Properties

Label 546.2.o.b.265.4
Level $546$
Weight $2$
Character 546.265
Analytic conductor $4.360$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 546.o (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(4.35983195036\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(i)\)
Coefficient field: 8.0.836829184.2
Defining polynomial: \(x^{8} + 14 x^{6} + 61 x^{4} + 84 x^{2} + 4\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 265.4
Root \(-0.222191i\) of defining polynomial
Character \(\chi\) \(=\) 546.265
Dual form 546.2.o.b.307.4

$q$-expansion

\(f(q)\) \(=\) \(q+(0.707107 - 0.707107i) q^{2} -1.00000i q^{3} -1.00000i q^{4} +(0.864220 + 0.864220i) q^{5} +(-0.707107 - 0.707107i) q^{6} +(-2.02133 - 1.70711i) q^{7} +(-0.707107 - 0.707107i) q^{8} -1.00000 q^{9} +O(q^{10})\) \(q+(0.707107 - 0.707107i) q^{2} -1.00000i q^{3} -1.00000i q^{4} +(0.864220 + 0.864220i) q^{5} +(-0.707107 - 0.707107i) q^{6} +(-2.02133 - 1.70711i) q^{7} +(-0.707107 - 0.707107i) q^{8} -1.00000 q^{9} +1.22219 q^{10} +(-3.50062 - 3.50062i) q^{11} -1.00000 q^{12} +(3.37930 - 1.25710i) q^{13} +(-2.63640 + 0.222191i) q^{14} +(0.864220 - 0.864220i) q^{15} -1.00000 q^{16} -0.322179 q^{17} +(-0.707107 + 0.707107i) q^{18} +(-1.77219 - 1.77219i) q^{19} +(0.864220 - 0.864220i) q^{20} +(-1.70711 + 2.02133i) q^{21} -4.95063 q^{22} -2.70799i q^{23} +(-0.707107 + 0.707107i) q^{24} -3.50625i q^{25} +(1.50062 - 3.27843i) q^{26} +1.00000i q^{27} +(-1.70711 + 2.02133i) q^{28} +4.82047 q^{29} -1.22219i q^{30} +(1.72844 + 1.72844i) q^{31} +(-0.707107 + 0.707107i) q^{32} +(-3.50062 + 3.50062i) q^{33} +(-0.227815 + 0.227815i) q^{34} +(-0.271560 - 3.22219i) q^{35} +1.00000i q^{36} +(2.27843 + 2.27843i) q^{37} -2.50625 q^{38} +(-1.25710 - 3.37930i) q^{39} -1.22219i q^{40} +(6.46483 + 6.46483i) q^{41} +(0.222191 + 2.63640i) q^{42} +0.393764i q^{43} +(-3.50062 + 3.50062i) q^{44} +(-0.864220 - 0.864220i) q^{45} +(-1.91484 - 1.91484i) q^{46} +(-1.41421 + 1.41421i) q^{47} +1.00000i q^{48} +(1.17157 + 6.90126i) q^{49} +(-2.47929 - 2.47929i) q^{50} +0.322179i q^{51} +(-1.25710 - 3.37930i) q^{52} -2.03142 q^{53} +(0.707107 + 0.707107i) q^{54} -6.05062i q^{55} +(0.222191 + 2.63640i) q^{56} +(-1.77219 + 1.77219i) q^{57} +(3.40859 - 3.40859i) q^{58} +(-10.7599 + 10.7599i) q^{59} +(-0.864220 - 0.864220i) q^{60} -10.6389i q^{61} +2.44438 q^{62} +(2.02133 + 1.70711i) q^{63} +1.00000i q^{64} +(4.00687 + 1.83405i) q^{65} +4.95063i q^{66} +(5.38404 - 5.38404i) q^{67} +0.322179i q^{68} -2.70799 q^{69} +(-2.47046 - 2.08641i) q^{70} +(-0.647652 + 0.647652i) q^{71} +(0.707107 + 0.707107i) q^{72} +(6.85297 - 6.85297i) q^{73} +3.22219 q^{74} -3.50625 q^{75} +(-1.77219 + 1.77219i) q^{76} +(1.09999 + 13.0519i) q^{77} +(-3.27843 - 1.50062i) q^{78} +8.81718 q^{79} +(-0.864220 - 0.864220i) q^{80} +1.00000 q^{81} +9.14265 q^{82} +(6.09203 + 6.09203i) q^{83} +(2.02133 + 1.70711i) q^{84} +(-0.278433 - 0.278433i) q^{85} +(0.278433 + 0.278433i) q^{86} -4.82047i q^{87} +4.95063i q^{88} +(-3.68702 + 3.68702i) q^{89} -1.22219 q^{90} +(-8.97670 - 3.22781i) q^{91} -2.70799 q^{92} +(1.72844 - 1.72844i) q^{93} +2.00000i q^{94} -3.06311i q^{95} +(0.707107 + 0.707107i) q^{96} +(-5.20299 - 5.20299i) q^{97} +(5.70836 + 4.05150i) q^{98} +(3.50062 + 3.50062i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q - 4q^{5} - 8q^{9} + O(q^{10}) \) \( 8q - 4q^{5} - 8q^{9} + 4q^{10} - 8q^{12} + 16q^{13} - 4q^{14} - 4q^{15} - 8q^{16} + 4q^{17} - 8q^{19} - 4q^{20} - 8q^{21} - 12q^{22} - 16q^{26} - 8q^{28} + 12q^{29} - 8q^{31} - 8q^{34} - 24q^{35} - 4q^{37} - 4q^{38} - 4q^{39} + 12q^{41} - 4q^{42} + 4q^{45} + 24q^{46} + 32q^{49} - 8q^{50} - 4q^{52} + 40q^{53} - 4q^{56} - 8q^{57} + 4q^{58} - 8q^{59} + 4q^{60} + 8q^{62} - 12q^{65} + 32q^{67} - 28q^{69} + 8q^{70} - 12q^{71} + 20q^{73} + 20q^{74} - 12q^{75} - 8q^{76} + 8q^{77} - 4q^{78} + 24q^{79} + 4q^{80} + 8q^{81} + 40q^{82} + 44q^{83} + 20q^{85} - 20q^{86} + 16q^{89} - 4q^{90} - 28q^{91} - 28q^{92} - 8q^{93} - 8q^{97} - 16q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/546\mathbb{Z}\right)^\times\).

\(n\) \(157\) \(365\) \(379\)
\(\chi(n)\) \(-1\) \(1\) \(e\left(\frac{3}{4}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.707107 0.707107i 0.500000 0.500000i
\(3\) 1.00000i 0.577350i
\(4\) 1.00000i 0.500000i
\(5\) 0.864220 + 0.864220i 0.386491 + 0.386491i 0.873434 0.486943i \(-0.161888\pi\)
−0.486943 + 0.873434i \(0.661888\pi\)
\(6\) −0.707107 0.707107i −0.288675 0.288675i
\(7\) −2.02133 1.70711i −0.763992 0.645226i
\(8\) −0.707107 0.707107i −0.250000 0.250000i
\(9\) −1.00000 −0.333333
\(10\) 1.22219 0.386491
\(11\) −3.50062 3.50062i −1.05548 1.05548i −0.998368 0.0571102i \(-0.981811\pi\)
−0.0571102 0.998368i \(-0.518189\pi\)
\(12\) −1.00000 −0.288675
\(13\) 3.37930 1.25710i 0.937250 0.348657i
\(14\) −2.63640 + 0.222191i −0.704609 + 0.0593831i
\(15\) 0.864220 0.864220i 0.223141 0.223141i
\(16\) −1.00000 −0.250000
\(17\) −0.322179 −0.0781399 −0.0390699 0.999236i \(-0.512440\pi\)
−0.0390699 + 0.999236i \(0.512440\pi\)
\(18\) −0.707107 + 0.707107i −0.166667 + 0.166667i
\(19\) −1.77219 1.77219i −0.406567 0.406567i 0.473972 0.880540i \(-0.342820\pi\)
−0.880540 + 0.473972i \(0.842820\pi\)
\(20\) 0.864220 0.864220i 0.193245 0.193245i
\(21\) −1.70711 + 2.02133i −0.372521 + 0.441091i
\(22\) −4.95063 −1.05548
\(23\) 2.70799i 0.564655i −0.959318 0.282328i \(-0.908894\pi\)
0.959318 0.282328i \(-0.0911065\pi\)
\(24\) −0.707107 + 0.707107i −0.144338 + 0.144338i
\(25\) 3.50625i 0.701250i
\(26\) 1.50062 3.27843i 0.294297 0.642954i
\(27\) 1.00000i 0.192450i
\(28\) −1.70711 + 2.02133i −0.322613 + 0.381996i
\(29\) 4.82047 0.895140 0.447570 0.894249i \(-0.352290\pi\)
0.447570 + 0.894249i \(0.352290\pi\)
\(30\) 1.22219i 0.223141i
\(31\) 1.72844 + 1.72844i 0.310437 + 0.310437i 0.845079 0.534642i \(-0.179553\pi\)
−0.534642 + 0.845079i \(0.679553\pi\)
\(32\) −0.707107 + 0.707107i −0.125000 + 0.125000i
\(33\) −3.50062 + 3.50062i −0.609381 + 0.609381i
\(34\) −0.227815 + 0.227815i −0.0390699 + 0.0390699i
\(35\) −0.271560 3.22219i −0.0459021 0.544650i
\(36\) 1.00000i 0.166667i
\(37\) 2.27843 + 2.27843i 0.374572 + 0.374572i 0.869139 0.494567i \(-0.164673\pi\)
−0.494567 + 0.869139i \(0.664673\pi\)
\(38\) −2.50625 −0.406567
\(39\) −1.25710 3.37930i −0.201297 0.541122i
\(40\) 1.22219i 0.193245i
\(41\) 6.46483 + 6.46483i 1.00964 + 1.00964i 0.999953 + 0.00968403i \(0.00308257\pi\)
0.00968403 + 0.999953i \(0.496917\pi\)
\(42\) 0.222191 + 2.63640i 0.0342849 + 0.406806i
\(43\) 0.393764i 0.0600485i 0.999549 + 0.0300242i \(0.00955845\pi\)
−0.999549 + 0.0300242i \(0.990442\pi\)
\(44\) −3.50062 + 3.50062i −0.527739 + 0.527739i
\(45\) −0.864220 0.864220i −0.128830 0.128830i
\(46\) −1.91484 1.91484i −0.282328 0.282328i
\(47\) −1.41421 + 1.41421i −0.206284 + 0.206284i −0.802686 0.596402i \(-0.796597\pi\)
0.596402 + 0.802686i \(0.296597\pi\)
\(48\) 1.00000i 0.144338i
\(49\) 1.17157 + 6.90126i 0.167368 + 0.985895i
\(50\) −2.47929 2.47929i −0.350625 0.350625i
\(51\) 0.322179i 0.0451141i
\(52\) −1.25710 3.37930i −0.174328 0.468625i
\(53\) −2.03142 −0.279037 −0.139518 0.990219i \(-0.544555\pi\)
−0.139518 + 0.990219i \(0.544555\pi\)
\(54\) 0.707107 + 0.707107i 0.0962250 + 0.0962250i
\(55\) 6.05062i 0.815865i
\(56\) 0.222191 + 2.63640i 0.0296916 + 0.352304i
\(57\) −1.77219 + 1.77219i −0.234732 + 0.234732i
\(58\) 3.40859 3.40859i 0.447570 0.447570i
\(59\) −10.7599 + 10.7599i −1.40081 + 1.40081i −0.603300 + 0.797515i \(0.706148\pi\)
−0.797515 + 0.603300i \(0.793852\pi\)
\(60\) −0.864220 0.864220i −0.111570 0.111570i
\(61\) 10.6389i 1.36217i −0.732203 0.681086i \(-0.761508\pi\)
0.732203 0.681086i \(-0.238492\pi\)
\(62\) 2.44438 0.310437
\(63\) 2.02133 + 1.70711i 0.254664 + 0.215075i
\(64\) 1.00000i 0.125000i
\(65\) 4.00687 + 1.83405i 0.496991 + 0.227486i
\(66\) 4.95063i 0.609381i
\(67\) 5.38404 5.38404i 0.657766 0.657766i −0.297085 0.954851i \(-0.596015\pi\)
0.954851 + 0.297085i \(0.0960146\pi\)
\(68\) 0.322179i 0.0390699i
\(69\) −2.70799 −0.326004
\(70\) −2.47046 2.08641i −0.295276 0.249374i
\(71\) −0.647652 + 0.647652i −0.0768621 + 0.0768621i −0.744493 0.667631i \(-0.767309\pi\)
0.667631 + 0.744493i \(0.267309\pi\)
\(72\) 0.707107 + 0.707107i 0.0833333 + 0.0833333i
\(73\) 6.85297 6.85297i 0.802080 0.802080i −0.181341 0.983420i \(-0.558044\pi\)
0.983420 + 0.181341i \(0.0580436\pi\)
\(74\) 3.22219 0.374572
\(75\) −3.50625 −0.404867
\(76\) −1.77219 + 1.77219i −0.203284 + 0.203284i
\(77\) 1.09999 + 13.0519i 0.125355 + 1.48740i
\(78\) −3.27843 1.50062i −0.371209 0.169912i
\(79\) 8.81718 0.992010 0.496005 0.868320i \(-0.334800\pi\)
0.496005 + 0.868320i \(0.334800\pi\)
\(80\) −0.864220 0.864220i −0.0966227 0.0966227i
\(81\) 1.00000 0.111111
\(82\) 9.14265 1.00964
\(83\) 6.09203 + 6.09203i 0.668688 + 0.668688i 0.957412 0.288725i \(-0.0932312\pi\)
−0.288725 + 0.957412i \(0.593231\pi\)
\(84\) 2.02133 + 1.70711i 0.220545 + 0.186261i
\(85\) −0.278433 0.278433i −0.0302003 0.0302003i
\(86\) 0.278433 + 0.278433i 0.0300242 + 0.0300242i
\(87\) 4.82047i 0.516809i
\(88\) 4.95063i 0.527739i
\(89\) −3.68702 + 3.68702i −0.390824 + 0.390824i −0.874981 0.484157i \(-0.839126\pi\)
0.484157 + 0.874981i \(0.339126\pi\)
\(90\) −1.22219 −0.128830
\(91\) −8.97670 3.22781i −0.941014 0.338367i
\(92\) −2.70799 −0.282328
\(93\) 1.72844 1.72844i 0.179231 0.179231i
\(94\) 2.00000i 0.206284i
\(95\) 3.06311i 0.314269i
\(96\) 0.707107 + 0.707107i 0.0721688 + 0.0721688i
\(97\) −5.20299 5.20299i −0.528284 0.528284i 0.391777 0.920060i \(-0.371861\pi\)
−0.920060 + 0.391777i \(0.871861\pi\)
\(98\) 5.70836 + 4.05150i 0.576631 + 0.409264i
\(99\) 3.50062 + 3.50062i 0.351826 + 0.351826i
\(100\) −3.50625 −0.350625
\(101\) 7.82968 0.779082 0.389541 0.921009i \(-0.372634\pi\)
0.389541 + 0.921009i \(0.372634\pi\)
\(102\) 0.227815 + 0.227815i 0.0225570 + 0.0225570i
\(103\) 14.8501 1.46323 0.731613 0.681720i \(-0.238768\pi\)
0.731613 + 0.681720i \(0.238768\pi\)
\(104\) −3.27843 1.50062i −0.321477 0.147148i
\(105\) −3.22219 + 0.271560i −0.314454 + 0.0265016i
\(106\) −1.43643 + 1.43643i −0.139518 + 0.139518i
\(107\) 13.8184 1.33588 0.667939 0.744216i \(-0.267177\pi\)
0.667939 + 0.744216i \(0.267177\pi\)
\(108\) 1.00000 0.0962250
\(109\) 5.19435 5.19435i 0.497529 0.497529i −0.413139 0.910668i \(-0.635568\pi\)
0.910668 + 0.413139i \(0.135568\pi\)
\(110\) −4.27843 4.27843i −0.407933 0.407933i
\(111\) 2.27843 2.27843i 0.216259 0.216259i
\(112\) 2.02133 + 1.70711i 0.190998 + 0.161306i
\(113\) 3.41598 0.321348 0.160674 0.987007i \(-0.448633\pi\)
0.160674 + 0.987007i \(0.448633\pi\)
\(114\) 2.50625i 0.234732i
\(115\) 2.34030 2.34030i 0.218234 0.218234i
\(116\) 4.82047i 0.447570i
\(117\) −3.37930 + 1.25710i −0.312417 + 0.116219i
\(118\) 15.2167i 1.40081i
\(119\) 0.651231 + 0.549994i 0.0596982 + 0.0504178i
\(120\) −1.22219 −0.111570
\(121\) 13.5087i 1.22807i
\(122\) −7.52284 7.52284i −0.681086 0.681086i
\(123\) 6.46483 6.46483i 0.582914 0.582914i
\(124\) 1.72844 1.72844i 0.155218 0.155218i
\(125\) 7.35127 7.35127i 0.657517 0.657517i
\(126\) 2.63640 0.222191i 0.234870 0.0197944i
\(127\) 9.70595i 0.861263i 0.902528 + 0.430632i \(0.141709\pi\)
−0.902528 + 0.430632i \(0.858291\pi\)
\(128\) 0.707107 + 0.707107i 0.0625000 + 0.0625000i
\(129\) 0.393764 0.0346690
\(130\) 4.13016 1.53642i 0.362239 0.134753i
\(131\) 18.3963i 1.60729i 0.595110 + 0.803644i \(0.297109\pi\)
−0.595110 + 0.803644i \(0.702891\pi\)
\(132\) 3.50062 + 3.50062i 0.304690 + 0.304690i
\(133\) 0.556867 + 6.60749i 0.0482865 + 0.572942i
\(134\) 7.61419i 0.657766i
\(135\) −0.864220 + 0.864220i −0.0743802 + 0.0743802i
\(136\) 0.227815 + 0.227815i 0.0195350 + 0.0195350i
\(137\) −1.93705 1.93705i −0.165494 0.165494i 0.619502 0.784995i \(-0.287335\pi\)
−0.784995 + 0.619502i \(0.787335\pi\)
\(138\) −1.91484 + 1.91484i −0.163002 + 0.163002i
\(139\) 15.4569i 1.31104i −0.755180 0.655518i \(-0.772450\pi\)
0.755180 0.655518i \(-0.227550\pi\)
\(140\) −3.22219 + 0.271560i −0.272325 + 0.0229510i
\(141\) 1.41421 + 1.41421i 0.119098 + 0.119098i
\(142\) 0.915918i 0.0768621i
\(143\) −16.2303 7.42904i −1.35725 0.621247i
\(144\) 1.00000 0.0833333
\(145\) 4.16595 + 4.16595i 0.345963 + 0.345963i
\(146\) 9.69157i 0.802080i
\(147\) 6.90126 1.17157i 0.569206 0.0966297i
\(148\) 2.27843 2.27843i 0.187286 0.187286i
\(149\) −3.16185 + 3.16185i −0.259029 + 0.259029i −0.824659 0.565630i \(-0.808633\pi\)
0.565630 + 0.824659i \(0.308633\pi\)
\(150\) −2.47929 + 2.47929i −0.202433 + 0.202433i
\(151\) −15.8872 15.8872i −1.29288 1.29288i −0.932998 0.359881i \(-0.882817\pi\)
−0.359881 0.932998i \(-0.617183\pi\)
\(152\) 2.50625i 0.203284i
\(153\) 0.322179 0.0260466
\(154\) 10.0069 + 8.45126i 0.806377 + 0.681022i
\(155\) 2.98750i 0.239962i
\(156\) −3.37930 + 1.25710i −0.270561 + 0.100649i
\(157\) 10.9376i 0.872917i 0.899724 + 0.436458i \(0.143767\pi\)
−0.899724 + 0.436458i \(0.856233\pi\)
\(158\) 6.23469 6.23469i 0.496005 0.496005i
\(159\) 2.03142i 0.161102i
\(160\) −1.22219 −0.0966227
\(161\) −4.62283 + 5.47375i −0.364330 + 0.431392i
\(162\) 0.707107 0.707107i 0.0555556 0.0555556i
\(163\) −0.687541 0.687541i −0.0538524 0.0538524i 0.679668 0.733520i \(-0.262124\pi\)
−0.733520 + 0.679668i \(0.762124\pi\)
\(164\) 6.46483 6.46483i 0.504819 0.504819i
\(165\) −6.05062 −0.471040
\(166\) 8.61544 0.668688
\(167\) −11.5592 + 11.5592i −0.894477 + 0.894477i −0.994941 0.100463i \(-0.967967\pi\)
0.100463 + 0.994941i \(0.467967\pi\)
\(168\) 2.63640 0.222191i 0.203403 0.0171424i
\(169\) 9.83940 8.49625i 0.756877 0.653558i
\(170\) −0.393764 −0.0302003
\(171\) 1.77219 + 1.77219i 0.135522 + 0.135522i
\(172\) 0.393764 0.0300242
\(173\) −10.4694 −0.795972 −0.397986 0.917392i \(-0.630291\pi\)
−0.397986 + 0.917392i \(0.630291\pi\)
\(174\) −3.40859 3.40859i −0.258405 0.258405i
\(175\) −5.98554 + 7.08729i −0.452464 + 0.535749i
\(176\) 3.50062 + 3.50062i 0.263870 + 0.263870i
\(177\) 10.7599 + 10.7599i 0.808760 + 0.808760i
\(178\) 5.21424i 0.390824i
\(179\) 22.4990i 1.68166i −0.541302 0.840828i \(-0.682068\pi\)
0.541302 0.840828i \(-0.317932\pi\)
\(180\) −0.864220 + 0.864220i −0.0644151 + 0.0644151i
\(181\) −24.5008 −1.82113 −0.910565 0.413366i \(-0.864353\pi\)
−0.910565 + 0.413366i \(0.864353\pi\)
\(182\) −8.62990 + 4.06508i −0.639691 + 0.301324i
\(183\) −10.6389 −0.786450
\(184\) −1.91484 + 1.91484i −0.141164 + 0.141164i
\(185\) 3.93813i 0.289537i
\(186\) 2.44438i 0.179231i
\(187\) 1.12783 + 1.12783i 0.0824749 + 0.0824749i
\(188\) 1.41421 + 1.41421i 0.103142 + 0.103142i
\(189\) 1.70711 2.02133i 0.124174 0.147030i
\(190\) −2.16595 2.16595i −0.157134 0.157134i
\(191\) 0.869566 0.0629196 0.0314598 0.999505i \(-0.489984\pi\)
0.0314598 + 0.999505i \(0.489984\pi\)
\(192\) 1.00000 0.0721688
\(193\) −6.38377 6.38377i −0.459514 0.459514i 0.438982 0.898496i \(-0.355339\pi\)
−0.898496 + 0.438982i \(0.855339\pi\)
\(194\) −7.35814 −0.528284
\(195\) 1.83405 4.00687i 0.131339 0.286938i
\(196\) 6.90126 1.17157i 0.492947 0.0836838i
\(197\) −10.5087 + 10.5087i −0.748717 + 0.748717i −0.974238 0.225521i \(-0.927592\pi\)
0.225521 + 0.974238i \(0.427592\pi\)
\(198\) 4.95063 0.351826
\(199\) 16.9105 1.19875 0.599376 0.800468i \(-0.295416\pi\)
0.599376 + 0.800468i \(0.295416\pi\)
\(200\) −2.47929 + 2.47929i −0.175312 + 0.175312i
\(201\) −5.38404 5.38404i −0.379761 0.379761i
\(202\) 5.53642 5.53642i 0.389541 0.389541i
\(203\) −9.74378 8.22906i −0.683879 0.577567i
\(204\) 0.322179 0.0225570
\(205\) 11.1741i 0.780431i
\(206\) 10.5006 10.5006i 0.731613 0.731613i
\(207\) 2.70799i 0.188218i
\(208\) −3.37930 + 1.25710i −0.234313 + 0.0871642i
\(209\) 12.4075i 0.858245i
\(210\) −2.08641 + 2.47046i −0.143976 + 0.170478i
\(211\) 4.96188 0.341590 0.170795 0.985307i \(-0.445366\pi\)
0.170795 + 0.985307i \(0.445366\pi\)
\(212\) 2.03142i 0.139518i
\(213\) 0.647652 + 0.647652i 0.0443764 + 0.0443764i
\(214\) 9.77111 9.77111i 0.667939 0.667939i
\(215\) −0.340299 + 0.340299i −0.0232082 + 0.0232082i
\(216\) 0.707107 0.707107i 0.0481125 0.0481125i
\(217\) −0.543121 6.44438i −0.0368694 0.437473i
\(218\) 7.34592i 0.497529i
\(219\) −6.85297 6.85297i −0.463081 0.463081i
\(220\) −6.05062 −0.407933
\(221\) −1.08874 + 0.405011i −0.0732366 + 0.0272440i
\(222\) 3.22219i 0.216259i
\(223\) 5.69799 + 5.69799i 0.381566 + 0.381566i 0.871666 0.490100i \(-0.163040\pi\)
−0.490100 + 0.871666i \(0.663040\pi\)
\(224\) 2.63640 0.222191i 0.176152 0.0148458i
\(225\) 3.50625i 0.233750i
\(226\) 2.41546 2.41546i 0.160674 0.160674i
\(227\) −0.501705 0.501705i −0.0332993 0.0332993i 0.690261 0.723560i \(-0.257496\pi\)
−0.723560 + 0.690261i \(0.757496\pi\)
\(228\) 1.77219 + 1.77219i 0.117366 + 0.117366i
\(229\) 12.5167 12.5167i 0.827127 0.827127i −0.159992 0.987118i \(-0.551147\pi\)
0.987118 + 0.159992i \(0.0511467\pi\)
\(230\) 3.30968i 0.218234i
\(231\) 13.0519 1.09999i 0.858750 0.0723739i
\(232\) −3.40859 3.40859i −0.223785 0.223785i
\(233\) 5.52846i 0.362182i 0.983466 + 0.181091i \(0.0579628\pi\)
−0.983466 + 0.181091i \(0.942037\pi\)
\(234\) −1.50062 + 3.27843i −0.0980989 + 0.214318i
\(235\) −2.44438 −0.159454
\(236\) 10.7599 + 10.7599i 0.700407 + 0.700407i
\(237\) 8.81718i 0.572737i
\(238\) 0.849394 0.0715854i 0.0550580 0.00464019i
\(239\) 10.2332 10.2332i 0.661928 0.661928i −0.293906 0.955834i \(-0.594955\pi\)
0.955834 + 0.293906i \(0.0949553\pi\)
\(240\) −0.864220 + 0.864220i −0.0557851 + 0.0557851i
\(241\) −16.8108 + 16.8108i −1.08288 + 1.08288i −0.0866358 + 0.996240i \(0.527612\pi\)
−0.996240 + 0.0866358i \(0.972388\pi\)
\(242\) 9.55213 + 9.55213i 0.614034 + 0.614034i
\(243\) 1.00000i 0.0641500i
\(244\) −10.6389 −0.681086
\(245\) −4.95171 + 6.97670i −0.316353 + 0.445725i
\(246\) 9.14265i 0.582914i
\(247\) −8.21657 3.76094i −0.522808 0.239303i
\(248\) 2.44438i 0.155218i
\(249\) 6.09203 6.09203i 0.386067 0.386067i
\(250\) 10.3963i 0.657517i
\(251\) 13.3838 0.844776 0.422388 0.906415i \(-0.361192\pi\)
0.422388 + 0.906415i \(0.361192\pi\)
\(252\) 1.70711 2.02133i 0.107538 0.127332i
\(253\) −9.47966 + 9.47966i −0.595981 + 0.595981i
\(254\) 6.86314 + 6.86314i 0.430632 + 0.430632i
\(255\) −0.278433 + 0.278433i −0.0174362 + 0.0174362i
\(256\) 1.00000 0.0625000
\(257\) 11.3581 0.708501 0.354251 0.935150i \(-0.384736\pi\)
0.354251 + 0.935150i \(0.384736\pi\)
\(258\) 0.278433 0.278433i 0.0173345 0.0173345i
\(259\) −0.715943 8.49500i −0.0444865 0.527854i
\(260\) 1.83405 4.00687i 0.113743 0.248496i
\(261\) −4.82047 −0.298380
\(262\) 13.0081 + 13.0081i 0.803644 + 0.803644i
\(263\) −28.4021 −1.75135 −0.875673 0.482905i \(-0.839582\pi\)
−0.875673 + 0.482905i \(0.839582\pi\)
\(264\) 4.95063 0.304690
\(265\) −1.75559 1.75559i −0.107845 0.107845i
\(266\) 5.06596 + 4.27843i 0.310614 + 0.262328i
\(267\) 3.68702 + 3.68702i 0.225642 + 0.225642i
\(268\) −5.38404 5.38404i −0.328883 0.328883i
\(269\) 22.3912i 1.36522i −0.730785 0.682608i \(-0.760846\pi\)
0.730785 0.682608i \(-0.239154\pi\)
\(270\) 1.22219i 0.0743802i
\(271\) −1.82388 + 1.82388i −0.110793 + 0.110793i −0.760330 0.649537i \(-0.774963\pi\)
0.649537 + 0.760330i \(0.274963\pi\)
\(272\) 0.322179 0.0195350
\(273\) −3.22781 + 8.97670i −0.195356 + 0.543295i
\(274\) −2.73941 −0.165494
\(275\) −12.2741 + 12.2741i −0.740154 + 0.740154i
\(276\) 2.70799i 0.163002i
\(277\) 16.7343i 1.00547i 0.864441 + 0.502735i \(0.167673\pi\)
−0.864441 + 0.502735i \(0.832327\pi\)
\(278\) −10.9297 10.9297i −0.655518 0.655518i
\(279\) −1.72844 1.72844i −0.103479 0.103479i
\(280\) −2.08641 + 2.47046i −0.124687 + 0.147638i
\(281\) −5.38706 5.38706i −0.321365 0.321365i 0.527926 0.849291i \(-0.322970\pi\)
−0.849291 + 0.527926i \(0.822970\pi\)
\(282\) 2.00000 0.119098
\(283\) 17.0421 1.01305 0.506525 0.862225i \(-0.330930\pi\)
0.506525 + 0.862225i \(0.330930\pi\)
\(284\) 0.647652 + 0.647652i 0.0384311 + 0.0384311i
\(285\) −3.06311 −0.181443
\(286\) −16.7297 + 6.22344i −0.989247 + 0.368000i
\(287\) −2.03142 24.1037i −0.119911 1.42280i
\(288\) 0.707107 0.707107i 0.0416667 0.0416667i
\(289\) −16.8962 −0.993894
\(290\) 5.89154 0.345963
\(291\) −5.20299 + 5.20299i −0.305005 + 0.305005i
\(292\) −6.85297 6.85297i −0.401040 0.401040i
\(293\) 4.20174 4.20174i 0.245468 0.245468i −0.573639 0.819108i \(-0.694469\pi\)
0.819108 + 0.573639i \(0.194469\pi\)
\(294\) 4.05150 5.70836i 0.236288 0.332918i
\(295\) −18.5978 −1.08280
\(296\) 3.22219i 0.187286i
\(297\) 3.50062 3.50062i 0.203127 0.203127i
\(298\) 4.47154i 0.259029i
\(299\) −3.40422 9.15112i −0.196871 0.529223i
\(300\) 3.50625i 0.202433i
\(301\) 0.672198 0.795929i 0.0387448 0.0458766i
\(302\) −22.4678 −1.29288
\(303\) 7.82968i 0.449803i
\(304\) 1.77219 + 1.77219i 0.101642 + 0.101642i
\(305\) 9.19435 9.19435i 0.526467 0.526467i
\(306\) 0.227815 0.227815i 0.0130233 0.0130233i
\(307\) −17.0150 + 17.0150i −0.971097 + 0.971097i −0.999594 0.0284968i \(-0.990928\pi\)
0.0284968 + 0.999594i \(0.490928\pi\)
\(308\) 13.0519 1.09999i 0.743699 0.0626776i
\(309\) 14.8501i 0.844794i
\(310\) 2.11248 + 2.11248i 0.119981 + 0.119981i
\(311\) −13.7090 −0.777366 −0.388683 0.921372i \(-0.627070\pi\)
−0.388683 + 0.921372i \(0.627070\pi\)
\(312\) −1.50062 + 3.27843i −0.0849561 + 0.185605i
\(313\) 17.4456i 0.986085i 0.870005 + 0.493043i \(0.164115\pi\)
−0.870005 + 0.493043i \(0.835885\pi\)
\(314\) 7.73406 + 7.73406i 0.436458 + 0.436458i
\(315\) 0.271560 + 3.22219i 0.0153007 + 0.181550i
\(316\) 8.81718i 0.496005i
\(317\) −21.4771 + 21.4771i −1.20627 + 1.20627i −0.234046 + 0.972226i \(0.575197\pi\)
−0.972226 + 0.234046i \(0.924803\pi\)
\(318\) 1.43643 + 1.43643i 0.0805510 + 0.0805510i
\(319\) −16.8747 16.8747i −0.944800 0.944800i
\(320\) −0.864220 + 0.864220i −0.0483114 + 0.0483114i
\(321\) 13.8184i 0.771270i
\(322\) 0.601692 + 7.13936i 0.0335310 + 0.397861i
\(323\) 0.570961 + 0.570961i 0.0317691 + 0.0317691i
\(324\) 1.00000i 0.0555556i
\(325\) −4.40771 11.8487i −0.244496 0.657247i
\(326\) −0.972330 −0.0538524
\(327\) −5.19435 5.19435i −0.287248 0.287248i
\(328\) 9.14265i 0.504819i
\(329\) 5.27281 0.444383i 0.290699 0.0244996i
\(330\) −4.27843 + 4.27843i −0.235520 + 0.235520i
\(331\) −5.19998 + 5.19998i −0.285816 + 0.285816i −0.835423 0.549607i \(-0.814778\pi\)
0.549607 + 0.835423i \(0.314778\pi\)
\(332\) 6.09203 6.09203i 0.334344 0.334344i
\(333\) −2.27843 2.27843i −0.124857 0.124857i
\(334\) 16.3472i 0.894477i
\(335\) 9.30600 0.508441
\(336\) 1.70711 2.02133i 0.0931303 0.110273i
\(337\) 1.35058i 0.0735708i 0.999323 + 0.0367854i \(0.0117118\pi\)
−0.999323 + 0.0367854i \(0.988288\pi\)
\(338\) 0.949747 12.9653i 0.0516595 0.705217i
\(339\) 3.41598i 0.185531i
\(340\) −0.278433 + 0.278433i −0.0151002 + 0.0151002i
\(341\) 12.1012i 0.655319i
\(342\) 2.50625 0.135522
\(343\) 9.41305 15.9497i 0.508257 0.861205i
\(344\) 0.278433 0.278433i 0.0150121 0.0150121i
\(345\) −2.34030 2.34030i −0.125997 0.125997i
\(346\) −7.40297 + 7.40297i −0.397986 + 0.397986i
\(347\) 21.6050 1.15982 0.579910 0.814681i \(-0.303088\pi\)
0.579910 + 0.814681i \(0.303088\pi\)
\(348\) −4.82047 −0.258405
\(349\) −25.7255 + 25.7255i −1.37705 + 1.37705i −0.527496 + 0.849557i \(0.676869\pi\)
−0.849557 + 0.527496i \(0.823131\pi\)
\(350\) 0.779058 + 9.24389i 0.0416424 + 0.494107i
\(351\) 1.25710 + 3.37930i 0.0670991 + 0.180374i
\(352\) 4.95063 0.263870
\(353\) 9.77451 + 9.77451i 0.520245 + 0.520245i 0.917645 0.397400i \(-0.130088\pi\)
−0.397400 + 0.917645i \(0.630088\pi\)
\(354\) 15.2167 0.808760
\(355\) −1.11943 −0.0594130
\(356\) 3.68702 + 3.68702i 0.195412 + 0.195412i
\(357\) 0.549994 0.651231i 0.0291088 0.0344668i
\(358\) −15.9092 15.9092i −0.840828 0.840828i
\(359\) −4.56016 4.56016i −0.240676 0.240676i 0.576454 0.817130i \(-0.304436\pi\)
−0.817130 + 0.576454i \(0.804436\pi\)
\(360\) 1.22219i 0.0644151i
\(361\) 12.7187i 0.669406i
\(362\) −17.3247 + 17.3247i −0.910565 + 0.910565i
\(363\) 13.5087 0.709025
\(364\) −3.22781 + 8.97670i −0.169183 + 0.470507i
\(365\) 11.8449 0.619993
\(366\) −7.52284 + 7.52284i −0.393225 + 0.393225i
\(367\) 14.4983i 0.756805i 0.925641 + 0.378402i \(0.123526\pi\)
−0.925641 + 0.378402i \(0.876474\pi\)
\(368\) 2.70799i 0.141164i
\(369\) −6.46483 6.46483i −0.336546 0.336546i
\(370\) 2.78468 + 2.78468i 0.144769 + 0.144769i
\(371\) 4.10617 + 3.46785i 0.213182 + 0.180042i
\(372\) −1.72844 1.72844i −0.0896154 0.0896154i
\(373\) 21.2073 1.09807 0.549035 0.835799i \(-0.314995\pi\)
0.549035 + 0.835799i \(0.314995\pi\)
\(374\) 1.59499 0.0824749
\(375\) −7.35127 7.35127i −0.379618 0.379618i
\(376\) 2.00000 0.103142
\(377\) 16.2899 6.05982i 0.838970 0.312097i
\(378\) −0.222191 2.63640i −0.0114283 0.135602i
\(379\) 25.0372 25.0372i 1.28608 1.28608i 0.348924 0.937151i \(-0.386547\pi\)
0.937151 0.348924i \(-0.113453\pi\)
\(380\) −3.06311 −0.157134
\(381\) 9.70595 0.497251
\(382\) 0.614876 0.614876i 0.0314598 0.0314598i
\(383\) −14.5420 14.5420i −0.743064 0.743064i 0.230103 0.973166i \(-0.426094\pi\)
−0.973166 + 0.230103i \(0.926094\pi\)
\(384\) 0.707107 0.707107i 0.0360844 0.0360844i
\(385\) −10.3291 + 12.2303i −0.526417 + 0.623315i
\(386\) −9.02801 −0.459514
\(387\) 0.393764i 0.0200162i
\(388\) −5.20299 + 5.20299i −0.264142 + 0.264142i
\(389\) 30.6758i 1.55532i −0.628683 0.777662i \(-0.716406\pi\)
0.628683 0.777662i \(-0.283594\pi\)
\(390\) −1.53642 4.13016i −0.0777995 0.209139i
\(391\) 0.872457i 0.0441221i
\(392\) 4.05150 5.70836i 0.204632 0.288316i
\(393\) 18.3963 0.927969
\(394\) 14.8616i 0.748717i
\(395\) 7.61998 + 7.61998i 0.383403 + 0.383403i
\(396\) 3.50062 3.50062i 0.175913 0.175913i
\(397\) 1.78156 1.78156i 0.0894138 0.0894138i −0.660985 0.750399i \(-0.729861\pi\)
0.750399 + 0.660985i \(0.229861\pi\)
\(398\) 11.9575 11.9575i 0.599376 0.599376i
\(399\) 6.60749 0.556867i 0.330788 0.0278782i
\(400\) 3.50625i 0.175312i
\(401\) −2.02017 2.02017i −0.100883 0.100883i 0.654864 0.755747i \(-0.272726\pi\)
−0.755747 + 0.654864i \(0.772726\pi\)
\(402\) −7.61419 −0.379761
\(403\) 8.01375 + 3.66810i 0.399193 + 0.182721i
\(404\) 7.82968i 0.389541i
\(405\) 0.864220 + 0.864220i 0.0429434 + 0.0429434i
\(406\) −12.7087 + 1.07107i −0.630723 + 0.0531562i
\(407\) 15.9519i 0.790705i
\(408\) 0.227815 0.227815i 0.0112785 0.0112785i
\(409\) −11.7667 11.7667i −0.581827 0.581827i 0.353578 0.935405i \(-0.384965\pi\)
−0.935405 + 0.353578i \(0.884965\pi\)
\(410\) 7.90126 + 7.90126i 0.390216 + 0.390216i
\(411\) −1.93705 + 1.93705i −0.0955479 + 0.0955479i
\(412\) 14.8501i 0.731613i
\(413\) 40.1175 3.38103i 1.97405 0.166370i
\(414\) 1.91484 + 1.91484i 0.0941092 + 0.0941092i
\(415\) 10.5297i 0.516883i
\(416\) −1.50062 + 3.27843i −0.0735742 + 0.160738i
\(417\) −15.4569 −0.756927
\(418\) 8.77343 + 8.77343i 0.429123 + 0.429123i
\(419\) 9.34287i 0.456429i 0.973611 + 0.228214i \(0.0732887\pi\)
−0.973611 + 0.228214i \(0.926711\pi\)
\(420\) 0.271560 + 3.22219i 0.0132508 + 0.157227i
\(421\) 7.32190 7.32190i 0.356848 0.356848i −0.505802 0.862650i \(-0.668803\pi\)
0.862650 + 0.505802i \(0.168803\pi\)
\(422\) 3.50858 3.50858i 0.170795 0.170795i
\(423\) 1.41421 1.41421i 0.0687614 0.0687614i
\(424\) 1.43643 + 1.43643i 0.0697592 + 0.0697592i
\(425\) 1.12964i 0.0547955i
\(426\) 0.915918 0.0443764
\(427\) −18.1617 + 21.5048i −0.878908 + 1.04069i
\(428\) 13.8184i 0.667939i
\(429\) −7.42904 + 16.2303i −0.358677 + 0.783607i
\(430\) 0.481255i 0.0232082i
\(431\) −26.9180 + 26.9180i −1.29660 + 1.29660i −0.365968 + 0.930627i \(0.619262\pi\)
−0.930627 + 0.365968i \(0.880738\pi\)
\(432\) 1.00000i 0.0481125i
\(433\) −30.8370 −1.48193 −0.740965 0.671544i \(-0.765632\pi\)
−0.740965 + 0.671544i \(0.765632\pi\)
\(434\) −4.94091 4.17282i −0.237171 0.200302i
\(435\) 4.16595 4.16595i 0.199742 0.199742i
\(436\) −5.19435 5.19435i −0.248764 0.248764i
\(437\) −4.79906 + 4.79906i −0.229570 + 0.229570i
\(438\) −9.69157 −0.463081
\(439\) 14.3229 0.683595 0.341798 0.939774i \(-0.388964\pi\)
0.341798 + 0.939774i \(0.388964\pi\)
\(440\) −4.27843 + 4.27843i −0.203966 + 0.203966i
\(441\) −1.17157 6.90126i −0.0557892 0.328632i
\(442\) −0.483470 + 1.05624i −0.0229963 + 0.0502403i
\(443\) 21.5422 1.02350 0.511751 0.859134i \(-0.328997\pi\)
0.511751 + 0.859134i \(0.328997\pi\)
\(444\) −2.27843 2.27843i −0.108130 0.108130i
\(445\) −6.37280 −0.302100
\(446\) 8.05818 0.381566
\(447\) 3.16185 + 3.16185i 0.149551 + 0.149551i
\(448\) 1.70711 2.02133i 0.0806532 0.0954990i
\(449\) 28.2383 + 28.2383i 1.33265 + 1.33265i 0.902995 + 0.429651i \(0.141364\pi\)
0.429651 + 0.902995i \(0.358636\pi\)
\(450\) 2.47929 + 2.47929i 0.116875 + 0.116875i
\(451\) 45.2619i 2.13130i
\(452\) 3.41598i 0.160674i
\(453\) −15.8872 + 15.8872i −0.746444 + 0.746444i
\(454\) −0.709517 −0.0332993
\(455\) −4.96830 10.5474i −0.232918 0.494469i
\(456\) 2.50625 0.117366
\(457\) −12.7653 + 12.7653i −0.597136 + 0.597136i −0.939549 0.342413i \(-0.888756\pi\)
0.342413 + 0.939549i \(0.388756\pi\)
\(458\) 17.7013i 0.827127i
\(459\) 0.322179i 0.0150380i
\(460\) −2.34030 2.34030i −0.109117 0.109117i
\(461\) 13.3358 + 13.3358i 0.621108 + 0.621108i 0.945815 0.324707i \(-0.105266\pi\)
−0.324707 + 0.945815i \(0.605266\pi\)
\(462\) 8.45126 10.0069i 0.393188 0.465562i
\(463\) 21.3712 + 21.3712i 0.993204 + 0.993204i 0.999977 0.00677317i \(-0.00215598\pi\)
−0.00677317 + 0.999977i \(0.502156\pi\)
\(464\) −4.82047 −0.223785
\(465\) 2.98750 0.138542
\(466\) 3.90921 + 3.90921i 0.181091 + 0.181091i
\(467\) 41.0053 1.89750 0.948749 0.316031i \(-0.102350\pi\)
0.948749 + 0.316031i \(0.102350\pi\)
\(468\) 1.25710 + 3.37930i 0.0581095 + 0.156208i
\(469\) −20.0741 + 1.69181i −0.926935 + 0.0781204i
\(470\) −1.72844 + 1.72844i −0.0797270 + 0.0797270i
\(471\) 10.9376 0.503979
\(472\) 15.2167 0.700407
\(473\) 1.37842 1.37842i 0.0633799 0.0633799i
\(474\) −6.23469 6.23469i −0.286369 0.286369i
\(475\) −6.21372 + 6.21372i −0.285105 + 0.285105i
\(476\) 0.549994 0.651231i 0.0252089 0.0298491i
\(477\) 2.03142 0.0930123
\(478\) 14.4719i 0.661928i
\(479\) −6.94553 + 6.94553i −0.317349 + 0.317349i −0.847748 0.530399i \(-0.822042\pi\)
0.530399 + 0.847748i \(0.322042\pi\)
\(480\) 1.22219i 0.0557851i
\(481\) 10.5637 + 4.83530i 0.481665 + 0.220471i
\(482\) 23.7740i 1.08288i
\(483\) 5.47375 + 4.62283i 0.249064 + 0.210346i
\(484\) 13.5087 0.614034
\(485\) 8.99306i 0.408354i
\(486\) −0.707107 0.707107i −0.0320750 0.0320750i
\(487\) −23.1741 + 23.1741i −1.05012 + 1.05012i −0.0514414 + 0.998676i \(0.516382\pi\)
−0.998676 + 0.0514414i \(0.983618\pi\)
\(488\) −7.52284 + 7.52284i −0.340543 + 0.340543i
\(489\) −0.687541 + 0.687541i −0.0310917 + 0.0310917i
\(490\) 1.43189 + 8.43466i 0.0646860 + 0.381039i
\(491\) 15.6206i 0.704948i 0.935822 + 0.352474i \(0.114660\pi\)
−0.935822 + 0.352474i \(0.885340\pi\)
\(492\) −6.46483 6.46483i −0.291457 0.291457i
\(493\) −1.55306 −0.0699461
\(494\) −8.46938 + 3.15061i −0.381055 + 0.141752i
\(495\) 6.05062i 0.271955i
\(496\) −1.72844 1.72844i −0.0776092 0.0776092i
\(497\) 2.41473 0.203509i 0.108315 0.00912863i
\(498\) 8.61544i 0.386067i
\(499\) 25.6581 25.6581i 1.14861 1.14861i 0.161789 0.986825i \(-0.448274\pi\)
0.986825 0.161789i \(-0.0517264\pi\)
\(500\) −7.35127 7.35127i −0.328759 0.328759i
\(501\) 11.5592 + 11.5592i 0.516427 + 0.516427i
\(502\) 9.46375 9.46375i 0.422388 0.422388i
\(503\) 31.3187i 1.39643i −0.715887 0.698216i \(-0.753977\pi\)
0.715887 0.698216i \(-0.246023\pi\)
\(504\) −0.222191 2.63640i −0.00989719 0.117435i
\(505\) 6.76656 + 6.76656i 0.301108 + 0.301108i
\(506\) 13.4063i 0.595981i
\(507\) −8.49625 9.83940i −0.377332 0.436983i
\(508\) 9.70595 0.430632
\(509\) −20.3793 20.3793i −0.903296 0.903296i 0.0924241 0.995720i \(-0.470538\pi\)
−0.995720 + 0.0924241i \(0.970538\pi\)
\(510\) 0.393764i 0.0174362i
\(511\) −25.5509 + 2.15338i −1.13031 + 0.0952600i
\(512\) 0.707107 0.707107i 0.0312500 0.0312500i
\(513\) 1.77219 1.77219i 0.0782439 0.0782439i
\(514\) 8.03142 8.03142i 0.354251 0.354251i
\(515\) 12.8338 + 12.8338i 0.565524 + 0.565524i
\(516\) 0.393764i 0.0173345i
\(517\) 9.90126 0.435457
\(518\) −6.51312 5.50062i −0.286170 0.241684i
\(519\) 10.4694i 0.459555i
\(520\) −1.53642 4.13016i −0.0673764 0.181119i
\(521\) 33.7078i 1.47677i 0.674382 + 0.738383i \(0.264410\pi\)
−0.674382 + 0.738383i \(0.735590\pi\)
\(522\) −3.40859 + 3.40859i −0.149190 + 0.149190i
\(523\) 19.2350i 0.841086i 0.907273 + 0.420543i \(0.138160\pi\)
−0.907273 + 0.420543i \(0.861840\pi\)
\(524\) 18.3963 0.803644
\(525\) 7.08729 + 5.98554i 0.309315 + 0.261230i
\(526\) −20.0833 + 20.0833i −0.875673 + 0.875673i
\(527\) −0.556867 0.556867i −0.0242575 0.0242575i
\(528\) 3.50062 3.50062i 0.152345 0.152345i
\(529\) 15.6668 0.681165
\(530\) −2.48278 −0.107845
\(531\) 10.7599 10.7599i 0.466938 0.466938i
\(532\) 6.60749 0.556867i 0.286471 0.0241432i
\(533\) 29.9736 + 13.7197i 1.29830 + 0.594266i
\(534\) 5.21424 0.225642
\(535\) 11.9422 + 11.9422i 0.516305 + 0.516305i
\(536\) −7.61419 −0.328883
\(537\) −22.4990 −0.970905
\(538\) −15.8330 15.8330i −0.682608 0.682608i
\(539\) 20.0575 28.2600i 0.863937 1.21724i
\(540\) 0.864220 + 0.864220i 0.0371901 + 0.0371901i
\(541\) 24.8685 + 24.8685i 1.06918 + 1.06918i 0.997422 + 0.0717576i \(0.0228608\pi\)
0.0717576 + 0.997422i \(0.477139\pi\)
\(542\) 2.57936i 0.110793i
\(543\) 24.5008i 1.05143i
\(544\) 0.227815 0.227815i 0.00976748 0.00976748i
\(545\) 8.97812 0.384581
\(546\) 4.06508 + 8.62990i 0.173969 + 0.369326i
\(547\) 31.2150 1.33466 0.667328 0.744764i \(-0.267438\pi\)
0.667328 + 0.744764i \(0.267438\pi\)
\(548\) −1.93705 + 1.93705i −0.0827469 + 0.0827469i
\(549\) 10.6389i 0.454057i
\(550\) 17.3581i 0.740154i
\(551\) −8.54277 8.54277i −0.363934 0.363934i
\(552\) 1.91484 + 1.91484i 0.0815009 + 0.0815009i
\(553\) −17.8225 15.0519i −0.757888 0.640071i
\(554\) 11.8330 + 11.8330i 0.502735 + 0.502735i
\(555\) 3.93813 0.167165
\(556\) −15.4569 −0.655518
\(557\) 5.05010 + 5.05010i 0.213980 + 0.213980i 0.805956 0.591976i \(-0.201652\pi\)
−0.591976 + 0.805956i \(0.701652\pi\)
\(558\) −2.44438 −0.103479
\(559\) 0.495001 + 1.33065i 0.0209363 + 0.0562805i
\(560\) 0.271560 + 3.22219i 0.0114755 + 0.136162i
\(561\) 1.12783 1.12783i 0.0476169 0.0476169i
\(562\) −7.61845 −0.321365
\(563\) −33.9410 −1.43044 −0.715221 0.698899i \(-0.753674\pi\)
−0.715221 + 0.698899i \(0.753674\pi\)
\(564\) 1.41421 1.41421i 0.0595491 0.0595491i
\(565\) 2.95216 + 2.95216i 0.124198 + 0.124198i
\(566\) 12.0506 12.0506i 0.506525 0.506525i
\(567\) −2.02133 1.70711i −0.0848880 0.0716917i
\(568\) 0.915918 0.0384311
\(569\) 1.28622i 0.0539210i −0.999636 0.0269605i \(-0.991417\pi\)
0.999636 0.0269605i \(-0.00858283\pi\)
\(570\) −2.16595 + 2.16595i −0.0907216 + 0.0907216i
\(571\) 36.5188i 1.52826i 0.645060 + 0.764132i \(0.276833\pi\)
−0.645060 + 0.764132i \(0.723167\pi\)
\(572\) −7.42904 + 16.2303i −0.310624 + 0.678624i
\(573\) 0.869566i 0.0363266i
\(574\) −18.4803 15.6075i −0.771355 0.651444i
\(575\) −9.49489 −0.395964
\(576\) 1.00000i 0.0416667i
\(577\) 9.37228 + 9.37228i 0.390173 + 0.390173i 0.874749 0.484576i \(-0.161026\pi\)
−0.484576 + 0.874749i \(0.661026\pi\)
\(578\) −11.9474 + 11.9474i −0.496947 + 0.496947i
\(579\) −6.38377 + 6.38377i −0.265300 + 0.265300i
\(580\) 4.16595 4.16595i 0.172982 0.172982i
\(581\) −1.91428 22.7138i −0.0794176 0.942327i
\(582\) 7.35814i 0.305005i
\(583\) 7.11123 + 7.11123i 0.294517 + 0.294517i
\(584\) −9.69157 −0.401040
\(585\) −4.00687 1.83405i −0.165664 0.0758287i
\(586\) 5.94216i 0.245468i
\(587\) −19.0646 19.0646i −0.786880 0.786880i 0.194101 0.980982i \(-0.437821\pi\)
−0.980982 + 0.194101i \(0.937821\pi\)
\(588\) −1.17157 6.90126i −0.0483149 0.284603i
\(589\) 6.12623i 0.252427i
\(590\) −13.1506 + 13.1506i −0.541402 + 0.541402i
\(591\) 10.5087 + 10.5087i 0.432272 + 0.432272i
\(592\) −2.27843 2.27843i −0.0936430 0.0936430i
\(593\) 25.5883 25.5883i 1.05078 1.05078i 0.0521454 0.998640i \(-0.483394\pi\)
0.998640 0.0521454i \(-0.0166059\pi\)
\(594\) 4.95063i 0.203127i
\(595\) 0.0874910 + 1.03812i 0.00358678 + 0.0425589i
\(596\) 3.16185 + 3.16185i 0.129515 + 0.129515i
\(597\) 16.9105i 0.692099i
\(598\) −8.87797 4.06368i −0.363047 0.166176i
\(599\) 4.67868 0.191166 0.0955828 0.995421i \(-0.469529\pi\)
0.0955828 + 0.995421i \(0.469529\pi\)
\(600\) 2.47929 + 2.47929i 0.101217 + 0.101217i
\(601\) 18.8059i 0.767110i −0.923518 0.383555i \(-0.874700\pi\)
0.923518 0.383555i \(-0.125300\pi\)
\(602\) −0.0874910 1.03812i −0.00356587 0.0423107i
\(603\) −5.38404 + 5.38404i −0.219255 + 0.219255i
\(604\) −15.8872 + 15.8872i −0.646440 + 0.646440i
\(605\) −11.6745 + 11.6745i −0.474637 + 0.474637i
\(606\) −5.53642 5.53642i −0.224902 0.224902i
\(607\) 4.66106i 0.189187i 0.995516 + 0.0945933i \(0.0301551\pi\)
−0.995516 + 0.0945933i \(0.969845\pi\)
\(608\) 2.50625 0.101642
\(609\) −8.22906 + 9.74378i −0.333459 + 0.394838i
\(610\) 13.0028i 0.526467i
\(611\) −3.00125 + 6.55687i −0.121418 + 0.265262i
\(612\) 0.322179i 0.0130233i
\(613\) 31.7107 31.7107i 1.28078 1.28078i 0.340558 0.940224i \(-0.389384\pi\)
0.940224 0.340558i \(-0.110616\pi\)
\(614\) 24.0628i 0.971097i
\(615\) 11.1741 0.450582
\(616\) 8.45126 10.0069i 0.340511 0.403188i
\(617\) −5.26417 + 5.26417i −0.211927 + 0.211927i −0.805086 0.593158i \(-0.797881\pi\)
0.593158 + 0.805086i \(0.297881\pi\)
\(618\) −10.5006 10.5006i −0.422397 0.422397i
\(619\) 9.61527 9.61527i 0.386470 0.386470i −0.486956 0.873426i \(-0.661893\pi\)
0.873426 + 0.486956i \(0.161893\pi\)
\(620\) 2.98750 0.119981
\(621\) 2.70799 0.108668
\(622\) −9.69373 + 9.69373i −0.388683 + 0.388683i
\(623\) 13.7468 1.15856i 0.550756 0.0464167i
\(624\) 1.25710 + 3.37930i 0.0503243 + 0.135280i
\(625\) −4.82502 −0.193001
\(626\) 12.3359 + 12.3359i 0.493043 + 0.493043i
\(627\) 12.4075 0.495508
\(628\) 10.9376 0.436458
\(629\) −0.734063 0.734063i −0.0292690 0.0292690i
\(630\) 2.47046 + 2.08641i 0.0984253 + 0.0831246i
\(631\) −14.4462 14.4462i −0.575094 0.575094i 0.358454 0.933548i \(-0.383304\pi\)
−0.933548 + 0.358454i \(0.883304\pi\)
\(632\) −6.23469 6.23469i −0.248003 0.248003i
\(633\) 4.96188i 0.197217i
\(634\) 30.3731i 1.20627i
\(635\) −8.38807 + 8.38807i −0.332870 + 0.332870i
\(636\) 2.03142 0.0805510
\(637\) 12.6347 + 21.8487i 0.500604 + 0.865676i
\(638\) −23.8644 −0.944800
\(639\) 0.647652 0.647652i 0.0256207 0.0256207i
\(640\) 1.22219i 0.0483114i
\(641\) 4.88105i 0.192790i −0.995343 0.0963950i \(-0.969269\pi\)
0.995343 0.0963950i \(-0.0307312\pi\)
\(642\) −9.77111 9.77111i −0.385635 0.385635i
\(643\) 25.2403 + 25.2403i 0.995381 + 0.995381i 0.999989 0.00460867i \(-0.00146699\pi\)
−0.00460867 + 0.999989i \(0.501467\pi\)
\(644\) 5.47375 + 4.62283i 0.215696 + 0.182165i
\(645\) 0.340299 + 0.340299i 0.0133993 + 0.0133993i
\(646\) 0.807460 0.0317691
\(647\) −18.9818 −0.746252 −0.373126 0.927781i \(-0.621714\pi\)
−0.373126 + 0.927781i \(0.621714\pi\)
\(648\) −0.707107 0.707107i −0.0277778 0.0277778i
\(649\) 75.3325 2.95706
\(650\) −11.4950 5.26156i −0.450871 0.206375i
\(651\) −6.44438 + 0.543121i −0.252575 + 0.0212866i
\(652\) −0.687541 + 0.687541i −0.0269262 + 0.0269262i
\(653\) 28.5652 1.11784 0.558921 0.829221i \(-0.311216\pi\)
0.558921 + 0.829221i \(0.311216\pi\)
\(654\) −7.34592 −0.287248
\(655\) −15.8984 + 15.8984i −0.621202 + 0.621202i
\(656\) −6.46483 6.46483i −0.252409 0.252409i
\(657\) −6.85297 + 6.85297i −0.267360 + 0.267360i
\(658\) 3.41421 4.04267i 0.133100 0.157600i
\(659\) 11.6879 0.455295 0.227648 0.973744i \(-0.426897\pi\)
0.227648 + 0.973744i \(0.426897\pi\)
\(660\) 6.05062i 0.235520i
\(661\) 16.7977 16.7977i 0.653356 0.653356i −0.300443 0.953800i \(-0.597135\pi\)
0.953800 + 0.300443i \(0.0971346\pi\)
\(662\) 7.35388i 0.285816i
\(663\) 0.405011 + 1.08874i 0.0157293 + 0.0422832i
\(664\) 8.61544i 0.334344i
\(665\) −5.22906 + 6.19157i −0.202774 + 0.240099i
\(666\) −3.22219 −0.124857
\(667\) 13.0538i 0.505445i
\(668\) 11.5592 + 11.5592i 0.447239 + 0.447239i
\(669\) 5.69799 5.69799i 0.220297 0.220297i
\(670\) 6.58033 6.58033i 0.254220 0.254220i
\(671\) −37.2428 + 37.2428i −1.43774 + 1.43774i
\(672\) −0.222191 2.63640i −0.00857122 0.101702i
\(673\) 35.7487i 1.37801i 0.724756 + 0.689006i \(0.241953\pi\)
−0.724756 + 0.689006i \(0.758047\pi\)
\(674\) 0.955005 + 0.955005i 0.0367854 + 0.0367854i
\(675\) 3.50625 0.134956
\(676\) −8.49625 9.83940i −0.326779 0.378438i
\(677\) 31.5694i 1.21331i −0.794966 0.606655i \(-0.792511\pi\)
0.794966 0.606655i \(-0.207489\pi\)
\(678\) −2.41546 2.41546i −0.0927653 0.0927653i
\(679\) 1.63492 + 19.3990i 0.0627423 + 0.744467i
\(680\) 0.393764i 0.0151002i
\(681\) −0.501705 + 0.501705i −0.0192254 + 0.0192254i
\(682\) −8.55687 8.55687i −0.327659 0.327659i
\(683\) 23.7613 + 23.7613i 0.909200 + 0.909200i 0.996208 0.0870076i \(-0.0277305\pi\)
−0.0870076 + 0.996208i \(0.527730\pi\)
\(684\) 1.77219 1.77219i 0.0677612 0.0677612i
\(685\) 3.34808i 0.127924i
\(686\) −4.62214 17.9342i −0.176474 0.684731i
\(687\) −12.5167 12.5167i −0.477542 0.477542i
\(688\) 0.393764i 0.0150121i
\(689\) −6.86478 + 2.55370i −0.261527 + 0.0972881i
\(690\) −3.30968 −0.125997
\(691\) 2.90001 + 2.90001i 0.110322 + 0.110322i 0.760113 0.649791i \(-0.225144\pi\)
−0.649791 + 0.760113i \(0.725144\pi\)
\(692\) 10.4694i 0.397986i
\(693\) −1.09999 13.0519i −0.0417851 0.495799i
\(694\) 15.2771 15.2771i 0.579910 0.579910i
\(695\) 13.3581 13.3581i 0.506703 0.506703i
\(696\) −3.40859 + 3.40859i −0.129202 + 0.129202i
\(697\) −2.08283 2.08283i −0.0788929 0.0788929i
\(698\) 36.3813i 1.37705i
\(699\) 5.52846 0.209106
\(700\) 7.08729 + 5.98554i 0.267875 + 0.226232i
\(701\) 25.6279i 0.967954i −0.875081 0.483977i \(-0.839192\pi\)
0.875081 0.483977i \(-0.160808\pi\)
\(702\) 3.27843 + 1.50062i 0.123736 + 0.0566374i
\(703\) 8.07561i 0.304577i
\(704\) 3.50062 3.50062i 0.131935 0.131935i
\(705\) 2.44438i 0.0920608i
\(706\) 13.8233 0.520245
\(707\) −15.8264 13.3661i −0.595212 0.502684i
\(708\) 10.7599 10.7599i 0.404380 0.404380i
\(709\) −31.7063 31.7063i −1.19075 1.19075i −0.976856 0.213899i \(-0.931384\pi\)
−0.213899 0.976856i \(-0.568616\pi\)
\(710\) −0.791555 + 0.791555i −0.0297065 + 0.0297065i
\(711\) −8.81718 −0.330670
\(712\) 5.21424 0.195412
\(713\) 4.68060 4.68060i 0.175290 0.175290i
\(714\) −0.0715854 0.849394i −0.00267902 0.0317878i
\(715\) −7.60624 20.4469i −0.284457 0.764670i
\(716\) −22.4990 −0.840828
\(717\) −10.2332 10.2332i −0.382164 0.382164i
\(718\) −6.44904 −0.240676
\(719\) 0.852526 0.0317938 0.0158969 0.999874i \(-0.494940\pi\)
0.0158969 + 0.999874i \(0.494940\pi\)
\(720\) 0.864220 + 0.864220i 0.0322076 + 0.0322076i
\(721\) −30.0170 25.3508i −1.11789 0.944111i
\(722\) −8.99349 8.99349i −0.334703 0.334703i
\(723\) 16.8108 + 16.8108i 0.625199 + 0.625199i
\(724\) 24.5008i 0.910565i
\(725\) 16.9018i 0.627716i
\(726\) 9.55213 9.55213i 0.354513 0.354513i
\(727\) 8.14896 0.302228 0.151114 0.988516i \(-0.451714\pi\)
0.151114 + 0.988516i \(0.451714\pi\)
\(728\) 4.06508 + 8.62990i 0.150662 + 0.319845i
\(729\) −1.00000 −0.0370370
\(730\) 8.37564 8.37564i 0.309997 0.309997i
\(731\) 0.126863i 0.00469218i
\(732\) 10.6389i 0.393225i
\(733\) −6.44262 6.44262i −0.237963 0.237963i 0.578043 0.816006i \(-0.303817\pi\)
−0.816006 + 0.578043i \(0.803817\pi\)
\(734\) 10.2518 + 10.2518i 0.378402 + 0.378402i
\(735\) 6.97670 + 4.95171i 0.257340 + 0.182647i
\(736\) 1.91484 + 1.91484i 0.0705819 + 0.0705819i
\(737\) −37.6950 −1.38851
\(738\) −9.14265 −0.336546
\(739\) 20.2641 + 20.2641i 0.745426 + 0.745426i 0.973616 0.228191i \(-0.0732810\pi\)
−0.228191 + 0.973616i \(0.573281\pi\)
\(740\) 3.93813 0.144769
\(741\) −3.76094 + 8.21657i −0.138162 + 0.301843i
\(742\) 5.35564 0.451364i 0.196612 0.0165701i
\(743\) −32.6975 + 32.6975i −1.19955 + 1.19955i −0.225254 + 0.974300i \(0.572321\pi\)
−0.974300 + 0.225254i \(0.927679\pi\)
\(744\) −2.44438 −0.0896154
\(745\) −5.46507 −0.200225
\(746\) 14.9958 14.9958i 0.549035 0.549035i
\(747\) −6.09203 6.09203i −0.222896 0.222896i
\(748\) 1.12783 1.12783i 0.0412375 0.0412375i
\(749\) −27.9316 23.5895i −1.02060 0.861943i
\(750\) −10.3963 −0.379618
\(751\) 39.6528i 1.44695i −0.690351 0.723475i \(-0.742544\pi\)
0.690351 0.723475i \(-0.257456\pi\)
\(752\) 1.41421 1.41421i 0.0515711 0.0515711i
\(753\) 13.3838i 0.487732i
\(754\) 7.23372 15.8036i 0.263437 0.575533i
\(755\) 27.4600i 0.999372i
\(756\) −2.02133 1.70711i −0.0735152 0.0620869i
\(757\) −32.1926 −1.17006 −0.585030 0.811012i \(-0.698917\pi\)
−0.585030 + 0.811012i \(0.698917\pi\)
\(758\) 35.4080i 1.28608i
\(759\) 9.47966 + 9.47966i 0.344090 + 0.344090i
\(760\) −2.16595 + 2.16595i −0.0785672 + 0.0785672i
\(761\) −22.8646 + 22.8646i −0.828842 + 0.828842i −0.987357 0.158514i \(-0.949330\pi\)
0.158514 + 0.987357i \(0.449330\pi\)
\(762\) 6.86314 6.86314i 0.248625 0.248625i
\(763\) −19.3668 + 1.63220i −0.701126 + 0.0590896i
\(764\) 0.869566i 0.0314598i
\(765\) 0.278433 + 0.278433i 0.0100668 + 0.0100668i
\(766\) −20.5656 −0.743064
\(767\) −22.8346 + 49.8871i −0.824510 + 1.80132i
\(768\) 1.00000i 0.0360844i
\(769\) −13.5311 13.5311i −0.487943 0.487943i 0.419714 0.907657i \(-0.362130\pi\)
−0.907657 + 0.419714i \(0.862130\pi\)
\(770\) 1.34440 + 15.9519i 0.0484486 + 0.574866i
\(771\) 11.3581i 0.409053i
\(772\) −6.38377 + 6.38377i −0.229757 + 0.229757i
\(773\) −9.19917 9.19917i −0.330871 0.330871i 0.522046 0.852917i \(-0.325169\pi\)
−0.852917 + 0.522046i \(0.825169\pi\)
\(774\) −0.278433 0.278433i −0.0100081 0.0100081i
\(775\) 6.06034 6.06034i 0.217694 0.217694i
\(776\) 7.35814i 0.264142i
\(777\) −8.49500 + 0.715943i −0.304756 + 0.0256843i
\(778\) −21.6910 21.6910i −0.777662 0.777662i