Properties

Label 600.2.d.e.349.6
Level 600
Weight 2
Character 600.349
Analytic conductor 4.791
Analytic rank 0
Dimension 6
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) \(=\) \( 600 = 2^{3} \cdot 3 \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 600.d (of order \(2\), degree \(1\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(4.79102412128\)
Analytic rank: \(0\)
Dimension: \(6\)
Coefficient field: 6.0.399424.1
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{3} \)
Twist minimal: no (minimal twist has level 120)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 349.6
Root \(0.264658 + 1.38923i\) of \(x^{6} - 2 x^{5} + 3 x^{4} - 6 x^{3} + 6 x^{2} - 8 x + 8\)
Character \(\chi\) \(=\) 600.349
Dual form 600.2.d.e.349.5

$q$-expansion

\(f(q)\) \(=\) \(q+(1.38923 + 0.264658i) q^{2} -1.00000 q^{3} +(1.85991 + 0.735342i) q^{4} +(-1.38923 - 0.264658i) q^{6} +0.941367i q^{7} +(2.38923 + 1.51380i) q^{8} +1.00000 q^{9} +O(q^{10})\) \(q+(1.38923 + 0.264658i) q^{2} -1.00000 q^{3} +(1.85991 + 0.735342i) q^{4} +(-1.38923 - 0.264658i) q^{6} +0.941367i q^{7} +(2.38923 + 1.51380i) q^{8} +1.00000 q^{9} -4.49828i q^{11} +(-1.85991 - 0.735342i) q^{12} +5.55691 q^{13} +(-0.249141 + 1.30777i) q^{14} +(2.91855 + 2.73534i) q^{16} +7.55691i q^{17} +(1.38923 + 0.264658i) q^{18} +1.05863i q^{19} -0.941367i q^{21} +(1.19051 - 6.24914i) q^{22} +1.05863i q^{23} +(-2.38923 - 1.51380i) q^{24} +(7.71982 + 1.47068i) q^{26} -1.00000 q^{27} +(-0.692226 + 1.75086i) q^{28} -2.00000i q^{29} +3.55691 q^{31} +(3.33060 + 4.57243i) q^{32} +4.49828i q^{33} +(-2.00000 + 10.4983i) q^{34} +(1.85991 + 0.735342i) q^{36} -7.43965 q^{37} +(-0.280176 + 1.47068i) q^{38} -5.55691 q^{39} -3.88273 q^{41} +(0.249141 - 1.30777i) q^{42} +1.88273 q^{43} +(3.30777 - 8.36641i) q^{44} +(-0.280176 + 1.47068i) q^{46} -10.0552i q^{47} +(-2.91855 - 2.73534i) q^{48} +6.11383 q^{49} -7.55691i q^{51} +(10.3354 + 4.08623i) q^{52} -2.00000 q^{53} +(-1.38923 - 0.264658i) q^{54} +(-1.42504 + 2.24914i) q^{56} -1.05863i q^{57} +(0.529317 - 2.77846i) q^{58} -8.49828i q^{59} -8.99656i q^{61} +(4.94137 + 0.941367i) q^{62} +0.941367i q^{63} +(3.41683 + 7.23362i) q^{64} +(-1.19051 + 6.24914i) q^{66} -4.00000 q^{67} +(-5.55691 + 14.0552i) q^{68} -1.05863i q^{69} -12.9966 q^{71} +(2.38923 + 1.51380i) q^{72} +6.00000i q^{73} +(-10.3354 - 1.96896i) q^{74} +(-0.778457 + 1.96896i) q^{76} +4.23453 q^{77} +(-7.71982 - 1.47068i) q^{78} -11.5569 q^{79} +1.00000 q^{81} +(-5.39400 - 1.02760i) q^{82} -5.88273 q^{83} +(0.692226 - 1.75086i) q^{84} +(2.61555 + 0.498281i) q^{86} +2.00000i q^{87} +(6.80949 - 10.7474i) q^{88} +4.11727 q^{89} +5.23109i q^{91} +(-0.778457 + 1.96896i) q^{92} -3.55691 q^{93} +(2.66119 - 13.9690i) q^{94} +(-3.33060 - 4.57243i) q^{96} +17.1138i q^{97} +(8.49351 + 1.61808i) q^{98} -4.49828i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6q - 6q^{3} + 2q^{4} + 6q^{8} + 6q^{9} + O(q^{10}) \) \( 6q - 6q^{3} + 2q^{4} + 6q^{8} + 6q^{9} - 2q^{12} + 16q^{14} + 10q^{16} - 12q^{22} - 6q^{24} + 28q^{26} - 6q^{27} - 20q^{28} - 12q^{31} + 10q^{32} - 12q^{34} + 2q^{36} - 8q^{37} - 20q^{38} - 20q^{41} - 16q^{42} + 8q^{43} + 4q^{44} - 20q^{46} - 10q^{48} - 30q^{49} + 12q^{52} - 12q^{53} + 4q^{56} + 4q^{58} + 28q^{62} - 22q^{64} + 12q^{66} - 24q^{67} - 8q^{71} + 6q^{72} - 12q^{74} + 12q^{76} + 32q^{77} - 28q^{78} - 36q^{79} + 6q^{81} + 16q^{82} - 32q^{83} + 20q^{84} - 16q^{86} + 60q^{88} + 28q^{89} + 12q^{92} + 12q^{93} - 4q^{94} - 10q^{96} + 56q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/600\mathbb{Z}\right)^\times\).

\(n\) \(151\) \(301\) \(401\) \(577\)
\(\chi(n)\) \(1\) \(-1\) \(1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.38923 + 0.264658i 0.982333 + 0.187142i
\(3\) −1.00000 −0.577350
\(4\) 1.85991 + 0.735342i 0.929956 + 0.367671i
\(5\) 0 0
\(6\) −1.38923 0.264658i −0.567150 0.108046i
\(7\) 0.941367i 0.355803i 0.984048 + 0.177902i \(0.0569309\pi\)
−0.984048 + 0.177902i \(0.943069\pi\)
\(8\) 2.38923 + 1.51380i 0.844720 + 0.535209i
\(9\) 1.00000 0.333333
\(10\) 0 0
\(11\) 4.49828i 1.35628i −0.734931 0.678141i \(-0.762786\pi\)
0.734931 0.678141i \(-0.237214\pi\)
\(12\) −1.85991 0.735342i −0.536910 0.212275i
\(13\) 5.55691 1.54121 0.770605 0.637313i \(-0.219954\pi\)
0.770605 + 0.637313i \(0.219954\pi\)
\(14\) −0.249141 + 1.30777i −0.0665856 + 0.349517i
\(15\) 0 0
\(16\) 2.91855 + 2.73534i 0.729636 + 0.683835i
\(17\) 7.55691i 1.83282i 0.400240 + 0.916410i \(0.368927\pi\)
−0.400240 + 0.916410i \(0.631073\pi\)
\(18\) 1.38923 + 0.264658i 0.327444 + 0.0623806i
\(19\) 1.05863i 0.242867i 0.992600 + 0.121434i \(0.0387491\pi\)
−0.992600 + 0.121434i \(0.961251\pi\)
\(20\) 0 0
\(21\) 0.941367i 0.205423i
\(22\) 1.19051 6.24914i 0.253817 1.33232i
\(23\) 1.05863i 0.220740i 0.993891 + 0.110370i \(0.0352036\pi\)
−0.993891 + 0.110370i \(0.964796\pi\)
\(24\) −2.38923 1.51380i −0.487699 0.309003i
\(25\) 0 0
\(26\) 7.71982 + 1.47068i 1.51398 + 0.288425i
\(27\) −1.00000 −0.192450
\(28\) −0.692226 + 1.75086i −0.130818 + 0.330881i
\(29\) 2.00000i 0.371391i −0.982607 0.185695i \(-0.940546\pi\)
0.982607 0.185695i \(-0.0594537\pi\)
\(30\) 0 0
\(31\) 3.55691 0.638841 0.319420 0.947613i \(-0.396512\pi\)
0.319420 + 0.947613i \(0.396512\pi\)
\(32\) 3.33060 + 4.57243i 0.588772 + 0.808299i
\(33\) 4.49828i 0.783050i
\(34\) −2.00000 + 10.4983i −0.342997 + 1.80044i
\(35\) 0 0
\(36\) 1.85991 + 0.735342i 0.309985 + 0.122557i
\(37\) −7.43965 −1.22307 −0.611535 0.791217i \(-0.709448\pi\)
−0.611535 + 0.791217i \(0.709448\pi\)
\(38\) −0.280176 + 1.47068i −0.0454506 + 0.238576i
\(39\) −5.55691 −0.889818
\(40\) 0 0
\(41\) −3.88273 −0.606381 −0.303191 0.952930i \(-0.598052\pi\)
−0.303191 + 0.952930i \(0.598052\pi\)
\(42\) 0.249141 1.30777i 0.0384432 0.201794i
\(43\) 1.88273 0.287114 0.143557 0.989642i \(-0.454146\pi\)
0.143557 + 0.989642i \(0.454146\pi\)
\(44\) 3.30777 8.36641i 0.498666 1.26128i
\(45\) 0 0
\(46\) −0.280176 + 1.47068i −0.0413097 + 0.216840i
\(47\) 10.0552i 1.46670i −0.679851 0.733350i \(-0.737955\pi\)
0.679851 0.733350i \(-0.262045\pi\)
\(48\) −2.91855 2.73534i −0.421256 0.394813i
\(49\) 6.11383 0.873404
\(50\) 0 0
\(51\) 7.55691i 1.05818i
\(52\) 10.3354 + 4.08623i 1.43326 + 0.566658i
\(53\) −2.00000 −0.274721 −0.137361 0.990521i \(-0.543862\pi\)
−0.137361 + 0.990521i \(0.543862\pi\)
\(54\) −1.38923 0.264658i −0.189050 0.0360154i
\(55\) 0 0
\(56\) −1.42504 + 2.24914i −0.190429 + 0.300554i
\(57\) 1.05863i 0.140219i
\(58\) 0.529317 2.77846i 0.0695027 0.364829i
\(59\) 8.49828i 1.10638i −0.833054 0.553191i \(-0.813410\pi\)
0.833054 0.553191i \(-0.186590\pi\)
\(60\) 0 0
\(61\) 8.99656i 1.15189i −0.817488 0.575946i \(-0.804634\pi\)
0.817488 0.575946i \(-0.195366\pi\)
\(62\) 4.94137 + 0.941367i 0.627554 + 0.119554i
\(63\) 0.941367i 0.118601i
\(64\) 3.41683 + 7.23362i 0.427103 + 0.904203i
\(65\) 0 0
\(66\) −1.19051 + 6.24914i −0.146541 + 0.769216i
\(67\) −4.00000 −0.488678 −0.244339 0.969690i \(-0.578571\pi\)
−0.244339 + 0.969690i \(0.578571\pi\)
\(68\) −5.55691 + 14.0552i −0.673875 + 1.70444i
\(69\) 1.05863i 0.127444i
\(70\) 0 0
\(71\) −12.9966 −1.54241 −0.771204 0.636588i \(-0.780345\pi\)
−0.771204 + 0.636588i \(0.780345\pi\)
\(72\) 2.38923 + 1.51380i 0.281573 + 0.178403i
\(73\) 6.00000i 0.702247i 0.936329 + 0.351123i \(0.114200\pi\)
−0.936329 + 0.351123i \(0.885800\pi\)
\(74\) −10.3354 1.96896i −1.20146 0.228887i
\(75\) 0 0
\(76\) −0.778457 + 1.96896i −0.0892952 + 0.225856i
\(77\) 4.23453 0.482570
\(78\) −7.71982 1.47068i −0.874098 0.166522i
\(79\) −11.5569 −1.30025 −0.650127 0.759825i \(-0.725284\pi\)
−0.650127 + 0.759825i \(0.725284\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) −5.39400 1.02760i −0.595668 0.113479i
\(83\) −5.88273 −0.645714 −0.322857 0.946448i \(-0.604643\pi\)
−0.322857 + 0.946448i \(0.604643\pi\)
\(84\) 0.692226 1.75086i 0.0755281 0.191034i
\(85\) 0 0
\(86\) 2.61555 + 0.498281i 0.282042 + 0.0537310i
\(87\) 2.00000i 0.214423i
\(88\) 6.80949 10.7474i 0.725894 1.14568i
\(89\) 4.11727 0.436429 0.218215 0.975901i \(-0.429977\pi\)
0.218215 + 0.975901i \(0.429977\pi\)
\(90\) 0 0
\(91\) 5.23109i 0.548368i
\(92\) −0.778457 + 1.96896i −0.0811598 + 0.205279i
\(93\) −3.55691 −0.368835
\(94\) 2.66119 13.9690i 0.274481 1.44079i
\(95\) 0 0
\(96\) −3.33060 4.57243i −0.339927 0.466672i
\(97\) 17.1138i 1.73765i 0.495123 + 0.868823i \(0.335123\pi\)
−0.495123 + 0.868823i \(0.664877\pi\)
\(98\) 8.49351 + 1.61808i 0.857974 + 0.163450i
\(99\) 4.49828i 0.452094i
\(100\) 0 0
\(101\) 2.00000i 0.199007i −0.995037 0.0995037i \(-0.968274\pi\)
0.995037 0.0995037i \(-0.0317255\pi\)
\(102\) 2.00000 10.4983i 0.198030 1.03948i
\(103\) 10.1725i 1.00232i −0.865354 0.501161i \(-0.832906\pi\)
0.865354 0.501161i \(-0.167094\pi\)
\(104\) 13.2767 + 8.41205i 1.30189 + 0.824869i
\(105\) 0 0
\(106\) −2.77846 0.529317i −0.269868 0.0514118i
\(107\) −17.2311 −1.66579 −0.832896 0.553429i \(-0.813319\pi\)
−0.832896 + 0.553429i \(0.813319\pi\)
\(108\) −1.85991 0.735342i −0.178970 0.0707583i
\(109\) 1.88273i 0.180333i 0.995927 + 0.0901666i \(0.0287399\pi\)
−0.995927 + 0.0901666i \(0.971260\pi\)
\(110\) 0 0
\(111\) 7.43965 0.706140
\(112\) −2.57496 + 2.74742i −0.243311 + 0.259607i
\(113\) 15.3224i 1.44141i −0.693243 0.720704i \(-0.743819\pi\)
0.693243 0.720704i \(-0.256181\pi\)
\(114\) 0.280176 1.47068i 0.0262409 0.137742i
\(115\) 0 0
\(116\) 1.47068 3.71982i 0.136550 0.345377i
\(117\) 5.55691 0.513737
\(118\) 2.24914 11.8061i 0.207050 1.08684i
\(119\) −7.11383 −0.652124
\(120\) 0 0
\(121\) −9.23453 −0.839503
\(122\) 2.38101 12.4983i 0.215567 1.13154i
\(123\) 3.88273 0.350094
\(124\) 6.61555 + 2.61555i 0.594094 + 0.234883i
\(125\) 0 0
\(126\) −0.249141 + 1.30777i −0.0221952 + 0.116506i
\(127\) 18.1725i 1.61255i −0.591544 0.806273i \(-0.701481\pi\)
0.591544 0.806273i \(-0.298519\pi\)
\(128\) 2.83231 + 10.9534i 0.250344 + 0.968157i
\(129\) −1.88273 −0.165765
\(130\) 0 0
\(131\) 6.38101i 0.557512i 0.960362 + 0.278756i \(0.0899220\pi\)
−0.960362 + 0.278756i \(0.910078\pi\)
\(132\) −3.30777 + 8.36641i −0.287905 + 0.728202i
\(133\) −0.996562 −0.0864129
\(134\) −5.55691 1.05863i −0.480044 0.0914520i
\(135\) 0 0
\(136\) −11.4396 + 18.0552i −0.980942 + 1.54822i
\(137\) 4.44309i 0.379598i −0.981823 0.189799i \(-0.939216\pi\)
0.981823 0.189799i \(-0.0607837\pi\)
\(138\) 0.280176 1.47068i 0.0238502 0.125193i
\(139\) 20.1725i 1.71101i 0.517798 + 0.855503i \(0.326752\pi\)
−0.517798 + 0.855503i \(0.673248\pi\)
\(140\) 0 0
\(141\) 10.0552i 0.846800i
\(142\) −18.0552 3.43965i −1.51516 0.288649i
\(143\) 24.9966i 2.09032i
\(144\) 2.91855 + 2.73534i 0.243212 + 0.227945i
\(145\) 0 0
\(146\) −1.58795 + 8.33537i −0.131420 + 0.689840i
\(147\) −6.11383 −0.504260
\(148\) −13.8371 5.47068i −1.13740 0.449687i
\(149\) 2.00000i 0.163846i −0.996639 0.0819232i \(-0.973894\pi\)
0.996639 0.0819232i \(-0.0261062\pi\)
\(150\) 0 0
\(151\) 9.67418 0.787274 0.393637 0.919266i \(-0.371217\pi\)
0.393637 + 0.919266i \(0.371217\pi\)
\(152\) −1.60256 + 2.52932i −0.129985 + 0.205155i
\(153\) 7.55691i 0.610940i
\(154\) 5.88273 + 1.12070i 0.474044 + 0.0903089i
\(155\) 0 0
\(156\) −10.3354 4.08623i −0.827492 0.327160i
\(157\) 4.32582 0.345238 0.172619 0.984989i \(-0.444777\pi\)
0.172619 + 0.984989i \(0.444777\pi\)
\(158\) −16.0552 3.05863i −1.27728 0.243332i
\(159\) 2.00000 0.158610
\(160\) 0 0
\(161\) −0.996562 −0.0785401
\(162\) 1.38923 + 0.264658i 0.109148 + 0.0207935i
\(163\) 6.11727 0.479141 0.239571 0.970879i \(-0.422993\pi\)
0.239571 + 0.970879i \(0.422993\pi\)
\(164\) −7.22154 2.85514i −0.563908 0.222949i
\(165\) 0 0
\(166\) −8.17246 1.55691i −0.634306 0.120840i
\(167\) 6.05520i 0.468565i −0.972169 0.234283i \(-0.924726\pi\)
0.972169 0.234283i \(-0.0752741\pi\)
\(168\) 1.42504 2.24914i 0.109944 0.173525i
\(169\) 17.8793 1.37533
\(170\) 0 0
\(171\) 1.05863i 0.0809557i
\(172\) 3.50172 + 1.38445i 0.267004 + 0.105564i
\(173\) −16.8793 −1.28331 −0.641655 0.766994i \(-0.721752\pi\)
−0.641655 + 0.766994i \(0.721752\pi\)
\(174\) −0.529317 + 2.77846i −0.0401274 + 0.210634i
\(175\) 0 0
\(176\) 12.3043 13.1284i 0.927474 0.989593i
\(177\) 8.49828i 0.638770i
\(178\) 5.71982 + 1.08967i 0.428719 + 0.0816741i
\(179\) 10.6155i 0.793443i 0.917939 + 0.396722i \(0.129852\pi\)
−0.917939 + 0.396722i \(0.870148\pi\)
\(180\) 0 0
\(181\) 14.1173i 1.04933i −0.851309 0.524664i \(-0.824191\pi\)
0.851309 0.524664i \(-0.175809\pi\)
\(182\) −1.38445 + 7.26719i −0.102622 + 0.538680i
\(183\) 8.99656i 0.665045i
\(184\) −1.60256 + 2.52932i −0.118142 + 0.186464i
\(185\) 0 0
\(186\) −4.94137 0.941367i −0.362319 0.0690244i
\(187\) 33.9931 2.48582
\(188\) 7.39400 18.7018i 0.539263 1.36397i
\(189\) 0.941367i 0.0684744i
\(190\) 0 0
\(191\) −8.00000 −0.578860 −0.289430 0.957199i \(-0.593466\pi\)
−0.289430 + 0.957199i \(0.593466\pi\)
\(192\) −3.41683 7.23362i −0.246588 0.522042i
\(193\) 4.87930i 0.351219i 0.984460 + 0.175610i \(0.0561897\pi\)
−0.984460 + 0.175610i \(0.943810\pi\)
\(194\) −4.52932 + 23.7750i −0.325186 + 1.70695i
\(195\) 0 0
\(196\) 11.3712 + 4.49575i 0.812227 + 0.321125i
\(197\) −2.88617 −0.205631 −0.102816 0.994700i \(-0.532785\pi\)
−0.102816 + 0.994700i \(0.532785\pi\)
\(198\) 1.19051 6.24914i 0.0846057 0.444107i
\(199\) 17.6742 1.25289 0.626445 0.779466i \(-0.284509\pi\)
0.626445 + 0.779466i \(0.284509\pi\)
\(200\) 0 0
\(201\) 4.00000 0.282138
\(202\) 0.529317 2.77846i 0.0372426 0.195492i
\(203\) 1.88273 0.132142
\(204\) 5.55691 14.0552i 0.389062 0.984061i
\(205\) 0 0
\(206\) 2.69223 14.1319i 0.187576 0.984614i
\(207\) 1.05863i 0.0735801i
\(208\) 16.2181 + 15.2001i 1.12452 + 1.05393i
\(209\) 4.76203 0.329396
\(210\) 0 0
\(211\) 23.9379i 1.64795i 0.566623 + 0.823977i \(0.308250\pi\)
−0.566623 + 0.823977i \(0.691750\pi\)
\(212\) −3.71982 1.47068i −0.255479 0.101007i
\(213\) 12.9966 0.890510
\(214\) −23.9379 4.56035i −1.63636 0.311739i
\(215\) 0 0
\(216\) −2.38923 1.51380i −0.162566 0.103001i
\(217\) 3.34836i 0.227302i
\(218\) −0.498281 + 2.61555i −0.0337479 + 0.177147i
\(219\) 6.00000i 0.405442i
\(220\) 0 0
\(221\) 41.9931i 2.82476i
\(222\) 10.3354 + 1.96896i 0.693665 + 0.132148i
\(223\) 24.0552i 1.61086i 0.592694 + 0.805428i \(0.298064\pi\)
−0.592694 + 0.805428i \(0.701936\pi\)
\(224\) −4.30434 + 3.13531i −0.287596 + 0.209487i
\(225\) 0 0
\(226\) 4.05520 21.2863i 0.269748 1.41594i
\(227\) 11.1138 0.737651 0.368825 0.929499i \(-0.379760\pi\)
0.368825 + 0.929499i \(0.379760\pi\)
\(228\) 0.778457 1.96896i 0.0515546 0.130398i
\(229\) 17.2311i 1.13866i −0.822108 0.569331i \(-0.807202\pi\)
0.822108 0.569331i \(-0.192798\pi\)
\(230\) 0 0
\(231\) −4.23453 −0.278612
\(232\) 3.02760 4.77846i 0.198772 0.313721i
\(233\) 8.44309i 0.553125i 0.960996 + 0.276562i \(0.0891953\pi\)
−0.960996 + 0.276562i \(0.910805\pi\)
\(234\) 7.71982 + 1.47068i 0.504661 + 0.0961416i
\(235\) 0 0
\(236\) 6.24914 15.8061i 0.406784 1.02889i
\(237\) 11.5569 0.750702
\(238\) −9.88273 1.88273i −0.640602 0.122039i
\(239\) −10.1173 −0.654432 −0.327216 0.944950i \(-0.606110\pi\)
−0.327216 + 0.944950i \(0.606110\pi\)
\(240\) 0 0
\(241\) 16.8793 1.08729 0.543646 0.839315i \(-0.317044\pi\)
0.543646 + 0.839315i \(0.317044\pi\)
\(242\) −12.8289 2.44400i −0.824671 0.157106i
\(243\) −1.00000 −0.0641500
\(244\) 6.61555 16.7328i 0.423517 1.07121i
\(245\) 0 0
\(246\) 5.39400 + 1.02760i 0.343909 + 0.0655172i
\(247\) 5.88273i 0.374309i
\(248\) 8.49828 + 5.38445i 0.539641 + 0.341913i
\(249\) 5.88273 0.372803
\(250\) 0 0
\(251\) 11.8466i 0.747753i −0.927478 0.373877i \(-0.878028\pi\)
0.927478 0.373877i \(-0.121972\pi\)
\(252\) −0.692226 + 1.75086i −0.0436062 + 0.110294i
\(253\) 4.76203 0.299386
\(254\) 4.80949 25.2457i 0.301774 1.58406i
\(255\) 0 0
\(256\) 1.03581 + 15.9664i 0.0647382 + 0.997902i
\(257\) 10.6707i 0.665623i −0.942993 0.332811i \(-0.892003\pi\)
0.942993 0.332811i \(-0.107997\pi\)
\(258\) −2.61555 0.498281i −0.162837 0.0310216i
\(259\) 7.00344i 0.435172i
\(260\) 0 0
\(261\) 2.00000i 0.123797i
\(262\) −1.68879 + 8.86469i −0.104334 + 0.547662i
\(263\) 1.94480i 0.119922i 0.998201 + 0.0599609i \(0.0190976\pi\)
−0.998201 + 0.0599609i \(0.980902\pi\)
\(264\) −6.80949 + 10.7474i −0.419095 + 0.661458i
\(265\) 0 0
\(266\) −1.38445 0.263748i −0.0848862 0.0161715i
\(267\) −4.11727 −0.251973
\(268\) −7.43965 2.94137i −0.454449 0.179673i
\(269\) 9.76547i 0.595411i 0.954658 + 0.297706i \(0.0962214\pi\)
−0.954658 + 0.297706i \(0.903779\pi\)
\(270\) 0 0
\(271\) 3.44652 0.209361 0.104681 0.994506i \(-0.466618\pi\)
0.104681 + 0.994506i \(0.466618\pi\)
\(272\) −20.6707 + 22.0552i −1.25335 + 1.33729i
\(273\) 5.23109i 0.316600i
\(274\) 1.17590 6.17246i 0.0710387 0.372892i
\(275\) 0 0
\(276\) 0.778457 1.96896i 0.0468576 0.118518i
\(277\) −18.7880 −1.12886 −0.564431 0.825480i \(-0.690904\pi\)
−0.564431 + 0.825480i \(0.690904\pi\)
\(278\) −5.33881 + 28.0242i −0.320200 + 1.68078i
\(279\) 3.55691 0.212947
\(280\) 0 0
\(281\) −16.8793 −1.00693 −0.503467 0.864014i \(-0.667943\pi\)
−0.503467 + 0.864014i \(0.667943\pi\)
\(282\) −2.66119 + 13.9690i −0.158472 + 0.831840i
\(283\) −20.0000 −1.18888 −0.594438 0.804141i \(-0.702626\pi\)
−0.594438 + 0.804141i \(0.702626\pi\)
\(284\) −24.1725 9.55691i −1.43437 0.567099i
\(285\) 0 0
\(286\) 6.61555 34.7259i 0.391186 2.05339i
\(287\) 3.65508i 0.215752i
\(288\) 3.33060 + 4.57243i 0.196257 + 0.269433i
\(289\) −40.1070 −2.35923
\(290\) 0 0
\(291\) 17.1138i 1.00323i
\(292\) −4.41205 + 11.1595i −0.258196 + 0.653059i
\(293\) 20.2277 1.18171 0.590856 0.806777i \(-0.298790\pi\)
0.590856 + 0.806777i \(0.298790\pi\)
\(294\) −8.49351 1.61808i −0.495351 0.0943681i
\(295\) 0 0
\(296\) −17.7750 11.2621i −1.03315 0.654598i
\(297\) 4.49828i 0.261017i
\(298\) 0.529317 2.77846i 0.0306625 0.160952i
\(299\) 5.88273i 0.340207i
\(300\) 0 0
\(301\) 1.77234i 0.102156i
\(302\) 13.4396 + 2.56035i 0.773365 + 0.147332i
\(303\) 2.00000i 0.114897i
\(304\) −2.89572 + 3.08967i −0.166081 + 0.177205i
\(305\) 0 0
\(306\) −2.00000 + 10.4983i −0.114332 + 0.600147i
\(307\) 8.11039 0.462884 0.231442 0.972849i \(-0.425656\pi\)
0.231442 + 0.972849i \(0.425656\pi\)
\(308\) 7.87586 + 3.11383i 0.448769 + 0.177427i
\(309\) 10.1725i 0.578691i
\(310\) 0 0
\(311\) 31.8759 1.80751 0.903757 0.428046i \(-0.140798\pi\)
0.903757 + 0.428046i \(0.140798\pi\)
\(312\) −13.2767 8.41205i −0.751647 0.476239i
\(313\) 5.11383i 0.289051i 0.989501 + 0.144525i \(0.0461655\pi\)
−0.989501 + 0.144525i \(0.953834\pi\)
\(314\) 6.00955 + 1.14486i 0.339139 + 0.0646084i
\(315\) 0 0
\(316\) −21.4948 8.49828i −1.20918 0.478066i
\(317\) 24.6448 1.38419 0.692094 0.721807i \(-0.256688\pi\)
0.692094 + 0.721807i \(0.256688\pi\)
\(318\) 2.77846 + 0.529317i 0.155808 + 0.0296826i
\(319\) −8.99656 −0.503711
\(320\) 0 0
\(321\) 17.2311 0.961746
\(322\) −1.38445 0.263748i −0.0771525 0.0146981i
\(323\) −8.00000 −0.445132
\(324\) 1.85991 + 0.735342i 0.103328 + 0.0408523i
\(325\) 0 0
\(326\) 8.49828 + 1.61899i 0.470676 + 0.0896673i
\(327\) 1.88273i 0.104115i
\(328\) −9.27674 5.87768i −0.512222 0.324540i
\(329\) 9.46563 0.521857
\(330\) 0 0
\(331\) 11.0518i 0.607460i 0.952758 + 0.303730i \(0.0982320\pi\)
−0.952758 + 0.303730i \(0.901768\pi\)
\(332\) −10.9414 4.32582i −0.600486 0.237410i
\(333\) −7.43965 −0.407690
\(334\) 1.60256 8.41205i 0.0876881 0.460287i
\(335\) 0 0
\(336\) 2.57496 2.74742i 0.140476 0.149884i
\(337\) 19.9931i 1.08909i −0.838730 0.544547i \(-0.816701\pi\)
0.838730 0.544547i \(-0.183299\pi\)
\(338\) 24.8384 + 4.73190i 1.35103 + 0.257382i
\(339\) 15.3224i 0.832198i
\(340\) 0 0
\(341\) 16.0000i 0.866449i
\(342\) −0.280176 + 1.47068i −0.0151502 + 0.0795255i
\(343\) 12.3449i 0.666563i
\(344\) 4.49828 + 2.85008i 0.242531 + 0.153666i
\(345\) 0 0
\(346\) −23.4492 4.46725i −1.26064 0.240161i
\(347\) −6.87930 −0.369300 −0.184650 0.982804i \(-0.559115\pi\)
−0.184650 + 0.982804i \(0.559115\pi\)
\(348\) −1.47068 + 3.71982i −0.0788369 + 0.199403i
\(349\) 4.76203i 0.254906i −0.991845 0.127453i \(-0.959320\pi\)
0.991845 0.127453i \(-0.0406801\pi\)
\(350\) 0 0
\(351\) −5.55691 −0.296606
\(352\) 20.5681 14.9820i 1.09628 0.798541i
\(353\) 3.79145i 0.201798i 0.994897 + 0.100899i \(0.0321720\pi\)
−0.994897 + 0.100899i \(0.967828\pi\)
\(354\) −2.24914 + 11.8061i −0.119540 + 0.627485i
\(355\) 0 0
\(356\) 7.65775 + 3.02760i 0.405860 + 0.160462i
\(357\) 7.11383 0.376504
\(358\) −2.80949 + 14.7474i −0.148486 + 0.779425i
\(359\) 12.9966 0.685932 0.342966 0.939348i \(-0.388568\pi\)
0.342966 + 0.939348i \(0.388568\pi\)
\(360\) 0 0
\(361\) 17.8793 0.941016
\(362\) 3.73625 19.6121i 0.196373 1.03079i
\(363\) 9.23453 0.484687
\(364\) −3.84664 + 9.72938i −0.201619 + 0.509958i
\(365\) 0 0
\(366\) −2.38101 + 12.4983i −0.124458 + 0.653296i
\(367\) 22.9345i 1.19717i 0.801059 + 0.598585i \(0.204270\pi\)
−0.801059 + 0.598585i \(0.795730\pi\)
\(368\) −2.89572 + 3.08967i −0.150950 + 0.161060i
\(369\) −3.88273 −0.202127
\(370\) 0 0
\(371\) 1.88273i 0.0977467i
\(372\) −6.61555 2.61555i −0.343000 0.135610i
\(373\) −15.4396 −0.799435 −0.399717 0.916638i \(-0.630892\pi\)
−0.399717 + 0.916638i \(0.630892\pi\)
\(374\) 47.2242 + 8.99656i 2.44191 + 0.465201i
\(375\) 0 0
\(376\) 15.2215 24.0242i 0.784991 1.23895i
\(377\) 11.1138i 0.572391i
\(378\) 0.249141 1.30777i 0.0128144 0.0672646i
\(379\) 6.28973i 0.323082i −0.986866 0.161541i \(-0.948354\pi\)
0.986866 0.161541i \(-0.0516463\pi\)
\(380\) 0 0
\(381\) 18.1725i 0.931003i
\(382\) −11.1138 2.11727i −0.568633 0.108329i
\(383\) 2.94137i 0.150297i −0.997172 0.0751484i \(-0.976057\pi\)
0.997172 0.0751484i \(-0.0239431\pi\)
\(384\) −2.83231 10.9534i −0.144536 0.558966i
\(385\) 0 0
\(386\) −1.29135 + 6.77846i −0.0657278 + 0.345014i
\(387\) 1.88273 0.0957047
\(388\) −12.5845 + 31.8302i −0.638882 + 1.61593i
\(389\) 12.2277i 0.619967i 0.950742 + 0.309983i \(0.100324\pi\)
−0.950742 + 0.309983i \(0.899676\pi\)
\(390\) 0 0
\(391\) −8.00000 −0.404577
\(392\) 14.6073 + 9.25511i 0.737782 + 0.467453i
\(393\) 6.38101i 0.321880i
\(394\) −4.00955 0.763849i −0.201998 0.0384822i
\(395\) 0 0
\(396\) 3.30777 8.36641i 0.166222 0.420428i
\(397\) −5.32238 −0.267123 −0.133561 0.991041i \(-0.542641\pi\)
−0.133561 + 0.991041i \(0.542641\pi\)
\(398\) 24.5535 + 4.67762i 1.23075 + 0.234468i
\(399\) 0.996562 0.0498905
\(400\) 0 0
\(401\) 6.99656 0.349392 0.174696 0.984622i \(-0.444106\pi\)
0.174696 + 0.984622i \(0.444106\pi\)
\(402\) 5.55691 + 1.05863i 0.277154 + 0.0527998i
\(403\) 19.7655 0.984588
\(404\) 1.47068 3.71982i 0.0731692 0.185068i
\(405\) 0 0
\(406\) 2.61555 + 0.498281i 0.129807 + 0.0247293i
\(407\) 33.4656i 1.65883i
\(408\) 11.4396 18.0552i 0.566347 0.893865i
\(409\) −16.2277 −0.802406 −0.401203 0.915989i \(-0.631408\pi\)
−0.401203 + 0.915989i \(0.631408\pi\)
\(410\) 0 0
\(411\) 4.44309i 0.219161i
\(412\) 7.48024 18.9199i 0.368525 0.932116i
\(413\) 8.00000 0.393654
\(414\) −0.280176 + 1.47068i −0.0137699 + 0.0722801i
\(415\) 0 0
\(416\) 18.5078 + 25.4086i 0.907421 + 1.24576i
\(417\) 20.1725i 0.987850i
\(418\) 6.61555 + 1.26031i 0.323577 + 0.0616438i
\(419\) 15.6121i 0.762701i −0.924430 0.381351i \(-0.875459\pi\)
0.924430 0.381351i \(-0.124541\pi\)
\(420\) 0 0
\(421\) 33.2311i 1.61958i −0.586717 0.809792i \(-0.699580\pi\)
0.586717 0.809792i \(-0.300420\pi\)
\(422\) −6.33537 + 33.2553i −0.308401 + 1.61884i
\(423\) 10.0552i 0.488900i
\(424\) −4.77846 3.02760i −0.232062 0.147033i
\(425\) 0 0
\(426\) 18.0552 + 3.43965i 0.874777 + 0.166651i
\(427\) 8.46907 0.409847
\(428\) −32.0483 12.6707i −1.54911 0.612463i
\(429\) 24.9966i 1.20685i
\(430\) 0 0
\(431\) −12.9966 −0.626022 −0.313011 0.949749i \(-0.601338\pi\)
−0.313011 + 0.949749i \(0.601338\pi\)
\(432\) −2.91855 2.73534i −0.140419 0.131604i
\(433\) 20.2277i 0.972079i −0.873937 0.486040i \(-0.838441\pi\)
0.873937 0.486040i \(-0.161559\pi\)
\(434\) −0.886172 + 4.65164i −0.0425376 + 0.223286i
\(435\) 0 0
\(436\) −1.38445 + 3.50172i −0.0663033 + 0.167702i
\(437\) −1.12070 −0.0536106
\(438\) 1.58795 8.33537i 0.0758752 0.398279i
\(439\) 5.43965 0.259620 0.129810 0.991539i \(-0.458563\pi\)
0.129810 + 0.991539i \(0.458563\pi\)
\(440\) 0 0
\(441\) 6.11383 0.291135
\(442\) −11.1138 + 58.3380i −0.528631 + 2.77486i
\(443\) 15.3484 0.729223 0.364611 0.931160i \(-0.381202\pi\)
0.364611 + 0.931160i \(0.381202\pi\)
\(444\) 13.8371 + 5.47068i 0.656679 + 0.259627i
\(445\) 0 0
\(446\) −6.36641 + 33.4182i −0.301458 + 1.58240i
\(447\) 2.00000i 0.0945968i
\(448\) −6.80949 + 3.21649i −0.321718 + 0.151965i
\(449\) −4.22766 −0.199515 −0.0997577 0.995012i \(-0.531807\pi\)
−0.0997577 + 0.995012i \(0.531807\pi\)
\(450\) 0 0
\(451\) 17.4656i 0.822424i
\(452\) 11.2672 28.4983i 0.529964 1.34045i
\(453\) −9.67418 −0.454533
\(454\) 15.4396 + 2.94137i 0.724619 + 0.138045i
\(455\) 0 0
\(456\) 1.60256 2.52932i 0.0750466 0.118446i
\(457\) 2.65164i 0.124038i 0.998075 + 0.0620192i \(0.0197540\pi\)
−0.998075 + 0.0620192i \(0.980246\pi\)
\(458\) 4.56035 23.9379i 0.213091 1.11855i
\(459\) 7.55691i 0.352727i
\(460\) 0 0
\(461\) 10.2345i 0.476670i 0.971183 + 0.238335i \(0.0766016\pi\)
−0.971183 + 0.238335i \(0.923398\pi\)
\(462\) −5.88273 1.12070i −0.273690 0.0521399i
\(463\) 19.0586i 0.885730i −0.896588 0.442865i \(-0.853962\pi\)
0.896588 0.442865i \(-0.146038\pi\)
\(464\) 5.47068 5.83709i 0.253970 0.270980i
\(465\) 0 0
\(466\) −2.23453 + 11.7294i −0.103513 + 0.543353i
\(467\) −4.11039 −0.190206 −0.0951031 0.995467i \(-0.530318\pi\)
−0.0951031 + 0.995467i \(0.530318\pi\)
\(468\) 10.3354 + 4.08623i 0.477753 + 0.188886i
\(469\) 3.76547i 0.173873i
\(470\) 0 0
\(471\) −4.32582 −0.199323
\(472\) 12.8647 20.3043i 0.592145 0.934583i
\(473\) 8.46907i 0.389408i
\(474\) 16.0552 + 3.05863i 0.737440 + 0.140488i
\(475\) 0 0
\(476\) −13.2311 5.23109i −0.606446 0.239767i
\(477\) −2.00000 −0.0915737
\(478\) −14.0552 2.67762i −0.642870 0.122471i
\(479\) 25.2311 1.15284 0.576419 0.817154i \(-0.304450\pi\)
0.576419 + 0.817154i \(0.304450\pi\)
\(480\) 0 0
\(481\) −41.3415 −1.88501
\(482\) 23.4492 + 4.46725i 1.06808 + 0.203477i
\(483\) 0.996562 0.0453451
\(484\) −17.1754 6.79054i −0.780701 0.308661i
\(485\) 0 0
\(486\) −1.38923 0.264658i −0.0630167 0.0120051i
\(487\) 21.9379i 0.994102i −0.867721 0.497051i \(-0.834416\pi\)
0.867721 0.497051i \(-0.165584\pi\)
\(488\) 13.6190 21.4948i 0.616502 0.973026i
\(489\) −6.11727 −0.276632
\(490\) 0 0
\(491\) 7.50172i 0.338548i 0.985569 + 0.169274i \(0.0541423\pi\)
−0.985569 + 0.169274i \(0.945858\pi\)
\(492\) 7.22154 + 2.85514i 0.325572 + 0.128719i
\(493\) 15.1138 0.680693
\(494\) −1.55691 + 8.17246i −0.0700489 + 0.367696i
\(495\) 0 0
\(496\) 10.3810 + 9.72938i 0.466121 + 0.436862i
\(497\) 12.2345i 0.548794i
\(498\) 8.17246 + 1.55691i 0.366217 + 0.0697670i
\(499\) 29.1690i 1.30578i −0.757451 0.652892i \(-0.773555\pi\)
0.757451 0.652892i \(-0.226445\pi\)
\(500\) 0 0
\(501\) 6.05520i 0.270526i
\(502\) 3.13531 16.4577i 0.139936 0.734543i
\(503\) 23.9379i 1.06734i 0.845693 + 0.533670i \(0.179187\pi\)
−0.845693 + 0.533670i \(0.820813\pi\)
\(504\) −1.42504 + 2.24914i −0.0634763 + 0.100185i
\(505\) 0 0
\(506\) 6.61555 + 1.26031i 0.294097 + 0.0560276i
\(507\) −17.8793 −0.794047
\(508\) 13.3630 33.7992i 0.592886 1.49960i
\(509\) 28.6967i 1.27196i 0.771706 + 0.635980i \(0.219404\pi\)
−0.771706 + 0.635980i \(0.780596\pi\)
\(510\) 0 0
\(511\) −5.64820 −0.249862
\(512\) −2.78667 + 22.4552i −0.123155 + 0.992387i
\(513\) 1.05863i 0.0467398i
\(514\) 2.82410 14.8241i 0.124566 0.653863i
\(515\) 0 0
\(516\) −3.50172 1.38445i −0.154155 0.0609471i
\(517\) −45.2311 −1.98926
\(518\) 1.85352 9.72938i 0.0814389 0.427484i
\(519\) 16.8793 0.740919
\(520\) 0 0
\(521\) 10.0000 0.438108 0.219054 0.975713i \(-0.429703\pi\)
0.219054 + 0.975713i \(0.429703\pi\)
\(522\) 0.529317 2.77846i 0.0231676 0.121610i
\(523\) −25.7586 −1.12634 −0.563172 0.826340i \(-0.690419\pi\)
−0.563172 + 0.826340i \(0.690419\pi\)
\(524\) −4.69223 + 11.8681i −0.204981 + 0.518461i
\(525\) 0 0
\(526\) −0.514709 + 2.70178i −0.0224424 + 0.117803i
\(527\) 26.8793i 1.17088i
\(528\) −12.3043 + 13.1284i −0.535477 + 0.571342i
\(529\) 21.8793 0.951274
\(530\) 0 0
\(531\) 8.49828i 0.368794i
\(532\) −1.85352 0.732814i −0.0803602 0.0317715i
\(533\) −21.5760 −0.934561
\(534\) −5.71982 1.08967i −0.247521 0.0471546i
\(535\) 0 0
\(536\) −9.55691 6.05520i −0.412796 0.261545i
\(537\) 10.6155i 0.458095i
\(538\) −2.58451 + 13.5665i −0.111426 + 0.584892i
\(539\) 27.5017i 1.18458i
\(540\) 0 0
\(541\) 12.3449i 0.530750i −0.964145 0.265375i \(-0.914504\pi\)
0.964145 0.265375i \(-0.0854957\pi\)
\(542\) 4.78801 + 0.912151i 0.205663 + 0.0391802i
\(543\) 14.1173i 0.605830i
\(544\) −34.5535 + 25.1690i −1.48147 + 1.07911i
\(545\) 0 0
\(546\) 1.38445 7.26719i 0.0592491 0.311007i
\(547\) −19.8759 −0.849830 −0.424915 0.905233i \(-0.639696\pi\)
−0.424915 + 0.905233i \(0.639696\pi\)
\(548\) 3.26719 8.26375i 0.139567 0.353010i
\(549\) 8.99656i 0.383964i
\(550\) 0 0
\(551\) 2.11727 0.0901986
\(552\) 1.60256 2.52932i 0.0682094 0.107655i
\(553\) 10.8793i 0.462635i
\(554\) −26.1008 4.97240i −1.10892 0.211257i
\(555\) 0 0
\(556\) −14.8337 + 37.5190i −0.629087 + 1.59116i
\(557\) 3.12070 0.132228 0.0661142 0.997812i \(-0.478940\pi\)
0.0661142 + 0.997812i \(0.478940\pi\)
\(558\) 4.94137 + 0.941367i 0.209185 + 0.0398512i
\(559\) 10.4622 0.442503
\(560\) 0 0
\(561\) −33.9931 −1.43519
\(562\) −23.4492 4.46725i −0.989145 0.188439i
\(563\) 0.651639 0.0274633 0.0137317 0.999906i \(-0.495629\pi\)
0.0137317 + 0.999906i \(0.495629\pi\)
\(564\) −7.39400 + 18.7018i −0.311344 + 0.787487i
\(565\) 0 0
\(566\) −27.7846 5.29317i −1.16787 0.222488i
\(567\) 0.941367i 0.0395337i
\(568\) −31.0518 19.6742i −1.30290 0.825510i
\(569\) −26.9966 −1.13175 −0.565877 0.824489i \(-0.691462\pi\)
−0.565877 + 0.824489i \(0.691462\pi\)
\(570\) 0 0
\(571\) 14.9414i 0.625277i −0.949872 0.312638i \(-0.898787\pi\)
0.949872 0.312638i \(-0.101213\pi\)
\(572\) 18.3810 46.4914i 0.768549 1.94390i
\(573\) 8.00000 0.334205
\(574\) 0.967346 5.07774i 0.0403763 0.211941i
\(575\) 0 0
\(576\) 3.41683 + 7.23362i 0.142368 + 0.301401i
\(577\) 8.87930i 0.369650i −0.982771 0.184825i \(-0.940828\pi\)
0.982771 0.184825i \(-0.0591718\pi\)
\(578\) −55.7177 10.6146i −2.31755 0.441511i
\(579\) 4.87930i 0.202777i
\(580\) 0 0
\(581\) 5.53781i 0.229747i
\(582\) 4.52932 23.7750i 0.187746 0.985506i
\(583\) 8.99656i 0.372600i
\(584\) −9.08279 + 14.3354i −0.375849 + 0.593202i
\(585\) 0 0
\(586\) 28.1008 + 5.35342i 1.16083 + 0.221148i
\(587\) 1.23109 0.0508127 0.0254064 0.999677i \(-0.491912\pi\)
0.0254064 + 0.999677i \(0.491912\pi\)
\(588\) −11.3712 4.49575i −0.468940 0.185402i
\(589\) 3.76547i 0.155153i
\(590\) 0 0
\(591\) 2.88617 0.118721
\(592\) −21.7129 20.3500i −0.892397 0.836379i
\(593\) 3.55691i 0.146065i −0.997330 0.0730325i \(-0.976732\pi\)
0.997330 0.0730325i \(-0.0232677\pi\)
\(594\) −1.19051 + 6.24914i −0.0488471 + 0.256405i
\(595\) 0 0
\(596\) 1.47068 3.71982i 0.0602415 0.152370i
\(597\) −17.6742 −0.723356
\(598\) −1.55691 + 8.17246i −0.0636670 + 0.334197i
\(599\) 19.2242 0.785480 0.392740 0.919649i \(-0.371527\pi\)
0.392740 + 0.919649i \(0.371527\pi\)
\(600\) 0 0
\(601\) −27.7586 −1.13230 −0.566148 0.824303i \(-0.691567\pi\)
−0.566148 + 0.824303i \(0.691567\pi\)
\(602\) −0.469065 + 2.46219i −0.0191177 + 0.100351i
\(603\) −4.00000 −0.162893
\(604\) 17.9931 + 7.11383i 0.732130 + 0.289458i
\(605\) 0 0
\(606\) −0.529317 + 2.77846i −0.0215020 + 0.112867i
\(607\) 7.16902i 0.290982i 0.989360 + 0.145491i \(0.0464761\pi\)
−0.989360 + 0.145491i \(0.953524\pi\)
\(608\) −4.84053 + 3.52588i −0.196309 + 0.142993i
\(609\) −1.88273 −0.0762922
\(610\) 0 0
\(611\) 55.8759i 2.26050i
\(612\) −5.55691 + 14.0552i −0.224625 + 0.568148i
\(613\) −9.55691 −0.386000 −0.193000 0.981199i \(-0.561822\pi\)
−0.193000 + 0.981199i \(0.561822\pi\)
\(614\) 11.2672 + 2.14648i 0.454707 + 0.0866250i
\(615\) 0 0
\(616\) 10.1173 + 6.41023i 0.407636 + 0.258276i
\(617\) 1.32926i 0.0535139i 0.999642 + 0.0267569i \(0.00851802\pi\)
−0.999642 + 0.0267569i \(0.991482\pi\)
\(618\) −2.69223 + 14.1319i −0.108297 + 0.568467i
\(619\) 28.1725i 1.13235i 0.824286 + 0.566173i \(0.191577\pi\)
−0.824286 + 0.566173i \(0.808423\pi\)
\(620\) 0 0
\(621\) 1.05863i 0.0424815i
\(622\) 44.2829 + 8.43621i 1.77558 + 0.338261i
\(623\) 3.87586i 0.155283i
\(624\) −16.2181 15.2001i −0.649244 0.608489i
\(625\) 0 0
\(626\) −1.35342 + 7.10428i −0.0540934 + 0.283944i
\(627\) −4.76203 −0.190177
\(628\) 8.04564 + 3.18096i 0.321056 + 0.126934i
\(629\) 56.2208i 2.24167i
\(630\) 0 0
\(631\) −23.3224 −0.928449 −0.464225 0.885717i \(-0.653667\pi\)
−0.464225 + 0.885717i \(0.653667\pi\)
\(632\) −27.6121 17.4948i −1.09835 0.695907i
\(633\) 23.9379i 0.951447i
\(634\) 34.2372 + 6.52244i 1.35973 + 0.259039i
\(635\) 0 0
\(636\) 3.71982 + 1.47068i 0.147501 + 0.0583164i
\(637\) 33.9740 1.34610
\(638\) −12.4983 2.38101i −0.494812 0.0942653i
\(639\) −12.9966 −0.514136
\(640\) 0 0
\(641\) 27.1070 1.07066 0.535330 0.844643i \(-0.320187\pi\)
0.535330 + 0.844643i \(0.320187\pi\)
\(642\) 23.9379 + 4.56035i 0.944755 + 0.179983i
\(643\) −20.3449 −0.802325 −0.401163 0.916007i \(-0.631394\pi\)
−0.401163 + 0.916007i \(0.631394\pi\)
\(644\) −1.85352 0.732814i −0.0730388 0.0288769i
\(645\) 0 0
\(646\) −11.1138 2.11727i −0.437268 0.0833027i
\(647\) 37.6965i 1.48200i 0.671503 + 0.741002i \(0.265649\pi\)
−0.671503 + 0.741002i \(0.734351\pi\)
\(648\) 2.38923 + 1.51380i 0.0938578 + 0.0594676i
\(649\) −38.2277 −1.50057
\(650\) 0 0
\(651\) 3.34836i 0.131233i
\(652\) 11.3776 + 4.49828i 0.445580 + 0.176166i
\(653\) 8.64476 0.338296 0.169148 0.985591i \(-0.445898\pi\)
0.169148 + 0.985591i \(0.445898\pi\)
\(654\) 0.498281 2.61555i 0.0194843 0.102276i
\(655\) 0 0
\(656\) −11.3319 10.6206i −0.442438 0.414665i
\(657\) 6.00000i 0.234082i
\(658\) 13.1499 + 2.50516i 0.512637 + 0.0976612i
\(659\) 29.2603i 1.13982i 0.821707 + 0.569910i \(0.193022\pi\)
−0.821707 + 0.569910i \(0.806978\pi\)
\(660\) 0 0
\(661\) 28.7620i 1.11871i −0.828927 0.559357i \(-0.811048\pi\)
0.828927 0.559357i \(-0.188952\pi\)
\(662\) −2.92494 + 15.3534i −0.113681 + 0.596728i
\(663\) 41.9931i 1.63088i
\(664\) −14.0552 8.90528i −0.545447 0.345592i
\(665\) 0 0
\(666\) −10.3354 1.96896i −0.400488 0.0762958i
\(667\) 2.11727 0.0819809
\(668\) 4.45264 11.2621i 0.172278 0.435745i
\(669\) 24.0552i 0.930028i
\(670\) 0 0
\(671\) −40.4691 −1.56229
\(672\) 4.30434 3.13531i 0.166043 0.120947i
\(673\) 18.0000i 0.693849i 0.937893 + 0.346925i \(0.112774\pi\)
−0.937893 + 0.346925i \(0.887226\pi\)
\(674\) 5.29135 27.7750i 0.203815 1.06985i
\(675\) 0 0
\(676\) 33.2539 + 13.1474i 1.27900 + 0.505669i
\(677\) −42.8724 −1.64772 −0.823860 0.566793i \(-0.808184\pi\)
−0.823860 + 0.566793i \(0.808184\pi\)
\(678\) −4.05520 + 21.2863i −0.155739 + 0.817495i
\(679\) −16.1104 −0.618260
\(680\) 0 0
\(681\) −11.1138 −0.425883
\(682\) 4.23453 22.2277i 0.162149 0.851141i
\(683\) 26.1173 0.999349 0.499675 0.866213i \(-0.333453\pi\)
0.499675 + 0.866213i \(0.333453\pi\)
\(684\) −0.778457 + 1.96896i −0.0297651 + 0.0752852i
\(685\) 0 0
\(686\) −3.26719 + 17.1499i −0.124742 + 0.654787i
\(687\) 17.2311i 0.657407i
\(688\) 5.49484 + 5.14992i 0.209489 + 0.196339i
\(689\) −11.1138 −0.423403
\(690\) 0 0
\(691\) 5.29317i 0.201362i 0.994919 + 0.100681i \(0.0321021\pi\)
−0.994919 + 0.100681i \(0.967898\pi\)
\(692\) −31.3940 12.4121i −1.19342 0.471835i
\(693\) 4.23453 0.160857
\(694\) −9.55691 1.82066i −0.362776 0.0691114i
\(695\) 0 0
\(696\) −3.02760 + 4.77846i −0.114761 + 0.181127i
\(697\) 29.3415i 1.11139i
\(698\) 1.26031 6.61555i 0.0477035 0.250402i
\(699\) 8.44309i 0.319347i
\(700\) 0 0
\(701\) 7.99312i 0.301896i −0.988542 0.150948i \(-0.951767\pi\)
0.988542 0.150948i \(-0.0482326\pi\)
\(702\) −7.71982 1.47068i −0.291366 0.0555074i
\(703\) 7.87586i 0.297044i
\(704\) 32.5389 15.3698i 1.22635 0.579273i
\(705\) 0 0
\(706\) −1.00344 + 5.26719i −0.0377649 + 0.198233i
\(707\) 1.88273 0.0708075
\(708\) −6.24914 + 15.8061i −0.234857 + 0.594028i
\(709\) 28.9966i 1.08899i −0.838764 0.544494i \(-0.816722\pi\)
0.838764 0.544494i \(-0.183278\pi\)
\(710\) 0 0
\(711\) −11.5569 −0.433418
\(712\) 9.83709 + 6.23271i 0.368661 + 0.233581i
\(713\) 3.76547i 0.141018i
\(714\) 9.88273 + 1.88273i 0.369852 + 0.0704595i
\(715\) 0 0
\(716\) −7.80605 + 19.7440i −0.291726 + 0.737867i
\(717\) 10.1173 0.377836
\(718\) 18.0552 + 3.43965i 0.673814 + 0.128367i
\(719\) −26.8793 −1.00243 −0.501214 0.865323i \(-0.667113\pi\)
−0.501214 + 0.865323i \(0.667113\pi\)
\(720\) 0 0
\(721\) 9.57602 0.356630
\(722\) 24.8384 + 4.73190i 0.924391 + 0.176103i
\(723\) −16.8793 −0.627748
\(724\) 10.3810 26.2569i 0.385807 0.975829i
\(725\) 0 0
\(726\) 12.8289 + 2.44400i 0.476124 + 0.0907052i
\(727\) 41.8138i 1.55079i 0.631478 + 0.775394i \(0.282449\pi\)
−0.631478 + 0.775394i \(0.717551\pi\)
\(728\) −7.91883 + 12.4983i −0.293491 + 0.463217i
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) 14.2277i 0.526229i
\(732\) −6.61555 + 16.7328i −0.244518 + 0.618463i
\(733\) −30.0844 −1.11119 −0.555597 0.831452i \(-0.687510\pi\)
−0.555597 + 0.831452i \(0.687510\pi\)
\(734\) −6.06980 + 31.8613i −0.224041 + 1.17602i
\(735\) 0 0
\(736\) −4.84053 + 3.52588i −0.178424 + 0.129966i
\(737\) 17.9931i 0.662785i
\(738\) −5.39400 1.02760i −0.198556 0.0378264i
\(739\) 29.0449i 1.06843i 0.845348 + 0.534217i \(0.179393\pi\)
−0.845348 + 0.534217i \(0.820607\pi\)
\(740\) 0 0
\(741\) 5.88273i 0.216108i
\(742\) 0.498281 2.61555i 0.0182925 0.0960198i
\(743\) 43.2863i 1.58802i 0.607905 + 0.794010i \(0.292010\pi\)
−0.607905 + 0.794010i \(0.707990\pi\)
\(744\) −8.49828 5.38445i −0.311562 0.197404i
\(745\) 0 0
\(746\) −21.4492 4.08623i −0.785311 0.149608i
\(747\) −5.88273 −0.215238
\(748\) 63.2242 + 24.9966i 2.31171 + 0.913965i
\(749\) 16.2208i 0.592694i
\(750\) 0 0
\(751\) 41.7846 1.52474 0.762370 0.647141i \(-0.224036\pi\)
0.762370 + 0.647141i \(0.224036\pi\)
\(752\) 27.5044 29.3465i 1.00298 1.07016i
\(753\) 11.8466i 0.431716i
\(754\) 2.94137 15.4396i 0.107118 0.562279i
\(755\) 0 0
\(756\) 0.692226 1.75086i 0.0251760 0.0636781i
\(757\) −16.3258 −0.593372 −0.296686 0.954975i \(-0.595881\pi\)
−0.296686 + 0.954975i \(0.595881\pi\)
\(758\) 1.66463 8.73787i 0.0604620 0.317374i
\(759\) −4.76203 −0.172851
\(760\) 0 0
\(761\) 50.2208 1.82050 0.910251 0.414057i \(-0.135889\pi\)
0.910251 + 0.414057i \(0.135889\pi\)
\(762\) −4.80949 + 25.2457i −0.174230 + 0.914555i
\(763\) −1.77234 −0.0641631
\(764\) −14.8793 5.88273i −0.538314 0.212830i
\(765\) 0 0
\(766\) 0.778457 4.08623i 0.0281268 0.147642i
\(767\) 47.2242i 1.70517i
\(768\) −1.03581 15.9664i −0.0373766 0.576139i
\(769\) 31.3415 1.13020 0.565101 0.825021i \(-0.308837\pi\)
0.565101 + 0.825021i \(0.308837\pi\)
\(770\) 0 0
\(771\) 10.6707i 0.384297i
\(772\) −3.58795 + 9.07506i −0.129133 + 0.326619i
\(773\) 9.11383 0.327802 0.163901 0.986477i \(-0.447592\pi\)
0.163901 + 0.986477i \(0.447592\pi\)
\(774\) 2.61555 + 0.498281i 0.0940139 + 0.0179103i
\(775\) 0 0
\(776\) −25.9069 + 40.8888i −0.930003 + 1.46782i
\(777\) 7.00344i 0.251247i
\(778\) −3.23615 + 16.9870i −0.116022 + 0.609014i
\(779\) 4.11039i 0.147270i
\(780\) 0 0
\(781\) 58.4622i 2.09194i
\(782\) −11.1138 2.11727i −0.397430 0.0757133i
\(783\) 2.00000i 0.0714742i
\(784\) 17.8435 + 16.7234i 0.637267 + 0.597265i
\(785\) 0 0
\(786\) 1.68879 8.86469i 0.0602371 0.316193i
\(787\) 36.2208 1.29113 0.645566 0.763705i \(-0.276622\pi\)
0.645566 + 0.763705i \(0.276622\pi\)
\(788\) −5.36802 2.12232i −0.191228 0.0756046i
\(789\) 1.94480i 0.0692369i
\(790\) 0 0
\(791\) 14.4240