)
\(500\) −0.707107 0.707107i −0.0316228 0.0316228i
\(501\) −3.95998 + 16.8535i −0.176919 + 0.752957i
\(502\) 9.91666i 0.442602i
\(503\) 17.6402 + 17.6402i 0.786536 + 0.786536i 0.980925 0.194388i \(-0.0622721\pi\)
−0.194388 + 0.980925i \(0.562272\pi\)
\(504\) −1.03476 + 0.347325i −0.0460919 + 0.0154711i
\(505\) −0.614366 0.614366i −0.0273389 0.0273389i
\(506\) −0.799257 −0.0355313
\(507\) 0.0347590 0.0215324i 0.00154370 0.000956289i
\(508\) 18.9130i 0.839127i
\(509\) 24.0229 1.06480 0.532398 0.846494i \(-0.321291\pi\)
0.532398 + 0.846494i \(0.321291\pi\)
\(510\) 1.56574 6.66370i 0.0693320 0.295074i
\(511\) 0.584833i 0.0258715i
\(512\) −0.707107 + 0.707107i −0.0312500 + 0.0312500i
\(513\) 6.57785 7.93207i 0.290419 0.350210i
\(514\) 20.0960 0.886395
\(515\) 10.8748i 0.479203i
\(516\) −2.66386 + 11.3373i −0.117270 + 0.499096i
\(517\) 1.98435i 0.0872716i
\(518\) −0.440529 + 2.16882i −0.0193557 + 0.0952924i
\(519\) 5.95531 + 9.61342i 0.261409 + 0.421982i
\(520\) −2.54719 2.54719i −0.111702 0.111702i
\(521\) 15.1389 0.663247 0.331623 0.943412i \(-0.392404\pi\)
0.331623 + 0.943412i \(0.392404\pi\)
\(522\) 6.12463 + 3.04633i 0.268068 + 0.133334i
\(523\) −1.01795 + 1.01795i −0.0445119 + 0.0445119i −0.729012 0.684500i \(-0.760020\pi\)
0.684500 + 0.729012i \(0.260020\pi\)
\(524\) −1.74566 1.74566i −0.0762596 0.0762596i
\(525\) 0.535713 0.331863i 0.0233804 0.0144837i
\(526\) −13.5662 + 13.5662i −0.591514 + 0.591514i
\(527\) 0.913594i 0.0397968i
\(528\) 1.12803 + 1.82093i 0.0490911 + 0.0792457i
\(529\) 22.5823i 0.981840i
\(530\) 8.02046i 0.348386i
\(531\) 25.9727 8.71793i 1.12712 0.378326i
\(532\) −0.510197 0.510197i −0.0221198 0.0221198i
\(533\) −1.38864 + 1.38864i −0.0601488 + 0.0601488i
\(534\) −1.14582 + 0.709809i −0.0495843 + 0.0307165i
\(535\) −5.69825 + 5.69825i −0.246357 + 0.246357i
\(536\) 3.50006 3.50006i 0.151180 0.151180i
\(537\) 12.0300 + 2.82664i 0.519134 + 0.121978i
\(538\) −19.8432 19.8432i −0.855499 0.855499i
\(539\) −8.49314 −0.365825
\(540\) −3.31690 + 3.99977i −0.142737 + 0.172123i
\(541\) 8.31756 8.31756i 0.357600 0.357600i −0.505328 0.862928i \(-0.668628\pi\)
0.862928 + 0.505328i \(0.168628\pi\)
\(542\) −11.5487 + 11.5487i −0.496060 + 0.496060i
\(543\) −1.52809 2.46673i −0.0655765 0.105857i
\(544\) 3.95206 0.169443
\(545\) −1.25137 −0.0536030
\(546\) 1.92979 1.19546i 0.0825873 0.0511611i
\(547\) −11.6801 11.6801i −0.499403 0.499403i 0.411849 0.911252i \(-0.364883\pi\)
−0.911252 + 0.411849i \(0.864883\pi\)
\(548\) 8.31134 0.355043
\(549\) −10.4974 + 3.52353i −0.448019 + 0.150381i
\(550\) −0.874474 0.874474i −0.0372877 0.0372877i
\(551\) 4.52181i 0.192636i
\(552\) 0.951603 0.589498i 0.0405029 0.0250907i
\(553\) 0.844660 0.844660i 0.0359186 0.0359186i
\(554\) 4.69968 0.199670
\(555\) 3.65445 + 9.88155i 0.155123 + 0.419448i
\(556\) −2.62959 −0.111520
\(557\) 31.2058 31.2058i 1.32223 1.32223i 0.410270 0.911964i \(-0.365434\pi\)
0.911964 0.410270i \(-0.134566\pi\)
\(558\) 0.308849 0.620938i 0.0130746 0.0262864i
\(559\) 24.2211i 1.02444i
\(560\) 0.257268 + 0.257268i 0.0108716 + 0.0108716i
\(561\) 1.93634 8.24095i 0.0817522 0.347933i
\(562\) −3.19146 −0.134624
\(563\) −2.07352 2.07352i −0.0873885 0.0873885i 0.662061 0.749450i \(-0.269682\pi\)
−0.749450 + 0.662061i \(0.769682\pi\)
\(564\) −1.46357 2.36259i −0.0616275 0.0994828i
\(565\) −10.4652 −0.440276
\(566\) −19.7177 −0.828796
\(567\) −1.97563 2.61136i −0.0829685 0.109667i
\(568\) 10.4722 10.4722i 0.439404 0.439404i
\(569\) 14.1395 14.1395i 0.592758 0.592758i −0.345617 0.938376i \(-0.612330\pi\)
0.938376 + 0.345617i \(0.112330\pi\)
\(570\) −3.34382 0.785681i −0.140057 0.0329086i
\(571\) −17.4906 −0.731960 −0.365980 0.930623i \(-0.619266\pi\)
−0.365980 + 0.930623i \(0.619266\pi\)
\(572\) −3.15010 3.15010i −0.131712 0.131712i
\(573\) −3.51874 + 14.9756i −0.146998 + 0.625615i
\(574\) 0.140254 0.140254i 0.00585408 0.00585408i
\(575\) −0.456993 + 0.456993i −0.0190579 + 0.0190579i
\(576\) −2.68608 1.33603i −0.111920 0.0556679i
\(577\) 23.1142 23.1142i 0.962256 0.962256i −0.0370574 0.999313i \(-0.511798\pi\)
0.999313 + 0.0370574i \(0.0117984\pi\)
\(578\) 0.976650 + 0.976650i 0.0406233 + 0.0406233i
\(579\) −9.88532 2.32271i −0.410820 0.0965284i
\(580\) 2.28014i 0.0946776i
\(581\) 3.07066i 0.127392i
\(582\) −1.81299 + 1.12311i −0.0751507 + 0.0465543i
\(583\) 9.91884i 0.410796i
\(584\) 1.13662 1.13662i 0.0470337 0.0470337i
\(585\) 4.81275 9.67600i 0.198983 0.400053i
\(586\) 12.3265 + 12.3265i 0.509203 + 0.509203i
\(587\) 16.8989 16.8989i 0.697491 0.697491i −0.266378 0.963869i \(-0.585827\pi\)
0.963869 + 0.266378i \(0.0858268\pi\)
\(588\) 10.1120 6.26418i 0.417013 0.258330i
\(589\) 0.458438 0.0188896
\(590\) −6.45749 6.45749i −0.265851 0.265851i
\(591\) 26.3670 16.3338i 1.08459 0.671883i
\(592\) −5.07126 + 3.35892i −0.208427 + 0.138051i
\(593\) 35.3242i 1.45059i 0.688438 + 0.725295i \(0.258297\pi\)
−0.688438 + 0.725295i \(0.741703\pi\)
\(594\) −4.10199 + 4.94649i −0.168307 + 0.202957i
\(595\) 1.43789i 0.0589477i
\(596\) 10.2673 0.420566
\(597\) −9.49372 + 40.4048i −0.388552 + 1.65366i
\(598\) −1.64622 + 1.64622i −0.0673188 + 0.0673188i
\(599\) 14.7052i 0.600838i 0.953807 + 0.300419i \(0.0971264\pi\)
−0.953807 + 0.300419i \(0.902874\pi\)
\(600\) 1.68613 + 0.396182i 0.0688360 + 0.0161741i
\(601\) −5.81380 −0.237150 −0.118575 0.992945i \(-0.537833\pi\)
−0.118575 + 0.992945i \(0.537833\pi\)
\(602\) 2.44635i 0.0997057i
\(603\) 13.2957 + 6.61313i 0.541441 + 0.269308i
\(604\) 5.53248 0.225113
\(605\) 6.69672 + 6.69672i 0.272260 + 0.272260i
\(606\) 1.46499 + 0.344221i 0.0595110 + 0.0139830i
\(607\) −4.11260 4.11260i −0.166925 0.166925i 0.618701 0.785626i \(-0.287659\pi\)
−0.785626 + 0.618701i \(0.787659\pi\)
\(608\) 1.98313i 0.0804266i
\(609\) 1.39879 + 0.328668i 0.0566820 + 0.0133183i
\(610\) 2.60993 + 2.60993i 0.105673 + 0.105673i
\(611\) 4.08713 + 4.08713i 0.165348 + 0.165348i
\(612\) 3.77275 + 11.2399i 0.152504 + 0.454346i
\(613\) 9.41341i 0.380204i 0.981764 + 0.190102i \(0.0608819\pi\)
−0.981764 + 0.190102i \(0.939118\pi\)
\(614\) 3.67626 + 3.67626i 0.148362 + 0.148362i
\(615\) 0.215985 0.919221i 0.00870936 0.0370666i
\(616\) 0.318162 + 0.318162i 0.0128191 + 0.0128191i
\(617\) −24.1161 −0.970877 −0.485438 0.874271i \(-0.661340\pi\)
−0.485438 + 0.874271i \(0.661340\pi\)
\(618\) 9.91928 + 16.0123i 0.399012 + 0.644109i
\(619\) 36.1762i 1.45404i 0.686614 + 0.727022i \(0.259096\pi\)
−0.686614 + 0.727022i \(0.740904\pi\)
\(620\) −0.231169 −0.00928397
\(621\) 2.58500 + 2.14367i 0.103732 + 0.0860224i
\(622\) 5.40903i 0.216882i
\(623\) −0.200203 + 0.200203i −0.00802096 + 0.00802096i
\(624\) 6.07391 + 1.42716i 0.243151 + 0.0571320i
\(625\) −1.00000 −0.0400000
\(626\) 33.3908i 1.33457i
\(627\) −4.13528 0.971646i −0.165147 0.0388038i
\(628\) 7.35707i 0.293579i
\(629\) 23.5584 + 4.78516i 0.939335 + 0.190797i
\(630\) −0.486091 + 0.977282i −0.0193663 + 0.0389359i
\(631\) −21.7680 21.7680i −0.866571 0.866571i 0.125520 0.992091i \(-0.459940\pi\)
−0.992091 + 0.125520i \(0.959940\pi\)
\(632\) 3.28319 0.130598
\(633\) −19.8136 31.9844i −0.787521 1.27126i
\(634\) 10.3584 10.3584i 0.411384 0.411384i
\(635\) −13.3735 13.3735i −0.530710 0.530710i
\(636\) 7.31572 + 11.8095i 0.290087 + 0.468276i
\(637\) −17.4932 + 17.4932i −0.693105 + 0.693105i
\(638\) 2.81983i 0.111638i
\(639\) 39.7807 + 19.7865i 1.57370 + 0.782744i
\(640\) 1.00000i 0.0395285i
\(641\) 4.70643i 0.185893i −0.995671 0.0929463i \(-0.970371\pi\)
0.995671 0.0929463i \(-0.0296285\pi\)
\(642\) 3.19265 13.5878i 0.126004 0.536266i
\(643\) −17.4164 17.4164i −0.686836 0.686836i 0.274695 0.961531i \(-0.411423\pi\)
−0.961531 + 0.274695i \(0.911423\pi\)
\(644\) 0.166269 0.166269i 0.00655191 0.00655191i
\(645\) 6.13303 + 9.90030i 0.241488 + 0.389824i
\(646\) −5.54192 + 5.54192i −0.218044 + 0.218044i
\(647\) 4.39908 4.39908i 0.172946 0.172946i −0.615327 0.788272i \(-0.710976\pi\)
0.788272 + 0.615327i \(0.210976\pi\)
\(648\) 1.23555 8.91479i 0.0485368 0.350206i
\(649\) −7.98593 7.98593i −0.313475 0.313475i
\(650\) −3.60228 −0.141293
\(651\) 0.0333216 0.141815i 0.00130598 0.00555817i
\(652\) 8.15725 8.15725i 0.319463 0.319463i
\(653\) −29.2611 + 29.2611i −1.14507 + 1.14507i −0.157567 + 0.987508i \(0.550365\pi\)
−0.987508 + 0.157567i \(0.949635\pi\)
\(654\) 1.84255 1.14142i 0.0720492 0.0446330i
\(655\) −2.46874 −0.0964616
\(656\) 0.545166 0.0212851
\(657\) 4.31767 + 2.14757i 0.168448 + 0.0837847i
\(658\) −0.412803 0.412803i −0.0160927 0.0160927i
\(659\) −1.26482 −0.0492703 −0.0246351 0.999697i \(-0.507842\pi\)
−0.0246351 + 0.999697i \(0.507842\pi\)
\(660\) 2.08523 + 0.489956i 0.0811673 + 0.0190715i
\(661\) −14.4067 14.4067i −0.560357 0.560357i 0.369052 0.929409i \(-0.379682\pi\)
−0.929409 + 0.369052i \(0.879682\pi\)
\(662\) 3.92816i 0.152672i
\(663\) −12.9855 20.9620i −0.504315 0.814096i
\(664\) 5.96781 5.96781i 0.231596 0.231596i
\(665\) −0.721527 −0.0279796
\(666\) −14.3941 11.2164i −0.557762 0.434628i
\(667\) −1.47362 −0.0570588
\(668\) −7.06777 + 7.06777i −0.273460 + 0.273460i
\(669\) −6.60940 10.6693i −0.255534 0.412499i
\(670\) 4.94984i 0.191229i
\(671\) 3.22768 + 3.22768i 0.124603 + 0.124603i
\(672\) −0.613469 0.144144i −0.0236651 0.00556047i
\(673\) −4.92341 −0.189784 −0.0948918 0.995488i \(-0.530251\pi\)
−0.0948918 + 0.995488i \(0.530251\pi\)
\(674\) 8.28004 + 8.28004i 0.318935 + 0.318935i
\(675\) 0.482863 + 5.17367i 0.0185854 + 0.199135i
\(676\) 0.0236067 0.000907951
\(677\) 27.8288 1.06955 0.534775 0.844995i \(-0.320396\pi\)
0.534775 + 0.844995i \(0.320396\pi\)
\(678\) 15.4092 9.54569i 0.591788 0.366600i
\(679\) −0.316774 + 0.316774i −0.0121567 + 0.0121567i
\(680\) 2.79453 2.79453i 0.107165 0.107165i
\(681\) −4.04437 + 17.2126i −0.154980 + 0.659589i
\(682\) −0.285885 −0.0109471
\(683\) 0.306666 + 0.306666i 0.0117343 + 0.0117343i 0.712950 0.701215i \(-0.247359\pi\)
−0.701215 + 0.712950i \(0.747359\pi\)
\(684\) 5.64015 1.89315i 0.215656 0.0723865i
\(685\) 5.87700 5.87700i 0.224549 0.224549i
\(686\) 3.56770 3.56770i 0.136215 0.136215i
\(687\) 13.7706 + 22.2293i 0.525381 + 0.848102i
\(688\) −4.75447 + 4.75447i −0.181263 + 0.181263i
\(689\) −20.4297 20.4297i −0.778308 0.778308i
\(690\) 0.256047 1.08972i 0.00974754 0.0414851i
\(691\) 6.54668i 0.249048i 0.992217 + 0.124524i \(0.0397403\pi\)
−0.992217 + 0.124524i \(0.960260\pi\)
\(692\) 6.52900i 0.248195i
\(693\) −0.601145 + 1.20860i −0.0228356 + 0.0459108i
\(694\) 28.1966i 1.07033i
\(695\) −1.85940 + 1.85940i −0.0705312 + 0.0705312i
\(696\) 2.07979 + 3.35732i 0.0788341 + 0.127259i
\(697\) −1.52348 1.52348i −0.0577060 0.0577060i
\(698\) 14.6252 14.6252i 0.553574 0.553574i
\(699\) 1.52687 + 2.46477i 0.0577517 + 0.0932262i
\(700\) 0.363832 0.0137516
\(701\) −15.0325 15.0325i −0.567769 0.567769i 0.363734 0.931503i \(-0.381502\pi\)
−0.931503 + 0.363734i \(0.881502\pi\)
\(702\) 1.73940 + 18.6370i 0.0656496 + 0.703408i
\(703\) 2.40118 11.8215i 0.0905621 0.445857i
\(704\) 1.23669i 0.0466096i
\(705\) −2.70550 0.635699i −0.101895 0.0239418i
\(706\) 7.59069i 0.285680i
\(707\) 0.316114 0.0118887
\(708\) 15.3982 + 3.61804i 0.578700 + 0.135974i
\(709\) −36.1363 + 36.1363i −1.35713 + 1.35713i −0.479690 + 0.877438i \(0.659251\pi\)
−0.877438 + 0.479690i \(0.840749\pi\)
\(710\) 14.8100i 0.555808i
\(711\) 3.13422 + 9.33759i 0.117543 + 0.350187i
\(712\) −0.778187 −0.0291638
\(713\) 0.149401i 0.00559512i
\(714\) 1.31154 + 2.11717i 0.0490833 + 0.0792332i
\(715\) −4.45491 −0.166604
\(716\) 5.04499 + 5.04499i 0.188540 + 0.188540i
\(717\) 5.00885 21.3174i 0.187059 0.796113i
\(718\) −10.9701 10.9701i −0.409401 0.409401i
\(719\) 17.6902i 0.659734i 0.944027 + 0.329867i \(0.107004\pi\)
−0.944027 + 0.329867i \(0.892996\pi\)
\(720\) −2.84406 + 0.954629i −0.105992 + 0.0355769i
\(721\) 2.79775 + 2.79775i 0.104194 + 0.104194i
\(722\) −10.6541 10.6541i −0.396505 0.396505i
\(723\) 4.53172 + 1.06480i 0.168536 + 0.0396002i
\(724\) 1.67529i 0.0622617i
\(725\) −1.61230 1.61230i −0.0598793 0.0598793i
\(726\) −15.9687 3.75208i −0.592653 0.139253i
\(727\) −28.1049 28.1049i −1.04235 1.04235i −0.999063 0.0432905i \(-0.986216\pi\)
−0.0432905 0.999063i \(-0.513784\pi\)
\(728\) 1.31062 0.0485750
\(729\) 26.5337 4.99634i 0.982729 0.185050i
\(730\) 1.60743i 0.0594935i
\(731\) 26.5730 0.982839
\(732\) −6.22350 1.46231i −0.230027 0.0540484i
\(733\) 13.3828i 0.494305i 0.968977 + 0.247152i \(0.0794948\pi\)
−0.968977 + 0.247152i \(0.920505\pi\)
\(734\) 16.6273 16.6273i 0.613724 0.613724i
\(735\) 2.72083 11.5797i 0.100359 0.427124i
\(736\) 0.646286 0.0238224
\(737\) 6.12143i 0.225486i
\(738\) 0.520431 + 1.55048i 0.0191573 + 0.0570741i
\(739\) 16.3486i 0.601394i 0.953720 + 0.300697i \(0.0972192\pi\)
−0.953720 + 0.300697i \(0.902781\pi\)
\(740\) −1.21080 + 5.96104i −0.0445099 + 0.219132i
\(741\) −10.5186 + 6.51608i −0.386412 + 0.239374i
\(742\) 2.06341 + 2.06341i 0.0757501 + 0.0757501i
\(743\) −30.1894 −1.10754 −0.553770 0.832670i \(-0.686811\pi\)
−0.553770 + 0.832670i \(0.686811\pi\)
\(744\) 0.340377 0.210857i 0.0124788 0.00773038i
\(745\) 7.26009 7.26009i 0.265989 0.265989i
\(746\) −26.4460 26.4460i −0.968255 0.968255i
\(747\) 22.6699 + 11.2758i 0.829447 + 0.412559i
\(748\) 3.45598 3.45598i 0.126363 0.126363i
\(749\) 2.93196i 0.107131i
\(750\) 1.47242 0.912132i 0.0537651 0.0333063i
\(751\) 18.3159i 0.668356i 0.942510 + 0.334178i \(0.108459\pi\)
−0.942510 + 0.334178i \(0.891541\pi\)
\(752\) 1.60456i 0.0585124i
\(753\) −16.7208 3.92880i −0.609340 0.143174i
\(754\) −5.80795 5.80795i −0.211513 0.211513i
\(755\) 3.91205 3.91205i 0.142374 0.142374i
\(756\) −0.175681 1.88235i −0.00638946 0.0684603i
\(757\) −24.8581 + 24.8581i −0.903485 + 0.903485i −0.995736 0.0922511i \(-0.970594\pi\)
0.0922511 + 0.995736i \(0.470594\pi\)
\(758\) −21.4716 + 21.4716i −0.779883 + 0.779883i
\(759\) 0.316651 1.34765i 0.0114937 0.0489167i
\(760\) −1.40229 1.40229i −0.0508662 0.0508662i
\(761\) −5.56719 −0.201811 −0.100905 0.994896i \(-0.532174\pi\)
−0.100905 + 0.994896i \(0.532174\pi\)
\(762\) 31.8897 + 7.49298i 1.15524 + 0.271442i
\(763\) 0.321939 0.321939i 0.0116550 0.0116550i
\(764\) −6.28026 + 6.28026i −0.227212 + 0.227212i
\(765\) 10.6156 + 5.28008i 0.383806 + 0.190902i
\(766\) 4.90455 0.177209
\(767\) −32.8970 −1.18784
\(768\) −0.912132 1.47242i −0.0329137 0.0531313i
\(769\) −27.1725 27.1725i −0.979867 0.979867i 0.0199341 0.999801i \(-0.493654\pi\)
−0.999801 + 0.0199341i \(0.993654\pi\)
\(770\) 0.449949 0.0162150
\(771\) −7.96167 + 33.8845i −0.286732 + 1.22032i
\(772\) −4.14557 4.14557i −0.149202 0.149202i
\(773\) 33.3633i 1.19999i 0.800002 + 0.599997i \(0.204832\pi\)
−0.800002 + 0.599997i \(0.795168\pi\)
\(774\) −18.0608 8.98325i −0.649181 0.322896i
\(775\) −0.163461 + 0.163461i −0.00587170 + 0.00587170i
\(776\) −1.23130 −0.0442010
\(777\) −3.48238 1.60204i −0.124930 0.0574727i
\(778\) −10.7881