Properties

Label 600.2.d.g.349.5
Level 600
Weight 2
Character 600.349
Analytic conductor 4.791
Analytic rank 0
Dimension 8
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: \(8\)
Coefficient field: 8.0.214798336.3
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 349.5
Root \(1.23291 - 0.692769i\) of \(x^{8} - 2 x^{7} - 2 x^{5} + 9 x^{4} - 4 x^{3} - 16 x + 16\)
Character \(\chi\) \(=\) 600.349
Dual form 600.2.d.g.349.6

$q$-expansion

\(f(q)\) \(=\) \(q+(0.192769 - 1.40101i) q^{2} -1.00000 q^{3} +(-1.92568 - 0.540143i) q^{4} +(-0.192769 + 1.40101i) q^{6} +0.0802864i q^{7} +(-1.12796 + 2.59378i) q^{8} +1.00000 q^{9} +O(q^{10})\) \(q+(0.192769 - 1.40101i) q^{2} -1.00000 q^{3} +(-1.92568 - 0.540143i) q^{4} +(-0.192769 + 1.40101i) q^{6} +0.0802864i q^{7} +(-1.12796 + 2.59378i) q^{8} +1.00000 q^{9} +2.41649i q^{11} +(1.92568 + 0.540143i) q^{12} -5.26785 q^{13} +(0.112482 + 0.0154767i) q^{14} +(3.41649 + 2.08029i) q^{16} -0.255918i q^{17} +(0.192769 - 1.40101i) q^{18} +6.95864i q^{19} -0.0802864i q^{21} +(3.38554 + 0.465824i) q^{22} +1.64542i q^{23} +(1.12796 - 2.59378i) q^{24} +(-1.01548 + 7.38033i) q^{26} -1.00000 q^{27} +(0.0433661 - 0.154606i) q^{28} +4.51516i q^{29} +8.29484 q^{31} +(3.57310 - 4.38554i) q^{32} -2.41649i q^{33} +(-0.358545 - 0.0493330i) q^{34} +(-1.92568 - 0.540143i) q^{36} +2.67241 q^{37} +(9.74915 + 1.34141i) q^{38} +5.26785 q^{39} -8.11921 q^{41} +(-0.112482 - 0.0154767i) q^{42} +4.08890 q^{43} +(1.30525 - 4.65339i) q^{44} +(2.30525 + 0.317185i) q^{46} +5.70272i q^{47} +(-3.41649 - 2.08029i) q^{48} +6.99355 q^{49} +0.255918i q^{51} +(10.1442 + 2.84539i) q^{52} -11.5627 q^{53} +(-0.192769 + 1.40101i) q^{54} +(-0.208245 - 0.0905597i) q^{56} -6.95864i q^{57} +(6.32580 + 0.870381i) q^{58} +12.6963i q^{59} -11.9403i q^{61} +(1.59899 - 11.6212i) q^{62} +0.0802864i q^{63} +(-5.45542 - 5.85136i) q^{64} +(-3.38554 - 0.465824i) q^{66} -7.27979 q^{67} +(-0.138232 + 0.492816i) q^{68} -1.64542i q^{69} -11.3481 q^{71} +(-1.12796 + 2.59378i) q^{72} +12.0779i q^{73} +(0.515157 - 3.74408i) q^{74} +(3.75866 - 13.4001i) q^{76} -0.194011 q^{77} +(1.01548 - 7.38033i) q^{78} -5.50539 q^{79} +1.00000 q^{81} +(-1.56513 + 11.3751i) q^{82} +9.20811 q^{83} +(-0.0433661 + 0.154606i) q^{84} +(0.788212 - 5.72861i) q^{86} -4.51516i q^{87} +(-6.26785 - 2.72570i) q^{88} -11.9173 q^{89} -0.422937i q^{91} +(0.888760 - 3.16855i) q^{92} -8.29484 q^{93} +(7.98959 + 1.09931i) q^{94} +(-3.57310 + 4.38554i) q^{96} +8.50539i q^{97} +(1.34814 - 9.79807i) q^{98} +2.41649i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q - 2q^{2} - 8q^{3} - 4q^{4} + 2q^{6} - 8q^{8} + 8q^{9} + O(q^{10}) \) \( 8q - 2q^{2} - 8q^{3} - 4q^{4} + 2q^{6} - 8q^{8} + 8q^{9} + 4q^{12} + 6q^{14} + 8q^{16} - 2q^{18} + 20q^{22} + 8q^{24} - 2q^{26} - 8q^{27} + 24q^{28} + 8q^{31} - 12q^{32} - 12q^{34} - 4q^{36} + 14q^{38} - 6q^{42} - 8q^{43} + 12q^{44} + 20q^{46} - 8q^{48} + 24q^{52} + 8q^{53} + 2q^{54} + 8q^{56} - 20q^{58} + 26q^{62} + 32q^{64} - 20q^{66} + 24q^{67} + 36q^{68} - 40q^{71} - 8q^{72} - 8q^{74} - 20q^{76} - 24q^{77} + 2q^{78} + 16q^{79} + 8q^{81} - 16q^{82} - 32q^{83} - 24q^{84} - 18q^{86} - 8q^{88} + 28q^{92} - 8q^{93} + 4q^{94} + 12q^{96} - 40q^{98} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.192769 1.40101i 0.136308 0.990667i
\(3\) −1.00000 −0.577350
\(4\) −1.92568 0.540143i −0.962840 0.270072i
\(5\) 0 0
\(6\) −0.192769 + 1.40101i −0.0786975 + 0.571962i
\(7\) 0.0802864i 0.0303454i 0.999885 + 0.0151727i \(0.00482980\pi\)
−0.999885 + 0.0151727i \(0.995170\pi\)
\(8\) −1.12796 + 2.59378i −0.398794 + 0.917041i
\(9\) 1.00000 0.333333
\(10\) 0 0
\(11\) 2.41649i 0.728599i 0.931282 + 0.364300i \(0.118692\pi\)
−0.931282 + 0.364300i \(0.881308\pi\)
\(12\) 1.92568 + 0.540143i 0.555896 + 0.155926i
\(13\) −5.26785 −1.46104 −0.730520 0.682892i \(-0.760722\pi\)
−0.730520 + 0.682892i \(0.760722\pi\)
\(14\) 0.112482 + 0.0154767i 0.0300622 + 0.00413632i
\(15\) 0 0
\(16\) 3.41649 + 2.08029i 0.854123 + 0.520072i
\(17\) 0.255918i 0.0620692i −0.999518 0.0310346i \(-0.990120\pi\)
0.999518 0.0310346i \(-0.00988021\pi\)
\(18\) 0.192769 1.40101i 0.0454360 0.330222i
\(19\) 6.95864i 1.59642i 0.602378 + 0.798211i \(0.294220\pi\)
−0.602378 + 0.798211i \(0.705780\pi\)
\(20\) 0 0
\(21\) 0.0802864i 0.0175199i
\(22\) 3.38554 + 0.465824i 0.721799 + 0.0993139i
\(23\) 1.64542i 0.343093i 0.985176 + 0.171546i \(0.0548764\pi\)
−0.985176 + 0.171546i \(0.945124\pi\)
\(24\) 1.12796 2.59378i 0.230244 0.529454i
\(25\) 0 0
\(26\) −1.01548 + 7.38033i −0.199151 + 1.44740i
\(27\) −1.00000 −0.192450
\(28\) 0.0433661 0.154606i 0.00819543 0.0292178i
\(29\) 4.51516i 0.838444i 0.907884 + 0.419222i \(0.137697\pi\)
−0.907884 + 0.419222i \(0.862303\pi\)
\(30\) 0 0
\(31\) 8.29484 1.48980 0.744899 0.667177i \(-0.232498\pi\)
0.744899 + 0.667177i \(0.232498\pi\)
\(32\) 3.57310 4.38554i 0.631641 0.775261i
\(33\) 2.41649i 0.420657i
\(34\) −0.358545 0.0493330i −0.0614899 0.00846053i
\(35\) 0 0
\(36\) −1.92568 0.540143i −0.320947 0.0900239i
\(37\) 2.67241 0.439341 0.219671 0.975574i \(-0.429502\pi\)
0.219671 + 0.975574i \(0.429502\pi\)
\(38\) 9.74915 + 1.34141i 1.58152 + 0.217605i
\(39\) 5.26785 0.843531
\(40\) 0 0
\(41\) −8.11921 −1.26801 −0.634004 0.773330i \(-0.718590\pi\)
−0.634004 + 0.773330i \(0.718590\pi\)
\(42\) −0.112482 0.0154767i −0.0173564 0.00238811i
\(43\) 4.08890 0.623551 0.311776 0.950156i \(-0.399076\pi\)
0.311776 + 0.950156i \(0.399076\pi\)
\(44\) 1.30525 4.65339i 0.196774 0.701525i
\(45\) 0 0
\(46\) 2.30525 + 0.317185i 0.339891 + 0.0467663i
\(47\) 5.70272i 0.831827i 0.909404 + 0.415914i \(0.136538\pi\)
−0.909404 + 0.415914i \(0.863462\pi\)
\(48\) −3.41649 2.08029i −0.493128 0.300263i
\(49\) 6.99355 0.999079
\(50\) 0 0
\(51\) 0.255918i 0.0358357i
\(52\) 10.1442 + 2.84539i 1.40675 + 0.394585i
\(53\) −11.5627 −1.58826 −0.794129 0.607749i \(-0.792073\pi\)
−0.794129 + 0.607749i \(0.792073\pi\)
\(54\) −0.192769 + 1.40101i −0.0262325 + 0.190654i
\(55\) 0 0
\(56\) −0.208245 0.0905597i −0.0278280 0.0121016i
\(57\) 6.95864i 0.921694i
\(58\) 6.32580 + 0.870381i 0.830618 + 0.114287i
\(59\) 12.6963i 1.65291i 0.563000 + 0.826457i \(0.309647\pi\)
−0.563000 + 0.826457i \(0.690353\pi\)
\(60\) 0 0
\(61\) 11.9403i 1.52879i −0.644746 0.764397i \(-0.723037\pi\)
0.644746 0.764397i \(-0.276963\pi\)
\(62\) 1.59899 11.6212i 0.203071 1.47589i
\(63\) 0.0802864i 0.0101151i
\(64\) −5.45542 5.85136i −0.681927 0.731420i
\(65\) 0 0
\(66\) −3.38554 0.465824i −0.416731 0.0573389i
\(67\) −7.27979 −0.889367 −0.444684 0.895688i \(-0.646684\pi\)
−0.444684 + 0.895688i \(0.646684\pi\)
\(68\) −0.138232 + 0.492816i −0.0167631 + 0.0597628i
\(69\) 1.64542i 0.198085i
\(70\) 0 0
\(71\) −11.3481 −1.34678 −0.673388 0.739289i \(-0.735162\pi\)
−0.673388 + 0.739289i \(0.735162\pi\)
\(72\) −1.12796 + 2.59378i −0.132931 + 0.305680i
\(73\) 12.0779i 1.41361i 0.707411 + 0.706803i \(0.249863\pi\)
−0.707411 + 0.706803i \(0.750137\pi\)
\(74\) 0.515157 3.74408i 0.0598857 0.435241i
\(75\) 0 0
\(76\) 3.75866 13.4001i 0.431148 1.53710i
\(77\) −0.194011 −0.0221096
\(78\) 1.01548 7.38033i 0.114980 0.835658i
\(79\) −5.50539 −0.619405 −0.309702 0.950834i \(-0.600229\pi\)
−0.309702 + 0.950834i \(0.600229\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) −1.56513 + 11.3751i −0.172840 + 1.25617i
\(83\) 9.20811 1.01072 0.505361 0.862908i \(-0.331359\pi\)
0.505361 + 0.862908i \(0.331359\pi\)
\(84\) −0.0433661 + 0.154606i −0.00473163 + 0.0168689i
\(85\) 0 0
\(86\) 0.788212 5.72861i 0.0849950 0.617731i
\(87\) 4.51516i 0.484076i
\(88\) −6.26785 2.72570i −0.668155 0.290561i
\(89\) −11.9173 −1.26323 −0.631615 0.775283i \(-0.717607\pi\)
−0.631615 + 0.775283i \(0.717607\pi\)
\(90\) 0 0
\(91\) 0.422937i 0.0443358i
\(92\) 0.888760 3.16855i 0.0926597 0.330344i
\(93\) −8.29484 −0.860135
\(94\) 7.98959 + 1.09931i 0.824064 + 0.113385i
\(95\) 0 0
\(96\) −3.57310 + 4.38554i −0.364678 + 0.447597i
\(97\) 8.50539i 0.863592i 0.901971 + 0.431796i \(0.142120\pi\)
−0.901971 + 0.431796i \(0.857880\pi\)
\(98\) 1.34814 9.79807i 0.136183 0.989754i
\(99\) 2.41649i 0.242866i
\(100\) 0 0
\(101\) 7.56270i 0.752516i −0.926515 0.376258i \(-0.877211\pi\)
0.926515 0.376258i \(-0.122789\pi\)
\(102\) 0.358545 + 0.0493330i 0.0355012 + 0.00488469i
\(103\) 1.78544i 0.175925i 0.996124 + 0.0879624i \(0.0280355\pi\)
−0.996124 + 0.0879624i \(0.971964\pi\)
\(104\) 5.94192 13.6637i 0.582653 1.33983i
\(105\) 0 0
\(106\) −2.22893 + 16.1995i −0.216492 + 1.57343i
\(107\) −10.4705 −1.01222 −0.506110 0.862469i \(-0.668917\pi\)
−0.506110 + 0.862469i \(0.668917\pi\)
\(108\) 1.92568 + 0.540143i 0.185299 + 0.0519753i
\(109\) 3.64298i 0.348934i −0.984663 0.174467i \(-0.944180\pi\)
0.984663 0.174467i \(-0.0558203\pi\)
\(110\) 0 0
\(111\) −2.67241 −0.253654
\(112\) −0.167019 + 0.274298i −0.0157818 + 0.0259187i
\(113\) 8.83298i 0.830937i −0.909608 0.415468i \(-0.863618\pi\)
0.909608 0.415468i \(-0.136382\pi\)
\(114\) −9.74915 1.34141i −0.913092 0.125634i
\(115\) 0 0
\(116\) 2.43883 8.69475i 0.226440 0.807287i
\(117\) −5.26785 −0.487013
\(118\) 17.7877 + 2.44744i 1.63749 + 0.225305i
\(119\) 0.0205467 0.00188351
\(120\) 0 0
\(121\) 5.16057 0.469143
\(122\) −16.7285 2.30171i −1.51452 0.208387i
\(123\) 8.11921 0.732085
\(124\) −15.9732 4.48040i −1.43444 0.402352i
\(125\) 0 0
\(126\) 0.112482 + 0.0154767i 0.0100207 + 0.00137877i
\(127\) 8.69628i 0.771670i −0.922568 0.385835i \(-0.873913\pi\)
0.922568 0.385835i \(-0.126087\pi\)
\(128\) −9.24947 + 6.51516i −0.817546 + 0.575864i
\(129\) −4.08890 −0.360008
\(130\) 0 0
\(131\) 10.7916i 0.942868i 0.881901 + 0.471434i \(0.156264\pi\)
−0.881901 + 0.471434i \(0.843736\pi\)
\(132\) −1.30525 + 4.65339i −0.113608 + 0.405026i
\(133\) −0.558684 −0.0484440
\(134\) −1.40331 + 10.1991i −0.121228 + 0.881066i
\(135\) 0 0
\(136\) 0.663796 + 0.288665i 0.0569200 + 0.0247528i
\(137\) 11.5421i 0.986112i 0.869997 + 0.493056i \(0.164120\pi\)
−0.869997 + 0.493056i \(0.835880\pi\)
\(138\) −2.30525 0.317185i −0.196236 0.0270006i
\(139\) 0.214558i 0.0181986i 0.999959 + 0.00909928i \(0.00289643\pi\)
−0.999959 + 0.00909928i \(0.997104\pi\)
\(140\) 0 0
\(141\) 5.70272i 0.480256i
\(142\) −2.18757 + 15.8989i −0.183576 + 1.33421i
\(143\) 12.7297i 1.06451i
\(144\) 3.41649 + 2.08029i 0.284708 + 0.173357i
\(145\) 0 0
\(146\) 16.9212 + 2.32823i 1.40041 + 0.192686i
\(147\) −6.99355 −0.576819
\(148\) −5.14621 1.44348i −0.423015 0.118654i
\(149\) 23.0475i 1.88813i −0.329762 0.944064i \(-0.606969\pi\)
0.329762 0.944064i \(-0.393031\pi\)
\(150\) 0 0
\(151\) 9.48573 0.771938 0.385969 0.922512i \(-0.373867\pi\)
0.385969 + 0.922512i \(0.373867\pi\)
\(152\) −18.0492 7.84906i −1.46398 0.636643i
\(153\) 0.255918i 0.0206897i
\(154\) −0.0373993 + 0.271812i −0.00301372 + 0.0219033i
\(155\) 0 0
\(156\) −10.1442 2.84539i −0.812186 0.227814i
\(157\) −6.34413 −0.506316 −0.253158 0.967425i \(-0.581469\pi\)
−0.253158 + 0.967425i \(0.581469\pi\)
\(158\) −1.06127 + 7.71313i −0.0844298 + 0.613624i
\(159\) 11.5627 0.916981
\(160\) 0 0
\(161\) −0.132104 −0.0104113
\(162\) 0.192769 1.40101i 0.0151453 0.110074i
\(163\) 12.4100 0.972030 0.486015 0.873951i \(-0.338450\pi\)
0.486015 + 0.873951i \(0.338450\pi\)
\(164\) 15.6350 + 4.38554i 1.22089 + 0.342453i
\(165\) 0 0
\(166\) 1.77504 12.9007i 0.137769 1.00129i
\(167\) 23.2654i 1.80033i 0.435547 + 0.900166i \(0.356555\pi\)
−0.435547 + 0.900166i \(0.643445\pi\)
\(168\) 0.208245 + 0.0905597i 0.0160665 + 0.00698683i
\(169\) 14.7503 1.13464
\(170\) 0 0
\(171\) 6.95864i 0.532140i
\(172\) −7.87391 2.20859i −0.600380 0.168403i
\(173\) −8.63897 −0.656809 −0.328404 0.944537i \(-0.606511\pi\)
−0.328404 + 0.944537i \(0.606511\pi\)
\(174\) −6.32580 0.870381i −0.479557 0.0659834i
\(175\) 0 0
\(176\) −5.02699 + 8.25592i −0.378924 + 0.622313i
\(177\) 12.6963i 0.954311i
\(178\) −2.29728 + 16.6963i −0.172188 + 1.25144i
\(179\) 9.40544i 0.702996i −0.936189 0.351498i \(-0.885672\pi\)
0.936189 0.351498i \(-0.114328\pi\)
\(180\) 0 0
\(181\) 6.43487i 0.478300i 0.970983 + 0.239150i \(0.0768688\pi\)
−0.970983 + 0.239150i \(0.923131\pi\)
\(182\) −0.592540 0.0815289i −0.0439220 0.00604333i
\(183\) 11.9403i 0.882649i
\(184\) −4.26785 1.85596i −0.314630 0.136823i
\(185\) 0 0
\(186\) −1.59899 + 11.6212i −0.117243 + 0.852107i
\(187\) 0.618423 0.0452236
\(188\) 3.08029 10.9816i 0.224653 0.800917i
\(189\) 0.0802864i 0.00583997i
\(190\) 0 0
\(191\) −5.56270 −0.402503 −0.201251 0.979540i \(-0.564501\pi\)
−0.201251 + 0.979540i \(0.564501\pi\)
\(192\) 5.45542 + 5.85136i 0.393711 + 0.422286i
\(193\) 18.4227i 1.32609i 0.748578 + 0.663046i \(0.230737\pi\)
−0.748578 + 0.663046i \(0.769263\pi\)
\(194\) 11.9162 + 1.63957i 0.855531 + 0.117714i
\(195\) 0 0
\(196\) −13.4674 3.77752i −0.961954 0.269823i
\(197\) 18.0239 1.28415 0.642074 0.766643i \(-0.278074\pi\)
0.642074 + 0.766643i \(0.278074\pi\)
\(198\) 3.38554 + 0.465824i 0.240600 + 0.0331046i
\(199\) −20.1214 −1.42637 −0.713183 0.700977i \(-0.752747\pi\)
−0.713183 + 0.700977i \(0.752747\pi\)
\(200\) 0 0
\(201\) 7.27979 0.513476
\(202\) −10.5954 1.45785i −0.745493 0.102574i
\(203\) −0.362505 −0.0254429
\(204\) 0.138232 0.492816i 0.00967820 0.0345040i
\(205\) 0 0
\(206\) 2.50143 + 0.344177i 0.174283 + 0.0239800i
\(207\) 1.64542i 0.114364i
\(208\) −17.9976 10.9586i −1.24791 0.759845i
\(209\) −16.8155 −1.16315
\(210\) 0 0
\(211\) 3.25592i 0.224147i 0.993700 + 0.112073i \(0.0357492\pi\)
−0.993700 + 0.112073i \(0.964251\pi\)
\(212\) 22.2661 + 6.24551i 1.52924 + 0.428943i
\(213\) 11.3481 0.777562
\(214\) −2.01838 + 14.6693i −0.137974 + 1.00277i
\(215\) 0 0
\(216\) 1.12796 2.59378i 0.0767479 0.176485i
\(217\) 0.665963i 0.0452085i
\(218\) −5.10387 0.702253i −0.345678 0.0475626i
\(219\) 12.0779i 0.816146i
\(220\) 0 0
\(221\) 1.34814i 0.0906856i
\(222\) −0.515157 + 3.74408i −0.0345750 + 0.251286i
\(223\) 26.9911i 1.80746i −0.428104 0.903730i \(-0.640818\pi\)
0.428104 0.903730i \(-0.359182\pi\)
\(224\) 0.352099 + 0.286871i 0.0235256 + 0.0191674i
\(225\) 0 0
\(226\) −12.3751 1.70272i −0.823181 0.113263i
\(227\) 19.8219 1.31563 0.657814 0.753180i \(-0.271481\pi\)
0.657814 + 0.753180i \(0.271481\pi\)
\(228\) −3.75866 + 13.4001i −0.248923 + 0.887444i
\(229\) 21.6797i 1.43264i −0.697773 0.716319i \(-0.745826\pi\)
0.697773 0.716319i \(-0.254174\pi\)
\(230\) 0 0
\(231\) 0.194011 0.0127650
\(232\) −11.7113 5.09291i −0.768887 0.334366i
\(233\) 17.2733i 1.13161i −0.824538 0.565807i \(-0.808565\pi\)
0.824538 0.565807i \(-0.191435\pi\)
\(234\) −1.01548 + 7.38033i −0.0663838 + 0.482468i
\(235\) 0 0
\(236\) 6.85781 24.4490i 0.446405 1.59149i
\(237\) 5.50539 0.357614
\(238\) 0.00396076 0.0287862i 0.000256738 0.00186594i
\(239\) 16.3718 1.05900 0.529502 0.848309i \(-0.322379\pi\)
0.529502 + 0.848309i \(0.322379\pi\)
\(240\) 0 0
\(241\) −6.82654 −0.439736 −0.219868 0.975530i \(-0.570563\pi\)
−0.219868 + 0.975530i \(0.570563\pi\)
\(242\) 0.994797 7.23003i 0.0639480 0.464764i
\(243\) −1.00000 −0.0641500
\(244\) −6.44945 + 22.9931i −0.412884 + 1.47198i
\(245\) 0 0
\(246\) 1.56513 11.3751i 0.0997890 0.725252i
\(247\) 36.6571i 2.33243i
\(248\) −9.35624 + 21.5150i −0.594122 + 1.36621i
\(249\) −9.20811 −0.583540
\(250\) 0 0
\(251\) 2.96969i 0.187445i −0.995598 0.0937225i \(-0.970123\pi\)
0.995598 0.0937225i \(-0.0298766\pi\)
\(252\) 0.0433661 0.154606i 0.00273181 0.00973925i
\(253\) −3.97613 −0.249977
\(254\) −12.1836 1.67637i −0.764467 0.105185i
\(255\) 0 0
\(256\) 7.34482 + 14.2146i 0.459051 + 0.888410i
\(257\) 5.03031i 0.313782i 0.987616 + 0.156891i \(0.0501472\pi\)
−0.987616 + 0.156891i \(0.949853\pi\)
\(258\) −0.788212 + 5.72861i −0.0490719 + 0.356647i
\(259\) 0.214558i 0.0133320i
\(260\) 0 0
\(261\) 4.51516i 0.279481i
\(262\) 15.1192 + 2.08029i 0.934068 + 0.128521i
\(263\) 2.70585i 0.166850i 0.996514 + 0.0834248i \(0.0265859\pi\)
−0.996514 + 0.0834248i \(0.973414\pi\)
\(264\) 6.26785 + 2.72570i 0.385760 + 0.167755i
\(265\) 0 0
\(266\) −0.107697 + 0.782724i −0.00660331 + 0.0479919i
\(267\) 11.9173 0.729326
\(268\) 14.0185 + 3.93213i 0.856319 + 0.240193i
\(269\) 22.3718i 1.36403i 0.731337 + 0.682017i \(0.238897\pi\)
−0.731337 + 0.682017i \(0.761103\pi\)
\(270\) 0 0
\(271\) −0.869741 −0.0528330 −0.0264165 0.999651i \(-0.508410\pi\)
−0.0264165 + 0.999651i \(0.508410\pi\)
\(272\) 0.532383 0.874341i 0.0322804 0.0530147i
\(273\) 0.422937i 0.0255973i
\(274\) 16.1707 + 2.22496i 0.976908 + 0.134415i
\(275\) 0 0
\(276\) −0.888760 + 3.16855i −0.0534971 + 0.190724i
\(277\) 28.6733 1.72281 0.861406 0.507918i \(-0.169585\pi\)
0.861406 + 0.507918i \(0.169585\pi\)
\(278\) 0.300599 + 0.0413600i 0.0180287 + 0.00248061i
\(279\) 8.29484 0.496599
\(280\) 0 0
\(281\) 15.1429 0.903349 0.451674 0.892183i \(-0.350827\pi\)
0.451674 + 0.892183i \(0.350827\pi\)
\(282\) −7.98959 1.09931i −0.475773 0.0654627i
\(283\) 6.23225 0.370469 0.185234 0.982694i \(-0.440696\pi\)
0.185234 + 0.982694i \(0.440696\pi\)
\(284\) 21.8529 + 6.12962i 1.29673 + 0.363726i
\(285\) 0 0
\(286\) −17.8345 2.45389i −1.05458 0.145102i
\(287\) 0.651862i 0.0384782i
\(288\) 3.57310 4.38554i 0.210547 0.258420i
\(289\) 16.9345 0.996147
\(290\) 0 0
\(291\) 8.50539i 0.498595i
\(292\) 6.52377 23.2581i 0.381775 1.36108i
\(293\) 21.5054 1.25636 0.628179 0.778069i \(-0.283800\pi\)
0.628179 + 0.778069i \(0.283800\pi\)
\(294\) −1.34814 + 9.79807i −0.0786250 + 0.571435i
\(295\) 0 0
\(296\) −3.01437 + 6.93165i −0.175207 + 0.402894i
\(297\) 2.41649i 0.140219i
\(298\) −32.2899 4.44284i −1.87051 0.257367i
\(299\) 8.66781i 0.501272i
\(300\) 0 0
\(301\) 0.328283i 0.0189219i
\(302\) 1.82855 13.2896i 0.105221 0.764733i
\(303\) 7.56270i 0.434466i
\(304\) −14.4760 + 23.7741i −0.830253 + 1.36354i
\(305\) 0 0
\(306\) −0.358545 0.0493330i −0.0204966 0.00282018i
\(307\) 3.57706 0.204154 0.102077 0.994777i \(-0.467451\pi\)
0.102077 + 0.994777i \(0.467451\pi\)
\(308\) 0.373604 + 0.104794i 0.0212880 + 0.00597118i
\(309\) 1.78544i 0.101570i
\(310\) 0 0
\(311\) −2.49461 −0.141456 −0.0707282 0.997496i \(-0.522532\pi\)
−0.0707282 + 0.997496i \(0.522532\pi\)
\(312\) −5.94192 + 13.6637i −0.336395 + 0.773553i
\(313\) 9.57246i 0.541068i −0.962710 0.270534i \(-0.912800\pi\)
0.962710 0.270534i \(-0.0872002\pi\)
\(314\) −1.22295 + 8.88821i −0.0690150 + 0.501591i
\(315\) 0 0
\(316\) 10.6016 + 2.97370i 0.596388 + 0.167284i
\(317\) −3.16702 −0.177877 −0.0889387 0.996037i \(-0.528348\pi\)
−0.0889387 + 0.996037i \(0.528348\pi\)
\(318\) 2.22893 16.1995i 0.124992 0.908423i
\(319\) −10.9108 −0.610889
\(320\) 0 0
\(321\) 10.4705 0.584405
\(322\) −0.0254656 + 0.185080i −0.00141914 + 0.0103141i
\(323\) 1.78084 0.0990887
\(324\) −1.92568 0.540143i −0.106982 0.0300080i
\(325\) 0 0
\(326\) 2.39227 17.3866i 0.132495 0.962957i
\(327\) 3.64298i 0.201457i
\(328\) 9.15814 21.0595i 0.505674 1.16281i
\(329\) −0.457851 −0.0252421
\(330\) 0 0
\(331\) 16.5118i 0.907573i 0.891111 + 0.453786i \(0.149927\pi\)
−0.891111 + 0.453786i \(0.850073\pi\)
\(332\) −17.7319 4.97370i −0.973163 0.272967i
\(333\) 2.67241 0.146447
\(334\) 32.5952 + 4.48484i 1.78353 + 0.245400i
\(335\) 0 0
\(336\) 0.167019 0.274298i 0.00911161 0.0149642i
\(337\) 11.8330i 0.644584i −0.946640 0.322292i \(-0.895547\pi\)
0.946640 0.322292i \(-0.104453\pi\)
\(338\) 2.84339 20.6653i 0.154660 1.12405i
\(339\) 8.83298i 0.479742i
\(340\) 0 0
\(341\) 20.0444i 1.08547i
\(342\) 9.74915 + 1.34141i 0.527174 + 0.0725350i
\(343\) 1.12349i 0.0606628i
\(344\) −4.61211 + 10.6057i −0.248668 + 0.571822i
\(345\) 0 0
\(346\) −1.66532 + 12.1033i −0.0895283 + 0.650678i
\(347\) 23.9713 1.28684 0.643422 0.765511i \(-0.277514\pi\)
0.643422 + 0.765511i \(0.277514\pi\)
\(348\) −2.43883 + 8.69475i −0.130735 + 0.466087i
\(349\) 8.91570i 0.477247i 0.971112 + 0.238623i \(0.0766961\pi\)
−0.971112 + 0.238623i \(0.923304\pi\)
\(350\) 0 0
\(351\) 5.26785 0.281177
\(352\) 10.5976 + 8.63437i 0.564855 + 0.460213i
\(353\) 7.35606i 0.391524i 0.980651 + 0.195762i \(0.0627179\pi\)
−0.980651 + 0.195762i \(0.937282\pi\)
\(354\) −17.7877 2.44744i −0.945403 0.130080i
\(355\) 0 0
\(356\) 22.9489 + 6.43704i 1.21629 + 0.341162i
\(357\) −0.0205467 −0.00108745
\(358\) −13.1772 1.81307i −0.696434 0.0958240i
\(359\) −25.2114 −1.33061 −0.665304 0.746572i \(-0.731698\pi\)
−0.665304 + 0.746572i \(0.731698\pi\)
\(360\) 0 0
\(361\) −29.4227 −1.54856
\(362\) 9.01534 + 1.24044i 0.473836 + 0.0651961i
\(363\) −5.16057 −0.270860
\(364\) −0.228446 + 0.814441i −0.0119738 + 0.0426883i
\(365\) 0 0
\(366\) 16.7285 + 2.30171i 0.874411 + 0.120312i
\(367\) 5.86573i 0.306189i 0.988212 + 0.153094i \(0.0489238\pi\)
−0.988212 + 0.153094i \(0.951076\pi\)
\(368\) −3.42294 + 5.62155i −0.178433 + 0.293043i
\(369\) −8.11921 −0.422669
\(370\) 0 0
\(371\) 0.928327i 0.0481963i
\(372\) 15.9732 + 4.48040i 0.828173 + 0.232298i
\(373\) 27.5063 1.42422 0.712111 0.702067i \(-0.247739\pi\)
0.712111 + 0.702067i \(0.247739\pi\)
\(374\) 0.119213 0.866420i 0.00616434 0.0448015i
\(375\) 0 0
\(376\) −14.7916 6.43244i −0.762820 0.331728i
\(377\) 23.7852i 1.22500i
\(378\) −0.112482 0.0154767i −0.00578547 0.000796035i
\(379\) 11.7549i 0.603807i −0.953339 0.301903i \(-0.902378\pi\)
0.953339 0.301903i \(-0.0976220\pi\)
\(380\) 0 0
\(381\) 8.69628i 0.445524i
\(382\) −1.07231 + 7.79341i −0.0548643 + 0.398746i
\(383\) 34.3335i 1.75436i 0.480162 + 0.877180i \(0.340578\pi\)
−0.480162 + 0.877180i \(0.659422\pi\)
\(384\) 9.24947 6.51516i 0.472010 0.332475i
\(385\) 0 0
\(386\) 25.8104 + 3.55131i 1.31372 + 0.180757i
\(387\) 4.08890 0.207850
\(388\) 4.59413 16.3787i 0.233232 0.831501i
\(389\) 2.89515i 0.146790i −0.997303 0.0733951i \(-0.976617\pi\)
0.997303 0.0733951i \(-0.0233834\pi\)
\(390\) 0 0
\(391\) 0.421092 0.0212955
\(392\) −7.88844 + 18.1398i −0.398427 + 0.916196i
\(393\) 10.7916i 0.544365i
\(394\) 3.47444 25.2517i 0.175040 1.27216i
\(395\) 0 0
\(396\) 1.30525 4.65339i 0.0655913 0.233842i
\(397\) −22.9099 −1.14982 −0.574909 0.818218i \(-0.694962\pi\)
−0.574909 + 0.818218i \(0.694962\pi\)
\(398\) −3.87877 + 28.1903i −0.194425 + 1.41305i
\(399\) 0.558684 0.0279692
\(400\) 0 0
\(401\) −12.4337 −0.620910 −0.310455 0.950588i \(-0.600481\pi\)
−0.310455 + 0.950588i \(0.600481\pi\)
\(402\) 1.40331 10.1991i 0.0699910 0.508684i
\(403\) −43.6960 −2.17665
\(404\) −4.08494 + 14.5633i −0.203233 + 0.724553i
\(405\) 0 0
\(406\) −0.0698797 + 0.507875i −0.00346807 + 0.0252054i
\(407\) 6.45785i 0.320104i
\(408\) −0.663796 0.288665i −0.0328628 0.0142910i
\(409\) 32.0886 1.58668 0.793340 0.608778i \(-0.208340\pi\)
0.793340 + 0.608778i \(0.208340\pi\)
\(410\) 0 0
\(411\) 11.5421i 0.569332i
\(412\) 0.964394 3.43819i 0.0475123 0.169388i
\(413\) −1.01934 −0.0501583
\(414\) 2.30525 + 0.317185i 0.113297 + 0.0155888i
\(415\) 0 0
\(416\) −18.8226 + 23.1024i −0.922853 + 1.13269i
\(417\) 0.214558i 0.0105069i
\(418\) −3.24150 + 23.5587i −0.158547 + 1.15230i
\(419\) 16.1364i 0.788317i −0.919043 0.394158i \(-0.871036\pi\)
0.919043 0.394158i \(-0.128964\pi\)
\(420\) 0 0
\(421\) 28.7675i 1.40204i 0.713141 + 0.701021i \(0.247272\pi\)
−0.713141 + 0.701021i \(0.752728\pi\)
\(422\) 4.56159 + 0.627639i 0.222055 + 0.0305530i
\(423\) 5.70272i 0.277276i
\(424\) 13.0422 29.9911i 0.633388 1.45650i
\(425\) 0 0
\(426\) 2.18757 15.8989i 0.105988 0.770304i
\(427\) 0.958640 0.0463918
\(428\) 20.1628 + 5.65556i 0.974605 + 0.273372i
\(429\) 12.7297i 0.614596i
\(430\) 0 0
\(431\) 24.7297 1.19119 0.595594 0.803285i \(-0.296917\pi\)
0.595594 + 0.803285i \(0.296917\pi\)
\(432\) −3.41649 2.08029i −0.164376 0.100088i
\(433\) 4.48816i 0.215687i 0.994168 + 0.107844i \(0.0343946\pi\)
−0.994168 + 0.107844i \(0.965605\pi\)
\(434\) 0.933023 + 0.128377i 0.0447865 + 0.00616228i
\(435\) 0 0
\(436\) −1.96773 + 7.01522i −0.0942373 + 0.335968i
\(437\) −11.4499 −0.547721
\(438\) −16.9212 2.32823i −0.808528 0.111247i
\(439\) −5.96081 −0.284494 −0.142247 0.989831i \(-0.545433\pi\)
−0.142247 + 0.989831i \(0.545433\pi\)
\(440\) 0 0
\(441\) 6.99355 0.333026
\(442\) 1.88876 + 0.259879i 0.0898392 + 0.0123612i
\(443\) −14.2924 −0.679053 −0.339526 0.940597i \(-0.610267\pi\)
−0.339526 + 0.940597i \(0.610267\pi\)
\(444\) 5.14621 + 1.44348i 0.244228 + 0.0685047i
\(445\) 0 0
\(446\) −37.8149 5.20304i −1.79059 0.246371i
\(447\) 23.0475i 1.09011i
\(448\) 0.469784 0.437996i 0.0221952 0.0206933i
\(449\) −24.5529 −1.15872 −0.579362 0.815070i \(-0.696698\pi\)
−0.579362 + 0.815070i \(0.696698\pi\)
\(450\) 0 0
\(451\) 19.6200i 0.923870i
\(452\) −4.77107 + 17.0095i −0.224412 + 0.800060i
\(453\) −9.48573 −0.445678
\(454\) 3.82105 27.7708i 0.179331 1.30335i
\(455\) 0 0
\(456\) 18.0492 + 7.84906i 0.845231 + 0.367566i
\(457\) 28.9108i 1.35239i 0.736722 + 0.676196i \(0.236373\pi\)
−0.736722 + 0.676196i \(0.763627\pi\)
\(458\) −30.3736 4.17917i −1.41927 0.195280i
\(459\) 0.255918i 0.0119452i
\(460\) 0 0
\(461\) 4.35458i 0.202813i −0.994845 0.101407i \(-0.967666\pi\)
0.994845 0.101407i \(-0.0323343\pi\)
\(462\) 0.0373993 0.271812i 0.00173997 0.0126459i
\(463\) 11.1303i 0.517267i −0.965976 0.258634i \(-0.916728\pi\)
0.965976 0.258634i \(-0.0832722\pi\)
\(464\) −9.39282 + 15.4260i −0.436051 + 0.716134i
\(465\) 0 0
\(466\) −24.2002 3.32976i −1.12105 0.154248i
\(467\) −19.1257 −0.885030 −0.442515 0.896761i \(-0.645914\pi\)
−0.442515 + 0.896761i \(0.645914\pi\)
\(468\) 10.1442 + 2.84539i 0.468916 + 0.131528i
\(469\) 0.584467i 0.0269882i
\(470\) 0 0
\(471\) 6.34413 0.292322
\(472\) −32.9314 14.3209i −1.51579 0.659172i
\(473\) 9.88079i 0.454319i
\(474\) 1.06127 7.71313i 0.0487456 0.354276i
\(475\) 0 0
\(476\) −0.0395664 0.0110982i −0.00181352 0.000508684i
\(477\) −11.5627 −0.529419
\(478\) 3.15597 22.9371i 0.144351 1.04912i
\(479\) 25.6358 1.17133 0.585666 0.810553i \(-0.300833\pi\)
0.585666 + 0.810553i \(0.300833\pi\)
\(480\) 0 0
\(481\) −14.0779 −0.641895
\(482\) −1.31594 + 9.56407i −0.0599395 + 0.435632i
\(483\) 0.132104 0.00601096
\(484\) −9.93761 2.78745i −0.451710 0.126702i
\(485\) 0 0
\(486\) −0.192769 + 1.40101i −0.00874416 + 0.0635513i
\(487\) 12.8434i 0.581992i −0.956724 0.290996i \(-0.906013\pi\)
0.956724 0.290996i \(-0.0939866\pi\)
\(488\) 30.9704 + 13.4681i 1.40197 + 0.609673i
\(489\) −12.4100 −0.561202
\(490\) 0 0
\(491\) 16.9887i 0.766689i −0.923605 0.383344i \(-0.874772\pi\)
0.923605 0.383344i \(-0.125228\pi\)
\(492\) −15.6350 4.38554i −0.704881 0.197715i
\(493\) 1.15551 0.0520415
\(494\) −51.3571 7.06634i −2.31066 0.317930i
\(495\) 0 0
\(496\) 28.3393 + 17.2557i 1.27247 + 0.774802i
\(497\) 0.911101i 0.0408684i
\(498\) −1.77504 + 12.9007i −0.0795412 + 0.578094i
\(499\) 14.0521i 0.629060i −0.949248 0.314530i \(-0.898153\pi\)
0.949248 0.314530i \(-0.101847\pi\)
\(500\) 0 0
\(501\) 23.2654i 1.03942i
\(502\) −4.16057 0.572463i −0.185695 0.0255503i
\(503\) 9.53258i 0.425037i 0.977157 + 0.212518i \(0.0681665\pi\)
−0.977157 + 0.212518i \(0.931833\pi\)
\(504\) −0.208245 0.0905597i −0.00927599 0.00403385i
\(505\) 0 0
\(506\) −0.766474 + 5.57062i −0.0340739 + 0.247644i
\(507\) −14.7503 −0.655082
\(508\) −4.69723 + 16.7462i −0.208406 + 0.742995i
\(509\) 30.3450i 1.34502i 0.740088 + 0.672510i \(0.234784\pi\)
−0.740088 + 0.672510i \(0.765216\pi\)
\(510\) 0 0
\(511\) −0.969687 −0.0428964
\(512\) 21.3306 7.55007i 0.942690 0.333669i
\(513\) 6.95864i 0.307231i
\(514\) 7.04754 + 0.969687i 0.310854 + 0.0427710i
\(515\) 0 0
\(516\) 7.87391 + 2.20859i 0.346630 + 0.0972278i
\(517\) −13.7806 −0.606069
\(518\) 0.300599 + 0.0413600i 0.0132075 + 0.00181726i
\(519\) 8.63897 0.379209
\(520\) 0 0
\(521\) 14.4245 0.631949 0.315975 0.948768i \(-0.397669\pi\)
0.315975 + 0.948768i \(0.397669\pi\)
\(522\) 6.32580 + 0.870381i 0.276873 + 0.0380955i
\(523\) −28.2207 −1.23401 −0.617003 0.786961i \(-0.711654\pi\)
−0.617003 + 0.786961i \(0.711654\pi\)
\(524\) 5.82902 20.7812i 0.254642 0.907832i
\(525\) 0 0
\(526\) 3.79093 + 0.521603i 0.165292 + 0.0227430i
\(527\) 2.12280i 0.0924706i
\(528\) 5.02699 8.25592i 0.218772 0.359293i
\(529\) 20.2926 0.882287
\(530\) 0 0
\(531\) 12.6963i 0.550971i
\(532\) 1.07585 + 0.301769i 0.0466439 + 0.0130834i
\(533\) 42.7708 1.85261
\(534\) 2.29728 16.6963i 0.0994129 0.722519i
\(535\) 0 0
\(536\) 8.21130 18.8822i 0.354674 0.815586i
\(537\) 9.40544i 0.405875i
\(538\) 31.3432 + 4.31258i 1.35130 + 0.185929i
\(539\) 16.8999i 0.727928i
\(540\) 0 0
\(541\) 13.4695i 0.579100i 0.957163 + 0.289550i \(0.0935056\pi\)
−0.957163 + 0.289550i \(0.906494\pi\)
\(542\) −0.167659 + 1.21852i −0.00720156 + 0.0523399i
\(543\) 6.43487i 0.276147i
\(544\) −1.12234 0.914421i −0.0481198 0.0392055i
\(545\) 0 0
\(546\) 0.592540 + 0.0815289i 0.0253584 + 0.00348912i
\(547\) 4.42773 0.189316 0.0946581 0.995510i \(-0.469824\pi\)
0.0946581 + 0.995510i \(0.469824\pi\)
\(548\) 6.23441 22.2265i 0.266321 0.949469i
\(549\) 11.9403i 0.509598i
\(550\) 0 0
\(551\) −31.4193 −1.33851
\(552\) 4.26785 + 1.85596i 0.181652 + 0.0789950i
\(553\) 0.442008i 0.0187961i
\(554\) 5.52731 40.1717i 0.234833 1.70673i
\(555\) 0 0
\(556\) 0.115892 0.413170i 0.00491492 0.0175223i
\(557\) −40.2017 −1.70340 −0.851700 0.524030i \(-0.824428\pi\)
−0.851700 + 0.524030i \(0.824428\pi\)
\(558\) 1.59899 11.6212i 0.0676905 0.491964i
\(559\) −21.5397 −0.911033
\(560\) 0 0
\(561\) −0.618423 −0.0261099
\(562\) 2.91907 21.2154i 0.123134 0.894917i
\(563\) −13.1128 −0.552637 −0.276319 0.961066i \(-0.589115\pi\)
−0.276319 + 0.961066i \(0.589115\pi\)
\(564\) −3.08029 + 10.9816i −0.129703 + 0.462410i
\(565\) 0 0
\(566\) 1.20138 8.73146i 0.0504978 0.367011i
\(567\) 0.0802864i 0.00337171i
\(568\) 12.8002 29.4346i 0.537086 1.23505i
\(569\) 11.0257 0.462222 0.231111 0.972927i \(-0.425764\pi\)
0.231111 + 0.972927i \(0.425764\pi\)
\(570\) 0 0
\(571\) 45.6960i 1.91232i −0.292847 0.956159i \(-0.594603\pi\)
0.292847 0.956159i \(-0.405397\pi\)
\(572\) −6.87587 + 24.5134i −0.287495 + 1.02496i
\(573\) 5.56270 0.232385
\(574\) −0.913268 0.125659i −0.0381191 0.00524489i
\(575\) 0 0
\(576\) −5.45542 5.85136i −0.227309 0.243807i
\(577\) 17.2685i 0.718899i 0.933165 + 0.359449i \(0.117035\pi\)
−0.933165 + 0.359449i \(0.882965\pi\)
\(578\) 3.26444 23.7255i 0.135783 0.986850i
\(579\) 18.4227i 0.765620i
\(580\) 0 0
\(581\) 0.739286i 0.0306707i
\(582\) −11.9162 1.63957i −0.493941 0.0679625i
\(583\) 27.9411i 1.15720i
\(584\) −31.3273 13.6233i −1.29633 0.563737i
\(585\) 0 0
\(586\) 4.14557 30.1294i 0.171252 1.24463i
\(587\) −34.7155 −1.43286 −0.716432 0.697657i \(-0.754226\pi\)
−0.716432 + 0.697657i \(0.754226\pi\)
\(588\) 13.4674 + 3.77752i 0.555384 + 0.155782i
\(589\) 57.7208i 2.37835i
\(590\) 0 0
\(591\) −18.0239 −0.741403
\(592\) 9.13026 + 5.55938i 0.375251 + 0.228489i
\(593\) 9.34022i 0.383557i −0.981438 0.191778i \(-0.938575\pi\)
0.981438 0.191778i \(-0.0614255\pi\)
\(594\) −3.38554 0.465824i −0.138910 0.0191130i
\(595\) 0 0
\(596\) −12.4490 + 44.3822i −0.509930 + 1.81797i
\(597\) 20.1214 0.823513
\(598\) −12.1437 1.67088i −0.496594 0.0683274i
\(599\) 13.9110 0.568389 0.284195 0.958767i \(-0.408274\pi\)
0.284195 + 0.958767i \(0.408274\pi\)
\(600\) 0 0
\(601\) 11.7330 0.478600 0.239300 0.970946i \(-0.423082\pi\)
0.239300 + 0.970946i \(0.423082\pi\)
\(602\) 0.459929 + 0.0632826i 0.0187453 + 0.00257921i
\(603\) −7.27979 −0.296456
\(604\) −18.2665 5.12365i −0.743253 0.208478i
\(605\) 0 0
\(606\) 10.5954 + 1.45785i 0.430410 + 0.0592211i
\(607\) 10.8158i 0.438998i 0.975613 + 0.219499i \(0.0704423\pi\)
−0.975613 + 0.219499i \(0.929558\pi\)
\(608\) 30.5174 + 24.8639i 1.23764 + 1.00837i
\(609\) 0.362505 0.0146895
\(610\) 0 0
\(611\) 30.0411i 1.21533i
\(612\) −0.138232 + 0.492816i −0.00558771 + 0.0199209i
\(613\) 17.9632 0.725528 0.362764 0.931881i \(-0.381833\pi\)
0.362764 + 0.931881i \(0.381833\pi\)
\(614\) 0.689546 5.01152i 0.0278278 0.202248i
\(615\) 0 0
\(616\) 0.218837 0.503223i 0.00881718 0.0202754i
\(617\) 12.3576i 0.497500i −0.968568 0.248750i \(-0.919980\pi\)
0.968568 0.248750i \(-0.0800197\pi\)
\(618\) −2.50143 0.344177i −0.100622 0.0138448i
\(619\) 4.99540i 0.200782i 0.994948 + 0.100391i \(0.0320094\pi\)
−0.994948 + 0.100391i \(0.967991\pi\)
\(620\) 0 0
\(621\) 1.64542i 0.0660283i
\(622\) −0.480883 + 3.49498i −0.0192816 + 0.140136i
\(623\) 0.956795i 0.0383332i
\(624\) 17.9976 + 10.9586i 0.720479 + 0.438697i
\(625\) 0 0
\(626\) −13.4112 1.84527i −0.536018 0.0737519i
\(627\) 16.8155 0.671546
\(628\) 12.2168 + 3.42674i 0.487502 + 0.136742i
\(629\) 0.683917i 0.0272696i
\(630\) 0 0
\(631\) −17.9674 −0.715273 −0.357636 0.933861i \(-0.616417\pi\)
−0.357636 + 0.933861i \(0.616417\pi\)
\(632\) 6.20985 14.2798i 0.247015 0.568019i
\(633\) 3.25592i 0.129411i
\(634\) −0.610502 + 4.43704i −0.0242461 + 0.176217i
\(635\) 0 0
\(636\) −22.2661 6.24551i −0.882907 0.247651i
\(637\) −36.8410 −1.45969
\(638\) −2.10327 + 15.2862i −0.0832691 + 0.605188i
\(639\) −11.3481 −0.448925
\(640\) 0 0
\(641\) 27.3638 1.08081 0.540403 0.841406i \(-0.318272\pi\)
0.540403 + 0.841406i \(0.318272\pi\)
\(642\) 2.01838 14.6693i 0.0796591 0.578950i
\(643\) −2.27518 −0.0897245 −0.0448623 0.998993i \(-0.514285\pi\)
−0.0448623 + 0.998993i \(0.514285\pi\)
\(644\) 0.254391 + 0.0713553i 0.0100244 + 0.00281179i
\(645\) 0 0
\(646\) 0.343290 2.49498i 0.0135066 0.0981638i
\(647\) 12.4769i 0.490516i −0.969458 0.245258i \(-0.921127\pi\)
0.969458 0.245258i \(-0.0788726\pi\)
\(648\) −1.12796 + 2.59378i −0.0443104 + 0.101893i
\(649\) −30.6804 −1.20431
\(650\) 0 0
\(651\) 0.665963i 0.0261011i
\(652\) −23.8978 6.70320i −0.935909 0.262518i
\(653\) −29.3055 −1.14681 −0.573406 0.819271i \(-0.694378\pi\)
−0.573406 + 0.819271i \(0.694378\pi\)
\(654\) 5.10387 + 0.702253i 0.199577 + 0.0274603i
\(655\) 0 0
\(656\) −27.7392 16.8903i −1.08303 0.659455i
\(657\) 12.0779i 0.471202i
\(658\) −0.0882593 + 0.641455i −0.00344070 + 0.0250065i
\(659\) 18.6009i 0.724589i 0.932064 + 0.362295i \(0.118007\pi\)
−0.932064 + 0.362295i \(0.881993\pi\)
\(660\) 0 0
\(661\) 16.1318i 0.627456i −0.949513 0.313728i \(-0.898422\pi\)
0.949513 0.313728i \(-0.101578\pi\)
\(662\) 23.1333 + 3.18296i 0.899102 + 0.123709i
\(663\) 1.34814i 0.0523573i
\(664\) −10.3864 + 23.8838i −0.403069 + 0.926873i
\(665\) 0 0
\(666\) 0.515157 3.74408i 0.0199619 0.145080i
\(667\) −7.42931 −0.287664
\(668\) 12.5667 44.8018i 0.486219 1.73343i
\(669\) 26.9911i 1.04354i
\(670\) 0 0
\(671\) 28.8535 1.11388
\(672\) −0.352099 0.286871i −0.0135825 0.0110663i
\(673\) 34.1385i 1.31594i −0.753043 0.657971i \(-0.771415\pi\)
0.753043 0.657971i \(-0.228585\pi\)
\(674\) −16.5782 2.28103i −0.638567 0.0878619i
\(675\) 0 0
\(676\) −28.4043 7.96725i −1.09247 0.306433i
\(677\) 12.1940 0.468654 0.234327 0.972158i \(-0.424711\pi\)
0.234327 + 0.972158i \(0.424711\pi\)
\(678\) 12.3751 + 1.70272i 0.475264 + 0.0653926i
\(679\) −0.682867 −0.0262060
\(680\) 0 0
\(681\) −19.8219 −0.759578
\(682\) 28.0825 + 3.86393i 1.07533 + 0.147958i
\(683\) −21.8567 −0.836322 −0.418161 0.908373i \(-0.637325\pi\)
−0.418161 + 0.908373i \(0.637325\pi\)
\(684\) 3.75866 13.4001i 0.143716 0.512366i
\(685\) 0 0
\(686\) 1.57403 + 0.216574i 0.0600966 + 0.00826883i
\(687\) 21.6797i 0.827134i
\(688\) 13.9697 + 8.50608i 0.532589 + 0.324291i
\(689\) 60.9106 2.32051
\(690\) 0 0
\(691\) 6.17780i 0.235015i −0.993072 0.117507i \(-0.962510\pi\)
0.993072 0.117507i \(-0.0374903\pi\)
\(692\) 16.6359 + 4.66628i 0.632402 + 0.177385i
\(693\) −0.194011 −0.00736988
\(694\) 4.62091 33.5841i 0.175407 1.27483i
\(695\) 0 0
\(696\) 11.7113 + 5.09291i 0.443917 + 0.193046i
\(697\) 2.07785i 0.0787043i
\(698\) 12.4910 + 1.71867i 0.472792 + 0.0650525i
\(699\) 17.2733i 0.653338i
\(700\) 0 0
\(701\) 33.9746i 1.28320i −0.767038 0.641601i \(-0.778270\pi\)
0.767038 0.641601i \(-0.221730\pi\)
\(702\) 1.01548 7.38033i 0.0383267 0.278553i
\(703\) 18.5963i 0.701374i
\(704\) 14.1398 13.1830i 0.532912 0.496852i
\(705\) 0 0
\(706\) 10.3059 + 1.41802i 0.387869 + 0.0533678i
\(707\) 0.607181 0.0228354
\(708\) −6.85781 + 24.4490i −0.257732 + 0.918849i
\(709\) 22.3441i 0.839151i −0.907720 0.419576i \(-0.862179\pi\)
0.907720 0.419576i \(-0.137821\pi\)
\(710\) 0 0
\(711\) −5.50539 −0.206468
\(712\) 13.4422 30.9108i 0.503768 1.15843i
\(713\) 13.6485i 0.511139i
\(714\) −0.00396076 + 0.0287862i −0.000148228 + 0.00107730i
\(715\) 0 0
\(716\) −5.08029 + 18.1119i −0.189859 + 0.676873i
\(717\) −16.3718 −0.611416
\(718\) −4.85997 + 35.3216i −0.181373 + 1.31819i
\(719\) 17.8427 0.665422 0.332711 0.943029i \(-0.392037\pi\)
0.332711 + 0.943029i \(0.392037\pi\)
\(720\) 0 0
\(721\) −0.143347 −0.00533851
\(722\) −5.67177 + 41.2216i −0.211081 + 1.53411i
\(723\) 6.82654 0.253882
\(724\) 3.47575 12.3915i 0.129175 0.460527i
\(725\) 0 0
\(726\) −0.994797 + 7.23003i −0.0369204 + 0.268332i
\(727\) 23.9148i 0.886953i 0.896286 + 0.443476i \(0.146255\pi\)
−0.896286 + 0.443476i \(0.853745\pi\)
\(728\) 1.09701 + 0.477055i 0.0406577 + 0.0176808i
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) 1.04642i 0.0387034i
\(732\) 6.44945 22.9931i 0.238379 0.849850i
\(733\) −15.6789 −0.579112 −0.289556 0.957161i \(-0.593508\pi\)
−0.289556 + 0.957161i \(0.593508\pi\)
\(734\) 8.21797 + 1.13073i 0.303331 + 0.0417360i
\(735\) 0 0
\(736\) 7.21603 + 5.87924i 0.265987 + 0.216712i
\(737\) 17.5915i 0.647992i
\(738\) −1.56513 + 11.3751i −0.0576132 + 0.418724i
\(739\) 22.3083i 0.820622i 0.911946 + 0.410311i \(0.134580\pi\)
−0.911946 + 0.410311i \(0.865420\pi\)
\(740\) 0 0
\(741\) 36.6571i 1.34663i
\(742\) −1.30060 0.178952i −0.0477465 0.00656955i
\(743\) 9.78057i 0.358814i 0.983775 + 0.179407i \(0.0574180\pi\)
−0.983775 + 0.179407i \(0.942582\pi\)
\(744\) 9.35624 21.5150i 0.343017 0.788779i
\(745\) 0 0
\(746\) 5.30235 38.5367i 0.194133 1.41093i
\(747\) 9.20811 0.336907
\(748\) −1.19089 0.334037i −0.0435431 0.0122136i
\(749\) 0.840636i 0.0307162i
\(750\) 0 0
\(751\) −8.05399 −0.293894 −0.146947 0.989144i \(-0.546945\pi\)
−0.146947 + 0.989144i \(0.546945\pi\)
\(752\) −11.8633 + 19.4833i −0.432610 + 0.710483i
\(753\) 2.96969i 0.108221i
\(754\) −33.3234 4.58504i −1.21357 0.166977i
\(755\) 0 0
\(756\) −0.0433661 + 0.154606i −0.00157721 + 0.00562296i
\(757\) 28.4889 1.03545 0.517723 0.855549i \(-0.326780\pi\)
0.517723 + 0.855549i \(0.326780\pi\)
\(758\) −16.4687 2.26597i −0.598171 0.0823037i
\(759\) 3.97613 0.144324
\(760\) 0 0
\(761\) −21.5005 −0.779393 −0.389697 0.920943i \(-0.627420\pi\)
−0.389697 + 0.920943i \(0.627420\pi\)
\(762\) 12.1836 + 1.67637i 0.441365 + 0.0607285i
\(763\) 0.292482 0.0105886
\(764\) 10.7120 + 3.00465i 0.387546 + 0.108705i
\(765\) 0 0
\(766\) 48.1017 + 6.61842i 1.73799 + 0.239133i
\(767\) 66.8821i 2.41497i
\(768\) −7.34482 14.2146i −0.265033 0.512924i
\(769\) −23.5596 −0.849580 −0.424790 0.905292i \(-0.639652\pi\)
−0.424790 + 0.905292i \(0.639652\pi\)
\(770\) 0 0
\(771\) 5.03031i 0.181162i
\(772\) 9.95088 35.4762i 0.358140 1.27682i
\(773\) 31.1655 1.12094 0.560472 0.828173i \(-0.310620\pi\)
0.560472 + 0.828173i \(0.310620\pi\)
\(774\) 0.788212 5.72861i 0.0283317 0.205910i
\(775\) 0 0
\(776\) −22.0611 9.59373i −0.791949 0.344395i
\(777\) 0.214558i 0.00769722i
\(778\) −4.05615 0.558095i −0.145420 0.0200087i
\(779\) 56.4987i 2.02428i
\(780\) 0 0
\(781\) 27.4227i 0.981260i
\(782\) 0.0811733 0.589955i 0.00290275 0.0210968i
\(783\) 4.51516i 0.161359i
\(784\) 23.8934 + 14.5486i 0.853336 + 0.519593i
\(785\) 0 0
\(786\) −15.1192 2.08029i −0.539284 0.0742014i
\(787\) −5.07812 −0.181015 −0.0905077 0.995896i \(-0.528849\pi\)
−0.0905077 + 0.995896i