Properties

Label 280.2.h.b.251.15
Level $280$
Weight $2$
Character 280.251
Analytic conductor $2.236$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 280 = 2^{3} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 280.h (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.23581125660\)
Analytic rank: \(0\)
Dimension: \(16\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
Defining polynomial: \(x^{16} - x^{15} - 2 x^{12} + 6 x^{11} - 12 x^{9} + 8 x^{8} - 24 x^{7} + 48 x^{5} - 32 x^{4} - 128 x + 256\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{4} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 251.15
Root \(1.41214 + 0.0765298i\) of defining polynomial
Character \(\chi\) \(=\) 280.251
Dual form 280.2.h.b.251.16

$q$-expansion

\(f(q)\) \(=\) \(q+(1.41214 - 0.0765298i) q^{2} -2.21915i q^{3} +(1.98829 - 0.216142i) q^{4} +1.00000 q^{5} +(-0.169831 - 3.13376i) q^{6} +(1.20923 + 2.35325i) q^{7} +(2.79120 - 0.457386i) q^{8} -1.92464 q^{9} +O(q^{10})\) \(q+(1.41214 - 0.0765298i) q^{2} -2.21915i q^{3} +(1.98829 - 0.216142i) q^{4} +1.00000 q^{5} +(-0.169831 - 3.13376i) q^{6} +(1.20923 + 2.35325i) q^{7} +(2.79120 - 0.457386i) q^{8} -1.92464 q^{9} +(1.41214 - 0.0765298i) q^{10} -3.88394 q^{11} +(-0.479652 - 4.41231i) q^{12} -5.67503 q^{13} +(1.88769 + 3.23057i) q^{14} -2.21915i q^{15} +(3.90657 - 0.859503i) q^{16} +5.63892i q^{17} +(-2.71786 + 0.147292i) q^{18} -1.31134i q^{19} +(1.98829 - 0.216142i) q^{20} +(5.22221 - 2.68346i) q^{21} +(-5.48468 + 0.297237i) q^{22} -7.37559i q^{23} +(-1.01501 - 6.19410i) q^{24} +1.00000 q^{25} +(-8.01395 + 0.434309i) q^{26} -2.38639i q^{27} +(2.91293 + 4.41756i) q^{28} +9.07201i q^{29} +(-0.169831 - 3.13376i) q^{30} -2.23073 q^{31} +(5.45085 - 1.51271i) q^{32} +8.61906i q^{33} +(0.431546 + 7.96296i) q^{34} +(1.20923 + 2.35325i) q^{35} +(-3.82673 + 0.415995i) q^{36} -6.98438i q^{37} +(-0.100356 - 1.85179i) q^{38} +12.5938i q^{39} +(2.79120 - 0.457386i) q^{40} +7.47757i q^{41} +(7.16914 - 4.18908i) q^{42} -1.46735 q^{43} +(-7.72239 + 0.839482i) q^{44} -1.92464 q^{45} +(-0.564452 - 10.4154i) q^{46} +0.567314 q^{47} +(-1.90737 - 8.66927i) q^{48} +(-4.07554 + 5.69122i) q^{49} +(1.41214 - 0.0765298i) q^{50} +12.5136 q^{51} +(-11.2836 + 1.22661i) q^{52} -0.100950i q^{53} +(-0.182630 - 3.36992i) q^{54} -3.88394 q^{55} +(4.45154 + 6.01530i) q^{56} -2.91006 q^{57} +(0.694279 + 12.8110i) q^{58} +2.93497i q^{59} +(-0.479652 - 4.41231i) q^{60} +13.8324 q^{61} +(-3.15011 + 0.170717i) q^{62} +(-2.32733 - 4.52915i) q^{63} +(7.58160 - 2.55331i) q^{64} -5.67503 q^{65} +(0.659615 + 12.1713i) q^{66} +5.54736 q^{67} +(1.21881 + 11.2118i) q^{68} -16.3676 q^{69} +(1.88769 + 3.23057i) q^{70} -2.42368i q^{71} +(-5.37205 + 0.880303i) q^{72} -6.08011i q^{73} +(-0.534513 - 9.86293i) q^{74} -2.21915i q^{75} +(-0.283435 - 2.60731i) q^{76} +(-4.69657 - 9.13987i) q^{77} +(0.963798 + 17.7842i) q^{78} +2.83370i q^{79} +(3.90657 - 0.859503i) q^{80} -11.0697 q^{81} +(0.572257 + 10.5594i) q^{82} -2.52687i q^{83} +(9.80325 - 6.46423i) q^{84} +5.63892i q^{85} +(-2.07211 + 0.112296i) q^{86} +20.1322 q^{87} +(-10.8409 + 1.77646i) q^{88} -10.9114i q^{89} +(-2.71786 + 0.147292i) q^{90} +(-6.86240 - 13.3547i) q^{91} +(-1.59417 - 14.6648i) q^{92} +4.95033i q^{93} +(0.801127 - 0.0434164i) q^{94} -1.31134i q^{95} +(-3.35693 - 12.0963i) q^{96} -9.93165i q^{97} +(-5.31969 + 8.34871i) q^{98} +7.47519 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q + q^{2} + q^{4} + 16q^{5} + q^{8} - 16q^{9} + O(q^{10}) \) \( 16q + q^{2} + q^{4} + 16q^{5} + q^{8} - 16q^{9} + q^{10} - 4q^{11} + 14q^{12} - q^{14} + 9q^{16} - 15q^{18} + q^{20} - 4q^{21} + 6q^{22} + 22q^{24} + 16q^{25} - 20q^{26} + q^{28} - 16q^{31} - 19q^{32} - 14q^{34} + 15q^{36} - 30q^{38} + q^{40} + 44q^{42} - 4q^{43} - 20q^{44} - 16q^{45} + 6q^{46} - 34q^{48} - 8q^{49} + q^{50} - 40q^{51} - 38q^{52} + 26q^{54} - 4q^{55} + 33q^{56} - 16q^{57} + 18q^{58} + 14q^{60} - 8q^{61} + 28q^{62} + 28q^{63} - 23q^{64} + 46q^{66} + 20q^{67} + 12q^{68} - 40q^{69} - q^{70} - 13q^{72} - 28q^{74} + 34q^{76} - 4q^{77} - 6q^{78} + 9q^{80} + 24q^{81} - 16q^{82} - 42q^{84} - 24q^{86} + 72q^{87} - 44q^{88} - 15q^{90} - 32q^{91} - 30q^{92} - 58q^{94} - 30q^{96} + 5q^{98} + 20q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/280\mathbb{Z}\right)^\times\).

\(n\) \(57\) \(71\) \(141\) \(241\)
\(\chi(n)\) \(1\) \(-1\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.41214 0.0765298i 0.998535 0.0541147i
\(3\) 2.21915i 1.28123i −0.767863 0.640614i \(-0.778680\pi\)
0.767863 0.640614i \(-0.221320\pi\)
\(4\) 1.98829 0.216142i 0.994143 0.108071i
\(5\) 1.00000 0.447214
\(6\) −0.169831 3.13376i −0.0693333 1.27935i
\(7\) 1.20923 + 2.35325i 0.457045 + 0.889444i
\(8\) 2.79120 0.457386i 0.986838 0.161710i
\(9\) −1.92464 −0.641546
\(10\) 1.41214 0.0765298i 0.446558 0.0242008i
\(11\) −3.88394 −1.17105 −0.585526 0.810653i \(-0.699112\pi\)
−0.585526 + 0.810653i \(0.699112\pi\)
\(12\) −0.479652 4.41231i −0.138463 1.27372i
\(13\) −5.67503 −1.57397 −0.786985 0.616972i \(-0.788359\pi\)
−0.786985 + 0.616972i \(0.788359\pi\)
\(14\) 1.88769 + 3.23057i 0.504507 + 0.863407i
\(15\) 2.21915i 0.572983i
\(16\) 3.90657 0.859503i 0.976641 0.214876i
\(17\) 5.63892i 1.36764i 0.729651 + 0.683820i \(0.239683\pi\)
−0.729651 + 0.683820i \(0.760317\pi\)
\(18\) −2.71786 + 0.147292i −0.640606 + 0.0347171i
\(19\) 1.31134i 0.300841i −0.988622 0.150421i \(-0.951937\pi\)
0.988622 0.150421i \(-0.0480628\pi\)
\(20\) 1.98829 0.216142i 0.444594 0.0483308i
\(21\) 5.22221 2.68346i 1.13958 0.585579i
\(22\) −5.48468 + 0.297237i −1.16934 + 0.0633712i
\(23\) 7.37559i 1.53792i −0.639299 0.768958i \(-0.720775\pi\)
0.639299 0.768958i \(-0.279225\pi\)
\(24\) −1.01501 6.19410i −0.207188 1.26437i
\(25\) 1.00000 0.200000
\(26\) −8.01395 + 0.434309i −1.57166 + 0.0851750i
\(27\) 2.38639i 0.459261i
\(28\) 2.91293 + 4.41756i 0.550491 + 0.834841i
\(29\) 9.07201i 1.68463i 0.538986 + 0.842315i \(0.318808\pi\)
−0.538986 + 0.842315i \(0.681192\pi\)
\(30\) −0.169831 3.13376i −0.0310068 0.572143i
\(31\) −2.23073 −0.400651 −0.200326 0.979729i \(-0.564200\pi\)
−0.200326 + 0.979729i \(0.564200\pi\)
\(32\) 5.45085 1.51271i 0.963582 0.267412i
\(33\) 8.61906i 1.50039i
\(34\) 0.431546 + 7.96296i 0.0740094 + 1.36564i
\(35\) 1.20923 + 2.35325i 0.204397 + 0.397771i
\(36\) −3.82673 + 0.415995i −0.637789 + 0.0693325i
\(37\) 6.98438i 1.14822i −0.818777 0.574112i \(-0.805347\pi\)
0.818777 0.574112i \(-0.194653\pi\)
\(38\) −0.100356 1.85179i −0.0162799 0.300400i
\(39\) 12.5938i 2.01662i
\(40\) 2.79120 0.457386i 0.441327 0.0723191i
\(41\) 7.47757i 1.16780i 0.811826 + 0.583900i \(0.198474\pi\)
−0.811826 + 0.583900i \(0.801526\pi\)
\(42\) 7.16914 4.18908i 1.10622 0.646389i
\(43\) −1.46735 −0.223769 −0.111884 0.993721i \(-0.535689\pi\)
−0.111884 + 0.993721i \(0.535689\pi\)
\(44\) −7.72239 + 0.839482i −1.16419 + 0.126557i
\(45\) −1.92464 −0.286908
\(46\) −0.564452 10.4154i −0.0832239 1.53566i
\(47\) 0.567314 0.0827512 0.0413756 0.999144i \(-0.486826\pi\)
0.0413756 + 0.999144i \(0.486826\pi\)
\(48\) −1.90737 8.66927i −0.275305 1.25130i
\(49\) −4.07554 + 5.69122i −0.582220 + 0.813032i
\(50\) 1.41214 0.0765298i 0.199707 0.0108229i
\(51\) 12.5136 1.75226
\(52\) −11.2836 + 1.22661i −1.56475 + 0.170100i
\(53\) 0.100950i 0.0138665i −0.999976 0.00693326i \(-0.997793\pi\)
0.999976 0.00693326i \(-0.00220694\pi\)
\(54\) −0.182630 3.36992i −0.0248528 0.458588i
\(55\) −3.88394 −0.523711
\(56\) 4.45154 + 6.01530i 0.594862 + 0.803828i
\(57\) −2.91006 −0.385446
\(58\) 0.694279 + 12.8110i 0.0911633 + 1.68216i
\(59\) 2.93497i 0.382101i 0.981580 + 0.191050i \(0.0611894\pi\)
−0.981580 + 0.191050i \(0.938811\pi\)
\(60\) −0.479652 4.41231i −0.0619228 0.569627i
\(61\) 13.8324 1.77106 0.885531 0.464580i \(-0.153795\pi\)
0.885531 + 0.464580i \(0.153795\pi\)
\(62\) −3.15011 + 0.170717i −0.400064 + 0.0216811i
\(63\) −2.32733 4.52915i −0.293216 0.570619i
\(64\) 7.58160 2.55331i 0.947700 0.319164i
\(65\) −5.67503 −0.703901
\(66\) 0.659615 + 12.1713i 0.0811930 + 1.49819i
\(67\) 5.54736 0.677718 0.338859 0.940837i \(-0.389959\pi\)
0.338859 + 0.940837i \(0.389959\pi\)
\(68\) 1.21881 + 11.2118i 0.147802 + 1.35963i
\(69\) −16.3676 −1.97042
\(70\) 1.88769 + 3.23057i 0.225623 + 0.386128i
\(71\) 2.42368i 0.287638i −0.989604 0.143819i \(-0.954062\pi\)
0.989604 0.143819i \(-0.0459384\pi\)
\(72\) −5.37205 + 0.880303i −0.633102 + 0.103745i
\(73\) 6.08011i 0.711623i −0.934558 0.355811i \(-0.884205\pi\)
0.934558 0.355811i \(-0.115795\pi\)
\(74\) −0.534513 9.86293i −0.0621359 1.14654i
\(75\) 2.21915i 0.256246i
\(76\) −0.283435 2.60731i −0.0325122 0.299079i
\(77\) −4.69657 9.13987i −0.535224 1.04159i
\(78\) 0.963798 + 17.7842i 0.109129 + 2.01366i
\(79\) 2.83370i 0.318816i 0.987213 + 0.159408i \(0.0509586\pi\)
−0.987213 + 0.159408i \(0.949041\pi\)
\(80\) 3.90657 0.859503i 0.436767 0.0960954i
\(81\) −11.0697 −1.22996
\(82\) 0.572257 + 10.5594i 0.0631952 + 1.16609i
\(83\) 2.52687i 0.277360i −0.990337 0.138680i \(-0.955714\pi\)
0.990337 0.138680i \(-0.0442860\pi\)
\(84\) 9.80325 6.46423i 1.06962 0.705305i
\(85\) 5.63892i 0.611627i
\(86\) −2.07211 + 0.112296i −0.223441 + 0.0121092i
\(87\) 20.1322 2.15840
\(88\) −10.8409 + 1.77646i −1.15564 + 0.189371i
\(89\) 10.9114i 1.15661i −0.815822 0.578303i \(-0.803715\pi\)
0.815822 0.578303i \(-0.196285\pi\)
\(90\) −2.71786 + 0.147292i −0.286488 + 0.0155260i
\(91\) −6.86240 13.3547i −0.719375 1.39996i
\(92\) −1.59417 14.6648i −0.166204 1.52891i
\(93\) 4.95033i 0.513326i
\(94\) 0.801127 0.0434164i 0.0826299 0.00447806i
\(95\) 1.31134i 0.134540i
\(96\) −3.35693 12.0963i −0.342615 1.23457i
\(97\) 9.93165i 1.00841i −0.863585 0.504203i \(-0.831786\pi\)
0.863585 0.504203i \(-0.168214\pi\)
\(98\) −5.31969 + 8.34871i −0.537370 + 0.843347i
\(99\) 7.47519 0.751285
\(100\) 1.98829 0.216142i 0.198829 0.0216142i
\(101\) 3.07042 0.305519 0.152759 0.988263i \(-0.451184\pi\)
0.152759 + 0.988263i \(0.451184\pi\)
\(102\) 17.6710 0.957665i 1.74969 0.0948230i
\(103\) 5.89112 0.580470 0.290235 0.956955i \(-0.406267\pi\)
0.290235 + 0.956955i \(0.406267\pi\)
\(104\) −15.8401 + 2.59568i −1.55325 + 0.254527i
\(105\) 5.22221 2.68346i 0.509636 0.261879i
\(106\) −0.00772567 0.142555i −0.000750383 0.0138462i
\(107\) −11.0481 −1.06806 −0.534032 0.845464i \(-0.679324\pi\)
−0.534032 + 0.845464i \(0.679324\pi\)
\(108\) −0.515799 4.74483i −0.0496327 0.456571i
\(109\) 4.12606i 0.395205i −0.980282 0.197603i \(-0.936684\pi\)
0.980282 0.197603i \(-0.0633156\pi\)
\(110\) −5.48468 + 0.297237i −0.522943 + 0.0283405i
\(111\) −15.4994 −1.47114
\(112\) 6.74655 + 8.15378i 0.637489 + 0.770459i
\(113\) −5.28550 −0.497218 −0.248609 0.968604i \(-0.579973\pi\)
−0.248609 + 0.968604i \(0.579973\pi\)
\(114\) −4.10941 + 0.222706i −0.384882 + 0.0208583i
\(115\) 7.37559i 0.687777i
\(116\) 1.96084 + 18.0378i 0.182059 + 1.67476i
\(117\) 10.9224 1.00977
\(118\) 0.224613 + 4.14460i 0.0206773 + 0.381541i
\(119\) −13.2698 + 6.81874i −1.21644 + 0.625073i
\(120\) −1.01501 6.19410i −0.0926572 0.565441i
\(121\) 4.08501 0.371364
\(122\) 19.5334 1.05859i 1.76847 0.0958406i
\(123\) 16.5939 1.49622
\(124\) −4.43533 + 0.482154i −0.398305 + 0.0432987i
\(125\) 1.00000 0.0894427
\(126\) −3.63313 6.21769i −0.323665 0.553916i
\(127\) 7.13436i 0.633072i −0.948580 0.316536i \(-0.897480\pi\)
0.948580 0.316536i \(-0.102520\pi\)
\(128\) 10.5109 4.18585i 0.929039 0.369981i
\(129\) 3.25627i 0.286699i
\(130\) −8.01395 + 0.434309i −0.702870 + 0.0380914i
\(131\) 6.86654i 0.599932i 0.953950 + 0.299966i \(0.0969754\pi\)
−0.953950 + 0.299966i \(0.903025\pi\)
\(132\) 1.86294 + 17.1372i 0.162148 + 1.49160i
\(133\) 3.08590 1.58570i 0.267581 0.137498i
\(134\) 7.83366 0.424538i 0.676725 0.0366745i
\(135\) 2.38639i 0.205388i
\(136\) 2.57916 + 15.7394i 0.221161 + 1.34964i
\(137\) 5.74697 0.490996 0.245498 0.969397i \(-0.421048\pi\)
0.245498 + 0.969397i \(0.421048\pi\)
\(138\) −23.1133 + 1.25261i −1.96753 + 0.106629i
\(139\) 12.6356i 1.07174i −0.844301 0.535869i \(-0.819984\pi\)
0.844301 0.535869i \(-0.180016\pi\)
\(140\) 2.91293 + 4.41756i 0.246187 + 0.373352i
\(141\) 1.25896i 0.106023i
\(142\) −0.185484 3.42258i −0.0155655 0.287217i
\(143\) 22.0415 1.84320
\(144\) −7.51873 + 1.65423i −0.626561 + 0.137853i
\(145\) 9.07201i 0.753389i
\(146\) −0.465309 8.58597i −0.0385093 0.710580i
\(147\) 12.6297 + 9.04424i 1.04168 + 0.745956i
\(148\) −1.50962 13.8869i −0.124090 1.14150i
\(149\) 11.9402i 0.978181i 0.872233 + 0.489091i \(0.162671\pi\)
−0.872233 + 0.489091i \(0.837329\pi\)
\(150\) −0.169831 3.13376i −0.0138667 0.255870i
\(151\) 7.62474i 0.620493i 0.950656 + 0.310246i \(0.100412\pi\)
−0.950656 + 0.310246i \(0.899588\pi\)
\(152\) −0.599787 3.66020i −0.0486491 0.296882i
\(153\) 10.8529i 0.877404i
\(154\) −7.33169 12.5474i −0.590805 1.01110i
\(155\) −2.23073 −0.179177
\(156\) 2.72204 + 25.0400i 0.217937 + 2.00480i
\(157\) −15.2157 −1.21435 −0.607174 0.794569i \(-0.707697\pi\)
−0.607174 + 0.794569i \(0.707697\pi\)
\(158\) 0.216862 + 4.00159i 0.0172527 + 0.318349i
\(159\) −0.224023 −0.0177662
\(160\) 5.45085 1.51271i 0.430927 0.119590i
\(161\) 17.3566 8.91876i 1.36789 0.702897i
\(162\) −15.6320 + 0.847160i −1.22816 + 0.0665592i
\(163\) −0.486426 −0.0380998 −0.0190499 0.999819i \(-0.506064\pi\)
−0.0190499 + 0.999819i \(0.506064\pi\)
\(164\) 1.61621 + 14.8675i 0.126205 + 1.16096i
\(165\) 8.61906i 0.670993i
\(166\) −0.193381 3.56830i −0.0150093 0.276954i
\(167\) −19.6159 −1.51793 −0.758963 0.651134i \(-0.774294\pi\)
−0.758963 + 0.651134i \(0.774294\pi\)
\(168\) 13.3489 9.87864i 1.02989 0.762154i
\(169\) 19.2060 1.47738
\(170\) 0.431546 + 7.96296i 0.0330980 + 0.610731i
\(171\) 2.52385i 0.193004i
\(172\) −2.91751 + 0.317156i −0.222458 + 0.0241829i
\(173\) 8.14454 0.619218 0.309609 0.950864i \(-0.399802\pi\)
0.309609 + 0.950864i \(0.399802\pi\)
\(174\) 28.4295 1.54071i 2.15523 0.116801i
\(175\) 1.20923 + 2.35325i 0.0914090 + 0.177889i
\(176\) −15.1729 + 3.33826i −1.14370 + 0.251631i
\(177\) 6.51315 0.489558
\(178\) −0.835047 15.4084i −0.0625894 1.15491i
\(179\) −20.3812 −1.52336 −0.761680 0.647953i \(-0.775625\pi\)
−0.761680 + 0.647953i \(0.775625\pi\)
\(180\) −3.82673 + 0.415995i −0.285228 + 0.0310064i
\(181\) −6.68992 −0.497258 −0.248629 0.968599i \(-0.579980\pi\)
−0.248629 + 0.968599i \(0.579980\pi\)
\(182\) −10.7127 18.3336i −0.794080 1.35898i
\(183\) 30.6963i 2.26914i
\(184\) −3.37349 20.5867i −0.248697 1.51767i
\(185\) 6.98438i 0.513502i
\(186\) 0.378848 + 6.99057i 0.0277785 + 0.512573i
\(187\) 21.9012i 1.60158i
\(188\) 1.12798 0.122620i 0.0822665 0.00894299i
\(189\) 5.61576 2.88569i 0.408487 0.209903i
\(190\) −0.100356 1.85179i −0.00728061 0.134343i
\(191\) 5.95641i 0.430991i 0.976505 + 0.215495i \(0.0691366\pi\)
−0.976505 + 0.215495i \(0.930863\pi\)
\(192\) −5.66619 16.8247i −0.408922 1.21422i
\(193\) 10.9141 0.785617 0.392808 0.919620i \(-0.371504\pi\)
0.392808 + 0.919620i \(0.371504\pi\)
\(194\) −0.760067 14.0249i −0.0545696 1.00693i
\(195\) 12.5938i 0.901858i
\(196\) −6.87323 + 12.1967i −0.490945 + 0.871191i
\(197\) 3.76694i 0.268384i −0.990955 0.134192i \(-0.957156\pi\)
0.990955 0.134192i \(-0.0428438\pi\)
\(198\) 10.5560 0.572074i 0.750184 0.0406556i
\(199\) 7.52925 0.533734 0.266867 0.963733i \(-0.414012\pi\)
0.266867 + 0.963733i \(0.414012\pi\)
\(200\) 2.79120 0.457386i 0.197368 0.0323421i
\(201\) 12.3104i 0.868311i
\(202\) 4.33587 0.234979i 0.305071 0.0165331i
\(203\) −21.3487 + 10.9701i −1.49838 + 0.769952i
\(204\) 24.8807 2.70472i 1.74200 0.189368i
\(205\) 7.47757i 0.522256i
\(206\) 8.31910 0.450847i 0.579619 0.0314120i
\(207\) 14.1953i 0.986644i
\(208\) −22.1699 + 4.87771i −1.53720 + 0.338208i
\(209\) 5.09315i 0.352301i
\(210\) 7.16914 4.18908i 0.494718 0.289074i
\(211\) −3.93687 −0.271026 −0.135513 0.990776i \(-0.543268\pi\)
−0.135513 + 0.990776i \(0.543268\pi\)
\(212\) −0.0218195 0.200717i −0.00149857 0.0137853i
\(213\) −5.37852 −0.368530
\(214\) −15.6015 + 0.845512i −1.06650 + 0.0577980i
\(215\) −1.46735 −0.100072
\(216\) −1.09150 6.66089i −0.0742672 0.453216i
\(217\) −2.69746 5.24946i −0.183116 0.356357i
\(218\) −0.315767 5.82658i −0.0213864 0.394626i
\(219\) −13.4927 −0.911752
\(220\) −7.72239 + 0.839482i −0.520643 + 0.0565979i
\(221\) 32.0011i 2.15262i
\(222\) −21.8873 + 1.18617i −1.46898 + 0.0796102i
\(223\) 17.3868 1.16431 0.582154 0.813078i \(-0.302210\pi\)
0.582154 + 0.813078i \(0.302210\pi\)
\(224\) 10.1511 + 10.9980i 0.678248 + 0.734833i
\(225\) −1.92464 −0.128309
\(226\) −7.46388 + 0.404499i −0.496490 + 0.0269068i
\(227\) 22.9676i 1.52441i 0.647334 + 0.762206i \(0.275884\pi\)
−0.647334 + 0.762206i \(0.724116\pi\)
\(228\) −5.78602 + 0.628985i −0.383189 + 0.0416555i
\(229\) 14.1945 0.938000 0.469000 0.883198i \(-0.344614\pi\)
0.469000 + 0.883198i \(0.344614\pi\)
\(230\) −0.564452 10.4154i −0.0372189 0.686769i
\(231\) −20.2828 + 10.4224i −1.33451 + 0.685744i
\(232\) 4.14941 + 25.3218i 0.272422 + 1.66246i
\(233\) 14.0393 0.919743 0.459872 0.887985i \(-0.347895\pi\)
0.459872 + 0.887985i \(0.347895\pi\)
\(234\) 15.4240 0.835888i 1.00830 0.0546437i
\(235\) 0.567314 0.0370075
\(236\) 0.634370 + 5.83557i 0.0412940 + 0.379863i
\(237\) 6.28841 0.408476
\(238\) −18.2170 + 10.6446i −1.18083 + 0.689984i
\(239\) 12.7467i 0.824517i 0.911067 + 0.412259i \(0.135260\pi\)
−0.911067 + 0.412259i \(0.864740\pi\)
\(240\) −1.90737 8.66927i −0.123120 0.559599i
\(241\) 5.80924i 0.374206i −0.982340 0.187103i \(-0.940090\pi\)
0.982340 0.187103i \(-0.0599098\pi\)
\(242\) 5.76861 0.312625i 0.370820 0.0200963i
\(243\) 17.4061i 1.11660i
\(244\) 27.5029 2.98977i 1.76069 0.191400i
\(245\) −4.07554 + 5.69122i −0.260377 + 0.363599i
\(246\) 23.4329 1.26992i 1.49403 0.0809675i
\(247\) 7.44187i 0.473515i
\(248\) −6.22642 + 1.02030i −0.395378 + 0.0647894i
\(249\) −5.60752 −0.355362
\(250\) 1.41214 0.0765298i 0.0893117 0.00484017i
\(251\) 26.0680i 1.64540i 0.568478 + 0.822698i \(0.307532\pi\)
−0.568478 + 0.822698i \(0.692468\pi\)
\(252\) −5.60633 8.50221i −0.353166 0.535589i
\(253\) 28.6464i 1.80098i
\(254\) −0.545991 10.0747i −0.0342585 0.632145i
\(255\) 12.5136 0.783634
\(256\) 14.5225 6.71541i 0.907657 0.419713i
\(257\) 18.1281i 1.13080i 0.824816 + 0.565401i \(0.191278\pi\)
−0.824816 + 0.565401i \(0.808722\pi\)
\(258\) 0.249202 + 4.59832i 0.0155146 + 0.286279i
\(259\) 16.4360 8.44570i 1.02128 0.524790i
\(260\) −11.2836 + 1.22661i −0.699778 + 0.0760712i
\(261\) 17.4603i 1.08077i
\(262\) 0.525495 + 9.69652i 0.0324652 + 0.599053i
\(263\) 22.7053i 1.40007i −0.714110 0.700034i \(-0.753168\pi\)
0.714110 0.700034i \(-0.246832\pi\)
\(264\) 3.94224 + 24.0575i 0.242628 + 1.48064i
\(265\) 0.100950i 0.00620130i
\(266\) 4.23637 2.47540i 0.259749 0.151777i
\(267\) −24.2140 −1.48188
\(268\) 11.0297 1.19902i 0.673749 0.0732416i
\(269\) −9.24420 −0.563629 −0.281814 0.959469i \(-0.590936\pi\)
−0.281814 + 0.959469i \(0.590936\pi\)
\(270\) −0.182630 3.36992i −0.0111145 0.205087i
\(271\) −14.5888 −0.886206 −0.443103 0.896471i \(-0.646122\pi\)
−0.443103 + 0.896471i \(0.646122\pi\)
\(272\) 4.84667 + 22.0288i 0.293873 + 1.33569i
\(273\) −29.6362 + 15.2287i −1.79367 + 0.921684i
\(274\) 8.11553 0.439814i 0.490277 0.0265701i
\(275\) −3.88394 −0.234211
\(276\) −32.5434 + 3.53771i −1.95888 + 0.212945i
\(277\) 17.6637i 1.06131i −0.847588 0.530654i \(-0.821946\pi\)
0.847588 0.530654i \(-0.178054\pi\)
\(278\) −0.967000 17.8433i −0.0579968 1.07017i
\(279\) 4.29335 0.257036
\(280\) 4.45154 + 6.01530i 0.266030 + 0.359483i
\(281\) −20.0874 −1.19832 −0.599158 0.800631i \(-0.704498\pi\)
−0.599158 + 0.800631i \(0.704498\pi\)
\(282\) −0.0963476 1.77782i −0.00573742 0.105868i
\(283\) 1.40295i 0.0833969i −0.999130 0.0416985i \(-0.986723\pi\)
0.999130 0.0416985i \(-0.0132769\pi\)
\(284\) −0.523859 4.81898i −0.0310853 0.285954i
\(285\) −2.91006 −0.172377
\(286\) 31.1257 1.68683i 1.84050 0.0997444i
\(287\) −17.5966 + 9.04208i −1.03869 + 0.533737i
\(288\) −10.4909 + 2.91142i −0.618183 + 0.171557i
\(289\) −14.7974 −0.870438
\(290\) 0.694279 + 12.8110i 0.0407695 + 0.752286i
\(291\) −22.0399 −1.29200
\(292\) −1.31417 12.0890i −0.0769057 0.707455i
\(293\) −14.9167 −0.871446 −0.435723 0.900081i \(-0.643507\pi\)
−0.435723 + 0.900081i \(0.643507\pi\)
\(294\) 18.5271 + 11.8052i 1.08052 + 0.688493i
\(295\) 2.93497i 0.170881i
\(296\) −3.19455 19.4948i −0.185680 1.13311i
\(297\) 9.26860i 0.537819i
\(298\) 0.913783 + 16.8613i 0.0529340 + 0.976748i
\(299\) 41.8567i 2.42063i
\(300\) −0.479652 4.41231i −0.0276927 0.254745i
\(301\) −1.77436 3.45304i −0.102272 0.199030i
\(302\) 0.583520 + 10.7672i 0.0335778 + 0.619584i
\(303\) 6.81374i 0.391439i
\(304\) −1.12710 5.12282i −0.0646435 0.293814i
\(305\) 13.8324 0.792043
\(306\) −0.830569 15.3258i −0.0474805 0.876119i
\(307\) 3.67891i 0.209966i 0.994474 + 0.104983i \(0.0334789\pi\)
−0.994474 + 0.104983i \(0.966521\pi\)
\(308\) −11.3136 17.1576i −0.644654 0.977643i
\(309\) 13.0733i 0.743714i
\(310\) −3.15011 + 0.170717i −0.178914 + 0.00969609i
\(311\) 31.1614 1.76700 0.883501 0.468429i \(-0.155180\pi\)
0.883501 + 0.468429i \(0.155180\pi\)
\(312\) 5.76021 + 35.1517i 0.326108 + 1.99007i
\(313\) 24.0566i 1.35976i −0.733323 0.679880i \(-0.762032\pi\)
0.733323 0.679880i \(-0.237968\pi\)
\(314\) −21.4868 + 1.16446i −1.21257 + 0.0657141i
\(315\) −2.32733 4.52915i −0.131130 0.255189i
\(316\) 0.612481 + 5.63421i 0.0344547 + 0.316949i
\(317\) 19.3274i 1.08554i 0.839883 + 0.542768i \(0.182624\pi\)
−0.839883 + 0.542768i \(0.817376\pi\)
\(318\) −0.316352 + 0.0171444i −0.0177401 + 0.000961412i
\(319\) 35.2352i 1.97279i
\(320\) 7.58160 2.55331i 0.423824 0.142734i
\(321\) 24.5175i 1.36843i
\(322\) 23.8274 13.9228i 1.32785 0.775890i
\(323\) 7.39452 0.411442
\(324\) −22.0097 + 2.39262i −1.22276 + 0.132923i
\(325\) −5.67503 −0.314794
\(326\) −0.686903 + 0.0372261i −0.0380440 + 0.00206176i
\(327\) −9.15636 −0.506348
\(328\) 3.42013 + 20.8714i 0.188845 + 1.15243i
\(329\) 0.686011 + 1.33503i 0.0378210 + 0.0736025i
\(330\) 0.659615 + 12.1713i 0.0363106 + 0.670010i
\(331\) 19.5607 1.07515 0.537576 0.843216i \(-0.319340\pi\)
0.537576 + 0.843216i \(0.319340\pi\)
\(332\) −0.546163 5.02415i −0.0299746 0.275736i
\(333\) 13.4424i 0.736639i
\(334\) −27.7005 + 1.50120i −1.51570 + 0.0821422i
\(335\) 5.54736 0.303085
\(336\) 18.0945 14.9716i 0.987135 0.816769i
\(337\) −10.2860 −0.560314 −0.280157 0.959954i \(-0.590387\pi\)
−0.280157 + 0.959954i \(0.590387\pi\)
\(338\) 27.1216 1.46983i 1.47522 0.0799482i
\(339\) 11.7293i 0.637050i
\(340\) 1.21881 + 11.2118i 0.0660991 + 0.608045i
\(341\) 8.66403 0.469183
\(342\) 0.193150 + 3.56403i 0.0104443 + 0.192721i
\(343\) −18.3211 2.70876i −0.989246 0.146260i
\(344\) −4.09567 + 0.671145i −0.220824 + 0.0361857i
\(345\) −16.3676 −0.881199
\(346\) 11.5012 0.623300i 0.618311 0.0335088i
\(347\) 3.49360 0.187546 0.0937732 0.995594i \(-0.470107\pi\)
0.0937732 + 0.995594i \(0.470107\pi\)
\(348\) 40.0285 4.35140i 2.14575 0.233260i
\(349\) 10.8420 0.580361 0.290180 0.956972i \(-0.406285\pi\)
0.290180 + 0.956972i \(0.406285\pi\)
\(350\) 1.88769 + 3.23057i 0.100901 + 0.172681i
\(351\) 13.5428i 0.722863i
\(352\) −21.1708 + 5.87527i −1.12841 + 0.313153i
\(353\) 0.494060i 0.0262961i −0.999914 0.0131481i \(-0.995815\pi\)
0.999914 0.0131481i \(-0.00418528\pi\)
\(354\) 9.19749 0.498450i 0.488841 0.0264923i
\(355\) 2.42368i 0.128636i
\(356\) −2.35841 21.6950i −0.124995 1.14983i
\(357\) 15.1318 + 29.4477i 0.800861 + 1.55854i
\(358\) −28.7811 + 1.55977i −1.52113 + 0.0824362i
\(359\) 4.33537i 0.228812i −0.993434 0.114406i \(-0.963503\pi\)
0.993434 0.114406i \(-0.0364965\pi\)
\(360\) −5.37205 + 0.880303i −0.283132 + 0.0463960i
\(361\) 17.2804 0.909495
\(362\) −9.44711 + 0.511978i −0.496529 + 0.0269090i
\(363\) 9.06525i 0.475802i
\(364\) −16.5309 25.0698i −0.866457 1.31401i
\(365\) 6.08011i 0.318247i
\(366\) −2.34918 43.3475i −0.122794 2.26581i
\(367\) −32.9836 −1.72173 −0.860866 0.508832i \(-0.830077\pi\)
−0.860866 + 0.508832i \(0.830077\pi\)
\(368\) −6.33934 28.8132i −0.330461 1.50199i
\(369\) 14.3916i 0.749198i
\(370\) −0.534513 9.86293i −0.0277880 0.512749i
\(371\) 0.237560 0.122071i 0.0123335 0.00633762i
\(372\) 1.06997 + 9.84268i 0.0554755 + 0.510319i
\(373\) 14.2525i 0.737967i 0.929436 + 0.368984i \(0.120294\pi\)
−0.929436 + 0.368984i \(0.879706\pi\)
\(374\) −1.67610 30.9277i −0.0866690 1.59923i
\(375\) 2.21915i 0.114597i
\(376\) 1.58349 0.259481i 0.0816621 0.0133817i
\(377\) 51.4839i 2.65156i
\(378\) 7.70941 4.50477i 0.396529 0.231701i
\(379\) 20.1528 1.03518 0.517590 0.855629i \(-0.326829\pi\)
0.517590 + 0.855629i \(0.326829\pi\)
\(380\) −0.283435 2.60731i −0.0145399 0.133752i
\(381\) −15.8322 −0.811110
\(382\) 0.455843 + 8.41130i 0.0233230 + 0.430359i
\(383\) 6.39302 0.326668 0.163334 0.986571i \(-0.447775\pi\)
0.163334 + 0.986571i \(0.447775\pi\)
\(384\) −9.28905 23.3253i −0.474030 1.19031i
\(385\) −4.69657 9.13987i −0.239359 0.465811i
\(386\) 15.4123 0.835257i 0.784466 0.0425134i
\(387\) 2.82412 0.143558
\(388\) −2.14664 19.7470i −0.108979 1.00250i
\(389\) 15.2150i 0.771432i 0.922618 + 0.385716i \(0.126045\pi\)
−0.922618 + 0.385716i \(0.873955\pi\)
\(390\) 0.963798 + 17.7842i 0.0488038 + 0.900536i
\(391\) 41.5904 2.10332
\(392\) −8.77256 + 17.7494i −0.443081 + 0.896482i
\(393\) 15.2379 0.768650
\(394\) −0.288283 5.31946i −0.0145235 0.267990i
\(395\) 2.83370i 0.142579i
\(396\) 14.8628 1.61570i 0.746884 0.0811920i
\(397\) 27.8429 1.39739 0.698696 0.715418i \(-0.253764\pi\)
0.698696 + 0.715418i \(0.253764\pi\)
\(398\) 10.6324 0.576212i 0.532952 0.0288829i
\(399\) −3.51892 6.84808i −0.176166 0.342833i
\(400\) 3.90657 0.859503i 0.195328 0.0429752i
\(401\) 4.49415 0.224427 0.112214 0.993684i \(-0.464206\pi\)
0.112214 + 0.993684i \(0.464206\pi\)
\(402\) −0.942115 17.3841i −0.0469884 0.867039i
\(403\) 12.6595 0.630613
\(404\) 6.10488 0.663647i 0.303729 0.0330177i
\(405\) −11.0697 −0.550057
\(406\) −29.3078 + 17.1252i −1.45452 + 0.849908i
\(407\) 27.1269i 1.34463i
\(408\) 34.9280 5.72356i 1.72920 0.283358i
\(409\) 9.16042i 0.452954i −0.974017 0.226477i \(-0.927279\pi\)
0.974017 0.226477i \(-0.0727207\pi\)
\(410\) 0.572257 + 10.5594i 0.0282617 + 0.521491i
\(411\) 12.7534i 0.629079i
\(412\) 11.7132 1.27332i 0.577070 0.0627319i
\(413\) −6.90671 + 3.54905i −0.339857 + 0.174637i
\(414\) 1.08637 + 20.0458i 0.0533920 + 0.985199i
\(415\) 2.52687i 0.124039i
\(416\) −30.9337 + 8.58467i −1.51665 + 0.420898i
\(417\) −28.0403 −1.37314
\(418\) 0.389778 + 7.19225i 0.0190647 + 0.351785i
\(419\) 18.8059i 0.918726i −0.888249 0.459363i \(-0.848078\pi\)
0.888249 0.459363i \(-0.151922\pi\)
\(420\) 9.80325 6.46423i 0.478350 0.315422i
\(421\) 34.3816i 1.67566i −0.545934 0.837828i \(-0.683825\pi\)
0.545934 0.837828i \(-0.316175\pi\)
\(422\) −5.55942 + 0.301288i −0.270628 + 0.0146665i
\(423\) −1.09187 −0.0530887
\(424\) −0.0461730 0.281771i −0.00224236 0.0136840i
\(425\) 5.63892i 0.273528i
\(426\) −7.59524 + 0.411617i −0.367990 + 0.0199429i
\(427\) 16.7266 + 32.5511i 0.809455 + 1.57526i
\(428\) −21.9669 + 2.38796i −1.06181 + 0.115427i
\(429\) 48.9134i 2.36156i
\(430\) −2.07211 + 0.112296i −0.0999258 + 0.00541539i
\(431\) 3.54360i 0.170689i 0.996351 + 0.0853447i \(0.0271991\pi\)
−0.996351 + 0.0853447i \(0.972801\pi\)
\(432\) −2.05111 9.32259i −0.0986841 0.448533i
\(433\) 35.6627i 1.71384i 0.515451 + 0.856919i \(0.327624\pi\)
−0.515451 + 0.856919i \(0.672376\pi\)
\(434\) −4.21094 7.20654i −0.202131 0.345925i
\(435\) 20.1322 0.965264
\(436\) −0.891815 8.20380i −0.0427102 0.392891i
\(437\) −9.67188 −0.462669
\(438\) −19.0536 + 1.03259i −0.910416 + 0.0493392i
\(439\) −12.9572 −0.618415 −0.309207 0.950995i \(-0.600064\pi\)
−0.309207 + 0.950995i \(0.600064\pi\)
\(440\) −10.8409 + 1.77646i −0.516818 + 0.0846894i
\(441\) 7.84394 10.9535i 0.373521 0.521597i
\(442\) −2.44903 45.1900i −0.116489 2.14947i
\(443\) 0.593530 0.0281994 0.0140997 0.999901i \(-0.495512\pi\)
0.0140997 + 0.999901i \(0.495512\pi\)
\(444\) −30.8172 + 3.35007i −1.46252 + 0.158987i
\(445\) 10.9114i 0.517250i
\(446\) 24.5527 1.33061i 1.16260 0.0630063i
\(447\) 26.4972 1.25327
\(448\) 15.1764 + 14.7538i 0.717020 + 0.697053i
\(449\) 26.9305 1.27093 0.635464 0.772130i \(-0.280809\pi\)
0.635464 + 0.772130i \(0.280809\pi\)
\(450\) −2.71786 + 0.147292i −0.128121 + 0.00694342i
\(451\) 29.0424i 1.36756i
\(452\) −10.5091 + 1.14242i −0.494306 + 0.0537348i
\(453\) 16.9205 0.794993
\(454\) 1.75770 + 32.4335i 0.0824932 + 1.52218i
\(455\) −6.86240 13.3547i −0.321714 0.626080i
\(456\) −8.12255 + 1.33102i −0.380373 + 0.0623306i
\(457\) 30.8127 1.44136 0.720678 0.693270i \(-0.243831\pi\)
0.720678 + 0.693270i \(0.243831\pi\)
\(458\) 20.0447 1.08630i 0.936626 0.0507596i
\(459\) 13.4567 0.628104
\(460\) −1.59417 14.6648i −0.0743287 0.683749i
\(461\) 0.701982 0.0326946 0.0163473 0.999866i \(-0.494796\pi\)
0.0163473 + 0.999866i \(0.494796\pi\)
\(462\) −27.8445 + 16.2701i −1.29544 + 0.756956i
\(463\) 26.4984i 1.23148i 0.787948 + 0.615742i \(0.211143\pi\)
−0.787948 + 0.615742i \(0.788857\pi\)
\(464\) 7.79742 + 35.4404i 0.361986 + 1.64528i
\(465\) 4.95033i 0.229566i
\(466\) 19.8254 1.07442i 0.918396 0.0497717i
\(467\) 41.6876i 1.92907i −0.263947 0.964537i \(-0.585024\pi\)
0.263947 0.964537i \(-0.414976\pi\)
\(468\) 21.7168 2.36078i 1.00386 0.109127i
\(469\) 6.70802 + 13.0543i 0.309748 + 0.602792i
\(470\) 0.801127 0.0434164i 0.0369532 0.00200265i
\(471\) 33.7660i 1.55586i
\(472\) 1.34241 + 8.19209i 0.0617896 + 0.377072i
\(473\) 5.69910 0.262045
\(474\) 8.88013 0.481251i 0.407878 0.0221046i
\(475\) 1.31134i 0.0601682i
\(476\) −24.9103 + 16.4258i −1.14176 + 0.752873i
\(477\) 0.194292i 0.00889602i
\(478\) 0.975504 + 18.0002i 0.0446185 + 0.823309i
\(479\) −1.36128 −0.0621983 −0.0310991 0.999516i \(-0.509901\pi\)
−0.0310991 + 0.999516i \(0.509901\pi\)
\(480\) −3.35693 12.0963i −0.153222 0.552116i
\(481\) 39.6366i 1.80727i
\(482\) −0.444580 8.20346i −0.0202500 0.373657i
\(483\) −19.7921 38.5169i −0.900572 1.75258i
\(484\) 8.12216 0.882940i 0.369189 0.0401337i
\(485\) 9.93165i 0.450973i
\(486\) 1.33209 + 24.5799i 0.0604248 + 1.11497i
\(487\) 10.7466i 0.486976i −0.969904 0.243488i \(-0.921708\pi\)
0.969904 0.243488i \(-0.0782916\pi\)
\(488\) 38.6091 6.32676i 1.74775 0.286399i
\(489\) 1.07945i 0.0488146i
\(490\) −5.31969 + 8.34871i −0.240319 + 0.377156i
\(491\) 23.1188 1.04334 0.521670 0.853148i \(-0.325309\pi\)
0.521670 + 0.853148i \(0.325309\pi\)
\(492\) 32.9934 3.58663i 1.48746 0.161698i
\(493\) −51.1564 −2.30397
\(494\) 0.569525 + 10.5090i 0.0256241 + 0.472821i
\(495\) 7.47519 0.335985
\(496\) −8.71450 + 1.91732i −0.391292 + 0.0860902i
\(497\) 5.70353 2.93079i 0.255838 0.131464i
\(498\) −7.91861 + 0.429142i −0.354841 + 0.0192303i
\(499\) −23.5311 −1.05340 −0.526698 0.850053i \(-0.676570\pi\)
−0.526698 + 0.850053i \(0.676570\pi\)
\(500\) 1.98829 0.216142i 0.0889189 0.00966615i
\(501\) 43.5307i 1.94481i
\(502\) 1.99498 + 36.8117i 0.0890402 + 1.64299i
\(503\) −20.3215 −0.906093 −0.453046 0.891487i \(-0.649663\pi\)
−0.453046 + 0.891487i \(0.649663\pi\)
\(504\) −8.56760 11.5773i −0.381631 0.515693i
\(505\) 3.07042 0.136632
\(506\) 2.19230 + 40.4527i 0.0974596 + 1.79834i
\(507\) 42.6210i 1.89286i
\(508\) −1.54203 14.1852i −0.0684167 0.629365i
\(509\) 32.6233 1.44600 0.723001 0.690847i \(-0.242762\pi\)
0.723001 + 0.690847i \(0.242762\pi\)
\(510\) 17.6710 0.957665i 0.782486 0.0424061i
\(511\) 14.3080 7.35224i 0.632948 0.325244i
\(512\) 19.9939 10.5945i 0.883614 0.468216i
\(513\) −3.12936 −0.138165
\(514\) 1.38734 + 25.5995i 0.0611930 + 1.12914i
\(515\) 5.89112 0.259594
\(516\) 0.703817 + 6.47441i 0.0309838 + 0.285020i
\(517\) −2.20341 −0.0969060
\(518\) 22.5636 13.1844i 0.991385 0.579288i
\(519\) 18.0740i 0.793360i
\(520\) −15.8401 + 2.59568i −0.694636 + 0.113828i
\(521\) 30.2799i 1.32659i −0.748360 0.663293i \(-0.769158\pi\)
0.748360 0.663293i \(-0.230842\pi\)
\(522\) −1.33624 24.6565i −0.0584855 1.07918i
\(523\) 4.23380i 0.185131i −0.995707 0.0925655i \(-0.970493\pi\)
0.995707 0.0925655i \(-0.0295067\pi\)
\(524\) 1.48415 + 13.6526i 0.0648352 + 0.596418i
\(525\) 5.22221 2.68346i 0.227916 0.117116i
\(526\) −1.73763 32.0631i −0.0757643 1.39802i
\(527\) 12.5789i 0.547946i
\(528\) 7.40811 + 33.6709i 0.322397 + 1.46534i
\(529\) −31.3993 −1.36519
\(530\) −0.00772567 0.142555i −0.000335581 0.00619221i
\(531\) 5.64876i 0.245135i
\(532\) 5.79291 3.81983i 0.251155 0.165610i
\(533\) 42.4354i 1.83808i
\(534\) −34.1937 + 1.85310i −1.47970 + 0.0801913i
\(535\) −11.0481 −0.477653
\(536\) 15.4838 2.53728i 0.668798 0.109594i
\(537\) 45.2289i 1.95177i
\(538\) −13.0541 + 0.707457i −0.562803 + 0.0305006i
\(539\) 15.8292 22.1044i 0.681810 0.952103i
\(540\) −0.515799 4.74483i −0.0221964 0.204185i
\(541\) 20.3843i 0.876390i 0.898880 + 0.438195i \(0.144382\pi\)
−0.898880 + 0.438195i \(0.855618\pi\)
\(542\) −20.6014 + 1.11648i −0.884908 + 0.0479568i
\(543\) 14.8459i 0.637101i
\(544\) 8.53005 + 30.7369i 0.365723 + 1.31783i
\(545\) 4.12606i 0.176741i
\(546\) −40.6851 + 23.7732i −1.74116 + 1.01740i
\(547\) −38.6889 −1.65422 −0.827110 0.562041i \(-0.810016\pi\)
−0.827110 + 0.562041i \(0.810016\pi\)
\(548\) 11.4266 1.24216i 0.488121 0.0530624i
\(549\) −26.6225 −1.13622
\(550\) −5.48468 + 0.297237i −0.233867 + 0.0126742i
\(551\) 11.8965 0.506806
\(552\) −45.6851 + 7.48629i −1.94449 + 0.318638i
\(553\) −6.66839 + 3.42659i −0.283569 + 0.145713i
\(554\) −1.35180 24.9436i −0.0574324 1.05975i
\(555\) −15.4994 −0.657913
\(556\) −2.73108 25.1232i −0.115824 1.06546i
\(557\) 27.3750i 1.15991i 0.814647 + 0.579957i \(0.196931\pi\)
−0.814647 + 0.579957i \(0.803069\pi\)
\(558\) 6.06282 0.328569i 0.256660 0.0139094i
\(559\) 8.32726 0.352206
\(560\) 6.74655 + 8.15378i 0.285094 + 0.344560i
\(561\) −48.6022 −2.05199
\(562\) −28.3663 + 1.53729i −1.19656 + 0.0648466i
\(563\) 13.1643i 0.554811i 0.960753 + 0.277405i \(0.0894745\pi\)
−0.960753 + 0.277405i \(0.910526\pi\)
\(564\) −0.272113 2.50316i −0.0114580 0.105402i
\(565\) −5.28550 −0.222363
\(566\) −0.107368 1.98117i −0.00451300 0.0832747i
\(567\) −13.3858 26.0497i −0.562149 1.09398i
\(568\) −1.10856 6.76499i −0.0465141 0.283853i
\(569\) −16.3200 −0.684168 −0.342084 0.939669i \(-0.611133\pi\)
−0.342084 + 0.939669i \(0.611133\pi\)
\(570\) −4.10941 + 0.222706i −0.172124 + 0.00932813i
\(571\) −23.5552 −0.985754 −0.492877 0.870099i \(-0.664055\pi\)
−0.492877 + 0.870099i \(0.664055\pi\)
\(572\) 43.8248 4.76409i 1.83241 0.199196i
\(573\) 13.2182 0.552198
\(574\) −24.1568 + 14.1154i −1.00829 + 0.589164i
\(575\) 7.37559i 0.307583i
\(576\) −14.5918 + 4.91420i −0.607993 + 0.204758i
\(577\) 29.3020i 1.21986i 0.792457 + 0.609928i \(0.208802\pi\)
−0.792457 + 0.609928i \(0.791198\pi\)
\(578\) −20.8961 + 1.13245i −0.869163 + 0.0471035i
\(579\) 24.2201i 1.00655i
\(580\) 1.96084 + 18.0378i 0.0814195 + 0.748977i
\(581\) 5.94635 3.05556i 0.246696 0.126766i
\(582\) −31.1234 + 1.68671i −1.29011 + 0.0699162i
\(583\) 0.392083i 0.0162384i
\(584\) −2.78096 16.9708i −0.115077 0.702257i
\(585\) 10.9224 0.451585
\(586\) −21.0646 + 1.14158i −0.870169 + 0.0471580i
\(587\) 18.3219i 0.756225i 0.925760 + 0.378113i \(0.123427\pi\)
−0.925760 + 0.378113i \(0.876573\pi\)
\(588\) 27.0663 + 15.2527i 1.11619 + 0.629012i
\(589\) 2.92524i 0.120532i
\(590\) 0.224613 + 4.14460i 0.00924716 + 0.170630i
\(591\) −8.35942 −0.343861
\(592\) −6.00310 27.2849i −0.246726 1.12140i
\(593\) 35.9919i 1.47801i −0.673699 0.739006i \(-0.735296\pi\)
0.673699 0.739006i \(-0.264704\pi\)
\(594\) 0.709324 + 13.0886i 0.0291039 + 0.537031i
\(595\) −13.2698 + 6.81874i −0.544008 + 0.279541i
\(596\) 2.58078 + 23.7406i 0.105713 + 0.972452i
\(597\) 16.7085i 0.683835i
\(598\) 3.20328 + 59.1076i 0.130992 + 2.41709i
\(599\) 8.44016i 0.344856i 0.985022 + 0.172428i \(0.0551611\pi\)
−0.985022 + 0.172428i \(0.944839\pi\)
\(600\) −1.01501 6.19410i −0.0414376 0.252873i
\(601\) 1.25783i 0.0513079i −0.999671 0.0256539i \(-0.991833\pi\)
0.999671 0.0256539i \(-0.00816680\pi\)
\(602\) −2.76991 4.74039i −0.112893 0.193204i
\(603\) −10.6767 −0.434787
\(604\) 1.64803 + 15.1602i 0.0670572 + 0.616859i
\(605\) 4.08501 0.166079
\(606\) −0.521454 9.62196i −0.0211826 0.390865i
\(607\) −9.60051 −0.389673 −0.194836 0.980836i \(-0.562418\pi\)
−0.194836 + 0.980836i \(0.562418\pi\)
\(608\) −1.98367 7.14789i −0.0804485 0.289885i
\(609\) 24.3444 + 47.3760i 0.986484 + 1.91977i
\(610\) 19.5334 1.05859i 0.790883 0.0428612i
\(611\) −3.21952 −0.130248
\(612\) −2.34576 21.5787i −0.0948218 0.872265i
\(613\) 31.9083i 1.28877i 0.764703 + 0.644383i \(0.222886\pi\)
−0.764703 + 0.644383i \(0.777114\pi\)
\(614\) 0.281546 + 5.19513i 0.0113623 + 0.209659i
\(615\) 16.5939 0.669129
\(616\) −17.2895 23.3631i −0.696614 0.941325i
\(617\) 28.7928 1.15916 0.579578 0.814917i \(-0.303217\pi\)
0.579578 + 0.814917i \(0.303217\pi\)
\(618\) −1.00050 18.4614i −0.0402459 0.742625i
\(619\) 15.2907i 0.614586i 0.951615 + 0.307293i \(0.0994232\pi\)
−0.951615 + 0.307293i \(0.900577\pi\)
\(620\) −4.43533 + 0.482154i −0.178127 + 0.0193638i
\(621\) −17.6010 −0.706305
\(622\) 44.0043 2.38478i 1.76441 0.0956208i
\(623\) 25.6772 13.1944i 1.02874 0.528621i
\(624\) 10.8244 + 49.1984i 0.433322 + 1.96951i
\(625\) 1.00000 0.0400000
\(626\) −1.84105 33.9713i −0.0735831 1.35777i
\(627\) 11.3025 0.451378
\(628\) −30.2532 + 3.28876i −1.20724 + 0.131236i
\(629\) 39.3844 1.57036
\(630\) −3.63313 6.21769i −0.144747 0.247719i
\(631\) 38.9523i 1.55067i 0.631551 + 0.775334i \(0.282419\pi\)
−0.631551 + 0.775334i \(0.717581\pi\)
\(632\) 1.29609 + 7.90942i 0.0515559 + 0.314620i
\(633\) 8.73652i 0.347246i
\(634\) 1.47912 + 27.2930i 0.0587435 + 1.08394i
\(635\) 7.13436i 0.283119i
\(636\) −0.445422 + 0.0484207i −0.0176621 + 0.00192001i
\(637\) 23.1288 32.2979i 0.916397 1.27969i
\(638\) −2.69654 49.7570i −0.106757 1.96990i
\(639\) 4.66472i 0.184533i
\(640\) 10.5109 4.18585i 0.415479 0.165460i
\(641\) −8.27890 −0.326997 −0.163498 0.986544i \(-0.552278\pi\)
−0.163498 + 0.986544i \(0.552278\pi\)
\(642\) 1.87632 + 34.6222i 0.0740525 + 1.36643i
\(643\) 18.0050i 0.710048i −0.934857 0.355024i \(-0.884473\pi\)
0.934857 0.355024i \(-0.115527\pi\)
\(644\) 32.5821 21.4845i 1.28392 0.846609i
\(645\) 3.25627i 0.128216i
\(646\) 10.4421 0.565901i 0.410839 0.0222651i
\(647\) 36.7978 1.44667 0.723336 0.690496i \(-0.242608\pi\)
0.723336 + 0.690496i \(0.242608\pi\)
\(648\) −30.8977 + 5.06312i −1.21378 + 0.198898i
\(649\) 11.3993i 0.447460i
\(650\) −8.01395 + 0.434309i −0.314333 + 0.0170350i
\(651\) −11.6494 + 5.98608i −0.456574 + 0.234613i
\(652\) −0.967155 + 0.105137i −0.0378767 + 0.00411748i
\(653\) 13.5053i 0.528504i 0.964454 + 0.264252i \(0.0851250\pi\)
−0.964454 + 0.264252i \(0.914875\pi\)
\(654\) −12.9301 + 0.700735i −0.505606 + 0.0274009i
\(655\) 6.86654i 0.268298i
\(656\) 6.42699 + 29.2116i 0.250932 + 1.14052i
\(657\) 11.7020i 0.456539i
\(658\) 1.07091 + 1.83275i 0.0417486 + 0.0714480i
\(659\) −21.7852 −0.848629 −0.424315 0.905515i \(-0.639485\pi\)
−0.424315 + 0.905515i \(0.639485\pi\)
\(660\) 1.86294 + 17.1372i 0.0725148 + 0.667063i
\(661\) −27.4541 −1.06784 −0.533921 0.845534i \(-0.679282\pi\)
−0.533921 + 0.845534i \(0.679282\pi\)
\(662\) 27.6224 1.49697i 1.07358 0.0581815i
\(663\) −71.0152 −2.75800
\(664\) −1.15576 7.05301i −0.0448520 0.273710i
\(665\) 3.08590 1.58570i 0.119666 0.0614910i
\(666\) 1.02874 + 18.9826i 0.0398630 + 0.735560i
\(667\) 66.9114 2.59082
\(668\) −39.0021 + 4.23982i −1.50904 + 0.164044i
\(669\) 38.5841i 1.49175i
\(670\) 7.83366 0.424538i 0.302641 0.0164013i
\(671\) −53.7244 −2.07401
\(672\) 24.4062 22.5268i 0.941489 0.868991i
\(673\) −15.2602 −0.588238 −0.294119 0.955769i \(-0.595026\pi\)
−0.294119 + 0.955769i \(0.595026\pi\)
\(674\) −14.5253 + 0.787186i −0.559493 + 0.0303213i
\(675\) 2.38639i 0.0918522i
\(676\) 38.1870 4.15121i 1.46873 0.159662i
\(677\) −29.8069 −1.14557 −0.572787 0.819704i \(-0.694138\pi\)
−0.572787 + 0.819704i \(0.694138\pi\)
\(678\) 0.897644 + 16.5635i 0.0344738 + 0.636117i
\(679\) 23.3716 12.0096i 0.896921 0.460887i
\(680\) 2.57916 + 15.7394i 0.0989064 + 0.603577i
\(681\) 50.9686 1.95312
\(682\) 12.2348 0.663056i 0.468496 0.0253897i
\(683\) 45.4219 1.73802 0.869010 0.494795i \(-0.164757\pi\)
0.869010 + 0.494795i \(0.164757\pi\)
\(684\) 0.545509 + 5.01814i 0.0208581 + 0.191873i
\(685\) 5.74697 0.219580
\(686\) −26.0793 2.42305i −0.995712 0.0925124i
\(687\) 31.4998i 1.20179i
\(688\) −5.73230 + 1.26119i −0.218542 + 0.0480825i
\(689\) 0.572893i 0.0218255i
\(690\) −23.1133 + 1.25261i −0.879908 + 0.0476859i
\(691\) 25.4854i 0.969510i 0.874650 + 0.484755i \(0.161091\pi\)
−0.874650 + 0.484755i \(0.838909\pi\)
\(692\) 16.1937 1.76038i 0.615592 0.0669195i
\(693\) 9.03920 + 17.5910i 0.343371 + 0.668225i
\(694\) 4.93346 0.267365i 0.187272 0.0101490i
\(695\) 12.6356i 0.479296i
\(696\) 56.1929 9.20817i 2.12999 0.349035i
\(697\) −42.1654 −1.59713
\(698\) 15.3105 0.829739i 0.579510 0.0314061i
\(699\) 31.1553i 1.17840i
\(700\) 2.91293 + 4.41756i 0.110098 + 0.166968i
\(701\) 24.4503i 0.923473i 0.887017 + 0.461737i \(0.152773\pi\)
−0.887017 + 0.461737i \(0.847227\pi\)
\(702\) 1.03643 + 19.1244i 0.0391176 + 0.721804i
\(703\) −9.15887 −0.345433
\(704\) −29.4465 + 9.91691i −1.10981 + 0.373758i
\(705\) 1.25896i 0.0474150i
\(706\) −0.0378103 0.697682i −0.00142301 0.0262576i
\(707\) 3.71284 + 7.22546i 0.139636 + 0.271742i
\(708\) 12.9500 1.40776i 0.486691 0.0529070i
\(709\) 32.1784i 1.20848i 0.796801 + 0.604242i \(0.206524\pi\)
−0.796801 + 0.604242i \(0.793476\pi\)
\(710\) −0.185484 3.42258i −0.00696109 0.128447i
\(711\) 5.45385i 0.204535i
\(712\) −4.99072 30.4559i −0.187035 1.14138i
\(713\) 16.4529i 0.616168i
\(714\) 23.6219 + 40.4262i 0.884027 + 1.51291i
\(715\) 22.0415 0.824305
\(716\) −40.5236 + 4.40522i −1.51444 + 0.164631i
\(717\) 28.2869 1.05639
\(718\) −0.331785 6.12216i −0.0123821 0.228477i
\(719\) −14.5688 −0.543324 −0.271662 0.962393i \(-0.587573\pi\)
−0.271662 + 0.962393i \(0.587573\pi\)
\(720\) −7.51873 + 1.65423i −0.280206 + 0.0616497i
\(721\) 7.12371 + 13.8633i 0.265301 + 0.516295i
\(722\) 24.4024 1.32247i 0.908162 0.0492171i
\(723\) −12.8916 −0.479443
\(724\) −13.3015 + 1.44597i −0.494345 + 0.0537391i
\(725\) 9.07201i 0.336926i
\(726\) −0.693762 12.8014i −0.0257479 0.475105i
\(727\) 36.7720 1.36380 0.681899 0.731447i \(-0.261154\pi\)
0.681899 + 0.731447i \(0.261154\pi\)
\(728\) −25.2626 34.1370i −0.936295 1.26520i
\(729\) 5.41785 0.200661
\(730\) −0.465309 8.58597i −0.0172219 0.317781i
\(731\) 8.27428i 0.306035i
\(732\) −6.63475 61.0330i −0.245228 2.25585i
\(733\) −44.4405 −1.64145 −0.820725 0.571324i \(-0.806430\pi\)
−0.820725 + 0.571324i \(0.806430\pi\)
\(734\) −46.5775 + 2.52423i −1.71921 + 0.0931710i
\(735\) 12.6297 + 9.04424i 0.465853 + 0.333602i
\(736\) −11.1571 40.2032i −0.411257 1.48191i
\(737\) −21.5456 −0.793643
\(738\) −1.10139 20.3230i −0.0405426 0.748100i
\(739\) 4.41504 0.162410 0.0812049 0.996697i \(-0.474123\pi\)
0.0812049 + 0.996697i \(0.474123\pi\)
\(740\) −1.50962 13.8869i −0.0554946 0.510494i
\(741\) 16.5147 0.606681
\(742\) 0.326126 0.190562i 0.0119725 0.00699576i
\(743\) 47.0540i 1.72625i 0.504994 + 0.863123i \(0.331495\pi\)
−0.504994 + 0.863123i \(0.668505\pi\)
\(744\) 2.26421 + 13.8174i 0.0830100 + 0.506569i
\(745\) 11.9402i 0.437456i
\(746\) 1.09074 + 20.1266i 0.0399349 + 0.736886i
\(747\) 4.86332i 0.177939i
\(748\) −4.73377 43.5460i −0.173084 1.59220i
\(749\) −13.3597 25.9990i −0.488153 0.949983i
\(750\) −0.169831 3.13376i −0.00620136 0.114429i
\(751\) 32.7742i 1.19595i −0.801516 0.597974i \(-0.795973\pi\)
0.801516 0.597974i \(-0.204027\pi\)
\(752\) 2.21625 0.487608i 0.0808182 0.0177812i
\(753\) 57.8488 2.10813
\(754\) −3.94006 72.7026i −0.143488 2.64767i
\(755\) 7.62474i 0.277493i
\(756\) 10.5420 6.95138i 0.383410 0.252819i
\(757\) 40.7277i 1.48027i −0.672457 0.740136i \(-0.734761\pi\)
0.672457 0.740136i \(-0.265239\pi\)
\(758\) 28.4586 1.54229i 1.03366 0.0560184i
\(759\) 63.5706 2.30747
\(760\) −0.599787 3.66020i −0.0217566 0.132769i
\(761\) 17.5757i 0.637118i −0.947903 0.318559i \(-0.896801\pi\)
0.947903 0.318559i \(-0.103199\pi\)
\(762\) −22.3574 + 1.21164i −0.809922 + 0.0438930i
\(763\) 9.70964 4.98935i 0.351513 0.180627i
\(764\) 1.28743 + 11.8431i 0.0465776 + 0.428467i
\(765\) 10.8529i 0.392387i
\(766\) 9.02784 0.489256i 0.326189 0.0176775i
\(767\) 16.6561i 0.601415i
\(768\) −14.9025 32.2277i −0.537749 1.16292i
\(769\) 31.9583i 1.15245i 0.817292 + 0.576223i \(0.195474\pi\)
−0.817292 + 0.576223i \(0.804526\pi\)
\(770\) −7.33169 12.5474i −0.264216 0.452176i
\(771\) 40.2291 1.44882
\(772\) 21.7004 2.35900i 0.781016 0.0849023i
\(773\) 15.3325 0.551470 0.275735 0.961234i \(-0.411079\pi\)
0.275735 + 0.961234i \(0.411079\pi\)
\(774\) 3.98806 0.216129i 0.143348 0.00776861i
\(775\) −2.23073 −0.0801302
\(776\) −4.54260 27.7212i −0.163070 0.995134i
\(777\) −18.7423 36.4739i −0.672376 1.30849i
\(778\) 1.16440 + 21.4857i 0.0417458 + 0.770301i
\(779\) 9.80561