Properties

Label 280.2.h.b.251.7
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 251.7
Root \(-0.275585 + 1.38710i\) of defining polynomial
Character \(\chi\) \(=\) 280.251
Dual form 280.2.h.b.251.8

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.275585 - 1.38710i) q^{2} -3.19977i q^{3} +(-1.84811 + 0.764529i) q^{4} +1.00000 q^{5} +(-4.43840 + 0.881807i) q^{6} +(-2.59303 + 0.525543i) q^{7} +(1.56979 + 2.35282i) q^{8} -7.23851 q^{9} +O(q^{10})\) \(q+(-0.275585 - 1.38710i) q^{2} -3.19977i q^{3} +(-1.84811 + 0.764529i) q^{4} +1.00000 q^{5} +(-4.43840 + 0.881807i) q^{6} +(-2.59303 + 0.525543i) q^{7} +(1.56979 + 2.35282i) q^{8} -7.23851 q^{9} +(-0.275585 - 1.38710i) q^{10} -3.34588 q^{11} +(2.44631 + 5.91351i) q^{12} +3.90251 q^{13} +(1.44358 + 3.45197i) q^{14} -3.19977i q^{15} +(2.83099 - 2.82586i) q^{16} -2.92992i q^{17} +(1.99482 + 10.0406i) q^{18} -6.33672i q^{19} +(-1.84811 + 0.764529i) q^{20} +(1.68161 + 8.29709i) q^{21} +(0.922074 + 4.64108i) q^{22} -3.44642i q^{23} +(7.52847 - 5.02296i) q^{24} +1.00000 q^{25} +(-1.07547 - 5.41319i) q^{26} +13.5622i q^{27} +(4.39040 - 2.95370i) q^{28} +2.68130i q^{29} +(-4.43840 + 0.881807i) q^{30} -2.52241 q^{31} +(-4.69994 - 3.14811i) q^{32} +10.7060i q^{33} +(-4.06411 + 0.807443i) q^{34} +(-2.59303 + 0.525543i) q^{35} +(13.3775 - 5.53405i) q^{36} +4.70905i q^{37} +(-8.78968 + 1.74630i) q^{38} -12.4871i q^{39} +(1.56979 + 2.35282i) q^{40} -5.59232i q^{41} +(11.0455 - 4.61912i) q^{42} +8.62439 q^{43} +(6.18354 - 2.55802i) q^{44} -7.23851 q^{45} +(-4.78054 + 0.949782i) q^{46} -0.506742 q^{47} +(-9.04209 - 9.05851i) q^{48} +(6.44761 - 2.72550i) q^{49} +(-0.275585 - 1.38710i) q^{50} -9.37508 q^{51} +(-7.21226 + 2.98358i) q^{52} -11.4136i q^{53} +(18.8122 - 3.73755i) q^{54} -3.34588 q^{55} +(-5.30702 - 5.27594i) q^{56} -20.2760 q^{57} +(3.71924 - 0.738926i) q^{58} +0.802275i q^{59} +(2.44631 + 5.91351i) q^{60} -7.97236 q^{61} +(0.695136 + 3.49883i) q^{62} +(18.7697 - 3.80415i) q^{63} +(-3.07152 + 7.38686i) q^{64} +3.90251 q^{65} +(14.8504 - 2.95042i) q^{66} +6.37503 q^{67} +(2.24001 + 5.41481i) q^{68} -11.0278 q^{69} +(1.44358 + 3.45197i) q^{70} -1.11901i q^{71} +(-11.3629 - 17.0309i) q^{72} -5.91619i q^{73} +(6.53194 - 1.29774i) q^{74} -3.19977i q^{75} +(4.84460 + 11.7109i) q^{76} +(8.67597 - 1.75840i) q^{77} +(-17.3209 + 3.44126i) q^{78} +10.5412i q^{79} +(2.83099 - 2.82586i) q^{80} +21.6805 q^{81} +(-7.75712 + 1.54116i) q^{82} -4.29261i q^{83} +(-9.45117 - 14.0483i) q^{84} -2.92992i q^{85} +(-2.37675 - 11.9629i) q^{86} +8.57954 q^{87} +(-5.25233 - 7.87226i) q^{88} -2.00722i q^{89} +(1.99482 + 10.0406i) q^{90} +(-10.1193 + 2.05094i) q^{91} +(2.63489 + 6.36936i) q^{92} +8.07111i q^{93} +(0.139650 + 0.702903i) q^{94} -6.33672i q^{95} +(-10.0732 + 15.0387i) q^{96} +6.06903i q^{97} +(-5.55741 - 8.19239i) q^{98} +24.2192 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.275585 1.38710i −0.194868 0.980830i
\(3\) 3.19977i 1.84739i −0.383133 0.923693i \(-0.625155\pi\)
0.383133 0.923693i \(-0.374845\pi\)
\(4\) −1.84811 + 0.764529i −0.924053 + 0.382264i
\(5\) 1.00000 0.447214
\(6\) −4.43840 + 0.881807i −1.81197 + 0.359996i
\(7\) −2.59303 + 0.525543i −0.980073 + 0.198637i
\(8\) 1.56979 + 2.35282i 0.555004 + 0.831847i
\(9\) −7.23851 −2.41284
\(10\) −0.275585 1.38710i −0.0871476 0.438640i
\(11\) −3.34588 −1.00882 −0.504411 0.863464i \(-0.668290\pi\)
−0.504411 + 0.863464i \(0.668290\pi\)
\(12\) 2.44631 + 5.91351i 0.706190 + 1.70708i
\(13\) 3.90251 1.08236 0.541181 0.840906i \(-0.317977\pi\)
0.541181 + 0.840906i \(0.317977\pi\)
\(14\) 1.44358 + 3.45197i 0.385813 + 0.922577i
\(15\) 3.19977i 0.826176i
\(16\) 2.83099 2.82586i 0.707748 0.706465i
\(17\) 2.92992i 0.710611i −0.934750 0.355306i \(-0.884377\pi\)
0.934750 0.355306i \(-0.115623\pi\)
\(18\) 1.99482 + 10.0406i 0.470184 + 2.36658i
\(19\) 6.33672i 1.45374i −0.686774 0.726871i \(-0.740974\pi\)
0.686774 0.726871i \(-0.259026\pi\)
\(20\) −1.84811 + 0.764529i −0.413249 + 0.170954i
\(21\) 1.68161 + 8.29709i 0.366958 + 1.81057i
\(22\) 0.922074 + 4.64108i 0.196587 + 0.989481i
\(23\) 3.44642i 0.718629i −0.933216 0.359315i \(-0.883010\pi\)
0.933216 0.359315i \(-0.116990\pi\)
\(24\) 7.52847 5.02296i 1.53674 1.02531i
\(25\) 1.00000 0.200000
\(26\) −1.07547 5.41319i −0.210918 1.06161i
\(27\) 13.5622i 2.61005i
\(28\) 4.39040 2.95370i 0.829708 0.558198i
\(29\) 2.68130i 0.497905i 0.968516 + 0.248952i \(0.0800863\pi\)
−0.968516 + 0.248952i \(0.919914\pi\)
\(30\) −4.43840 + 0.881807i −0.810338 + 0.160995i
\(31\) −2.52241 −0.453037 −0.226519 0.974007i \(-0.572734\pi\)
−0.226519 + 0.974007i \(0.572734\pi\)
\(32\) −4.69994 3.14811i −0.830839 0.556513i
\(33\) 10.7060i 1.86368i
\(34\) −4.06411 + 0.807443i −0.696988 + 0.138475i
\(35\) −2.59303 + 0.525543i −0.438302 + 0.0888330i
\(36\) 13.3775 5.53405i 2.22959 0.922341i
\(37\) 4.70905i 0.774164i 0.922045 + 0.387082i \(0.126517\pi\)
−0.922045 + 0.387082i \(0.873483\pi\)
\(38\) −8.78968 + 1.74630i −1.42587 + 0.283288i
\(39\) 12.4871i 1.99954i
\(40\) 1.56979 + 2.35282i 0.248206 + 0.372013i
\(41\) 5.59232i 0.873374i −0.899614 0.436687i \(-0.856152\pi\)
0.899614 0.436687i \(-0.143848\pi\)
\(42\) 11.0455 4.61912i 1.70436 0.712746i
\(43\) 8.62439 1.31521 0.657604 0.753364i \(-0.271570\pi\)
0.657604 + 0.753364i \(0.271570\pi\)
\(44\) 6.18354 2.55802i 0.932204 0.385636i
\(45\) −7.23851 −1.07905
\(46\) −4.78054 + 0.949782i −0.704853 + 0.140038i
\(47\) −0.506742 −0.0739159 −0.0369580 0.999317i \(-0.511767\pi\)
−0.0369580 + 0.999317i \(0.511767\pi\)
\(48\) −9.04209 9.05851i −1.30511 1.30748i
\(49\) 6.44761 2.72550i 0.921087 0.389357i
\(50\) −0.275585 1.38710i −0.0389736 0.196166i
\(51\) −9.37508 −1.31277
\(52\) −7.21226 + 2.98358i −1.00016 + 0.413749i
\(53\) 11.4136i 1.56777i −0.620904 0.783886i \(-0.713235\pi\)
0.620904 0.783886i \(-0.286765\pi\)
\(54\) 18.8122 3.73755i 2.56002 0.508616i
\(55\) −3.34588 −0.451159
\(56\) −5.30702 5.27594i −0.709180 0.705027i
\(57\) −20.2760 −2.68562
\(58\) 3.71924 0.738926i 0.488360 0.0970257i
\(59\) 0.802275i 0.104447i 0.998635 + 0.0522236i \(0.0166309\pi\)
−0.998635 + 0.0522236i \(0.983369\pi\)
\(60\) 2.44631 + 5.91351i 0.315818 + 0.763431i
\(61\) −7.97236 −1.02076 −0.510378 0.859950i \(-0.670494\pi\)
−0.510378 + 0.859950i \(0.670494\pi\)
\(62\) 0.695136 + 3.49883i 0.0882824 + 0.444352i
\(63\) 18.7697 3.80415i 2.36476 0.479277i
\(64\) −3.07152 + 7.38686i −0.383940 + 0.923358i
\(65\) 3.90251 0.484047
\(66\) 14.8504 2.95042i 1.82795 0.363172i
\(67\) 6.37503 0.778834 0.389417 0.921062i \(-0.372677\pi\)
0.389417 + 0.921062i \(0.372677\pi\)
\(68\) 2.24001 + 5.41481i 0.271641 + 0.656642i
\(69\) −11.0278 −1.32759
\(70\) 1.44358 + 3.45197i 0.172541 + 0.412589i
\(71\) 1.11901i 0.132802i −0.997793 0.0664011i \(-0.978848\pi\)
0.997793 0.0664011i \(-0.0211517\pi\)
\(72\) −11.3629 17.0309i −1.33913 2.00711i
\(73\) 5.91619i 0.692438i −0.938154 0.346219i \(-0.887465\pi\)
0.938154 0.346219i \(-0.112535\pi\)
\(74\) 6.53194 1.29774i 0.759323 0.150860i
\(75\) 3.19977i 0.369477i
\(76\) 4.84460 + 11.7109i 0.555714 + 1.34334i
\(77\) 8.67597 1.75840i 0.988719 0.200389i
\(78\) −17.3209 + 3.44126i −1.96121 + 0.389646i
\(79\) 10.5412i 1.18598i 0.805211 + 0.592989i \(0.202052\pi\)
−0.805211 + 0.592989i \(0.797948\pi\)
\(80\) 2.83099 2.82586i 0.316515 0.315941i
\(81\) 21.6805 2.40894
\(82\) −7.75712 + 1.54116i −0.856631 + 0.170192i
\(83\) 4.29261i 0.471175i −0.971853 0.235588i \(-0.924299\pi\)
0.971853 0.235588i \(-0.0757014\pi\)
\(84\) −9.45117 14.0483i −1.03121 1.53279i
\(85\) 2.92992i 0.317795i
\(86\) −2.37675 11.9629i −0.256292 1.28999i
\(87\) 8.57954 0.919823
\(88\) −5.25233 7.87226i −0.559900 0.839185i
\(89\) 2.00722i 0.212764i −0.994325 0.106382i \(-0.966073\pi\)
0.994325 0.106382i \(-0.0339267\pi\)
\(90\) 1.99482 + 10.0406i 0.210273 + 1.05837i
\(91\) −10.1193 + 2.05094i −1.06079 + 0.214997i
\(92\) 2.63489 + 6.36936i 0.274706 + 0.664052i
\(93\) 8.07111i 0.836935i
\(94\) 0.139650 + 0.702903i 0.0144038 + 0.0724989i
\(95\) 6.33672i 0.650134i
\(96\) −10.0732 + 15.0387i −1.02809 + 1.53488i
\(97\) 6.06903i 0.616217i 0.951351 + 0.308108i \(0.0996959\pi\)
−0.951351 + 0.308108i \(0.900304\pi\)
\(98\) −5.55741 8.19239i −0.561383 0.827556i
\(99\) 24.2192 2.43412
\(100\) −1.84811 + 0.764529i −0.184811 + 0.0764529i
\(101\) 11.2324 1.11767 0.558834 0.829279i \(-0.311249\pi\)
0.558834 + 0.829279i \(0.311249\pi\)
\(102\) 2.58363 + 13.0042i 0.255817 + 1.28761i
\(103\) 0.403587 0.0397667 0.0198833 0.999802i \(-0.493671\pi\)
0.0198833 + 0.999802i \(0.493671\pi\)
\(104\) 6.12613 + 9.18191i 0.600716 + 0.900361i
\(105\) 1.68161 + 8.29709i 0.164109 + 0.809713i
\(106\) −15.8318 + 3.14540i −1.53772 + 0.305508i
\(107\) 17.9070 1.73114 0.865568 0.500791i \(-0.166957\pi\)
0.865568 + 0.500791i \(0.166957\pi\)
\(108\) −10.3687 25.0645i −0.997730 2.41183i
\(109\) 14.4062i 1.37986i 0.723874 + 0.689932i \(0.242359\pi\)
−0.723874 + 0.689932i \(0.757641\pi\)
\(110\) 0.922074 + 4.64108i 0.0879163 + 0.442510i
\(111\) 15.0679 1.43018
\(112\) −5.85574 + 8.81535i −0.553315 + 0.832972i
\(113\) −6.85909 −0.645249 −0.322625 0.946527i \(-0.604565\pi\)
−0.322625 + 0.946527i \(0.604565\pi\)
\(114\) 5.58776 + 28.1249i 0.523342 + 2.63414i
\(115\) 3.44642i 0.321381i
\(116\) −2.04993 4.95533i −0.190331 0.460091i
\(117\) −28.2484 −2.61156
\(118\) 1.11284 0.221095i 0.102445 0.0203534i
\(119\) 1.53980 + 7.59738i 0.141153 + 0.696451i
\(120\) 7.52847 5.02296i 0.687253 0.458531i
\(121\) 0.194920 0.0177200
\(122\) 2.19706 + 11.0585i 0.198913 + 1.00119i
\(123\) −17.8941 −1.61346
\(124\) 4.66167 1.92845i 0.418630 0.173180i
\(125\) 1.00000 0.0894427
\(126\) −10.4494 24.9871i −0.930904 2.22603i
\(127\) 5.87400i 0.521233i −0.965442 0.260617i \(-0.916074\pi\)
0.965442 0.260617i \(-0.0839259\pi\)
\(128\) 11.0928 + 2.22481i 0.980474 + 0.196647i
\(129\) 27.5960i 2.42970i
\(130\) −1.07547 5.41319i −0.0943253 0.474768i
\(131\) 4.47680i 0.391139i −0.980690 0.195570i \(-0.937344\pi\)
0.980690 0.195570i \(-0.0626556\pi\)
\(132\) −8.18507 19.7859i −0.712419 1.72214i
\(133\) 3.33022 + 16.4313i 0.288767 + 1.42477i
\(134\) −1.75686 8.84282i −0.151770 0.763903i
\(135\) 13.5622i 1.16725i
\(136\) 6.89358 4.59936i 0.591120 0.394392i
\(137\) 7.90390 0.675276 0.337638 0.941276i \(-0.390372\pi\)
0.337638 + 0.941276i \(0.390372\pi\)
\(138\) 3.03908 + 15.2966i 0.258704 + 1.30214i
\(139\) 9.80123i 0.831329i 0.909518 + 0.415665i \(0.136451\pi\)
−0.909518 + 0.415665i \(0.863549\pi\)
\(140\) 4.39040 2.95370i 0.371057 0.249634i
\(141\) 1.62146i 0.136551i
\(142\) −1.55218 + 0.308382i −0.130256 + 0.0258789i
\(143\) −13.0573 −1.09191
\(144\) −20.4922 + 20.4550i −1.70768 + 1.70458i
\(145\) 2.68130i 0.222670i
\(146\) −8.20636 + 1.63041i −0.679164 + 0.134934i
\(147\) −8.72096 20.6308i −0.719292 1.70160i
\(148\) −3.60021 8.70283i −0.295935 0.715368i
\(149\) 11.5613i 0.947135i −0.880758 0.473567i \(-0.842966\pi\)
0.880758 0.473567i \(-0.157034\pi\)
\(150\) −4.43840 + 0.881807i −0.362394 + 0.0719992i
\(151\) 0.509248i 0.0414420i −0.999785 0.0207210i \(-0.993404\pi\)
0.999785 0.0207210i \(-0.00659617\pi\)
\(152\) 14.9092 9.94731i 1.20929 0.806834i
\(153\) 21.2083i 1.71459i
\(154\) −4.83005 11.5499i −0.389217 0.930715i
\(155\) −2.52241 −0.202604
\(156\) 9.54677 + 23.0776i 0.764354 + 1.84768i
\(157\) 9.98993 0.797283 0.398642 0.917107i \(-0.369482\pi\)
0.398642 + 0.917107i \(0.369482\pi\)
\(158\) 14.6217 2.90500i 1.16324 0.231109i
\(159\) −36.5207 −2.89628
\(160\) −4.69994 3.14811i −0.371563 0.248880i
\(161\) 1.81124 + 8.93668i 0.142746 + 0.704309i
\(162\) −5.97481 30.0730i −0.469425 2.36276i
\(163\) 19.7736 1.54879 0.774393 0.632705i \(-0.218056\pi\)
0.774393 + 0.632705i \(0.218056\pi\)
\(164\) 4.27549 + 10.3352i 0.333860 + 0.807044i
\(165\) 10.7060i 0.833464i
\(166\) −5.95429 + 1.18298i −0.462142 + 0.0918169i
\(167\) −20.6423 −1.59735 −0.798673 0.601765i \(-0.794464\pi\)
−0.798673 + 0.601765i \(0.794464\pi\)
\(168\) −16.8818 + 16.9812i −1.30246 + 1.31013i
\(169\) 2.22962 0.171509
\(170\) −4.06411 + 0.807443i −0.311703 + 0.0619280i
\(171\) 45.8684i 3.50764i
\(172\) −15.9388 + 6.59360i −1.21532 + 0.502757i
\(173\) 12.1166 0.921205 0.460602 0.887607i \(-0.347633\pi\)
0.460602 + 0.887607i \(0.347633\pi\)
\(174\) −2.36439 11.9007i −0.179244 0.902189i
\(175\) −2.59303 + 0.525543i −0.196015 + 0.0397273i
\(176\) −9.47216 + 9.45499i −0.713991 + 0.712697i
\(177\) 2.56709 0.192954
\(178\) −2.78421 + 0.553158i −0.208686 + 0.0414610i
\(179\) −14.6327 −1.09370 −0.546851 0.837230i \(-0.684173\pi\)
−0.546851 + 0.837230i \(0.684173\pi\)
\(180\) 13.3775 5.53405i 0.997102 0.412483i
\(181\) 23.1384 1.71986 0.859932 0.510408i \(-0.170506\pi\)
0.859932 + 0.510408i \(0.170506\pi\)
\(182\) 5.63360 + 13.4713i 0.417590 + 0.998563i
\(183\) 25.5097i 1.88573i
\(184\) 8.10882 5.41016i 0.597790 0.398842i
\(185\) 4.70905i 0.346217i
\(186\) 11.1955 2.22427i 0.820890 0.163092i
\(187\) 9.80318i 0.716879i
\(188\) 0.936513 0.387419i 0.0683022 0.0282554i
\(189\) −7.12754 35.1673i −0.518452 2.55804i
\(190\) −8.78968 + 1.74630i −0.637670 + 0.126690i
\(191\) 2.41554i 0.174782i 0.996174 + 0.0873911i \(0.0278530\pi\)
−0.996174 + 0.0873911i \(0.972147\pi\)
\(192\) 23.6362 + 9.82816i 1.70580 + 0.709286i
\(193\) −7.38549 −0.531619 −0.265810 0.964026i \(-0.585639\pi\)
−0.265810 + 0.964026i \(0.585639\pi\)
\(194\) 8.41837 1.67253i 0.604403 0.120081i
\(195\) 12.4871i 0.894222i
\(196\) −9.83214 + 9.96639i −0.702296 + 0.711885i
\(197\) 20.9305i 1.49124i −0.666372 0.745619i \(-0.732154\pi\)
0.666372 0.745619i \(-0.267846\pi\)
\(198\) −6.67444 33.5945i −0.474332 2.38746i
\(199\) −4.89644 −0.347099 −0.173550 0.984825i \(-0.555524\pi\)
−0.173550 + 0.984825i \(0.555524\pi\)
\(200\) 1.56979 + 2.35282i 0.111001 + 0.166369i
\(201\) 20.3986i 1.43881i
\(202\) −3.09549 15.5805i −0.217798 1.09624i
\(203\) −1.40914 6.95269i −0.0989021 0.487983i
\(204\) 17.3261 7.16751i 1.21307 0.501826i
\(205\) 5.59232i 0.390585i
\(206\) −0.111223 0.559817i −0.00774924 0.0390043i
\(207\) 24.9470i 1.73393i
\(208\) 11.0480 11.0280i 0.766040 0.764651i
\(209\) 21.2019i 1.46657i
\(210\) 11.0455 4.61912i 0.762211 0.318750i
\(211\) 2.25447 0.155204 0.0776020 0.996984i \(-0.475274\pi\)
0.0776020 + 0.996984i \(0.475274\pi\)
\(212\) 8.72599 + 21.0935i 0.599303 + 1.44870i
\(213\) −3.58058 −0.245337
\(214\) −4.93490 24.8389i −0.337343 1.69795i
\(215\) 8.62439 0.588179
\(216\) −31.9095 + 21.2899i −2.17117 + 1.44859i
\(217\) 6.54067 1.32563i 0.444010 0.0899898i
\(218\) 19.9829 3.97013i 1.35341 0.268891i
\(219\) −18.9304 −1.27920
\(220\) 6.18354 2.55802i 0.416894 0.172462i
\(221\) 11.4341i 0.769139i
\(222\) −4.15248 20.9007i −0.278696 1.40276i
\(223\) 24.4820 1.63944 0.819718 0.572768i \(-0.194130\pi\)
0.819718 + 0.572768i \(0.194130\pi\)
\(224\) 13.8415 + 5.69313i 0.924827 + 0.380388i
\(225\) −7.23851 −0.482567
\(226\) 1.89026 + 9.51426i 0.125738 + 0.632879i
\(227\) 5.16178i 0.342599i 0.985219 + 0.171300i \(0.0547966\pi\)
−0.985219 + 0.171300i \(0.945203\pi\)
\(228\) 37.4722 15.5016i 2.48166 1.02662i
\(229\) 9.48995 0.627114 0.313557 0.949569i \(-0.398479\pi\)
0.313557 + 0.949569i \(0.398479\pi\)
\(230\) −4.78054 + 0.949782i −0.315220 + 0.0626268i
\(231\) −5.62648 27.7611i −0.370195 1.82655i
\(232\) −6.30862 + 4.20908i −0.414181 + 0.276339i
\(233\) −2.55217 −0.167198 −0.0835991 0.996499i \(-0.526642\pi\)
−0.0835991 + 0.996499i \(0.526642\pi\)
\(234\) 7.78482 + 39.1834i 0.508910 + 2.56150i
\(235\) −0.506742 −0.0330562
\(236\) −0.613362 1.48269i −0.0399265 0.0965148i
\(237\) 33.7294 2.19096
\(238\) 10.1140 4.22958i 0.655593 0.274163i
\(239\) 8.15573i 0.527550i −0.964584 0.263775i \(-0.915032\pi\)
0.964584 0.263775i \(-0.0849677\pi\)
\(240\) −9.04209 9.05851i −0.583665 0.584725i
\(241\) 2.66753i 0.171831i 0.996302 + 0.0859155i \(0.0273815\pi\)
−0.996302 + 0.0859155i \(0.972619\pi\)
\(242\) −0.0537170 0.270374i −0.00345306 0.0173803i
\(243\) 28.6857i 1.84019i
\(244\) 14.7338 6.09510i 0.943233 0.390199i
\(245\) 6.44761 2.72550i 0.411923 0.174126i
\(246\) 4.93135 + 24.8210i 0.314411 + 1.58253i
\(247\) 24.7291i 1.57348i
\(248\) −3.95964 5.93476i −0.251438 0.376858i
\(249\) −13.7353 −0.870442
\(250\) −0.275585 1.38710i −0.0174295 0.0877281i
\(251\) 8.52244i 0.537932i −0.963150 0.268966i \(-0.913318\pi\)
0.963150 0.268966i \(-0.0866819\pi\)
\(252\) −31.7800 + 21.3804i −2.00195 + 1.34684i
\(253\) 11.5313i 0.724968i
\(254\) −8.14784 + 1.61879i −0.511241 + 0.101572i
\(255\) −9.37508 −0.587090
\(256\) 0.0290305 16.0000i 0.00181440 0.999998i
\(257\) 14.1473i 0.882487i −0.897387 0.441244i \(-0.854538\pi\)
0.897387 0.441244i \(-0.145462\pi\)
\(258\) −38.2785 + 7.60505i −2.38312 + 0.473470i
\(259\) −2.47481 12.2107i −0.153777 0.758737i
\(260\) −7.21226 + 2.98358i −0.447285 + 0.185034i
\(261\) 19.4086i 1.20136i
\(262\) −6.20977 + 1.23374i −0.383641 + 0.0762205i
\(263\) 31.1418i 1.92029i 0.279510 + 0.960143i \(0.409828\pi\)
−0.279510 + 0.960143i \(0.590172\pi\)
\(264\) −25.1894 + 16.8062i −1.55030 + 1.03435i
\(265\) 11.4136i 0.701129i
\(266\) 21.8741 9.14757i 1.34119 0.560874i
\(267\) −6.42262 −0.393058
\(268\) −11.7817 + 4.87389i −0.719684 + 0.297720i
\(269\) −1.39567 −0.0850956 −0.0425478 0.999094i \(-0.513547\pi\)
−0.0425478 + 0.999094i \(0.513547\pi\)
\(270\) 18.8122 3.73755i 1.14487 0.227460i
\(271\) −22.4663 −1.36473 −0.682366 0.731011i \(-0.739049\pi\)
−0.682366 + 0.731011i \(0.739049\pi\)
\(272\) −8.27956 8.29459i −0.502022 0.502934i
\(273\) 6.56253 + 32.3795i 0.397182 + 1.95970i
\(274\) −2.17820 10.9635i −0.131590 0.662331i
\(275\) −3.34588 −0.201764
\(276\) 20.3805 8.43103i 1.22676 0.507489i
\(277\) 12.0828i 0.725985i 0.931792 + 0.362993i \(0.118245\pi\)
−0.931792 + 0.362993i \(0.881755\pi\)
\(278\) 13.5953 2.70107i 0.815392 0.161999i
\(279\) 18.2584 1.09310
\(280\) −5.30702 5.27594i −0.317155 0.315298i
\(281\) −5.84893 −0.348918 −0.174459 0.984664i \(-0.555818\pi\)
−0.174459 + 0.984664i \(0.555818\pi\)
\(282\) 2.24913 0.446849i 0.133933 0.0266094i
\(283\) 10.1804i 0.605164i −0.953123 0.302582i \(-0.902151\pi\)
0.953123 0.302582i \(-0.0978486\pi\)
\(284\) 0.855516 + 2.06805i 0.0507655 + 0.122716i
\(285\) −20.2760 −1.20105
\(286\) 3.59841 + 18.1119i 0.212778 + 1.07098i
\(287\) 2.93900 + 14.5011i 0.173484 + 0.855970i
\(288\) 34.0205 + 22.7876i 2.00468 + 1.34277i
\(289\) 8.41554 0.495032
\(290\) 3.71924 0.738926i 0.218401 0.0433912i
\(291\) 19.4195 1.13839
\(292\) 4.52310 + 10.9338i 0.264694 + 0.639849i
\(293\) −30.6832 −1.79253 −0.896266 0.443518i \(-0.853730\pi\)
−0.896266 + 0.443518i \(0.853730\pi\)
\(294\) −26.2137 + 17.7824i −1.52882 + 1.03709i
\(295\) 0.802275i 0.0467102i
\(296\) −11.0796 + 7.39222i −0.643986 + 0.429664i
\(297\) 45.3776i 2.63308i
\(298\) −16.0366 + 3.18611i −0.928978 + 0.184566i
\(299\) 13.4497i 0.777817i
\(300\) 2.44631 + 5.91351i 0.141238 + 0.341417i
\(301\) −22.3633 + 4.53249i −1.28900 + 0.261248i
\(302\) −0.706379 + 0.140341i −0.0406475 + 0.00807571i
\(303\) 35.9412i 2.06477i
\(304\) −17.9067 17.9392i −1.02702 1.02888i
\(305\) −7.97236 −0.456496
\(306\) 29.4181 5.84468i 1.68172 0.334118i
\(307\) 25.8632i 1.47609i 0.674750 + 0.738046i \(0.264251\pi\)
−0.674750 + 0.738046i \(0.735749\pi\)
\(308\) −14.6898 + 9.88275i −0.837027 + 0.563122i
\(309\) 1.29139i 0.0734644i
\(310\) 0.695136 + 3.49883i 0.0394811 + 0.198720i
\(311\) 10.8246 0.613806 0.306903 0.951741i \(-0.400707\pi\)
0.306903 + 0.951741i \(0.400707\pi\)
\(312\) 29.3800 19.6022i 1.66331 1.10975i
\(313\) 27.8999i 1.57699i 0.615038 + 0.788497i \(0.289141\pi\)
−0.615038 + 0.788497i \(0.710859\pi\)
\(314\) −2.75307 13.8571i −0.155365 0.781999i
\(315\) 18.7697 3.80415i 1.05755 0.214339i
\(316\) −8.05905 19.4813i −0.453357 1.09591i
\(317\) 7.49682i 0.421064i −0.977587 0.210532i \(-0.932480\pi\)
0.977587 0.210532i \(-0.0675195\pi\)
\(318\) 10.0646 + 50.6580i 0.564392 + 2.84076i
\(319\) 8.97131i 0.502297i
\(320\) −3.07152 + 7.38686i −0.171703 + 0.412938i
\(321\) 57.2983i 3.19808i
\(322\) 11.8969 4.97520i 0.662991 0.277257i
\(323\) −18.5661 −1.03305
\(324\) −40.0678 + 16.5753i −2.22599 + 0.920852i
\(325\) 3.90251 0.216473
\(326\) −5.44930 27.4280i −0.301809 1.51909i
\(327\) 46.0965 2.54914
\(328\) 13.1577 8.77876i 0.726514 0.484726i
\(329\) 1.31400 0.266315i 0.0724430 0.0146824i
\(330\) 14.8504 2.95042i 0.817486 0.162415i
\(331\) 12.3429 0.678429 0.339214 0.940709i \(-0.389839\pi\)
0.339214 + 0.940709i \(0.389839\pi\)
\(332\) 3.28182 + 7.93320i 0.180113 + 0.435391i
\(333\) 34.0865i 1.86793i
\(334\) 5.68869 + 28.6329i 0.311271 + 1.56672i
\(335\) 6.37503 0.348305
\(336\) 28.2071 + 18.7370i 1.53882 + 1.02219i
\(337\) 30.1764 1.64382 0.821908 0.569620i \(-0.192910\pi\)
0.821908 + 0.569620i \(0.192910\pi\)
\(338\) −0.614449 3.09271i −0.0334216 0.168221i
\(339\) 21.9475i 1.19202i
\(340\) 2.24001 + 5.41481i 0.121482 + 0.293659i
\(341\) 8.43967 0.457034
\(342\) 63.6241 12.6406i 3.44040 0.683527i
\(343\) −15.2865 + 10.4558i −0.825392 + 0.564560i
\(344\) 13.5385 + 20.2916i 0.729946 + 1.09405i
\(345\) −11.0278 −0.593714
\(346\) −3.33914 16.8069i −0.179513 0.903545i
\(347\) −21.3398 −1.14558 −0.572789 0.819703i \(-0.694139\pi\)
−0.572789 + 0.819703i \(0.694139\pi\)
\(348\) −15.8559 + 6.55930i −0.849965 + 0.351615i
\(349\) −16.3885 −0.877255 −0.438627 0.898669i \(-0.644535\pi\)
−0.438627 + 0.898669i \(0.644535\pi\)
\(350\) 1.44358 + 3.45197i 0.0771627 + 0.184515i
\(351\) 52.9268i 2.82502i
\(352\) 15.7254 + 10.5332i 0.838168 + 0.561422i
\(353\) 3.84670i 0.204739i 0.994746 + 0.102370i \(0.0326425\pi\)
−0.994746 + 0.102370i \(0.967358\pi\)
\(354\) −0.707451 3.56082i −0.0376006 0.189255i
\(355\) 1.11901i 0.0593910i
\(356\) 1.53457 + 3.70955i 0.0813323 + 0.196606i
\(357\) 24.3099 4.92700i 1.28661 0.260765i
\(358\) 4.03256 + 20.2971i 0.213127 + 1.07273i
\(359\) 27.6613i 1.45991i 0.683495 + 0.729955i \(0.260459\pi\)
−0.683495 + 0.729955i \(0.739541\pi\)
\(360\) −11.3629 17.0309i −0.598879 0.897607i
\(361\) −21.1540 −1.11337
\(362\) −6.37660 32.0954i −0.335146 1.68689i
\(363\) 0.623698i 0.0327357i
\(364\) 17.1336 11.5269i 0.898045 0.604172i
\(365\) 5.91619i 0.309668i
\(366\) 35.3845 7.03008i 1.84958 0.367468i
\(367\) 2.94732 0.153849 0.0769244 0.997037i \(-0.475490\pi\)
0.0769244 + 0.997037i \(0.475490\pi\)
\(368\) −9.73911 9.75680i −0.507686 0.508608i
\(369\) 40.4801i 2.10731i
\(370\) 6.53194 1.29774i 0.339579 0.0674665i
\(371\) 5.99831 + 29.5957i 0.311417 + 1.53653i
\(372\) −6.17059 14.9163i −0.319930 0.773372i
\(373\) 12.6247i 0.653683i −0.945079 0.326841i \(-0.894016\pi\)
0.945079 0.326841i \(-0.105984\pi\)
\(374\) 13.5980 2.70161i 0.703136 0.139697i
\(375\) 3.19977i 0.165235i
\(376\) −0.795478 1.19227i −0.0410236 0.0614868i
\(377\) 10.4638i 0.538914i
\(378\) −46.8164 + 19.5782i −2.40798 + 1.00699i
\(379\) −20.9882 −1.07809 −0.539045 0.842277i \(-0.681215\pi\)
−0.539045 + 0.842277i \(0.681215\pi\)
\(380\) 4.84460 + 11.7109i 0.248523 + 0.600758i
\(381\) −18.7954 −0.962919
\(382\) 3.35060 0.665686i 0.171432 0.0340595i
\(383\) −11.4237 −0.583724 −0.291862 0.956460i \(-0.594275\pi\)
−0.291862 + 0.956460i \(0.594275\pi\)
\(384\) 7.11887 35.4944i 0.363283 1.81131i
\(385\) 8.67597 1.75840i 0.442168 0.0896166i
\(386\) 2.03533 + 10.2444i 0.103596 + 0.521428i
\(387\) −62.4277 −3.17338
\(388\) −4.63995 11.2162i −0.235558 0.569417i
\(389\) 22.7966i 1.15583i 0.816096 + 0.577917i \(0.196134\pi\)
−0.816096 + 0.577917i \(0.803866\pi\)
\(390\) −17.3209 + 3.44126i −0.877080 + 0.174255i
\(391\) −10.0978 −0.510666
\(392\) 16.5340 + 10.8916i 0.835093 + 0.550109i
\(393\) −14.3247 −0.722586
\(394\) −29.0328 + 5.76814i −1.46265 + 0.290595i
\(395\) 10.5412i 0.530385i
\(396\) −44.7596 + 18.5163i −2.24926 + 0.930477i
\(397\) −29.8779 −1.49953 −0.749763 0.661706i \(-0.769833\pi\)
−0.749763 + 0.661706i \(0.769833\pi\)
\(398\) 1.34938 + 6.79186i 0.0676385 + 0.340445i
\(399\) 52.5763 10.6559i 2.63211 0.533463i
\(400\) 2.83099 2.82586i 0.141550 0.141293i
\(401\) −16.8397 −0.840933 −0.420467 0.907308i \(-0.638134\pi\)
−0.420467 + 0.907308i \(0.638134\pi\)
\(402\) −28.2950 + 5.62154i −1.41122 + 0.280377i
\(403\) −9.84372 −0.490351
\(404\) −20.7587 + 8.58752i −1.03279 + 0.427245i
\(405\) 21.6805 1.07731
\(406\) −9.25576 + 3.87068i −0.459356 + 0.192098i
\(407\) 15.7559i 0.780993i
\(408\) −14.7169 22.0579i −0.728595 1.09203i
\(409\) 26.9755i 1.33385i 0.745123 + 0.666927i \(0.232391\pi\)
−0.745123 + 0.666927i \(0.767609\pi\)
\(410\) −7.75712 + 1.54116i −0.383097 + 0.0761124i
\(411\) 25.2906i 1.24750i
\(412\) −0.745872 + 0.308554i −0.0367465 + 0.0152014i
\(413\) −0.421630 2.08032i −0.0207470 0.102366i
\(414\) 34.6040 6.87501i 1.70069 0.337888i
\(415\) 4.29261i 0.210716i
\(416\) −18.3416 12.2856i −0.899269 0.602349i
\(417\) 31.3616 1.53579
\(418\) 29.4092 5.84292i 1.43845 0.285787i
\(419\) 15.0474i 0.735114i 0.930001 + 0.367557i \(0.119806\pi\)
−0.930001 + 0.367557i \(0.880194\pi\)
\(420\) −9.45117 14.0483i −0.461170 0.685485i
\(421\) 27.5257i 1.34152i −0.741674 0.670761i \(-0.765968\pi\)
0.741674 0.670761i \(-0.234032\pi\)
\(422\) −0.621297 3.12718i −0.0302443 0.152229i
\(423\) 3.66806 0.178347
\(424\) 26.8540 17.9169i 1.30415 0.870121i
\(425\) 2.92992i 0.142122i
\(426\) 0.986752 + 4.96662i 0.0478083 + 0.240634i
\(427\) 20.6726 4.18982i 1.00042 0.202759i
\(428\) −33.0941 + 13.6904i −1.59966 + 0.661752i
\(429\) 41.7805i 2.01718i
\(430\) −2.37675 11.9629i −0.114617 0.576903i
\(431\) 22.5778i 1.08753i 0.839236 + 0.543767i \(0.183002\pi\)
−0.839236 + 0.543767i \(0.816998\pi\)
\(432\) 38.3250 + 38.3946i 1.84391 + 1.84726i
\(433\) 23.4737i 1.12808i −0.825749 0.564038i \(-0.809247\pi\)
0.825749 0.564038i \(-0.190753\pi\)
\(434\) −3.64130 8.70726i −0.174788 0.417962i
\(435\) 8.57954 0.411357
\(436\) −11.0140 26.6242i −0.527473 1.27507i
\(437\) −21.8390 −1.04470
\(438\) 5.21694 + 26.2585i 0.249275 + 1.25468i
\(439\) −12.3485 −0.589363 −0.294681 0.955596i \(-0.595214\pi\)
−0.294681 + 0.955596i \(0.595214\pi\)
\(440\) −5.25233 7.87226i −0.250395 0.375295i
\(441\) −46.6711 + 19.7285i −2.22243 + 0.939454i
\(442\) −15.8602 + 3.15106i −0.754394 + 0.149880i
\(443\) 24.9234 1.18415 0.592074 0.805883i \(-0.298309\pi\)
0.592074 + 0.805883i \(0.298309\pi\)
\(444\) −27.8470 + 11.5198i −1.32156 + 0.546707i
\(445\) 2.00722i 0.0951512i
\(446\) −6.74686 33.9590i −0.319473 1.60801i
\(447\) −36.9933 −1.74972
\(448\) 4.08244 20.7686i 0.192877 0.981223i
\(449\) 33.7360 1.59210 0.796051 0.605230i \(-0.206919\pi\)
0.796051 + 0.605230i \(0.206919\pi\)
\(450\) 1.99482 + 10.0406i 0.0940368 + 0.473316i
\(451\) 18.7112i 0.881078i
\(452\) 12.6763 5.24397i 0.596244 0.246656i
\(453\) −1.62947 −0.0765594
\(454\) 7.15992 1.42251i 0.336032 0.0667616i
\(455\) −10.1193 + 2.05094i −0.474402 + 0.0961495i
\(456\) −31.8291 47.7058i −1.49053 2.23403i
\(457\) −23.0696 −1.07915 −0.539576 0.841937i \(-0.681416\pi\)
−0.539576 + 0.841937i \(0.681416\pi\)
\(458\) −2.61529 13.1635i −0.122204 0.615092i
\(459\) 39.7363 1.85473
\(460\) 2.63489 + 6.36936i 0.122852 + 0.296973i
\(461\) 4.90911 0.228640 0.114320 0.993444i \(-0.463531\pi\)
0.114320 + 0.993444i \(0.463531\pi\)
\(462\) −36.9569 + 15.4550i −1.71939 + 0.719034i
\(463\) 30.9829i 1.43990i −0.694027 0.719949i \(-0.744165\pi\)
0.694027 0.719949i \(-0.255835\pi\)
\(464\) 7.57698 + 7.59074i 0.351752 + 0.352391i
\(465\) 8.07111i 0.374289i
\(466\) 0.703339 + 3.54012i 0.0325815 + 0.163993i
\(467\) 20.4881i 0.948078i −0.880504 0.474039i \(-0.842796\pi\)
0.880504 0.474039i \(-0.157204\pi\)
\(468\) 52.2060 21.5967i 2.41322 0.998308i
\(469\) −16.5306 + 3.35035i −0.763314 + 0.154705i
\(470\) 0.139650 + 0.702903i 0.00644159 + 0.0324225i
\(471\) 31.9655i 1.47289i
\(472\) −1.88761 + 1.25940i −0.0868842 + 0.0579687i
\(473\) −28.8562 −1.32681
\(474\) −9.29531 46.7861i −0.426948 2.14896i
\(475\) 6.33672i 0.290749i
\(476\) −8.65413 12.8635i −0.396661 0.589600i
\(477\) 82.6171i 3.78278i
\(478\) −11.3128 + 2.24759i −0.517437 + 0.102803i
\(479\) −35.1704 −1.60698 −0.803489 0.595319i \(-0.797026\pi\)
−0.803489 + 0.595319i \(0.797026\pi\)
\(480\) −10.0732 + 15.0387i −0.459778 + 0.686419i
\(481\) 18.3772i 0.837926i
\(482\) 3.70014 0.735132i 0.168537 0.0334843i
\(483\) 28.5953 5.79556i 1.30113 0.263707i
\(484\) −0.360233 + 0.149022i −0.0163742 + 0.00677372i
\(485\) 6.06903i 0.275580i
\(486\) −39.7901 + 7.90535i −1.80491 + 0.358594i
\(487\) 7.86977i 0.356614i −0.983975 0.178307i \(-0.942938\pi\)
0.983975 0.178307i \(-0.0570619\pi\)
\(488\) −12.5149 18.7575i −0.566524 0.849113i
\(489\) 63.2708i 2.86121i
\(490\) −5.55741 8.19239i −0.251058 0.370094i
\(491\) 2.88992 0.130420 0.0652102 0.997872i \(-0.479228\pi\)
0.0652102 + 0.997872i \(0.479228\pi\)
\(492\) 33.0702 13.6806i 1.49092 0.616768i
\(493\) 7.85601 0.353817
\(494\) −34.3018 + 6.81497i −1.54331 + 0.306620i
\(495\) 24.2192 1.08857
\(496\) −7.14091 + 7.12796i −0.320636 + 0.320055i
\(497\) 0.588089 + 2.90163i 0.0263794 + 0.130156i
\(498\) 3.78525 + 19.0523i 0.169621 + 0.853756i
\(499\) 16.5134 0.739240 0.369620 0.929183i \(-0.379488\pi\)
0.369620 + 0.929183i \(0.379488\pi\)
\(500\) −1.84811 + 0.764529i −0.0826498 + 0.0341908i
\(501\) 66.0504i 2.95092i
\(502\) −11.8215 + 2.34866i −0.527619 + 0.104826i
\(503\) −7.23320 −0.322513 −0.161256 0.986913i \(-0.551555\pi\)
−0.161256 + 0.986913i \(0.551555\pi\)
\(504\) 38.4149 + 38.1899i 1.71114 + 1.70112i
\(505\) 11.2324 0.499837
\(506\) 15.9951 3.17786i 0.711070 0.141273i
\(507\) 7.13426i 0.316843i
\(508\) 4.49084 + 10.8558i 0.199249 + 0.481647i
\(509\) 26.3986 1.17010 0.585048 0.810999i \(-0.301076\pi\)
0.585048 + 0.810999i \(0.301076\pi\)
\(510\) 2.58363 + 13.0042i 0.114405 + 0.575835i
\(511\) 3.10921 + 15.3409i 0.137543 + 0.678640i
\(512\) −22.2016 + 4.36908i −0.981181 + 0.193088i
\(513\) 85.9401 3.79435
\(514\) −19.6238 + 3.89879i −0.865569 + 0.171968i
\(515\) 0.403587 0.0177842
\(516\) 21.0980 + 51.0004i 0.928786 + 2.24517i
\(517\) 1.69550 0.0745679
\(518\) −16.2555 + 6.79790i −0.714226 + 0.298683i
\(519\) 38.7702i 1.70182i
\(520\) 6.12613 + 9.18191i 0.268648 + 0.402654i
\(521\) 29.5635i 1.29520i −0.761981 0.647599i \(-0.775773\pi\)
0.761981 0.647599i \(-0.224227\pi\)
\(522\) −26.9217 + 5.34872i −1.17833 + 0.234107i
\(523\) 21.6311i 0.945862i −0.881100 0.472931i \(-0.843196\pi\)
0.881100 0.472931i \(-0.156804\pi\)
\(524\) 3.42264 + 8.27359i 0.149519 + 0.361434i
\(525\) 1.68161 + 8.29709i 0.0733917 + 0.362115i
\(526\) 43.1969 8.58221i 1.88347 0.374202i
\(527\) 7.39046i 0.321933i
\(528\) 30.2538 + 30.3087i 1.31663 + 1.31902i
\(529\) 11.1222 0.483572
\(530\) −15.8318 + 3.14540i −0.687688 + 0.136628i
\(531\) 5.80727i 0.252014i
\(532\) −18.7168 27.8207i −0.811476 1.20618i
\(533\) 21.8241i 0.945307i
\(534\) 1.76998 + 8.90883i 0.0765944 + 0.385523i
\(535\) 17.9070 0.774188
\(536\) 10.0075 + 14.9993i 0.432256 + 0.647871i
\(537\) 46.8213i 2.02049i
\(538\) 0.384626 + 1.93594i 0.0165824 + 0.0834643i
\(539\) −21.5729 + 9.11919i −0.929212 + 0.392791i
\(540\) −10.3687 25.0645i −0.446199 1.07860i
\(541\) 3.88138i 0.166874i 0.996513 + 0.0834368i \(0.0265897\pi\)
−0.996513 + 0.0834368i \(0.973410\pi\)
\(542\) 6.19138 + 31.1631i 0.265942 + 1.33857i
\(543\) 74.0375i 3.17725i
\(544\) −9.22373 + 13.7705i −0.395464 + 0.590403i
\(545\) 14.4062i 0.617094i
\(546\) 43.1052 18.0262i 1.84473 0.771450i
\(547\) −4.88320 −0.208791 −0.104395 0.994536i \(-0.533291\pi\)
−0.104395 + 0.994536i \(0.533291\pi\)
\(548\) −14.6072 + 6.04276i −0.623991 + 0.258134i
\(549\) 57.7080 2.46292
\(550\) 0.922074 + 4.64108i 0.0393174 + 0.197896i
\(551\) 16.9906 0.723826
\(552\) −17.3113 25.9463i −0.736816 1.10435i
\(553\) −5.53985 27.3337i −0.235579 1.16235i
\(554\) 16.7601 3.32984i 0.712068 0.141471i
\(555\) 15.0679 0.639596
\(556\) −7.49332 18.1137i −0.317788 0.768192i
\(557\) 44.6377i 1.89136i −0.325099 0.945680i \(-0.605398\pi\)
0.325099 0.945680i \(-0.394602\pi\)
\(558\) −5.03175 25.3263i −0.213011 1.07215i
\(559\) 33.6568 1.42353
\(560\) −5.85574 + 8.81535i −0.247450 + 0.372516i
\(561\) 31.3679 1.32435
\(562\) 1.61188 + 8.11306i 0.0679928 + 0.342229i
\(563\) 28.5884i 1.20486i 0.798172 + 0.602429i \(0.205800\pi\)
−0.798172 + 0.602429i \(0.794200\pi\)
\(564\) −1.23965 2.99662i −0.0521987 0.126181i
\(565\) −6.85909 −0.288564
\(566\) −14.1213 + 2.80557i −0.593563 + 0.117927i
\(567\) −56.2181 + 11.3940i −2.36094 + 0.478504i
\(568\) 2.63283 1.75661i 0.110471 0.0737058i
\(569\) −5.12489 −0.214846 −0.107423 0.994213i \(-0.534260\pi\)
−0.107423 + 0.994213i \(0.534260\pi\)
\(570\) 5.58776 + 28.1249i 0.234046 + 1.17802i
\(571\) 36.7465 1.53779 0.768897 0.639373i \(-0.220806\pi\)
0.768897 + 0.639373i \(0.220806\pi\)
\(572\) 24.1314 9.98272i 1.00898 0.417398i
\(573\) 7.72916 0.322890
\(574\) 19.3045 8.07297i 0.805754 0.336959i
\(575\) 3.44642i 0.143726i
\(576\) 22.2332 53.4699i 0.926385 2.22791i
\(577\) 2.55301i 0.106283i −0.998587 0.0531417i \(-0.983076\pi\)
0.998587 0.0531417i \(-0.0169235\pi\)
\(578\) −2.31920 11.6732i −0.0964658 0.485542i
\(579\) 23.6319i 0.982106i
\(580\) −2.04993 4.95533i −0.0851187 0.205759i
\(581\) 2.25595 + 11.1309i 0.0935926 + 0.461786i
\(582\) −5.35171 26.9368i −0.221836 1.11657i
\(583\) 38.1884i 1.58160i
\(584\) 13.9197 9.28718i 0.576003 0.384306i
\(585\) −28.2484 −1.16793
\(586\) 8.45582 + 42.5607i 0.349307 + 1.75817i
\(587\) 33.3508i 1.37653i −0.725457 0.688267i \(-0.758372\pi\)
0.725457 0.688267i \(-0.241628\pi\)
\(588\) 31.8901 + 31.4606i 1.31513 + 1.29741i
\(589\) 15.9838i 0.658600i
\(590\) 1.11284 0.221095i 0.0458148 0.00910232i
\(591\) −66.9728 −2.75489
\(592\) 13.3071 + 13.3313i 0.546920 + 0.547913i
\(593\) 10.9350i 0.449048i −0.974469 0.224524i \(-0.927917\pi\)
0.974469 0.224524i \(-0.0720827\pi\)
\(594\) −62.9434 + 12.5054i −2.58260 + 0.513102i
\(595\) 1.53980 + 7.59738i 0.0631257 + 0.311462i
\(596\) 8.83891 + 21.3664i 0.362056 + 0.875203i
\(597\) 15.6675i 0.641227i
\(598\) −18.6561 + 3.70654i −0.762906 + 0.151572i
\(599\) 25.8459i 1.05603i 0.849234 + 0.528017i \(0.177064\pi\)
−0.849234 + 0.528017i \(0.822936\pi\)
\(600\) 7.52847 5.02296i 0.307349 0.205061i
\(601\) 6.70199i 0.273380i 0.990614 + 0.136690i \(0.0436464\pi\)
−0.990614 + 0.136690i \(0.956354\pi\)
\(602\) 12.4500 + 29.7711i 0.507425 + 1.21338i
\(603\) −46.1457 −1.87920
\(604\) 0.389334 + 0.941144i 0.0158418 + 0.0382946i
\(605\) 0.194920 0.00792462
\(606\) −49.8541 + 9.90484i −2.02518 + 0.402357i
\(607\) 37.4686 1.52080 0.760402 0.649453i \(-0.225002\pi\)
0.760402 + 0.649453i \(0.225002\pi\)
\(608\) −19.9487 + 29.7822i −0.809026 + 1.20783i
\(609\) −22.2470 + 4.50891i −0.901494 + 0.182710i
\(610\) 2.19706 + 11.0585i 0.0889564 + 0.447745i
\(611\) −1.97757 −0.0800038
\(612\) −16.2143 39.1952i −0.655426 1.58437i
\(613\) 20.0776i 0.810928i 0.914111 + 0.405464i \(0.132890\pi\)
−0.914111 + 0.405464i \(0.867110\pi\)
\(614\) 35.8750 7.12751i 1.44780 0.287643i
\(615\) −17.8941 −0.721561
\(616\) 17.7567 + 17.6527i 0.715436 + 0.711246i
\(617\) 27.8737 1.12215 0.561077 0.827764i \(-0.310387\pi\)
0.561077 + 0.827764i \(0.310387\pi\)
\(618\) −1.79128 + 0.355886i −0.0720560 + 0.0143158i
\(619\) 25.0328i 1.00615i −0.864242 0.503076i \(-0.832202\pi\)
0.864242 0.503076i \(-0.167798\pi\)
\(620\) 4.66167 1.92845i 0.187217 0.0774485i
\(621\) 46.7412 1.87566
\(622\) −2.98309 15.0148i −0.119611 0.602039i
\(623\) 1.05488 + 5.20477i 0.0422628 + 0.208525i
\(624\) −35.2869 35.3510i −1.41261 1.41517i
\(625\) 1.00000 0.0400000
\(626\) 38.7000 7.68879i 1.54676 0.307306i
\(627\) 67.8412 2.70931
\(628\) −18.4625 + 7.63759i −0.736732 + 0.304773i
\(629\) 13.7972 0.550129
\(630\) −10.4494 24.9871i −0.416313 0.995509i
\(631\) 17.2836i 0.688048i −0.938961 0.344024i \(-0.888210\pi\)
0.938961 0.344024i \(-0.111790\pi\)
\(632\) −24.8016 + 16.5475i −0.986553 + 0.658223i
\(633\) 7.21378i 0.286722i
\(634\) −10.3989 + 2.06601i −0.412992 + 0.0820518i
\(635\) 5.87400i 0.233103i
\(636\) 67.4942 27.9211i 2.67632 1.10714i
\(637\) 25.1619 10.6363i 0.996950 0.421425i
\(638\) −12.4441 + 2.47236i −0.492668 + 0.0978815i
\(639\) 8.09997i 0.320430i
\(640\) 11.0928 + 2.22481i 0.438481 + 0.0879433i
\(641\) −5.40646 −0.213542 −0.106771 0.994284i \(-0.534051\pi\)
−0.106771 + 0.994284i \(0.534051\pi\)
\(642\) −79.4786 + 15.7905i −3.13677 + 0.623203i
\(643\) 8.51562i 0.335823i 0.985802 + 0.167912i \(0.0537024\pi\)
−0.985802 + 0.167912i \(0.946298\pi\)
\(644\) −10.1797 15.1312i −0.401137 0.596252i
\(645\) 27.5960i 1.08659i
\(646\) 5.11654 + 25.7531i 0.201307 + 1.01324i
\(647\) 9.29106 0.365269 0.182635 0.983181i \(-0.441537\pi\)
0.182635 + 0.983181i \(0.441537\pi\)
\(648\) 34.0338 + 51.0102i 1.33697 + 2.00387i
\(649\) 2.68432i 0.105369i
\(650\) −1.07547 5.41319i −0.0421835 0.212323i
\(651\) −4.24171 20.9286i −0.166246 0.820257i
\(652\) −36.5437 + 15.1175i −1.43116 + 0.592045i
\(653\) 13.4994i 0.528272i 0.964486 + 0.264136i \(0.0850867\pi\)
−0.964486 + 0.264136i \(0.914913\pi\)
\(654\) −12.7035 63.9405i −0.496746 2.50027i
\(655\) 4.47680i 0.174923i
\(656\) −15.8031 15.8318i −0.617008 0.618128i
\(657\) 42.8244i 1.67074i
\(658\) −0.731523 1.74926i −0.0285177 0.0681931i
\(659\) −32.9215 −1.28244 −0.641219 0.767358i \(-0.721571\pi\)
−0.641219 + 0.767358i \(0.721571\pi\)
\(660\) −8.18507 19.7859i −0.318604 0.770165i
\(661\) −28.6462 −1.11421 −0.557104 0.830443i \(-0.688088\pi\)
−0.557104 + 0.830443i \(0.688088\pi\)
\(662\) −3.40152 17.1209i −0.132204 0.665423i
\(663\) −36.5864 −1.42090
\(664\) 10.0997 6.73849i 0.391946 0.261504i
\(665\) 3.33022 + 16.4313i 0.129140 + 0.637179i
\(666\) −47.2815 + 9.39373i −1.83212 + 0.364000i
\(667\) 9.24090 0.357809
\(668\) 38.1491 15.7816i 1.47603 0.610608i
\(669\) 78.3367i 3.02867i
\(670\) −1.75686 8.84282i −0.0678735 0.341628i
\(671\) 26.6746 1.02976
\(672\) 18.2167 44.2897i 0.702724 1.70851i
\(673\) 4.30988 0.166134 0.0830669 0.996544i \(-0.473528\pi\)
0.0830669 + 0.996544i \(0.473528\pi\)
\(674\) −8.31617 41.8578i −0.320327 1.61230i
\(675\) 13.5622i 0.522011i
\(676\) −4.12057 + 1.70461i −0.158483 + 0.0655618i
\(677\) −23.3619 −0.897870 −0.448935 0.893564i \(-0.648197\pi\)
−0.448935 + 0.893564i \(0.648197\pi\)
\(678\) 30.4434 6.04840i 1.16917 0.232287i
\(679\) −3.18954 15.7372i −0.122403 0.603937i
\(680\) 6.89358 4.59936i 0.264357 0.176378i
\(681\) 16.5165 0.632913
\(682\) −2.32584 11.7067i −0.0890612 0.448272i
\(683\) 40.0020 1.53063 0.765317 0.643653i \(-0.222582\pi\)
0.765317 + 0.643653i \(0.222582\pi\)
\(684\) −35.0677 84.7696i −1.34085 3.24125i
\(685\) 7.90390 0.301993
\(686\) 18.7160 + 18.3225i 0.714579 + 0.699554i
\(687\) 30.3656i 1.15852i
\(688\) 24.4156 24.3713i 0.930835 0.929148i
\(689\) 44.5416i 1.69690i
\(690\) 3.03908 + 15.2966i 0.115696 + 0.582333i
\(691\) 38.8983i 1.47976i 0.672738 + 0.739881i \(0.265118\pi\)
−0.672738 + 0.739881i \(0.734882\pi\)
\(692\) −22.3927 + 9.26346i −0.851242 + 0.352144i
\(693\) −62.8011 + 12.7282i −2.38562 + 0.483505i
\(694\) 5.88091 + 29.6004i 0.223236 + 1.12362i
\(695\) 9.80123i 0.371782i
\(696\) 13.4681 + 20.1861i 0.510506 + 0.765152i
\(697\) −16.3851 −0.620629
\(698\) 4.51641 + 22.7325i 0.170949 + 0.860437i
\(699\) 8.16634i 0.308880i
\(700\) 4.39040 2.95370i 0.165942 0.111640i
\(701\) 3.06613i 0.115806i 0.998322 + 0.0579031i \(0.0184415\pi\)
−0.998322 + 0.0579031i \(0.981559\pi\)
\(702\) 73.4149 14.5858i 2.77087 0.550507i
\(703\) 29.8400 1.12544
\(704\) 10.2769 24.7156i 0.387327 0.931503i
\(705\) 1.62146i 0.0610676i
\(706\) 5.33577 1.06009i 0.200814 0.0398971i
\(707\) −29.1260 + 5.90313i −1.09540 + 0.222010i
\(708\) −4.74426 + 1.96261i −0.178300 + 0.0737596i
\(709\) 38.5857i 1.44912i 0.689214 + 0.724558i \(0.257956\pi\)
−0.689214 + 0.724558i \(0.742044\pi\)
\(710\) −1.55218 + 0.308382i −0.0582524 + 0.0115734i
\(711\) 76.3026i 2.86157i
\(712\) 4.72262 3.15091i 0.176988 0.118085i
\(713\) 8.69328i 0.325566i
\(714\) −13.5337 32.3624i −0.506485 1.21113i
\(715\) −13.0573 −0.488317
\(716\) 27.0428 11.1871i 1.01064 0.418083i
\(717\) −26.0964 −0.974589
\(718\) 38.3691 7.62305i 1.43192 0.284490i
\(719\) 31.4806 1.17403 0.587014 0.809577i \(-0.300303\pi\)
0.587014 + 0.809577i \(0.300303\pi\)
\(720\) −20.4922 + 20.4550i −0.763698 + 0.762313i
\(721\) −1.04651 + 0.212103i −0.0389742 + 0.00789911i
\(722\) 5.82972 + 29.3428i 0.216960 + 1.09202i
\(723\) 8.53548 0.317438
\(724\) −42.7622 + 17.6900i −1.58925 + 0.657443i
\(725\) 2.68130i 0.0995810i
\(726\) −0.865133 + 0.171882i −0.0321081 + 0.00637913i
\(727\) −1.97285 −0.0731689 −0.0365844 0.999331i \(-0.511648\pi\)
−0.0365844 + 0.999331i \(0.511648\pi\)
\(728\) −20.7107 20.5894i −0.767590 0.763095i
\(729\) −26.7463 −0.990603
\(730\) −8.20636 + 1.63041i −0.303731 + 0.0603443i
\(731\) 25.2688i 0.934601i
\(732\) −19.5029 47.1446i −0.720847 1.74251i
\(733\) 1.04466 0.0385855 0.0192928 0.999814i \(-0.493859\pi\)
0.0192928 + 0.999814i \(0.493859\pi\)
\(734\) −0.812236 4.08823i −0.0299802 0.150899i
\(735\) −8.72096 20.6308i −0.321677 0.760980i
\(736\) −10.8497 + 16.1980i −0.399926 + 0.597065i
\(737\) −21.3301 −0.785704
\(738\) 56.1500 11.1557i 2.06691 0.410646i
\(739\) −33.3529 −1.22691 −0.613454 0.789730i \(-0.710220\pi\)
−0.613454 + 0.789730i \(0.710220\pi\)
\(740\) −3.60021 8.70283i −0.132346 0.319922i
\(741\) −79.1275 −2.90682
\(742\) 39.3992 16.4764i 1.44639 0.604868i
\(743\) 2.33616i 0.0857054i 0.999081 + 0.0428527i \(0.0136446\pi\)
−0.999081 + 0.0428527i \(0.986355\pi\)
\(744\) −18.9899 + 12.6699i −0.696202 + 0.464503i
\(745\) 11.5613i 0.423572i
\(746\) −17.5118 + 3.47918i −0.641151 + 0.127382i
\(747\) 31.0721i 1.13687i
\(748\) −7.49481 18.1173i −0.274037 0.662435i
\(749\) −46.4334 + 9.41091i −1.69664 + 0.343867i
\(750\) −4.43840 + 0.881807i −0.162068 + 0.0321990i
\(751\) 22.6980i 0.828261i 0.910218 + 0.414130i \(0.135914\pi\)
−0.910218 + 0.414130i \(0.864086\pi\)
\(752\) −1.43458 + 1.43198i −0.0523138 + 0.0522190i
\(753\) −27.2698 −0.993768
\(754\) 14.5144 2.88367i 0.528583 0.105017i
\(755\) 0.509248i 0.0185334i
\(756\) 40.0588 + 59.5437i 1.45693 + 2.16558i
\(757\) 0.859830i 0.0312510i 0.999878 + 0.0156255i \(0.00497396\pi\)
−0.999878 + 0.0156255i \(0.995026\pi\)
\(758\) 5.78402 + 29.1128i 0.210085 + 1.05742i
\(759\) 36.8976 1.33930
\(760\) 14.9092 9.94731i 0.540812 0.360827i
\(761\) 9.59745i 0.347907i 0.984754 + 0.173954i \(0.0556543\pi\)
−0.984754 + 0.173954i \(0.944346\pi\)
\(762\) 5.17974 + 26.0712i 0.187642 + 0.944460i
\(763\) −7.57108 37.3557i −0.274091 1.35237i
\(764\) −1.84675 4.46417i −0.0668130 0.161508i
\(765\) 21.2083i 0.766787i
\(766\) 3.14820 + 15.8458i 0.113749 + 0.572533i
\(767\) 3.13089i 0.113050i
\(768\) −51.1962 0.0928907i −1.84738 0.00335191i
\(769\) 46.0671i 1.66122i 0.556854 + 0.830610i \(0.312008\pi\)
−0.556854 + 0.830610i \(0.687992\pi\)
\(770\) −4.83005 11.5499i −0.174063 0.416228i
\(771\) −45.2682 −1.63029
\(772\) 13.6492 5.64642i 0.491244 0.203219i
\(773\) −7.98484 −0.287195 −0.143597 0.989636i \(-0.545867\pi\)
−0.143597 + 0.989636i \(0.545867\pi\)
\(774\) 17.2041 + 86.5937i 0.618390 + 3.11254i
\(775\) −2.52241 −0.0906075
\(776\) −14.2793 + 9.52710i −0.512598 + 0.342003i
\(777\) −39.0715 + 7.91882i −1.40168 + 0.284086i
\(778\) 31.6212 6.28240i 1.13368 0.225235i
\(779\) −35.4370 −1.26966