Properties

Label 546.2.o.b.307.4
Level $546$
Weight $2$
Character 546.307
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 307.4
Root \(0.222191i\) of defining polynomial
Character \(\chi\) \(=\) 546.307
Dual form 546.2.o.b.265.4

$q$-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 \(\left(\mathbb{Z}/546\mathbb{Z}\right)^\times\).

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

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 −0.486943 0.873434i \(-0.661888\pi\)
0.873434 + 0.486943i \(0.161888\pi\)
\(6\) −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 −0.0571102 + 0.998368i \(0.518189\pi\)
−0.998368 + 0.0571102i \(0.981811\pi\)
\(12\) −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 −0.880540 0.473972i \(-0.842820\pi\)
0.473972 + 0.880540i \(0.342820\pi\)
\(20\) 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 \(0.0911065\pi\)
−0.959318 + 0.282328i \(0.908894\pi\)
\(24\) −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 −0.534642 0.845079i \(-0.679553\pi\)
0.845079 + 0.534642i \(0.179553\pi\)
\(32\) −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 −0.494567 0.869139i \(-0.664673\pi\)
0.869139 + 0.494567i \(0.164673\pi\)
\(38\) −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 0.00968403 0.999953i \(-0.496917\pi\)
0.999953 0.00968403i \(-0.00308257\pi\)
\(42\) 0.222191 2.63640i 0.0342849 0.406806i
\(43\) 0.393764i 0.0600485i −0.999549 0.0300242i \(-0.990442\pi\)
0.999549 0.0300242i \(-0.00955845\pi\)
\(44\) −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 0.596402 0.802686i \(-0.296597\pi\)
−0.802686 + 0.596402i \(0.796597\pi\)
\(48\) 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 −0.797515 0.603300i \(-0.793852\pi\)
−0.603300 0.797515i \(-0.706148\pi\)
\(60\) −0.864220 + 0.864220i −0.111570 + 0.111570i
\(61\) 10.6389i 1.36217i 0.732203 + 0.681086i \(0.238492\pi\)
−0.732203 + 0.681086i \(0.761508\pi\)
\(62\) 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 0.954851 0.297085i \(-0.0960146\pi\)
−0.297085 + 0.954851i \(0.596015\pi\)
\(68\) 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 0.667631 0.744493i \(-0.267309\pi\)
−0.744493 + 0.667631i \(0.767309\pi\)
\(72\) 0.707107 0.707107i 0.0833333 0.0833333i
\(73\) 6.85297 + 6.85297i 0.802080 + 0.802080i 0.983420 0.181341i \(-0.0580436\pi\)
−0.181341 + 0.983420i \(0.558044\pi\)
\(74\) 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 −0.288725 0.957412i \(-0.593231\pi\)
0.957412 + 0.288725i \(0.0932312\pi\)
\(84\) 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 0.484157 0.874981i \(-0.339126\pi\)
−0.874981 + 0.484157i \(0.839126\pi\)
\(90\) −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 −0.920060 0.391777i \(-0.871861\pi\)
0.391777 + 0.920060i \(0.371861\pi\)
\(98\) 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 0.910668 0.413139i \(-0.135568\pi\)
−0.413139 + 0.910668i \(0.635568\pi\)
\(110\) −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 \(-0.858291\pi\)
0.902528 0.430632i \(-0.141709\pi\)
\(128\) 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 \(-0.702891\pi\)
0.595110 0.803644i \(-0.297109\pi\)
\(132\) 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 −0.784995 0.619502i \(-0.787335\pi\)
0.619502 + 0.784995i \(0.287335\pi\)
\(138\) −1.91484 1.91484i −0.163002 0.163002i
\(139\) 15.4569i 1.31104i 0.755180 + 0.655518i \(0.227550\pi\)
−0.755180 + 0.655518i \(0.772450\pi\)
\(140\) −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 0.565630 0.824659i \(-0.308633\pi\)
−0.824659 + 0.565630i \(0.808633\pi\)
\(150\) −2.47929 2.47929i −0.202433 0.202433i
\(151\) −15.8872 + 15.8872i −1.29288 + 1.29288i −0.359881 + 0.932998i \(0.617183\pi\)
−0.932998 + 0.359881i \(0.882817\pi\)
\(152\) 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 \(-0.856233\pi\)
0.899724 0.436458i \(-0.143767\pi\)
\(158\) 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 −0.733520 0.679668i \(-0.762124\pi\)
0.679668 + 0.733520i \(0.262124\pi\)
\(164\) 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 0.100463 0.994941i \(-0.467967\pi\)
−0.994941 + 0.100463i \(0.967967\pi\)
\(168\) 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 \(0.317932\pi\)
−0.541302 + 0.840828i \(0.682068\pi\)
\(180\) −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 −0.898496 0.438982i \(-0.855339\pi\)
0.438982 + 0.898496i \(0.355339\pi\)
\(194\) −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 0.225521 0.974238i \(-0.427592\pi\)
−0.974238 + 0.225521i \(0.927592\pi\)
\(198\) 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 −0.490100 0.871666i \(-0.663040\pi\)
0.871666 + 0.490100i \(0.163040\pi\)
\(224\) 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 −0.723560 0.690261i \(-0.757496\pi\)
0.690261 + 0.723560i \(0.257496\pi\)
\(228\) 1.77219 1.77219i 0.117366 0.117366i
\(229\) 12.5167 + 12.5167i 0.827127 + 0.827127i 0.987118 0.159992i \(-0.0511467\pi\)
−0.159992 + 0.987118i \(0.551147\pi\)
\(230\) 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 \(-0.942037\pi\)
0.983466 0.181091i \(-0.0579628\pi\)
\(234\) −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 0.955834 0.293906i \(-0.0949553\pi\)
−0.293906 + 0.955834i \(0.594955\pi\)
\(240\) −0.864220 0.864220i −0.0557851 0.0557851i
\(241\) −16.8108 16.8108i −1.08288 1.08288i −0.996240 0.0866358i \(-0.972388\pi\)
−0.0866358 0.996240i \(-0.527612\pi\)
\(242\) 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 \(0.239154\pi\)
−0.730785 + 0.682608i \(0.760846\pi\)
\(270\) 1.22219i 0.0743802i
\(271\) −1.82388 1.82388i −0.110793 0.110793i 0.649537 0.760330i \(-0.274963\pi\)
−0.760330 + 0.649537i \(0.774963\pi\)
\(272\) 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 \(-0.832327\pi\)
0.864441 0.502735i \(-0.167673\pi\)
\(278\) −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 −0.849291 0.527926i \(-0.822970\pi\)
0.527926 + 0.849291i \(0.322970\pi\)
\(282\) 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 0.819108 0.573639i \(-0.194469\pi\)
−0.573639 + 0.819108i \(0.694469\pi\)
\(294\) 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 0.0284968 0.999594i \(-0.490928\pi\)
−0.999594 + 0.0284968i \(0.990928\pi\)
\(308\) 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 \(-0.835885\pi\)
0.870005 0.493043i \(-0.164115\pi\)
\(314\) 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 −0.972226 0.234046i \(-0.924803\pi\)
−0.234046 0.972226i \(-0.575197\pi\)
\(318\) 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 0.549607 0.835423i \(-0.314778\pi\)
−0.835423 + 0.549607i \(0.814778\pi\)
\(332\) 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 \(-0.988288\pi\)
0.999323 0.0367854i \(-0.0117118\pi\)
\(338\) 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 −0.849557 0.527496i \(-0.823131\pi\)
−0.527496 0.849557i \(-0.676869\pi\)
\(350\) 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 −0.397400 0.917645i \(-0.630088\pi\)
0.917645 + 0.397400i \(0.130088\pi\)
\(354\) 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 −0.817130 0.576454i \(-0.804436\pi\)
0.576454 + 0.817130i \(0.304436\pi\)
\(360\) 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 \(-0.876474\pi\)
0.925641 0.378402i \(-0.123526\pi\)
\(368\) 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 0.937151 + 0.348924i \(0.113453\pi\)
0.348924 + 0.937151i \(0.386547\pi\)
\(380\) −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 −0.973166 0.230103i \(-0.926094\pi\)
0.230103 + 0.973166i \(0.426094\pi\)
\(384\) 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 \(0.283594\pi\)
−0.628683 + 0.777662i \(0.716406\pi\)
\(390\) −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 0.750399 0.660985i \(-0.229861\pi\)
−0.660985 + 0.750399i \(0.729861\pi\)
\(398\) 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 −0.755747 0.654864i \(-0.772726\pi\)
0.654864 + 0.755747i \(0.272726\pi\)
\(402\) −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 −0.935405 0.353578i \(-0.884965\pi\)
0.353578 + 0.935405i \(0.384965\pi\)
\(410\) 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 \(-0.926711\pi\)
0.973611 0.228214i \(-0.0732887\pi\)
\(420\) 0.271560 3.22219i 0.0132508 0.157227i
\(421\) 7.32190 + 7.32190i 0.356848 + 0.356848i 0.862650 0.505802i \(-0.168803\pi\)
−0.505802 + 0.862650i \(0.668803\pi\)
\(422\) 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 −0.930627 0.365968i \(-0.880738\pi\)
−0.365968 0.930627i \(-0.619262\pi\)
\(432\) 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 0.429651 0.902995i \(-0.358636\pi\)
0.902995 0.429651i \(-0.141364\pi\)
\(450\) 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 0.342413 0.939549i \(-0.388756\pi\)
−0.939549 + 0.342413i \(0.888756\pi\)
\(458\) 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 −0.324707 0.945815i \(-0.605266\pi\)
0.945815 + 0.324707i \(0.105266\pi\)
\(462\) 8.45126 + 10.0069i 0.393188 + 0.465562i
\(463\) 21.3712 21.3712i 0.993204 0.993204i −0.00677317 0.999977i \(-0.502156\pi\)
0.999977 + 0.00677317i \(0.00215598\pi\)
\(464\) −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 0.530399 0.847748i \(-0.322042\pi\)
−0.847748 + 0.530399i \(0.822042\pi\)
\(480\) 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 −0.998676 0.0514414i \(-0.983618\pi\)
−0.0514414 0.998676i \(-0.516382\pi\)
\(488\) −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 \(-0.885340\pi\)
0.935822 0.352474i \(-0.114660\pi\)
\(492\) −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 0.986825 + 0.161789i \(0.0517264\pi\)
0.161789 + 0.986825i \(0.448274\pi\)
\(500\) −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 \(0.246023\pi\)
−0.715887 + 0.698216i \(0.753977\pi\)
\(504\) −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 −0.995720 0.0924241i \(-0.970538\pi\)
0.0924241 + 0.995720i \(0.470538\pi\)
\(510\) 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 \(-0.735590\pi\)
0.674382 0.738383i \(-0.264410\pi\)
\(522\) −3.40859 3.40859i −0.149190 0.149190i
\(523\) 19.2350i 0.841086i −0.907273 0.420543i \(-0.861840\pi\)
0.907273 0.420543i \(-0.138160\pi\)
\(524\) 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 0.0717576 0.997422i \(-0.477139\pi\)
0.997422 0.0717576i \(-0.0228608\pi\)
\(542\) 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 −0.591976 0.805956i \(-0.701652\pi\)
0.805956 + 0.591976i \(0.201652\pi\)
\(558\) −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 \(0.00858283\pi\)
−0.999636 + 0.0269605i \(0.991417\pi\)
\(570\) −2.16595 2.16595i −0.0907216 0.0907216i
\(571\) 36.5188i 1.52826i −0.645060 0.764132i \(-0.723167\pi\)
0.645060 0.764132i \(-0.276833\pi\)
\(572\) −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 −0.484576 0.874749i \(-0.661026\pi\)
0.874749 + 0.484576i \(0.161026\pi\)
\(578\) −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 −0.980982 0.194101i \(-0.937821\pi\)
0.194101 + 0.980982i \(0.437821\pi\)
\(588\) −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 0.998640 + 0.0521454i \(0.0166059\pi\)
0.0521454 + 0.998640i \(0.483394\pi\)
\(594\) 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 \(0.125300\pi\)
−0.923518 + 0.383555i \(0.874700\pi\)
\(602\) −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 \(-0.969845\pi\)
0.995516 0.0945933i \(-0.0301551\pi\)
\(608\) 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 0.940224 + 0.340558i \(0.110616\pi\)
0.340558 + 0.940224i \(0.389384\pi\)
\(614\) 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 0.593158 0.805086i \(-0.297881\pi\)
−0.805086 + 0.593158i \(0.797881\pi\)
\(618\) −10.5006 + 10.5006i −0.422397 + 0.422397i
\(619\) 9.61527 + 9.61527i 0.386470 + 0.386470i 0.873426 0.486956i \(-0.161893\pi\)
−0.486956 + 0.873426i \(0.661893\pi\)
\(620\) 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 −0.933548 0.358454i \(-0.883304\pi\)
0.358454 + 0.933548i \(0.383304\pi\)
\(632\) −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 \(0.0307312\pi\)
−0.995343 + 0.0963950i \(0.969269\pi\)
\(642\) −9.77111 + 9.77111i −0.385635 + 0.385635i
\(643\) 25.2403 25.2403i 0.995381 0.995381i −0.00460867 0.999989i \(-0.501467\pi\)
0.999989 + 0.00460867i \(0.00146699\pi\)
\(644\) 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 0.953800 0.300443i \(-0.0971346\pi\)
−0.300443 + 0.953800i \(0.597135\pi\)
\(662\) 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 \(-0.758047\pi\)
0.724756 0.689006i \(-0.241953\pi\)
\(674\) 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 \(0.207489\pi\)
−0.794966 + 0.606655i \(0.792511\pi\)
\(678\) −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 −0.0870076 0.996208i \(-0.527730\pi\)
0.996208 + 0.0870076i \(0.0277305\pi\)
\(684\) 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 −0.649791 0.760113i \(-0.725144\pi\)
0.760113 + 0.649791i \(0.225144\pi\)
\(692\) 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 \(0.160808\pi\)
−0.875081 + 0.483977i \(0.839192\pi\)
\(702\) 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 −0.213899 + 0.976856i \(0.568616\pi\)
−0.976856 + 0.213899i \(0.931384\pi\)
\(710\) −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 −0.816006 0.578043i \(-0.803817\pi\)
0.578043 + 0.816006i \(0.303817\pi\)
\(734\) 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 −0.228191 0.973616i \(-0.573281\pi\)
0.973616 + 0.228191i \(0.0732810\pi\)
\(740\) 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 −0.974300 0.225254i \(-0.927679\pi\)
−0.225254 0.974300i \(-0.572321\pi\)
\(744\) −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 \(0.257456\pi\)
−0.690351 + 0.723475i \(0.742544\pi\)
\(752\) 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 0.158514 0.987357i \(-0.449330\pi\)
−0.987357 + 0.158514i \(0.949330\pi\)
\(762\) 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 −0.907657 0.419714i \(-0.862130\pi\)
0.419714 + 0.907657i \(0.362130\pi\)
\(770\) 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 −0.852917 0.522046i \(-0.825169\pi\)
0.522046 + 0.852917i \(0.325169\pi\)
\(774\) −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 +