Properties

Label 804.2.c.b.671.15
Level 804
Weight 2
Character 804.671
Analytic conductor 6.420
Analytic rank 0
Dimension 128
CM no
Inner twists 4

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Newspace parameters

Level: \( N \) = \( 804 = 2^{2} \cdot 3 \cdot 67 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 804.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.41997232251\)
Analytic rank: \(0\)
Dimension: \(128\)
Coefficient ring index: multiple of None
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 671.15
Character \(\chi\) = 804.671
Dual form 804.2.c.b.671.16

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.28652 - 0.587251i) q^{2} +(1.29382 - 1.15153i) q^{3} +(1.31027 + 1.51102i) q^{4} +1.10955i q^{5} +(-2.34077 + 0.721672i) q^{6} -0.262541i q^{7} +(-0.798342 - 2.71342i) q^{8} +(0.347946 - 2.97975i) q^{9} +O(q^{10})\) \(q+(-1.28652 - 0.587251i) q^{2} +(1.29382 - 1.15153i) q^{3} +(1.31027 + 1.51102i) q^{4} +1.10955i q^{5} +(-2.34077 + 0.721672i) q^{6} -0.262541i q^{7} +(-0.798342 - 2.71342i) q^{8} +(0.347946 - 2.97975i) q^{9} +(0.651585 - 1.42746i) q^{10} -2.52769 q^{11} +(3.43525 + 0.446172i) q^{12} +2.54523 q^{13} +(-0.154178 + 0.337765i) q^{14} +(1.27768 + 1.43556i) q^{15} +(-0.566377 + 3.95970i) q^{16} -1.62641i q^{17} +(-2.19750 + 3.62918i) q^{18} -7.27510i q^{19} +(-1.67656 + 1.45381i) q^{20} +(-0.302325 - 0.339681i) q^{21} +(3.25193 + 1.48439i) q^{22} -2.35289 q^{23} +(-4.15750 - 2.59136i) q^{24} +3.76890 q^{25} +(-3.27450 - 1.49469i) q^{26} +(-2.98110 - 4.25594i) q^{27} +(0.396706 - 0.344000i) q^{28} -2.37144i q^{29} +(-0.800732 - 2.59720i) q^{30} -4.13270i q^{31} +(3.05399 - 4.76163i) q^{32} +(-3.27038 + 2.91072i) q^{33} +(-0.955110 + 2.09241i) q^{34} +0.291303 q^{35} +(4.95838 - 3.37853i) q^{36} +9.94276 q^{37} +(-4.27231 + 9.35956i) q^{38} +(3.29308 - 2.93092i) q^{39} +(3.01068 - 0.885801i) q^{40} -0.158753i q^{41} +(0.189469 + 0.614548i) q^{42} +0.426938i q^{43} +(-3.31196 - 3.81940i) q^{44} +(3.30619 + 0.386064i) q^{45} +(3.02704 + 1.38174i) q^{46} +6.49415 q^{47} +(3.82693 + 5.77534i) q^{48} +6.93107 q^{49} +(-4.84876 - 2.21329i) q^{50} +(-1.87286 - 2.10428i) q^{51} +(3.33495 + 3.84590i) q^{52} -2.11312i q^{53} +(1.33595 + 7.22601i) q^{54} -2.80460i q^{55} +(-0.712385 + 0.209598i) q^{56} +(-8.37751 - 9.41267i) q^{57} +(-1.39263 + 3.05091i) q^{58} +1.36081 q^{59} +(-0.495051 + 3.81158i) q^{60} -5.75065 q^{61} +(-2.42693 + 5.31680i) q^{62} +(-0.782308 - 0.0913501i) q^{63} +(-6.72530 + 4.33247i) q^{64} +2.82407i q^{65} +(5.91673 - 1.82416i) q^{66} -1.00000i q^{67} +(2.45754 - 2.13103i) q^{68} +(-3.04421 + 2.70943i) q^{69} +(-0.374767 - 0.171068i) q^{70} +4.23883 q^{71} +(-8.36311 + 1.43474i) q^{72} -15.0927 q^{73} +(-12.7916 - 5.83890i) q^{74} +(4.87628 - 4.34001i) q^{75} +(10.9928 - 9.53235i) q^{76} +0.663623i q^{77} +(-5.95780 + 1.83682i) q^{78} +11.8105i q^{79} +(-4.39349 - 0.628424i) q^{80} +(-8.75787 - 2.07359i) q^{81} +(-0.0932279 + 0.204239i) q^{82} +0.252949 q^{83} +(0.117139 - 0.901894i) q^{84} +1.80458 q^{85} +(0.250720 - 0.549264i) q^{86} +(-2.73079 - 3.06822i) q^{87} +(2.01796 + 6.85869i) q^{88} -7.08186i q^{89} +(-4.02676 - 2.43824i) q^{90} -0.668229i q^{91} +(-3.08292 - 3.55526i) q^{92} +(-4.75893 - 5.34697i) q^{93} +(-8.35486 - 3.81370i) q^{94} +8.07209 q^{95} +(-1.53185 - 9.67747i) q^{96} -9.60577 q^{97} +(-8.91697 - 4.07028i) q^{98} +(-0.879500 + 7.53190i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 128q + 4q^{4} - 6q^{6} - 4q^{9} + O(q^{10}) \) \( 128q + 4q^{4} - 6q^{6} - 4q^{9} - 4q^{10} + 4q^{12} - 8q^{13} - 4q^{16} + 18q^{18} - 8q^{21} - 8q^{22} - 24q^{24} - 136q^{25} + 14q^{30} - 32q^{33} + 34q^{36} - 48q^{37} + 16q^{40} - 28q^{42} - 16q^{45} - 28q^{46} - 22q^{48} - 152q^{49} + 8q^{52} - 16q^{54} - 32q^{57} - 20q^{58} - 14q^{60} + 8q^{61} + 16q^{64} + 14q^{66} + 56q^{69} - 4q^{70} - 8q^{72} - 48q^{73} - 36q^{76} + 40q^{78} + 44q^{81} + 60q^{82} + 46q^{84} + 64q^{85} - 28q^{88} - 14q^{90} + 32q^{93} - 8q^{96} + 64q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/804\mathbb{Z}\right)^\times\).

\(n\) \(269\) \(337\) \(403\)
\(\chi(n)\) \(-1\) \(1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.28652 0.587251i −0.909708 0.415249i
\(3\) 1.29382 1.15153i 0.746988 0.664838i
\(4\) 1.31027 + 1.51102i 0.655136 + 0.755511i
\(5\) 1.10955i 0.496206i 0.968734 + 0.248103i \(0.0798072\pi\)
−0.968734 + 0.248103i \(0.920193\pi\)
\(6\) −2.34077 + 0.721672i −0.955614 + 0.294621i
\(7\) 0.262541i 0.0992313i −0.998768 0.0496156i \(-0.984200\pi\)
0.998768 0.0496156i \(-0.0157996\pi\)
\(8\) −0.798342 2.71342i −0.282256 0.959339i
\(9\) 0.347946 2.97975i 0.115982 0.993251i
\(10\) 0.651585 1.42746i 0.206049 0.451403i
\(11\) −2.52769 −0.762127 −0.381064 0.924549i \(-0.624442\pi\)
−0.381064 + 0.924549i \(0.624442\pi\)
\(12\) 3.43525 + 0.446172i 0.991671 + 0.128799i
\(13\) 2.54523 0.705921 0.352960 0.935638i \(-0.385175\pi\)
0.352960 + 0.935638i \(0.385175\pi\)
\(14\) −0.154178 + 0.337765i −0.0412057 + 0.0902714i
\(15\) 1.27768 + 1.43556i 0.329897 + 0.370660i
\(16\) −0.566377 + 3.95970i −0.141594 + 0.989925i
\(17\) 1.62641i 0.394462i −0.980357 0.197231i \(-0.936805\pi\)
0.980357 0.197231i \(-0.0631948\pi\)
\(18\) −2.19750 + 3.62918i −0.517957 + 0.855407i
\(19\) 7.27510i 1.66902i −0.550992 0.834511i \(-0.685750\pi\)
0.550992 0.834511i \(-0.314250\pi\)
\(20\) −1.67656 + 1.45381i −0.374889 + 0.325082i
\(21\) −0.302325 0.339681i −0.0659727 0.0741245i
\(22\) 3.25193 + 1.48439i 0.693313 + 0.316473i
\(23\) −2.35289 −0.490611 −0.245305 0.969446i \(-0.578888\pi\)
−0.245305 + 0.969446i \(0.578888\pi\)
\(24\) −4.15750 2.59136i −0.848647 0.528960i
\(25\) 3.76890 0.753779
\(26\) −3.27450 1.49469i −0.642182 0.293133i
\(27\) −2.98110 4.25594i −0.573714 0.819056i
\(28\) 0.396706 0.344000i 0.0749703 0.0650099i
\(29\) 2.37144i 0.440366i −0.975459 0.220183i \(-0.929335\pi\)
0.975459 0.220183i \(-0.0706654\pi\)
\(30\) −0.800732 2.59720i −0.146193 0.474182i
\(31\) 4.13270i 0.742254i −0.928582 0.371127i \(-0.878971\pi\)
0.928582 0.371127i \(-0.121029\pi\)
\(32\) 3.05399 4.76163i 0.539875 0.841745i
\(33\) −3.27038 + 2.91072i −0.569300 + 0.506691i
\(34\) −0.955110 + 2.09241i −0.163800 + 0.358845i
\(35\) 0.291303 0.0492392
\(36\) 4.95838 3.37853i 0.826396 0.563089i
\(37\) 9.94276 1.63458 0.817290 0.576226i \(-0.195475\pi\)
0.817290 + 0.576226i \(0.195475\pi\)
\(38\) −4.27231 + 9.35956i −0.693060 + 1.51832i
\(39\) 3.29308 2.93092i 0.527314 0.469323i
\(40\) 3.01068 0.885801i 0.476030 0.140057i
\(41\) 0.158753i 0.0247931i −0.999923 0.0123965i \(-0.996054\pi\)
0.999923 0.0123965i \(-0.00394604\pi\)
\(42\) 0.189469 + 0.614548i 0.0292357 + 0.0948268i
\(43\) 0.426938i 0.0651074i 0.999470 + 0.0325537i \(0.0103640\pi\)
−0.999470 + 0.0325537i \(0.989636\pi\)
\(44\) −3.31196 3.81940i −0.499297 0.575796i
\(45\) 3.30619 + 0.386064i 0.492858 + 0.0575510i
\(46\) 3.02704 + 1.38174i 0.446312 + 0.203726i
\(47\) 6.49415 0.947270 0.473635 0.880721i \(-0.342942\pi\)
0.473635 + 0.880721i \(0.342942\pi\)
\(48\) 3.82693 + 5.77534i 0.552370 + 0.833599i
\(49\) 6.93107 0.990153
\(50\) −4.84876 2.21329i −0.685719 0.313006i
\(51\) −1.87286 2.10428i −0.262253 0.294658i
\(52\) 3.33495 + 3.84590i 0.462474 + 0.533331i
\(53\) 2.11312i 0.290259i −0.989413 0.145129i \(-0.953640\pi\)
0.989413 0.145129i \(-0.0463599\pi\)
\(54\) 1.33595 + 7.22601i 0.181799 + 0.983336i
\(55\) 2.80460i 0.378172i
\(56\) −0.712385 + 0.209598i −0.0951964 + 0.0280087i
\(57\) −8.37751 9.41267i −1.10963 1.24674i
\(58\) −1.39263 + 3.05091i −0.182862 + 0.400604i
\(59\) 1.36081 0.177162 0.0885810 0.996069i \(-0.471767\pi\)
0.0885810 + 0.996069i \(0.471767\pi\)
\(60\) −0.495051 + 3.81158i −0.0639108 + 0.492073i
\(61\) −5.75065 −0.736295 −0.368148 0.929767i \(-0.620008\pi\)
−0.368148 + 0.929767i \(0.620008\pi\)
\(62\) −2.42693 + 5.31680i −0.308221 + 0.675234i
\(63\) −0.782308 0.0913501i −0.0985616 0.0115090i
\(64\) −6.72530 + 4.33247i −0.840663 + 0.541559i
\(65\) 2.82407i 0.350282i
\(66\) 5.91673 1.82416i 0.728300 0.224539i
\(67\) 1.00000i 0.122169i
\(68\) 2.45754 2.13103i 0.298020 0.258426i
\(69\) −3.04421 + 2.70943i −0.366480 + 0.326177i
\(70\) −0.374767 0.171068i −0.0447932 0.0204465i
\(71\) 4.23883 0.503056 0.251528 0.967850i \(-0.419067\pi\)
0.251528 + 0.967850i \(0.419067\pi\)
\(72\) −8.36311 + 1.43474i −0.985601 + 0.169086i
\(73\) −15.0927 −1.76647 −0.883236 0.468929i \(-0.844640\pi\)
−0.883236 + 0.468929i \(0.844640\pi\)
\(74\) −12.7916 5.83890i −1.48699 0.678759i
\(75\) 4.87628 4.34001i 0.563064 0.501141i
\(76\) 10.9928 9.53235i 1.26096 1.09344i
\(77\) 0.663623i 0.0756269i
\(78\) −5.95780 + 1.83682i −0.674588 + 0.207979i
\(79\) 11.8105i 1.32878i 0.747386 + 0.664390i \(0.231309\pi\)
−0.747386 + 0.664390i \(0.768691\pi\)
\(80\) −4.39349 0.628424i −0.491207 0.0702599i
\(81\) −8.75787 2.07359i −0.973096 0.230398i
\(82\) −0.0932279 + 0.204239i −0.0102953 + 0.0225544i
\(83\) 0.252949 0.0277648 0.0138824 0.999904i \(-0.495581\pi\)
0.0138824 + 0.999904i \(0.495581\pi\)
\(84\) 0.117139 0.901894i 0.0127809 0.0984047i
\(85\) 1.80458 0.195734
\(86\) 0.250720 0.549264i 0.0270358 0.0592287i
\(87\) −2.73079 3.06822i −0.292772 0.328948i
\(88\) 2.01796 + 6.85869i 0.215115 + 0.731138i
\(89\) 7.08186i 0.750675i −0.926888 0.375338i \(-0.877527\pi\)
0.926888 0.375338i \(-0.122473\pi\)
\(90\) −4.02676 2.43824i −0.424458 0.257013i
\(91\) 0.668229i 0.0700494i
\(92\) −3.08292 3.55526i −0.321417 0.370662i
\(93\) −4.75893 5.34697i −0.493478 0.554455i
\(94\) −8.35486 3.81370i −0.861738 0.393353i
\(95\) 8.07209 0.828179
\(96\) −1.53185 9.67747i −0.156344 0.987703i
\(97\) −9.60577 −0.975318 −0.487659 0.873034i \(-0.662149\pi\)
−0.487659 + 0.873034i \(0.662149\pi\)
\(98\) −8.91697 4.07028i −0.900750 0.411161i
\(99\) −0.879500 + 7.53190i −0.0883930 + 0.756984i
\(100\) 4.93828 + 5.69489i 0.493828 + 0.569489i
\(101\) 0.353964i 0.0352207i −0.999845 0.0176104i \(-0.994394\pi\)
0.999845 0.0176104i \(-0.00560584\pi\)
\(102\) 1.17373 + 3.80704i 0.116217 + 0.376953i
\(103\) 0.502968i 0.0495589i 0.999693 + 0.0247794i \(0.00788835\pi\)
−0.999693 + 0.0247794i \(0.992112\pi\)
\(104\) −2.03197 6.90629i −0.199251 0.677217i
\(105\) 0.376894 0.335445i 0.0367811 0.0327360i
\(106\) −1.24093 + 2.71857i −0.120530 + 0.264051i
\(107\) −11.9462 −1.15488 −0.577440 0.816433i \(-0.695948\pi\)
−0.577440 + 0.816433i \(0.695948\pi\)
\(108\) 2.52476 10.0810i 0.242946 0.970040i
\(109\) 2.85495 0.273455 0.136727 0.990609i \(-0.456342\pi\)
0.136727 + 0.990609i \(0.456342\pi\)
\(110\) −1.64701 + 3.60818i −0.157036 + 0.344026i
\(111\) 12.8642 11.4494i 1.22101 1.08673i
\(112\) 1.03958 + 0.148697i 0.0982315 + 0.0140506i
\(113\) 4.89451i 0.460437i −0.973139 0.230218i \(-0.926056\pi\)
0.973139 0.230218i \(-0.0739440\pi\)
\(114\) 5.25023 + 17.0293i 0.491730 + 1.59494i
\(115\) 2.61065i 0.243444i
\(116\) 3.58330 3.10723i 0.332701 0.288499i
\(117\) 0.885604 7.58417i 0.0818741 0.701157i
\(118\) −1.75071 0.799136i −0.161166 0.0735664i
\(119\) −0.426999 −0.0391429
\(120\) 2.87525 4.61296i 0.262473 0.421104i
\(121\) −4.61078 −0.419162
\(122\) 7.39833 + 3.37708i 0.669814 + 0.305746i
\(123\) −0.182809 0.205398i −0.0164834 0.0185201i
\(124\) 6.24460 5.41495i 0.560781 0.486277i
\(125\) 9.72954i 0.870236i
\(126\) 0.952810 + 0.576935i 0.0848831 + 0.0513975i
\(127\) 7.16672i 0.635943i −0.948100 0.317972i \(-0.896998\pi\)
0.948100 0.317972i \(-0.103002\pi\)
\(128\) 11.1965 1.62437i 0.989639 0.143576i
\(129\) 0.491633 + 0.552381i 0.0432858 + 0.0486344i
\(130\) 1.65844 3.63322i 0.145455 0.318654i
\(131\) 18.8378 1.64586 0.822932 0.568140i \(-0.192337\pi\)
0.822932 + 0.568140i \(0.192337\pi\)
\(132\) −8.68324 1.12779i −0.755779 0.0981611i
\(133\) −1.91001 −0.165619
\(134\) −0.587251 + 1.28652i −0.0507308 + 0.111138i
\(135\) 4.72218 3.30769i 0.406421 0.284680i
\(136\) −4.41312 + 1.29843i −0.378422 + 0.111339i
\(137\) 19.8598i 1.69673i 0.529409 + 0.848367i \(0.322414\pi\)
−0.529409 + 0.848367i \(0.677586\pi\)
\(138\) 5.50756 1.69801i 0.468835 0.144544i
\(139\) 15.9768i 1.35514i 0.735459 + 0.677569i \(0.236966\pi\)
−0.735459 + 0.677569i \(0.763034\pi\)
\(140\) 0.381686 + 0.440165i 0.0322583 + 0.0372007i
\(141\) 8.40227 7.47823i 0.707599 0.629781i
\(142\) −5.45334 2.48926i −0.457634 0.208894i
\(143\) −6.43356 −0.538002
\(144\) 11.6019 + 3.06542i 0.966822 + 0.255452i
\(145\) 2.63123 0.218512
\(146\) 19.4171 + 8.86323i 1.60697 + 0.733526i
\(147\) 8.96757 7.98135i 0.739632 0.658291i
\(148\) 13.0277 + 15.0237i 1.07087 + 1.23494i
\(149\) 12.0139i 0.984216i 0.870534 + 0.492108i \(0.163773\pi\)
−0.870534 + 0.492108i \(0.836227\pi\)
\(150\) −8.82211 + 2.71991i −0.720322 + 0.222080i
\(151\) 6.15058i 0.500527i −0.968178 0.250263i \(-0.919483\pi\)
0.968178 0.250263i \(-0.0805172\pi\)
\(152\) −19.7404 + 5.80801i −1.60116 + 0.471092i
\(153\) −4.84629 0.565901i −0.391799 0.0457504i
\(154\) 0.389714 0.853765i 0.0314040 0.0687983i
\(155\) 4.58544 0.368311
\(156\) 8.74351 + 1.13561i 0.700041 + 0.0909218i
\(157\) 0.311590 0.0248676 0.0124338 0.999923i \(-0.496042\pi\)
0.0124338 + 0.999923i \(0.496042\pi\)
\(158\) 6.93571 15.1944i 0.551775 1.20880i
\(159\) −2.43332 2.73400i −0.192975 0.216820i
\(160\) 5.28327 + 3.38856i 0.417679 + 0.267889i
\(161\) 0.617730i 0.0486839i
\(162\) 10.0495 + 7.81078i 0.789560 + 0.613673i
\(163\) 8.18013i 0.640717i 0.947296 + 0.320358i \(0.103803\pi\)
−0.947296 + 0.320358i \(0.896197\pi\)
\(164\) 0.239879 0.208010i 0.0187314 0.0162428i
\(165\) −3.22959 3.62865i −0.251423 0.282490i
\(166\) −0.325425 0.148545i −0.0252579 0.0115293i
\(167\) −12.5370 −0.970143 −0.485072 0.874474i \(-0.661206\pi\)
−0.485072 + 0.874474i \(0.661206\pi\)
\(168\) −0.680340 + 1.09152i −0.0524894 + 0.0842123i
\(169\) −6.52179 −0.501676
\(170\) −2.32163 1.05974i −0.178061 0.0812786i
\(171\) −21.6780 2.53134i −1.65776 0.193576i
\(172\) −0.645112 + 0.559404i −0.0491894 + 0.0426542i
\(173\) 4.00346i 0.304378i −0.988351 0.152189i \(-0.951368\pi\)
0.988351 0.152189i \(-0.0486322\pi\)
\(174\) 1.71140 + 5.55099i 0.129741 + 0.420820i
\(175\) 0.989491i 0.0747985i
\(176\) 1.43163 10.0089i 0.107913 0.754449i
\(177\) 1.76064 1.56701i 0.132338 0.117784i
\(178\) −4.15883 + 9.11096i −0.311718 + 0.682895i
\(179\) 21.7282 1.62404 0.812020 0.583630i \(-0.198368\pi\)
0.812020 + 0.583630i \(0.198368\pi\)
\(180\) 3.74865 + 5.50157i 0.279408 + 0.410063i
\(181\) −14.5887 −1.08437 −0.542183 0.840260i \(-0.682402\pi\)
−0.542183 + 0.840260i \(0.682402\pi\)
\(182\) −0.392418 + 0.859690i −0.0290880 + 0.0637245i
\(183\) −7.44031 + 6.62206i −0.550004 + 0.489517i
\(184\) 1.87841 + 6.38437i 0.138478 + 0.470662i
\(185\) 11.0320i 0.811089i
\(186\) 2.98245 + 9.67368i 0.218684 + 0.709309i
\(187\) 4.11105i 0.300630i
\(188\) 8.50911 + 9.81281i 0.620590 + 0.715673i
\(189\) −1.11736 + 0.782663i −0.0812759 + 0.0569303i
\(190\) −10.3849 4.74035i −0.753401 0.343901i
\(191\) 21.8420 1.58043 0.790217 0.612827i \(-0.209968\pi\)
0.790217 + 0.612827i \(0.209968\pi\)
\(192\) −3.71235 + 13.3498i −0.267916 + 0.963442i
\(193\) 3.19092 0.229688 0.114844 0.993384i \(-0.463363\pi\)
0.114844 + 0.993384i \(0.463363\pi\)
\(194\) 12.3580 + 5.64100i 0.887254 + 0.405000i
\(195\) 3.25200 + 3.65384i 0.232881 + 0.261657i
\(196\) 9.08159 + 10.4730i 0.648685 + 0.748072i
\(197\) 4.90985i 0.349812i −0.984585 0.174906i \(-0.944038\pi\)
0.984585 0.174906i \(-0.0559622\pi\)
\(198\) 5.55461 9.17345i 0.394749 0.651929i
\(199\) 23.5288i 1.66791i 0.551832 + 0.833956i \(0.313929\pi\)
−0.551832 + 0.833956i \(0.686071\pi\)
\(200\) −3.00887 10.2266i −0.212759 0.723130i
\(201\) −1.15153 1.29382i −0.0812228 0.0912591i
\(202\) −0.207866 + 0.455382i −0.0146254 + 0.0320405i
\(203\) −0.622601 −0.0436980
\(204\) 0.725657 5.58711i 0.0508062 0.391176i
\(205\) 0.176145 0.0123025
\(206\) 0.295368 0.647078i 0.0205793 0.0450841i
\(207\) −0.818677 + 7.01102i −0.0569020 + 0.487300i
\(208\) −1.44156 + 10.0784i −0.0999543 + 0.698809i
\(209\) 18.3892i 1.27201i
\(210\) −0.681872 + 0.210225i −0.0470536 + 0.0145069i
\(211\) 3.78622i 0.260654i 0.991471 + 0.130327i \(0.0416028\pi\)
−0.991471 + 0.130327i \(0.958397\pi\)
\(212\) 3.19297 2.76876i 0.219294 0.190159i
\(213\) 5.48429 4.88115i 0.375777 0.334451i
\(214\) 15.3690 + 7.01541i 1.05060 + 0.479564i
\(215\) −0.473709 −0.0323067
\(216\) −9.16821 + 11.4867i −0.623818 + 0.781570i
\(217\) −1.08500 −0.0736548
\(218\) −3.67296 1.67657i −0.248764 0.113552i
\(219\) −19.5273 + 17.3798i −1.31953 + 1.17442i
\(220\) 4.23782 3.67479i 0.285713 0.247754i
\(221\) 4.13958i 0.278459i
\(222\) −23.2737 + 7.17542i −1.56203 + 0.481582i
\(223\) 3.36904i 0.225608i −0.993617 0.112804i \(-0.964017\pi\)
0.993617 0.112804i \(-0.0359832\pi\)
\(224\) −1.25012 0.801799i −0.0835274 0.0535725i
\(225\) 1.31137 11.2304i 0.0874248 0.748692i
\(226\) −2.87431 + 6.29689i −0.191196 + 0.418863i
\(227\) −19.5547 −1.29789 −0.648945 0.760835i \(-0.724789\pi\)
−0.648945 + 0.760835i \(0.724789\pi\)
\(228\) 3.24595 24.9918i 0.214968 1.65512i
\(229\) 5.62695 0.371839 0.185920 0.982565i \(-0.440474\pi\)
0.185920 + 0.982565i \(0.440474\pi\)
\(230\) −1.53311 + 3.35865i −0.101090 + 0.221463i
\(231\) 0.764183 + 0.858609i 0.0502796 + 0.0564923i
\(232\) −6.43472 + 1.89322i −0.422460 + 0.124296i
\(233\) 27.4599i 1.79896i 0.436961 + 0.899480i \(0.356055\pi\)
−0.436961 + 0.899480i \(0.643945\pi\)
\(234\) −5.59316 + 9.23712i −0.365636 + 0.603849i
\(235\) 7.20559i 0.470041i
\(236\) 1.78303 + 2.05621i 0.116065 + 0.133848i
\(237\) 13.6001 + 15.2806i 0.883423 + 0.992583i
\(238\) 0.549343 + 0.250756i 0.0356086 + 0.0162541i
\(239\) 18.0672 1.16867 0.584336 0.811512i \(-0.301355\pi\)
0.584336 + 0.811512i \(0.301355\pi\)
\(240\) −6.40804 + 4.24618i −0.413637 + 0.274089i
\(241\) 20.0664 1.29259 0.646294 0.763089i \(-0.276318\pi\)
0.646294 + 0.763089i \(0.276318\pi\)
\(242\) 5.93187 + 2.70769i 0.381315 + 0.174057i
\(243\) −13.7189 + 7.40212i −0.880069 + 0.474846i
\(244\) −7.53492 8.68936i −0.482374 0.556279i
\(245\) 7.69038i 0.491320i
\(246\) 0.114568 + 0.371604i 0.00730457 + 0.0236926i
\(247\) 18.5168i 1.17820i
\(248\) −11.2137 + 3.29930i −0.712073 + 0.209506i
\(249\) 0.327271 0.291280i 0.0207400 0.0184591i
\(250\) 5.71368 12.5173i 0.361365 0.791661i
\(251\) 0.410017 0.0258800 0.0129400 0.999916i \(-0.495881\pi\)
0.0129400 + 0.999916i \(0.495881\pi\)
\(252\) −0.887004 1.30178i −0.0558760 0.0820043i
\(253\) 5.94737 0.373908
\(254\) −4.20866 + 9.22013i −0.264075 + 0.578522i
\(255\) 2.33480 2.07803i 0.146211 0.130132i
\(256\) −15.3584 4.48536i −0.959902 0.280335i
\(257\) 28.2650i 1.76312i 0.472068 + 0.881562i \(0.343508\pi\)
−0.472068 + 0.881562i \(0.656492\pi\)
\(258\) −0.308109 0.999361i −0.0191820 0.0622175i
\(259\) 2.61039i 0.162201i
\(260\) −4.26723 + 3.70029i −0.264642 + 0.229482i
\(261\) −7.06631 0.825133i −0.437394 0.0510745i
\(262\) −24.2352 11.0625i −1.49725 0.683444i
\(263\) 10.9958 0.678033 0.339016 0.940780i \(-0.389906\pi\)
0.339016 + 0.940780i \(0.389906\pi\)
\(264\) 10.5089 + 6.55017i 0.646777 + 0.403135i
\(265\) 2.34461 0.144028
\(266\) 2.45727 + 1.12166i 0.150665 + 0.0687732i
\(267\) −8.15499 9.16266i −0.499077 0.560745i
\(268\) 1.51102 1.31027i 0.0923004 0.0800376i
\(269\) 0.709047i 0.0432314i 0.999766 + 0.0216157i \(0.00688102\pi\)
−0.999766 + 0.0216157i \(0.993119\pi\)
\(270\) −8.01763 + 1.48230i −0.487937 + 0.0902099i
\(271\) 8.50829i 0.516842i 0.966032 + 0.258421i \(0.0832022\pi\)
−0.966032 + 0.258421i \(0.916798\pi\)
\(272\) 6.44008 + 0.921159i 0.390487 + 0.0558535i
\(273\) −0.769487 0.864568i −0.0465715 0.0523261i
\(274\) 11.6627 25.5500i 0.704568 1.54353i
\(275\) −9.52660 −0.574476
\(276\) −8.08275 1.04979i −0.486524 0.0631901i
\(277\) 29.7481 1.78739 0.893695 0.448674i \(-0.148104\pi\)
0.893695 + 0.448674i \(0.148104\pi\)
\(278\) 9.38242 20.5545i 0.562720 1.23278i
\(279\) −12.3144 1.43795i −0.737245 0.0860881i
\(280\) −0.232559 0.790427i −0.0138981 0.0472371i
\(281\) 8.92122i 0.532195i −0.963946 0.266098i \(-0.914266\pi\)
0.963946 0.266098i \(-0.0857344\pi\)
\(282\) −15.2013 + 4.68665i −0.905224 + 0.279086i
\(283\) 5.10047i 0.303191i 0.988443 + 0.151596i \(0.0484412\pi\)
−0.988443 + 0.151596i \(0.951559\pi\)
\(284\) 5.55402 + 6.40496i 0.329570 + 0.380065i
\(285\) 10.4438 9.29527i 0.618640 0.550604i
\(286\) 8.27691 + 3.77812i 0.489424 + 0.223405i
\(287\) −0.0416792 −0.00246025
\(288\) −13.1259 10.7569i −0.773449 0.633859i
\(289\) 14.3548 0.844400
\(290\) −3.38514 1.54520i −0.198782 0.0907370i
\(291\) −12.4281 + 11.0614i −0.728551 + 0.648428i
\(292\) −19.7756 22.8055i −1.15728 1.33459i
\(293\) 22.5544i 1.31764i −0.752300 0.658820i \(-0.771056\pi\)
0.752300 0.658820i \(-0.228944\pi\)
\(294\) −16.2240 + 5.00196i −0.946204 + 0.291720i
\(295\) 1.50988i 0.0879089i
\(296\) −7.93772 26.9789i −0.461371 1.56812i
\(297\) 7.53531 + 10.7577i 0.437243 + 0.624225i
\(298\) 7.05517 15.4561i 0.408695 0.895349i
\(299\) −5.98865 −0.346332
\(300\) 12.9471 + 1.68158i 0.747501 + 0.0970859i
\(301\) 0.112089 0.00646069
\(302\) −3.61193 + 7.91284i −0.207843 + 0.455333i
\(303\) −0.407601 0.457966i −0.0234160 0.0263094i
\(304\) 28.8072 + 4.12045i 1.65221 + 0.236324i
\(305\) 6.38064i 0.365354i
\(306\) 5.90253 + 3.57404i 0.337425 + 0.204314i
\(307\) 22.0167i 1.25656i −0.777988 0.628280i \(-0.783759\pi\)
0.777988 0.628280i \(-0.216241\pi\)
\(308\) −1.00275 + 0.869526i −0.0571369 + 0.0495459i
\(309\) 0.579184 + 0.650750i 0.0329486 + 0.0370199i
\(310\) −5.89926 2.69280i −0.335055 0.152941i
\(311\) 17.5997 0.997986 0.498993 0.866606i \(-0.333703\pi\)
0.498993 + 0.866606i \(0.333703\pi\)
\(312\) −10.5818 6.59563i −0.599077 0.373404i
\(313\) 7.38797 0.417593 0.208796 0.977959i \(-0.433045\pi\)
0.208796 + 0.977959i \(0.433045\pi\)
\(314\) −0.400867 0.182982i −0.0226222 0.0103263i
\(315\) 0.101358 0.868011i 0.00571086 0.0489069i
\(316\) −17.8459 + 15.4749i −1.00391 + 0.870531i
\(317\) 28.7508i 1.61481i −0.590001 0.807403i \(-0.700873\pi\)
0.590001 0.807403i \(-0.299127\pi\)
\(318\) 1.52498 + 4.94631i 0.0855165 + 0.277376i
\(319\) 5.99427i 0.335615i
\(320\) −4.80710 7.46206i −0.268725 0.417142i
\(321\) −15.4562 + 13.7564i −0.862682 + 0.767808i
\(322\) 0.362763 0.794722i 0.0202160 0.0442881i
\(323\) −11.8323 −0.658365
\(324\) −8.34195 15.9503i −0.463442 0.886127i
\(325\) 9.59272 0.532109
\(326\) 4.80379 10.5239i 0.266057 0.582865i
\(327\) 3.69380 3.28757i 0.204267 0.181803i
\(328\) −0.430764 + 0.126739i −0.0237849 + 0.00699800i
\(329\) 1.70498i 0.0939988i
\(330\) 2.02400 + 6.56492i 0.111418 + 0.361387i
\(331\) 9.08046i 0.499107i −0.968361 0.249553i \(-0.919716\pi\)
0.968361 0.249553i \(-0.0802838\pi\)
\(332\) 0.331433 + 0.382212i 0.0181897 + 0.0209766i
\(333\) 3.45954 29.6270i 0.189582 1.62355i
\(334\) 16.1291 + 7.36238i 0.882547 + 0.402851i
\(335\) 1.10955 0.0606212
\(336\) 1.51627 1.00473i 0.0827191 0.0548124i
\(337\) −20.0677 −1.09316 −0.546579 0.837408i \(-0.684070\pi\)
−0.546579 + 0.837408i \(0.684070\pi\)
\(338\) 8.39041 + 3.82993i 0.456378 + 0.208321i
\(339\) −5.63618 6.33262i −0.306116 0.343941i
\(340\) 2.36449 + 2.72676i 0.128233 + 0.147879i
\(341\) 10.4462i 0.565692i
\(342\) 26.4027 + 15.9871i 1.42769 + 0.864481i
\(343\) 3.65748i 0.197485i
\(344\) 1.15846 0.340842i 0.0624600 0.0183770i
\(345\) −3.00625 3.37771i −0.161851 0.181850i
\(346\) −2.35104 + 5.15054i −0.126393 + 0.276895i
\(347\) −12.6600 −0.679625 −0.339812 0.940493i \(-0.610364\pi\)
−0.339812 + 0.940493i \(0.610364\pi\)
\(348\) 1.05807 8.14649i 0.0567186 0.436698i
\(349\) 11.0888 0.593571 0.296786 0.954944i \(-0.404085\pi\)
0.296786 + 0.954944i \(0.404085\pi\)
\(350\) −0.581080 + 1.27300i −0.0310600 + 0.0680447i
\(351\) −7.58761 10.8324i −0.404996 0.578189i
\(352\) −7.71955 + 12.0359i −0.411454 + 0.641517i
\(353\) 4.79771i 0.255356i 0.991816 + 0.127678i \(0.0407525\pi\)
−0.991816 + 0.127678i \(0.959248\pi\)
\(354\) −3.18533 + 0.982056i −0.169298 + 0.0521957i
\(355\) 4.70320i 0.249620i
\(356\) 10.7008 9.27916i 0.567144 0.491794i
\(357\) −0.552460 + 0.491703i −0.0292393 + 0.0260237i
\(358\) −27.9537 12.7599i −1.47740 0.674381i
\(359\) −27.5490 −1.45398 −0.726989 0.686649i \(-0.759081\pi\)
−0.726989 + 0.686649i \(0.759081\pi\)
\(360\) −1.59192 9.27929i −0.0839013 0.489062i
\(361\) −33.9270 −1.78563
\(362\) 18.7686 + 8.56721i 0.986456 + 0.450282i
\(363\) −5.96553 + 5.30946i −0.313109 + 0.278675i
\(364\) 1.00971 0.875561i 0.0529231 0.0458919i
\(365\) 16.7462i 0.876534i
\(366\) 13.4609 4.15009i 0.703614 0.216928i
\(367\) 32.3136i 1.68676i 0.537320 + 0.843379i \(0.319437\pi\)
−0.537320 + 0.843379i \(0.680563\pi\)
\(368\) 1.33262 9.31672i 0.0694677 0.485668i
\(369\) −0.473045 0.0552375i −0.0246257 0.00287555i
\(370\) 6.47856 14.1929i 0.336804 0.737854i
\(371\) −0.554780 −0.0288028
\(372\) 1.84389 14.1968i 0.0956015 0.736072i
\(373\) −5.16397 −0.267380 −0.133690 0.991023i \(-0.542683\pi\)
−0.133690 + 0.991023i \(0.542683\pi\)
\(374\) 2.41422 5.28895i 0.124836 0.273485i
\(375\) 11.2039 + 12.5883i 0.578566 + 0.650056i
\(376\) −5.18455 17.6214i −0.267373 0.908753i
\(377\) 6.03587i 0.310863i
\(378\) 1.89713 0.350741i 0.0975776 0.0180402i
\(379\) 14.0877i 0.723636i −0.932249 0.361818i \(-0.882156\pi\)
0.932249 0.361818i \(-0.117844\pi\)
\(380\) 10.5766 + 12.1971i 0.542570 + 0.625698i
\(381\) −8.25271 9.27245i −0.422799 0.475042i
\(382\) −28.1002 12.8268i −1.43773 0.656274i
\(383\) −7.22905 −0.369387 −0.184694 0.982796i \(-0.559129\pi\)
−0.184694 + 0.982796i \(0.559129\pi\)
\(384\) 12.6157 14.9948i 0.643794 0.765199i
\(385\) −0.736323 −0.0375265
\(386\) −4.10519 1.87387i −0.208949 0.0953776i
\(387\) 1.27217 + 0.148551i 0.0646680 + 0.00755128i
\(388\) −12.5862 14.5145i −0.638966 0.736864i
\(389\) 15.3857i 0.780085i 0.920797 + 0.390042i \(0.127540\pi\)
−0.920797 + 0.390042i \(0.872460\pi\)
\(390\) −2.03805 6.61048i −0.103201 0.334735i
\(391\) 3.82675i 0.193527i
\(392\) −5.53336 18.8069i −0.279477 0.949893i
\(393\) 24.3727 21.6923i 1.22944 1.09423i
\(394\) −2.88332 + 6.31662i −0.145259 + 0.318227i
\(395\) −13.1043 −0.659349
\(396\) −12.5332 + 8.53989i −0.629819 + 0.429145i
\(397\) 30.3383 1.52263 0.761317 0.648380i \(-0.224553\pi\)
0.761317 + 0.648380i \(0.224553\pi\)
\(398\) 13.8173 30.2703i 0.692599 1.51731i
\(399\) −2.47121 + 2.19944i −0.123715 + 0.110110i
\(400\) −2.13462 + 14.9237i −0.106731 + 0.746185i
\(401\) 32.8331i 1.63961i 0.572646 + 0.819803i \(0.305917\pi\)
−0.572646 + 0.819803i \(0.694083\pi\)
\(402\) 0.721672 + 2.34077i 0.0359937 + 0.116747i
\(403\) 10.5187i 0.523973i
\(404\) 0.534847 0.463789i 0.0266096 0.0230743i
\(405\) 2.30075 9.71730i 0.114325 0.482857i
\(406\) 0.800989 + 0.365623i 0.0397524 + 0.0181456i
\(407\) −25.1322 −1.24576
\(408\) −4.21461 + 6.76179i −0.208654 + 0.334759i
\(409\) −12.4009 −0.613184 −0.306592 0.951841i \(-0.599189\pi\)
−0.306592 + 0.951841i \(0.599189\pi\)
\(410\) −0.226614 0.103441i −0.0111916 0.00510859i
\(411\) 22.8692 + 25.6950i 1.12805 + 1.26744i
\(412\) −0.759995 + 0.659024i −0.0374423 + 0.0324678i
\(413\) 0.357268i 0.0175800i
\(414\) 5.17048 8.53906i 0.254115 0.419672i
\(415\) 0.280660i 0.0137771i
\(416\) 7.77313 12.1195i 0.381109 0.594205i
\(417\) 18.3978 + 20.6712i 0.900946 + 1.01227i
\(418\) 10.7991 23.6581i 0.528200 1.15715i
\(419\) 21.6380 1.05709 0.528543 0.848907i \(-0.322739\pi\)
0.528543 + 0.848907i \(0.322739\pi\)
\(420\) 1.00070 + 0.129971i 0.0488290 + 0.00634195i
\(421\) −22.6818 −1.10544 −0.552721 0.833366i \(-0.686411\pi\)
−0.552721 + 0.833366i \(0.686411\pi\)
\(422\) 2.22346 4.87105i 0.108237 0.237119i
\(423\) 2.25961 19.3510i 0.109866 0.940877i
\(424\) −5.73377 + 1.68699i −0.278457 + 0.0819274i
\(425\) 6.12976i 0.297337i
\(426\) −9.92211 + 3.05904i −0.480728 + 0.148211i
\(427\) 1.50978i 0.0730635i
\(428\) −15.6527 18.0509i −0.756604 0.872525i
\(429\) −8.32388 + 7.40846i −0.401881 + 0.357684i
\(430\) 0.609437 + 0.278186i 0.0293896 + 0.0134153i
\(431\) 22.4935 1.08347 0.541736 0.840549i \(-0.317767\pi\)
0.541736 + 0.840549i \(0.317767\pi\)
\(432\) 18.5407 9.39381i 0.892038 0.451960i
\(433\) −19.6531 −0.944468 −0.472234 0.881473i \(-0.656552\pi\)
−0.472234 + 0.881473i \(0.656552\pi\)
\(434\) 1.39588 + 0.637170i 0.0670043 + 0.0305851i
\(435\) 3.40435 3.02995i 0.163226 0.145275i
\(436\) 3.74076 + 4.31390i 0.179150 + 0.206598i
\(437\) 17.1175i 0.818840i
\(438\) 35.3286 10.8920i 1.68806 0.520440i
\(439\) 21.9774i 1.04892i 0.851434 + 0.524462i \(0.175733\pi\)
−0.851434 + 0.524462i \(0.824267\pi\)
\(440\) −7.61006 + 2.23903i −0.362795 + 0.106742i
\(441\) 2.41164 20.6529i 0.114840 0.983471i
\(442\) −2.43098 + 5.32566i −0.115630 + 0.253316i
\(443\) 1.97577 0.0938716 0.0469358 0.998898i \(-0.485054\pi\)
0.0469358 + 0.998898i \(0.485054\pi\)
\(444\) 34.1559 + 4.43619i 1.62097 + 0.210532i
\(445\) 7.85768 0.372490
\(446\) −1.97848 + 4.33435i −0.0936836 + 0.205237i
\(447\) 13.8344 + 15.5438i 0.654344 + 0.735197i
\(448\) 1.13745 + 1.76567i 0.0537396 + 0.0834200i
\(449\) 6.86064i 0.323774i −0.986809 0.161887i \(-0.948242\pi\)
0.986809 0.161887i \(-0.0517580\pi\)
\(450\) −8.28217 + 13.6780i −0.390425 + 0.644788i
\(451\) 0.401278i 0.0188955i
\(452\) 7.39571 6.41313i 0.347865 0.301648i
\(453\) −7.08259 7.95774i −0.332769 0.373887i
\(454\) 25.1575 + 11.4835i 1.18070 + 0.538948i
\(455\) 0.741434 0.0347590
\(456\) −18.8524 + 30.2462i −0.882846 + 1.41641i
\(457\) −7.92873 −0.370890 −0.185445 0.982655i \(-0.559373\pi\)
−0.185445 + 0.982655i \(0.559373\pi\)
\(458\) −7.23919 3.30443i −0.338265 0.154406i
\(459\) −6.92189 + 4.84849i −0.323086 + 0.226308i
\(460\) 3.94475 3.42066i 0.183925 0.159489i
\(461\) 27.6962i 1.28994i −0.764208 0.644970i \(-0.776870\pi\)
0.764208 0.644970i \(-0.223130\pi\)
\(462\) −0.478918 1.55339i −0.0222813 0.0722701i
\(463\) 39.6611i 1.84321i −0.388131 0.921604i \(-0.626879\pi\)
0.388131 0.921604i \(-0.373121\pi\)
\(464\) 9.39019 + 1.34313i 0.435929 + 0.0623532i
\(465\) 5.93274 5.28028i 0.275124 0.244867i
\(466\) 16.1259 35.3278i 0.747017 1.63653i
\(467\) −39.8079 −1.84209 −0.921045 0.389456i \(-0.872663\pi\)
−0.921045 + 0.389456i \(0.872663\pi\)
\(468\) 12.6202 8.59916i 0.583370 0.397496i
\(469\) −0.262541 −0.0121230
\(470\) 4.23150 9.27015i 0.195184 0.427600i
\(471\) 0.403142 0.358806i 0.0185758 0.0165329i
\(472\) −1.08639 3.69244i −0.0500051 0.169958i
\(473\) 1.07917i 0.0496201i
\(474\) −8.52328 27.6455i −0.391487 1.26980i
\(475\) 27.4191i 1.25807i
\(476\) −0.559484 0.645205i −0.0256439 0.0295729i
\(477\) −6.29657 0.735250i −0.288300 0.0336648i
\(478\) −23.2439 10.6100i −1.06315 0.485291i
\(479\) 6.76561 0.309129 0.154564 0.987983i \(-0.450603\pi\)
0.154564 + 0.987983i \(0.450603\pi\)
\(480\) 10.7376 1.69966i 0.490104 0.0775787i
\(481\) 25.3067 1.15388
\(482\) −25.8158 11.7840i −1.17588 0.536746i
\(483\) 0.711336 + 0.799232i 0.0323669 + 0.0363663i
\(484\) −6.04138 6.96699i −0.274608 0.316681i
\(485\) 10.6581i 0.483959i
\(486\) 21.9966 1.46653i 0.997785 0.0665231i
\(487\) 33.2472i 1.50658i 0.657690 + 0.753288i \(0.271534\pi\)
−0.657690 + 0.753288i \(0.728466\pi\)
\(488\) 4.59098 + 15.6039i 0.207824 + 0.706357i
\(489\) 9.41968 + 10.5836i 0.425973 + 0.478608i
\(490\) 4.51619 9.89383i 0.204020 0.446958i
\(491\) 9.36873 0.422805 0.211403 0.977399i \(-0.432197\pi\)
0.211403 + 0.977399i \(0.432197\pi\)
\(492\) 0.0708312 0.545356i 0.00319332 0.0245865i
\(493\) −3.85693 −0.173707
\(494\) −10.8740 + 23.8223i −0.489246 + 1.07181i
\(495\) −8.35702 0.975850i −0.375620 0.0438612i
\(496\) 16.3642 + 2.34066i 0.734776 + 0.105099i
\(497\) 1.11287i 0.0499189i
\(498\) −0.592096 + 0.182547i −0.0265324 + 0.00818011i
\(499\) 14.4248i 0.645742i 0.946443 + 0.322871i \(0.104648\pi\)
−0.946443 + 0.322871i \(0.895352\pi\)
\(500\) −14.7015 + 12.7483i −0.657473 + 0.570123i
\(501\) −16.2207 + 14.4368i −0.724685 + 0.644988i
\(502\) −0.527495 0.240783i −0.0235433 0.0107467i
\(503\) −31.2772 −1.39458 −0.697292 0.716787i \(-0.745612\pi\)
−0.697292 + 0.716787i \(0.745612\pi\)
\(504\) 0.376678 + 2.19566i 0.0167786 + 0.0978025i
\(505\) 0.392741 0.0174767
\(506\) −7.65142 3.49260i −0.340147 0.155265i
\(507\) −8.43802 + 7.51005i −0.374746 + 0.333533i
\(508\) 10.8291 9.39034i 0.480462 0.416629i
\(509\) 32.5296i 1.44185i 0.693014 + 0.720924i \(0.256282\pi\)
−0.693014 + 0.720924i \(0.743718\pi\)
\(510\) −4.22410 + 1.30232i −0.187046 + 0.0576675i
\(511\) 3.96247i 0.175289i
\(512\) 17.1249 + 14.7898i 0.756821 + 0.653622i
\(513\) −30.9624 + 21.6878i −1.36702 + 0.957540i
\(514\) 16.5987 36.3635i 0.732136 1.60393i
\(515\) −0.558068 −0.0245914
\(516\) −0.190488 + 1.46664i −0.00838575 + 0.0645651i
\(517\) −16.4152 −0.721940
\(518\) −1.53295 + 3.35831i −0.0673541 + 0.147556i
\(519\) −4.61012 5.17977i −0.202362 0.227367i
\(520\) 7.66288 2.25457i 0.336040 0.0988694i
\(521\) 11.5579i 0.506360i −0.967419 0.253180i \(-0.918524\pi\)
0.967419 0.253180i \(-0.0814764\pi\)
\(522\) 8.60640 + 5.21125i 0.376692 + 0.228090i
\(523\) 4.09487i 0.179056i −0.995984 0.0895281i \(-0.971464\pi\)
0.995984 0.0895281i \(-0.0285359\pi\)
\(524\) 24.6826 + 28.4643i 1.07826 + 1.24347i
\(525\) −1.13943 1.28022i −0.0497288 0.0558736i
\(526\) −14.1464 6.45732i −0.616812 0.281553i
\(527\) −6.72144 −0.292791
\(528\) −9.67330 14.5983i −0.420976 0.635309i
\(529\) −17.4639 −0.759301
\(530\) −3.01639 1.37688i −0.131024 0.0598077i
\(531\) 0.473487 4.05487i 0.0205476 0.175966i
\(532\) −2.50264 2.88607i −0.108503 0.125127i
\(533\) 0.404064i 0.0175019i
\(534\) 5.11078 + 16.5770i 0.221165 + 0.717356i
\(535\) 13.2549i 0.573059i
\(536\) −2.71342 + 0.798342i −0.117202 + 0.0344831i
\(537\) 28.1124 25.0207i 1.21314 1.07972i
\(538\) 0.416389 0.912204i 0.0179518 0.0393279i
\(539\) −17.5196 −0.754623
\(540\) 11.1853 + 2.80135i 0.481340 + 0.120551i
\(541\) 8.60038 0.369759 0.184880 0.982761i \(-0.440810\pi\)
0.184880 + 0.982761i \(0.440810\pi\)
\(542\) 4.99651 10.9461i 0.214618 0.470175i
\(543\) −18.8751 + 16.7993i −0.810008 + 0.720927i
\(544\) −7.74435 4.96704i −0.332036 0.212960i
\(545\) 3.16771i 0.135690i
\(546\) 0.482242 + 1.56417i 0.0206381 + 0.0669402i
\(547\) 19.3459i 0.827169i 0.910466 + 0.413585i \(0.135723\pi\)
−0.910466 + 0.413585i \(0.864277\pi\)
\(548\) −30.0085 + 26.0217i −1.28190 + 1.11159i
\(549\) −2.00092 + 17.1355i −0.0853970 + 0.731326i
\(550\) 12.2562 + 5.59451i 0.522605 + 0.238551i
\(551\) −17.2525 −0.734980
\(552\) 9.78213 + 6.09719i 0.416355 + 0.259514i
\(553\) 3.10073 0.131857
\(554\) −38.2716 17.4696i −1.62600 0.742213i
\(555\) 12.7037 + 14.2734i 0.539242 + 0.605874i
\(556\) −24.1414 + 20.9340i −1.02382 + 0.887799i
\(557\) 22.1267i 0.937536i −0.883321 0.468768i \(-0.844698\pi\)
0.883321 0.468768i \(-0.155302\pi\)
\(558\) 14.9983 + 9.08162i 0.634929 + 0.384456i
\(559\) 1.08666i 0.0459607i
\(560\) −0.164987 + 1.15347i −0.00697198 + 0.0487431i
\(561\) 4.73401 + 5.31897i 0.199870 + 0.224567i
\(562\) −5.23900 + 11.4773i −0.220994 + 0.484142i
\(563\) 32.7218 1.37906 0.689530 0.724257i \(-0.257817\pi\)
0.689530 + 0.724257i \(0.257817\pi\)
\(564\) 22.3090 + 2.89751i 0.939380 + 0.122007i
\(565\) 5.43071 0.228472
\(566\) 2.99526 6.56186i 0.125900 0.275815i
\(567\) −0.544402 + 2.29930i −0.0228627 + 0.0965616i
\(568\) −3.38403 11.5017i −0.141991 0.482602i
\(569\) 17.1204i 0.717725i 0.933390 + 0.358862i \(0.116835\pi\)
−0.933390 + 0.358862i \(0.883165\pi\)
\(570\) −18.8949 + 5.82540i −0.791419 + 0.243999i
\(571\) 27.6118i 1.15552i −0.816207 0.577760i \(-0.803927\pi\)
0.816207 0.577760i \(-0.196073\pi\)
\(572\) −8.42971 9.72126i −0.352464 0.406466i
\(573\) 28.2597 25.1518i 1.18057 1.05073i
\(574\) 0.0536212 + 0.0244762i 0.00223810 + 0.00102162i
\(575\) −8.86779 −0.369812
\(576\) 10.5697 + 21.5472i 0.440403 + 0.897800i
\(577\) −16.6041 −0.691237 −0.345618 0.938375i \(-0.612331\pi\)
−0.345618 + 0.938375i \(0.612331\pi\)
\(578\) −18.4678 8.42988i −0.768157 0.350637i
\(579\) 4.12848 3.67445i 0.171574 0.152705i
\(580\) 3.44763 + 3.97585i 0.143155 + 0.165088i
\(581\) 0.0664097i 0.00275514i
\(582\) 22.4849 6.93222i 0.932028 0.287350i
\(583\) 5.34131i 0.221214i
\(584\) 12.0492 + 40.9529i 0.498598 + 1.69464i
\(585\) 8.41502 + 0.982622i 0.347918 + 0.0406264i
\(586\) −13.2451 + 29.0167i −0.547150 + 1.19867i
\(587\) 29.1091 1.20146 0.600731 0.799451i \(-0.294876\pi\)
0.600731 + 0.799451i \(0.294876\pi\)
\(588\) 23.8100 + 3.09245i 0.981906 + 0.127531i
\(589\) −30.0658 −1.23884
\(590\) 0.886682 1.94250i 0.0365041 0.0799714i
\(591\) −5.65385 6.35247i −0.232568 0.261306i
\(592\) −5.63135 + 39.3704i −0.231447 + 1.61811i
\(593\) 22.6210i 0.928931i 0.885591 + 0.464466i \(0.153754\pi\)
−0.885591 + 0.464466i \(0.846246\pi\)
\(594\) −3.37686 18.2651i −0.138554 0.749427i
\(595\) 0.473777i 0.0194230i
\(596\) −18.1532 + 15.7415i −0.743586 + 0.644795i
\(597\) 27.0942 + 30.4420i 1.10889 + 1.24591i
\(598\) 7.70452 + 3.51684i 0.315061 + 0.143814i
\(599\) −11.2359 −0.459087 −0.229544 0.973298i \(-0.573723\pi\)
−0.229544 + 0.973298i \(0.573723\pi\)
\(600\) −15.6692 9.76658i −0.639692 0.398719i
\(601\) 4.66316 0.190214 0.0951071 0.995467i \(-0.469681\pi\)
0.0951071 + 0.995467i \(0.469681\pi\)
\(602\) −0.144204 0.0658243i −0.00587734 0.00268280i
\(603\) −2.97975 0.347946i −0.121345 0.0141695i
\(604\) 9.29366 8.05892i 0.378154 0.327913i
\(605\) 5.11590i 0.207991i
\(606\) 0.255446 + 0.828546i 0.0103768 + 0.0336574i
\(607\) 12.7184i 0.516223i −0.966115 0.258111i \(-0.916900\pi\)
0.966115 0.258111i \(-0.0831002\pi\)
\(608\) −34.6413 22.2181i −1.40489 0.901063i
\(609\) −0.805534 + 0.716945i −0.0326419 + 0.0290521i
\(610\) −3.74704 + 8.20883i −0.151713 + 0.332366i
\(611\) 16.5291 0.668697
\(612\) −5.49487 8.06434i −0.222117 0.325982i
\(613\) −4.53277 −0.183077 −0.0915385 0.995802i \(-0.529178\pi\)
−0.0915385 + 0.995802i \(0.529178\pi\)
\(614\) −12.9293 + 28.3249i −0.521786 + 1.14310i
\(615\) 0.227900 0.202836i 0.00918980 0.00817914i
\(616\) 1.80069 0.529798i 0.0725518 0.0213462i
\(617\) 2.32331i 0.0935328i −0.998906 0.0467664i \(-0.985108\pi\)
0.998906 0.0467664i \(-0.0148916\pi\)
\(618\) −0.362978 1.17733i −0.0146011 0.0473592i
\(619\) 8.70358i 0.349826i −0.984584 0.174913i \(-0.944036\pi\)
0.984584 0.174913i \(-0.0559645\pi\)
\(620\) 6.00817 + 6.92870i 0.241294 + 0.278263i
\(621\) 7.01420 + 10.0137i 0.281470 + 0.401838i
\(622\) −22.6423 10.3354i −0.907875 0.414413i
\(623\) −1.85928 −0.0744905
\(624\) 9.74044 + 14.6996i 0.389930 + 0.588455i
\(625\) 8.04907 0.321963
\(626\) −9.50477 4.33859i −0.379887 0.173405i
\(627\) 21.1757 + 23.7923i 0.845678 + 0.950174i
\(628\) 0.408267 + 0.470819i 0.0162916 + 0.0187877i
\(629\) 16.1710i 0.644779i
\(630\) −0.640139 + 1.05719i −0.0255038 + 0.0421195i
\(631\) 18.9935i 0.756119i −0.925781 0.378059i \(-0.876592\pi\)
0.925781 0.378059i \(-0.123408\pi\)
\(632\) 32.0467 9.42878i 1.27475 0.375057i
\(633\) 4.35996 + 4.89869i 0.173293 + 0.194706i
\(634\) −16.8839 + 36.9885i −0.670547 + 1.46900i
\(635\) 7.95184 0.315559
\(636\) 0.942814 7.25908i 0.0373850 0.287841i
\(637\) 17.6412 0.698970
\(638\) 3.52014 7.71175i 0.139364 0.305311i
\(639\) 1.47488 12.6307i 0.0583455 0.499661i
\(640\) 1.80233 + 12.4231i 0.0712432 + 0.491065i
\(641\) 6.25712i 0.247141i −0.992336 0.123571i \(-0.960565\pi\)
0.992336 0.123571i \(-0.0394346\pi\)
\(642\) 27.9632 8.62123i 1.10362 0.340253i
\(643\) 34.6109i 1.36492i −0.730923 0.682460i \(-0.760910\pi\)
0.730923 0.682460i \(-0.239090\pi\)
\(644\) −0.933404 + 0.809394i −0.0367813 + 0.0318946i
\(645\) −0.612895 + 0.545491i −0.0241327 + 0.0214787i
\(646\) 15.2225 + 6.94851i 0.598919 + 0.273386i
\(647\) −5.84844 −0.229926 −0.114963 0.993370i \(-0.536675\pi\)
−0.114963 + 0.993370i \(0.536675\pi\)
\(648\) 1.36526 + 25.4192i 0.0536324 + 0.998561i
\(649\) −3.43970 −0.135020
\(650\) −12.3412 5.63334i −0.484063 0.220958i
\(651\) −1.40380 + 1.24942i −0.0550193 + 0.0489685i
\(652\) −12.3604 + 10.7182i −0.484069 + 0.419757i
\(653\) 37.8822i 1.48244i 0.671260 + 0.741222i \(0.265753\pi\)
−0.671260 + 0.741222i \(0.734247\pi\)
\(654\) −6.68278 + 2.06034i −0.261317 + 0.0805657i
\(655\) 20.9015i 0.816688i
\(656\) 0.628614 + 0.0899140i 0.0245433 + 0.00351055i
\(657\) −5.25146 + 44.9726i −0.204879 + 1.75455i
\(658\) −1.00125 + 2.19350i −0.0390329 + 0.0855114i
\(659\) 22.5539 0.878574 0.439287 0.898347i \(-0.355231\pi\)
0.439287 + 0.898347i \(0.355231\pi\)
\(660\) 1.25134 9.63450i 0.0487082 0.375022i
\(661\) −3.76797 −0.146557 −0.0732786 0.997312i \(-0.523346\pi\)
−0.0732786 + 0.997312i \(0.523346\pi\)
\(662\) −5.33251 + 11.6822i −0.207254 + 0.454041i
\(663\) −4.76687 5.35588i −0.185130 0.208005i
\(664\) −0.201940 0.686358i −0.00783680 0.0266359i
\(665\) 2.11926i 0.0821812i
\(666\) −21.8493 + 36.0841i −0.846642 + 1.39823i
\(667\) 5.57973i 0.216048i
\(668\) −16.4269 18.9437i −0.635576 0.732954i
\(669\) −3.87956 4.35894i −0.149993 0.168526i
\(670\) −1.42746 0.651585i −0.0551476 0.0251729i
\(671\) 14.5359 0.561151
\(672\) −2.54073 + 0.402173i −0.0980110 + 0.0155142i
\(673\) −36.4192 −1.40386 −0.701929 0.712247i \(-0.747678\pi\)
−0.701929 + 0.712247i \(0.747678\pi\)
\(674\) 25.8175 + 11.7848i 0.994454 + 0.453933i
\(675\) −11.2355 16.0402i −0.432454 0.617387i
\(676\) −8.54531 9.85456i −0.328666 0.379022i
\(677\) 21.9603i 0.844004i −0.906595 0.422002i \(-0.861328\pi\)
0.906595 0.422002i \(-0.138672\pi\)
\(678\) 3.53223 + 11.4569i 0.135654 + 0.440000i
\(679\) 2.52191i 0.0967821i
\(680\) −1.44067 4.89659i −0.0552473 0.187776i
\(681\) −25.3003 + 22.5179i −0.969508 + 0.862886i
\(682\) 6.13453 13.4392i 0.234903 0.514615i
\(683\) −13.2126 −0.505566 −0.252783 0.967523i \(-0.581346\pi\)
−0.252783 + 0.967523i \(0.581346\pi\)
\(684\) −24.5792 36.0727i −0.939807 1.37927i
\(685\) −22.0354 −0.841930
\(686\) −2.14786 + 4.70542i −0.0820057 + 0.179654i
\(687\) 7.28027 6.47962i 0.277760 0.247213i
\(688\) −1.69054 0.241808i −0.0644514 0.00921883i
\(689\) 5.37838i 0.204900i
\(690\) 1.88403 + 6.11092i 0.0717239 + 0.232639i
\(691\) 37.0974i 1.41125i 0.708585 + 0.705626i \(0.249334\pi\)
−0.708585 + 0.705626i \(0.750666\pi\)
\(692\) 6.04932 5.24563i 0.229961 0.199409i
\(693\) 1.97743 + 0.230905i 0.0751165 + 0.00877135i
\(694\) 16.2874 + 7.43461i 0.618260 + 0.282214i
\(695\) −17.7271 −0.672428
\(696\) −6.14527 + 9.85927i −0.232936 + 0.373715i
\(697\) −0.258197 −0.00977991
\(698\) −14.2660 6.51193i −0.539976 0.246480i
\(699\) 31.6210 + 35.5283i 1.19602 + 1.34380i
\(700\) 1.49514 1.29650i 0.0565111 0.0490032i
\(701\) 17.0565i 0.644214i −0.946703 0.322107i \(-0.895609\pi\)
0.946703 0.322107i \(-0.104391\pi\)
\(702\) 3.40029 + 18.3919i 0.128336 + 0.694157i
\(703\) 72.3346i 2.72815i
\(704\) 16.9995 10.9512i 0.640692 0.412737i
\(705\) 8.29748 + 9.32275i 0.312501 + 0.351115i
\(706\) 2.81746 6.17235i 0.106037 0.232300i
\(707\) −0.0929301 −0.00349499
\(708\) 4.67471 + 0.607154i 0.175686 + 0.0228182i
\(709\) 37.6031 1.41222 0.706108 0.708104i \(-0.250449\pi\)
0.706108 + 0.708104i \(0.250449\pi\)
\(710\) 2.76196 6.05076i 0.103654 0.227081i
\(711\) 35.1923 + 4.10940i 1.31981 + 0.154115i
\(712\) −19.2161 + 5.65374i −0.720152 + 0.211883i
\(713\) 9.72377i 0.364158i
\(714\) 0.999505 0.308153i 0.0374055 0.0115323i
\(715\) 7.13837i 0.266960i
\(716\) 28.4698 + 32.8317i 1.06397 + 1.22698i
\(717\) 23.3758 20.8050i 0.872985 0.776978i
\(718\) 35.4423 + 16.1782i 1.32270 + 0.603764i
\(719\) −28.7377 −1.07174 −0.535868 0.844301i \(-0.680016\pi\)
−0.535868 + 0.844301i \(0.680016\pi\)
\(720\) −3.40124 + 12.8729i −0.126757 + 0.479743i
\(721\) 0.132050 0.00491779
\(722\) 43.6478 + 19.9237i 1.62440 + 0.741483i
\(723\) 25.9623 23.1071i 0.965548 0.859361i
\(724\) −19.1151 22.0438i −0.710407 0.819251i
\(725\) 8.93772i 0.331938i
\(726\) 10.7928 3.32747i 0.400557 0.123494i
\(727\) 46.5471i 1.72634i 0.504918 + 0.863168i \(0.331523\pi\)
−0.504918 + 0.863168i \(0.668477\pi\)
\(728\) −1.81319 + 0.533475i −0.0672011 + 0.0197719i
\(729\) −9.22604 + 25.3748i −0.341705 + 0.939807i
\(730\) −9.83421 + 21.5443i −0.363980 + 0.797390i
\(731\) 0.694374 0.0256824
\(732\) −19.7549 2.56578i −0.730163 0.0948340i
\(733\) 3.78994 0.139985 0.0699923 0.997548i \(-0.477703\pi\)
0.0699923 + 0.997548i \(0.477703\pi\)
\(734\) 18.9762 41.5721i 0.700425 1.53446i
\(735\) 8.85572 + 9.94997i 0.326648 + 0.367010i
\(736\) −7.18570 + 11.2036i −0.264869 + 0.412969i
\(737\) 2.52769i 0.0931087i
\(738\) 0.576144 + 0.348860i 0.0212081 + 0.0128417i
\(739\) 18.1767i 0.668641i −0.942460 0.334320i \(-0.891493\pi\)
0.942460 0.334320i \(-0.108507\pi\)
\(740\) −16.6696 + 14.4549i −0.612787 + 0.531373i
\(741\) −21.3227 23.9575i −0.783310 0.880099i
\(742\) 0.713736 + 0.325795i 0.0262021 + 0.0119603i
\(743\) 43.5376 1.59724 0.798619 0.601836i \(-0.205564\pi\)
0.798619 + 0.601836i \(0.205564\pi\)
\(744\) −10.7093 + 17.1817i −0.392623 + 0.629912i
\(745\) −13.3300 −0.488374
\(746\) 6.64355 + 3.03255i 0.243238 + 0.111029i
\(747\) 0.0880127 0.753727i 0.00322022 0.0275774i
\(748\) −6.21189 + 5.38660i −0.227129 + 0.196953i
\(749\) 3.13636i 0.114600i
\(750\) −7.02154 22.7746i −0.256390 0.831610i
\(751\) 36.0638i 1.31599i 0.753024 + 0.657993i \(0.228595\pi\)
−0.753024 + 0.657993i \(0.771405\pi\)
\(752\) −3.67814 + 25.7149i −0.134128 + 0.937726i
\(753\) 0.530488 0.472147i 0.0193321 0.0172060i
\(754\) −3.54457 + 7.76527i −0.129086 + 0.282795i
\(755\) 6.82438 0.248365
\(756\) −2.64667 0.662855i −0.0962583 0.0241078i
\(757\) 27.7730 1.00943 0.504713 0.863287i \(-0.331598\pi\)
0.504713 + 0.863287i \(0.331598\pi\)
\(758\) −8.27302 + 18.1241i −0.300490 + 0.658297i
\(759\) 7.69483 6.84859i 0.279305 0.248588i
\(760\) −6.44429 21.9030i −0.233759 0.794504i
\(761\) 19.2103i 0.696373i −0.937425 0.348186i \(-0.886798\pi\)
0.937425 0.348186i \(-0.113202\pi\)
\(762\) 5.17202 + 16.7756i 0.187362 + 0.607716i
\(763\) 0.749543i