Properties

Label 798.2.j.l.457.1
Level $798$
Weight $2$
Character 798.457
Analytic conductor $6.372$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 798 = 2 \cdot 3 \cdot 7 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 798.j (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.37206208130\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{3})\)
Coefficient field: 8.0.856615824.2
Defining polynomial: \(x^{8} + 11 x^{6} + 36 x^{4} + 32 x^{2} + 4\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 3 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 457.1
Root \(1.07834i\) of defining polynomial
Character \(\chi\) \(=\) 798.457
Dual form 798.2.j.l.571.1

$q$-expansion

\(f(q)\) \(=\) \(q+(0.500000 - 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.24624 + 2.15855i) q^{5} +1.00000 q^{6} +(2.47720 + 0.929227i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(q+(0.500000 - 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.24624 + 2.15855i) q^{5} +1.00000 q^{6} +(2.47720 + 0.929227i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(1.24624 + 2.15855i) q^{10} +(1.73096 + 2.99812i) q^{11} +(0.500000 - 0.866025i) q^{12} -4.98496 q^{13} +(2.04334 - 1.68071i) q^{14} -2.49248 q^{15} +(-0.500000 + 0.866025i) q^{16} +(-1.12150 - 1.94249i) q^{17} +(0.500000 + 0.866025i) q^{18} +(-0.500000 + 0.866025i) q^{19} +2.49248 q^{20} +(0.433868 + 2.60993i) q^{21} +3.46193 q^{22} +(-3.00202 + 5.19965i) q^{23} +(-0.500000 - 0.866025i) q^{24} +(-0.606223 - 1.05001i) q^{25} +(-2.49248 + 4.31710i) q^{26} -1.00000 q^{27} +(-0.433868 - 2.60993i) q^{28} -5.51156 q^{29} +(-1.24624 + 2.15855i) q^{30} +(3.64204 + 6.30819i) q^{31} +(0.500000 + 0.866025i) q^{32} +(-1.73096 + 2.99812i) q^{33} -2.24299 q^{34} +(-5.09297 + 4.18913i) q^{35} +1.00000 q^{36} +(4.58343 - 7.93873i) q^{37} +(0.500000 + 0.866025i) q^{38} +(-2.49248 - 4.31710i) q^{39} +(1.24624 - 2.15855i) q^{40} +4.64383 q^{41} +(2.47720 + 0.929227i) q^{42} +9.54211 q^{43} +(1.73096 - 2.99812i) q^{44} +(-1.24624 - 2.15855i) q^{45} +(3.00202 + 5.19965i) q^{46} +(-2.68011 + 4.64208i) q^{47} -1.00000 q^{48} +(5.27308 + 4.60377i) q^{49} -1.21245 q^{50} +(1.12150 - 1.94249i) q^{51} +(2.49248 + 4.31710i) q^{52} +(2.93711 + 5.08723i) q^{53} +(-0.500000 + 0.866025i) q^{54} -8.62878 q^{55} +(-2.47720 - 0.929227i) q^{56} -1.00000 q^{57} +(-2.75578 + 4.77315i) q^{58} +(4.33921 + 7.51573i) q^{59} +(1.24624 + 2.15855i) q^{60} +(-2.18763 + 3.78908i) q^{61} +7.28407 q^{62} +(-2.04334 + 1.68071i) q^{63} +1.00000 q^{64} +(6.21245 - 10.7603i) q^{65} +(1.73096 + 2.99812i) q^{66} +(-7.57915 - 13.1275i) q^{67} +(-1.12150 + 1.94249i) q^{68} -6.00404 q^{69} +(1.08141 + 6.50520i) q^{70} +12.0907 q^{71} +(0.500000 - 0.866025i) q^{72} +(-7.21019 - 12.4884i) q^{73} +(-4.58343 - 7.93873i) q^{74} +(0.606223 - 1.05001i) q^{75} +1.00000 q^{76} +(1.50202 + 9.03541i) q^{77} -4.98496 q^{78} +(3.54334 - 6.13724i) q^{79} +(-1.24624 - 2.15855i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(2.32191 - 4.02167i) q^{82} -5.59823 q^{83} +(2.04334 - 1.68071i) q^{84} +5.59061 q^{85} +(4.77106 - 8.26371i) q^{86} +(-2.75578 - 4.77315i) q^{87} +(-1.73096 - 2.99812i) q^{88} +(-3.76476 + 6.52075i) q^{89} -2.49248 q^{90} +(-12.3488 - 4.63215i) q^{91} +6.00404 q^{92} +(-3.64204 + 6.30819i) q^{93} +(2.68011 + 4.64208i) q^{94} +(-1.24624 - 2.15855i) q^{95} +(-0.500000 + 0.866025i) q^{96} +7.00404 q^{97} +(6.62352 - 2.26473i) q^{98} -3.46193 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q + 4q^{2} + 4q^{3} - 4q^{4} + 8q^{6} - 2q^{7} - 8q^{8} - 4q^{9} + O(q^{10}) \) \( 8q + 4q^{2} + 4q^{3} - 4q^{4} + 8q^{6} - 2q^{7} - 8q^{8} - 4q^{9} + 2q^{11} + 4q^{12} - q^{14} - 4q^{16} - 10q^{17} + 4q^{18} - 4q^{19} - q^{21} + 4q^{22} + 5q^{23} - 4q^{24} - 4q^{25} - 8q^{27} + q^{28} - 6q^{29} - 9q^{31} + 4q^{32} - 2q^{33} - 20q^{34} - 9q^{35} + 8q^{36} + 14q^{37} + 4q^{38} + 8q^{41} - 2q^{42} + 42q^{43} + 2q^{44} - 5q^{46} - 7q^{47} - 8q^{48} - 4q^{49} - 8q^{50} + 10q^{51} + 7q^{53} - 4q^{54} + 2q^{56} - 8q^{57} - 3q^{58} - 7q^{59} - 23q^{61} - 18q^{62} + q^{63} + 8q^{64} + 48q^{65} + 2q^{66} - 6q^{67} - 10q^{68} + 10q^{69} + 15q^{70} + 4q^{71} + 4q^{72} + 5q^{73} - 14q^{74} + 4q^{75} + 8q^{76} - 17q^{77} + 11q^{79} - 4q^{81} + 4q^{82} + 28q^{83} - q^{84} + 12q^{85} + 21q^{86} - 3q^{87} - 2q^{88} - 10q^{89} - 48q^{91} - 10q^{92} + 9q^{93} + 7q^{94} - 4q^{96} - 2q^{97} + 25q^{98} - 4q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/798\mathbb{Z}\right)^\times\).

\(n\) \(115\) \(211\) \(533\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.500000 0.866025i 0.353553 0.612372i
\(3\) 0.500000 + 0.866025i 0.288675 + 0.500000i
\(4\) −0.500000 0.866025i −0.250000 0.433013i
\(5\) −1.24624 + 2.15855i −0.557335 + 0.965333i 0.440383 + 0.897810i \(0.354843\pi\)
−0.997718 + 0.0675224i \(0.978491\pi\)
\(6\) 1.00000 0.408248
\(7\) 2.47720 + 0.929227i 0.936295 + 0.351215i
\(8\) −1.00000 −0.353553
\(9\) −0.500000 + 0.866025i −0.166667 + 0.288675i
\(10\) 1.24624 + 2.15855i 0.394095 + 0.682593i
\(11\) 1.73096 + 2.99812i 0.521906 + 0.903967i 0.999675 + 0.0254818i \(0.00811198\pi\)
−0.477770 + 0.878485i \(0.658555\pi\)
\(12\) 0.500000 0.866025i 0.144338 0.250000i
\(13\) −4.98496 −1.38258 −0.691289 0.722578i \(-0.742957\pi\)
−0.691289 + 0.722578i \(0.742957\pi\)
\(14\) 2.04334 1.68071i 0.546104 0.449188i
\(15\) −2.49248 −0.643555
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) −1.12150 1.94249i −0.272003 0.471123i 0.697372 0.716710i \(-0.254353\pi\)
−0.969375 + 0.245587i \(0.921019\pi\)
\(18\) 0.500000 + 0.866025i 0.117851 + 0.204124i
\(19\) −0.500000 + 0.866025i −0.114708 + 0.198680i
\(20\) 2.49248 0.557335
\(21\) 0.433868 + 2.60993i 0.0946777 + 0.569534i
\(22\) 3.46193 0.738086
\(23\) −3.00202 + 5.19965i −0.625964 + 1.08420i 0.362389 + 0.932027i \(0.381961\pi\)
−0.988354 + 0.152175i \(0.951372\pi\)
\(24\) −0.500000 0.866025i −0.102062 0.176777i
\(25\) −0.606223 1.05001i −0.121245 0.210002i
\(26\) −2.49248 + 4.31710i −0.488815 + 0.846653i
\(27\) −1.00000 −0.192450
\(28\) −0.433868 2.60993i −0.0819933 0.493231i
\(29\) −5.51156 −1.02347 −0.511736 0.859143i \(-0.670997\pi\)
−0.511736 + 0.859143i \(0.670997\pi\)
\(30\) −1.24624 + 2.15855i −0.227531 + 0.394095i
\(31\) 3.64204 + 6.30819i 0.654129 + 1.13298i 0.982111 + 0.188301i \(0.0602980\pi\)
−0.327982 + 0.944684i \(0.606369\pi\)
\(32\) 0.500000 + 0.866025i 0.0883883 + 0.153093i
\(33\) −1.73096 + 2.99812i −0.301322 + 0.521906i
\(34\) −2.24299 −0.384670
\(35\) −5.09297 + 4.18913i −0.860869 + 0.708092i
\(36\) 1.00000 0.166667
\(37\) 4.58343 7.93873i 0.753511 1.30512i −0.192601 0.981277i \(-0.561692\pi\)
0.946111 0.323842i \(-0.104974\pi\)
\(38\) 0.500000 + 0.866025i 0.0811107 + 0.140488i
\(39\) −2.49248 4.31710i −0.399116 0.691289i
\(40\) 1.24624 2.15855i 0.197048 0.341297i
\(41\) 4.64383 0.725244 0.362622 0.931936i \(-0.381882\pi\)
0.362622 + 0.931936i \(0.381882\pi\)
\(42\) 2.47720 + 0.929227i 0.382241 + 0.143383i
\(43\) 9.54211 1.45516 0.727579 0.686024i \(-0.240645\pi\)
0.727579 + 0.686024i \(0.240645\pi\)
\(44\) 1.73096 2.99812i 0.260953 0.451983i
\(45\) −1.24624 2.15855i −0.185778 0.321778i
\(46\) 3.00202 + 5.19965i 0.442624 + 0.766647i
\(47\) −2.68011 + 4.64208i −0.390934 + 0.677117i −0.992573 0.121651i \(-0.961181\pi\)
0.601639 + 0.798768i \(0.294515\pi\)
\(48\) −1.00000 −0.144338
\(49\) 5.27308 + 4.60377i 0.753297 + 0.657681i
\(50\) −1.21245 −0.171466
\(51\) 1.12150 1.94249i 0.157041 0.272003i
\(52\) 2.49248 + 4.31710i 0.345644 + 0.598674i
\(53\) 2.93711 + 5.08723i 0.403443 + 0.698785i 0.994139 0.108110i \(-0.0344799\pi\)
−0.590695 + 0.806895i \(0.701147\pi\)
\(54\) −0.500000 + 0.866025i −0.0680414 + 0.117851i
\(55\) −8.62878 −1.16350
\(56\) −2.47720 0.929227i −0.331030 0.124173i
\(57\) −1.00000 −0.132453
\(58\) −2.75578 + 4.77315i −0.361852 + 0.626746i
\(59\) 4.33921 + 7.51573i 0.564917 + 0.978464i 0.997057 + 0.0766583i \(0.0244251\pi\)
−0.432141 + 0.901806i \(0.642242\pi\)
\(60\) 1.24624 + 2.15855i 0.160889 + 0.278667i
\(61\) −2.18763 + 3.78908i −0.280097 + 0.485143i −0.971408 0.237415i \(-0.923700\pi\)
0.691311 + 0.722557i \(0.257033\pi\)
\(62\) 7.28407 0.925078
\(63\) −2.04334 + 1.68071i −0.257436 + 0.211749i
\(64\) 1.00000 0.125000
\(65\) 6.21245 10.7603i 0.770559 1.33465i
\(66\) 1.73096 + 2.99812i 0.213067 + 0.369043i
\(67\) −7.57915 13.1275i −0.925940 1.60378i −0.790042 0.613053i \(-0.789941\pi\)
−0.135899 0.990723i \(-0.543392\pi\)
\(68\) −1.12150 + 1.94249i −0.136001 + 0.235561i
\(69\) −6.00404 −0.722802
\(70\) 1.08141 + 6.50520i 0.129253 + 0.777521i
\(71\) 12.0907 1.43490 0.717452 0.696608i \(-0.245308\pi\)
0.717452 + 0.696608i \(0.245308\pi\)
\(72\) 0.500000 0.866025i 0.0589256 0.102062i
\(73\) −7.21019 12.4884i −0.843889 1.46166i −0.886583 0.462570i \(-0.846927\pi\)
0.0426940 0.999088i \(-0.486406\pi\)
\(74\) −4.58343 7.93873i −0.532813 0.922858i
\(75\) 0.606223 1.05001i 0.0700006 0.121245i
\(76\) 1.00000 0.114708
\(77\) 1.50202 + 9.03541i 0.171171 + 1.02968i
\(78\) −4.98496 −0.564435
\(79\) 3.54334 6.13724i 0.398656 0.690493i −0.594904 0.803797i \(-0.702810\pi\)
0.993560 + 0.113304i \(0.0361433\pi\)
\(80\) −1.24624 2.15855i −0.139334 0.241333i
\(81\) −0.500000 0.866025i −0.0555556 0.0962250i
\(82\) 2.32191 4.02167i 0.256412 0.444119i
\(83\) −5.59823 −0.614486 −0.307243 0.951631i \(-0.599406\pi\)
−0.307243 + 0.951631i \(0.599406\pi\)
\(84\) 2.04334 1.68071i 0.222946 0.183380i
\(85\) 5.59061 0.606387
\(86\) 4.77106 8.26371i 0.514476 0.891099i
\(87\) −2.75578 4.77315i −0.295451 0.511736i
\(88\) −1.73096 2.99812i −0.184521 0.319601i
\(89\) −3.76476 + 6.52075i −0.399064 + 0.691198i −0.993611 0.112862i \(-0.963998\pi\)
0.594547 + 0.804061i \(0.297331\pi\)
\(90\) −2.49248 −0.262730
\(91\) −12.3488 4.63215i −1.29450 0.485582i
\(92\) 6.00404 0.625964
\(93\) −3.64204 + 6.30819i −0.377662 + 0.654129i
\(94\) 2.68011 + 4.64208i 0.276432 + 0.478794i
\(95\) −1.24624 2.15855i −0.127861 0.221462i
\(96\) −0.500000 + 0.866025i −0.0510310 + 0.0883883i
\(97\) 7.00404 0.711153 0.355576 0.934647i \(-0.384285\pi\)
0.355576 + 0.934647i \(0.384285\pi\)
\(98\) 6.62352 2.26473i 0.669076 0.228773i
\(99\) −3.46193 −0.347937
\(100\) −0.606223 + 1.05001i −0.0606223 + 0.105001i
\(101\) −3.54784 6.14504i −0.353024 0.611455i 0.633754 0.773535i \(-0.281513\pi\)
−0.986778 + 0.162080i \(0.948180\pi\)
\(102\) −1.12150 1.94249i −0.111045 0.192335i
\(103\) −3.57567 + 6.19325i −0.352322 + 0.610239i −0.986656 0.162820i \(-0.947941\pi\)
0.634334 + 0.773059i \(0.281274\pi\)
\(104\) 4.98496 0.488815
\(105\) −6.17438 2.31608i −0.602557 0.226026i
\(106\) 5.87423 0.570555
\(107\) 7.86525 13.6230i 0.760362 1.31699i −0.182302 0.983243i \(-0.558355\pi\)
0.942664 0.333744i \(-0.108312\pi\)
\(108\) 0.500000 + 0.866025i 0.0481125 + 0.0833333i
\(109\) −4.15854 7.20279i −0.398315 0.689903i 0.595203 0.803576i \(-0.297072\pi\)
−0.993518 + 0.113673i \(0.963738\pi\)
\(110\) −4.31439 + 7.47274i −0.411361 + 0.712498i
\(111\) 9.16685 0.870079
\(112\) −2.04334 + 1.68071i −0.193077 + 0.158812i
\(113\) 13.3643 1.25720 0.628602 0.777727i \(-0.283628\pi\)
0.628602 + 0.777727i \(0.283628\pi\)
\(114\) −0.500000 + 0.866025i −0.0468293 + 0.0811107i
\(115\) −7.48247 12.9600i −0.697744 1.20853i
\(116\) 2.75578 + 4.77315i 0.255868 + 0.443176i
\(117\) 2.49248 4.31710i 0.230430 0.399116i
\(118\) 8.67842 0.798913
\(119\) −0.973163 5.85407i −0.0892097 0.536641i
\(120\) 2.49248 0.227531
\(121\) −0.492478 + 0.852997i −0.0447707 + 0.0775451i
\(122\) 2.18763 + 3.78908i 0.198059 + 0.343048i
\(123\) 2.32191 + 4.02167i 0.209360 + 0.362622i
\(124\) 3.64204 6.30819i 0.327065 0.566492i
\(125\) −9.44040 −0.844375
\(126\) 0.433868 + 2.60993i 0.0386520 + 0.232511i
\(127\) 6.09569 0.540905 0.270452 0.962733i \(-0.412827\pi\)
0.270452 + 0.962733i \(0.412827\pi\)
\(128\) 0.500000 0.866025i 0.0441942 0.0765466i
\(129\) 4.77106 + 8.26371i 0.420068 + 0.727579i
\(130\) −6.21245 10.7603i −0.544868 0.943738i
\(131\) −4.65708 + 8.06630i −0.406891 + 0.704756i −0.994540 0.104360i \(-0.966720\pi\)
0.587649 + 0.809116i \(0.300054\pi\)
\(132\) 3.46193 0.301322
\(133\) −2.04334 + 1.68071i −0.177180 + 0.145736i
\(134\) −15.1583 −1.30948
\(135\) 1.24624 2.15855i 0.107259 0.185778i
\(136\) 1.12150 + 1.94249i 0.0961676 + 0.166567i
\(137\) 3.89255 + 6.74210i 0.332563 + 0.576016i 0.983014 0.183532i \(-0.0587532\pi\)
−0.650450 + 0.759549i \(0.725420\pi\)
\(138\) −3.00202 + 5.19965i −0.255549 + 0.442624i
\(139\) 12.5882 1.06771 0.533857 0.845575i \(-0.320742\pi\)
0.533857 + 0.845575i \(0.320742\pi\)
\(140\) 6.17438 + 2.31608i 0.521830 + 0.195744i
\(141\) −5.36021 −0.451411
\(142\) 6.04536 10.4709i 0.507315 0.878695i
\(143\) −8.62878 14.9455i −0.721575 1.24980i
\(144\) −0.500000 0.866025i −0.0416667 0.0721688i
\(145\) 6.86872 11.8970i 0.570416 0.987990i
\(146\) −14.4204 −1.19344
\(147\) −1.35044 + 6.86850i −0.111383 + 0.566504i
\(148\) −9.16685 −0.753511
\(149\) −8.14608 + 14.1094i −0.667353 + 1.15589i 0.311289 + 0.950315i \(0.399239\pi\)
−0.978642 + 0.205573i \(0.934094\pi\)
\(150\) −0.606223 1.05001i −0.0494979 0.0857329i
\(151\) −9.98675 17.2976i −0.812710 1.40765i −0.910961 0.412493i \(-0.864658\pi\)
0.0982509 0.995162i \(-0.468675\pi\)
\(152\) 0.500000 0.866025i 0.0405554 0.0702439i
\(153\) 2.24299 0.181335
\(154\) 8.57590 + 3.21692i 0.691066 + 0.259227i
\(155\) −18.1554 −1.45828
\(156\) −2.49248 + 4.31710i −0.199558 + 0.345644i
\(157\) 0.369526 + 0.640038i 0.0294914 + 0.0510806i 0.880394 0.474242i \(-0.157278\pi\)
−0.850903 + 0.525323i \(0.823945\pi\)
\(158\) −3.54334 6.13724i −0.281893 0.488252i
\(159\) −2.93711 + 5.08723i −0.232928 + 0.403443i
\(160\) −2.49248 −0.197048
\(161\) −12.2683 + 10.0910i −0.966875 + 0.795285i
\(162\) −1.00000 −0.0785674
\(163\) 2.89904 5.02129i 0.227071 0.393298i −0.729868 0.683588i \(-0.760419\pi\)
0.956939 + 0.290290i \(0.0937519\pi\)
\(164\) −2.32191 4.02167i −0.181311 0.314040i
\(165\) −4.31439 7.47274i −0.335875 0.581752i
\(166\) −2.79912 + 4.84821i −0.217254 + 0.376294i
\(167\) 17.1058 1.32368 0.661842 0.749644i \(-0.269775\pi\)
0.661842 + 0.749644i \(0.269775\pi\)
\(168\) −0.433868 2.60993i −0.0334736 0.201361i
\(169\) 11.8498 0.911522
\(170\) 2.79531 4.84161i 0.214390 0.371335i
\(171\) −0.500000 0.866025i −0.0382360 0.0662266i
\(172\) −4.77106 8.26371i −0.363790 0.630102i
\(173\) 1.29206 2.23792i 0.0982336 0.170146i −0.812720 0.582654i \(-0.802014\pi\)
0.910954 + 0.412509i \(0.135347\pi\)
\(174\) −5.51156 −0.417830
\(175\) −0.526041 3.16440i −0.0397650 0.239206i
\(176\) −3.46193 −0.260953
\(177\) −4.33921 + 7.51573i −0.326155 + 0.564917i
\(178\) 3.76476 + 6.52075i 0.282181 + 0.488751i
\(179\) 1.62474 + 2.81414i 0.121439 + 0.210338i 0.920335 0.391130i \(-0.127916\pi\)
−0.798896 + 0.601469i \(0.794582\pi\)
\(180\) −1.24624 + 2.15855i −0.0928892 + 0.160889i
\(181\) 12.4559 0.925840 0.462920 0.886400i \(-0.346802\pi\)
0.462920 + 0.886400i \(0.346802\pi\)
\(182\) −10.1859 + 8.37825i −0.755032 + 0.621038i
\(183\) −4.37526 −0.323428
\(184\) 3.00202 5.19965i 0.221312 0.383323i
\(185\) 11.4241 + 19.7871i 0.839916 + 1.45478i
\(186\) 3.64204 + 6.30819i 0.267047 + 0.462539i
\(187\) 3.88254 6.72476i 0.283920 0.491763i
\(188\) 5.36021 0.390934
\(189\) −2.47720 0.929227i −0.180190 0.0675913i
\(190\) −2.49248 −0.180823
\(191\) 8.22222 14.2413i 0.594939 1.03046i −0.398617 0.917118i \(-0.630510\pi\)
0.993556 0.113347i \(-0.0361571\pi\)
\(192\) 0.500000 + 0.866025i 0.0360844 + 0.0625000i
\(193\) 9.34268 + 16.1820i 0.672501 + 1.16481i 0.977193 + 0.212355i \(0.0681133\pi\)
−0.304692 + 0.952451i \(0.598553\pi\)
\(194\) 3.50202 6.06568i 0.251430 0.435490i
\(195\) 12.4249 0.889765
\(196\) 1.35044 6.86850i 0.0964601 0.490607i
\(197\) −15.4965 −1.10408 −0.552041 0.833817i \(-0.686151\pi\)
−0.552041 + 0.833817i \(0.686151\pi\)
\(198\) −1.73096 + 2.99812i −0.123014 + 0.213067i
\(199\) 0.729740 + 1.26395i 0.0517299 + 0.0895988i 0.890731 0.454531i \(-0.150193\pi\)
−0.839001 + 0.544130i \(0.816860\pi\)
\(200\) 0.606223 + 1.05001i 0.0428664 + 0.0742468i
\(201\) 7.57915 13.1275i 0.534592 0.925940i
\(202\) −7.09569 −0.499251
\(203\) −13.6533 5.12149i −0.958271 0.359458i
\(204\) −2.24299 −0.157041
\(205\) −5.78732 + 10.0239i −0.404204 + 0.700102i
\(206\) 3.57567 + 6.19325i 0.249129 + 0.431504i
\(207\) −3.00202 5.19965i −0.208655 0.361401i
\(208\) 2.49248 4.31710i 0.172822 0.299337i
\(209\) −3.46193 −0.239467
\(210\) −5.09297 + 4.18913i −0.351448 + 0.289077i
\(211\) −23.3953 −1.61060 −0.805298 0.592870i \(-0.797995\pi\)
−0.805298 + 0.592870i \(0.797995\pi\)
\(212\) 2.93711 5.08723i 0.201722 0.349392i
\(213\) 6.04536 + 10.4709i 0.414221 + 0.717452i
\(214\) −7.86525 13.6230i −0.537657 0.931250i
\(215\) −11.8917 + 20.5971i −0.811011 + 1.40471i
\(216\) 1.00000 0.0680414
\(217\) 3.16033 + 19.0110i 0.214537 + 1.29055i
\(218\) −8.31707 −0.563303
\(219\) 7.21019 12.4884i 0.487219 0.843889i
\(220\) 4.31439 + 7.47274i 0.290876 + 0.503812i
\(221\) 5.59061 + 9.68323i 0.376065 + 0.651364i
\(222\) 4.58343 7.93873i 0.307619 0.532813i
\(223\) 14.8221 0.992564 0.496282 0.868161i \(-0.334698\pi\)
0.496282 + 0.868161i \(0.334698\pi\)
\(224\) 0.433868 + 2.60993i 0.0289890 + 0.174384i
\(225\) 1.21245 0.0808297
\(226\) 6.68213 11.5738i 0.444488 0.769877i
\(227\) −8.11473 14.0551i −0.538594 0.932872i −0.998980 0.0451531i \(-0.985622\pi\)
0.460386 0.887719i \(-0.347711\pi\)
\(228\) 0.500000 + 0.866025i 0.0331133 + 0.0573539i
\(229\) 3.19740 5.53806i 0.211290 0.365965i −0.740828 0.671694i \(-0.765567\pi\)
0.952119 + 0.305729i \(0.0989001\pi\)
\(230\) −14.9649 −0.986759
\(231\) −7.07388 + 5.81849i −0.465427 + 0.382829i
\(232\) 5.51156 0.361852
\(233\) 10.6899 18.5154i 0.700317 1.21299i −0.268038 0.963408i \(-0.586375\pi\)
0.968355 0.249577i \(-0.0802915\pi\)
\(234\) −2.49248 4.31710i −0.162938 0.282218i
\(235\) −6.68011 11.5703i −0.435762 0.754762i
\(236\) 4.33921 7.51573i 0.282458 0.489232i
\(237\) 7.08667 0.460329
\(238\) −5.55635 2.08425i −0.360165 0.135102i
\(239\) 18.8938 1.22214 0.611068 0.791578i \(-0.290740\pi\)
0.611068 + 0.791578i \(0.290740\pi\)
\(240\) 1.24624 2.15855i 0.0804444 0.139334i
\(241\) −2.02505 3.50748i −0.130445 0.225937i 0.793403 0.608696i \(-0.208307\pi\)
−0.923848 + 0.382759i \(0.874974\pi\)
\(242\) 0.492478 + 0.852997i 0.0316577 + 0.0548327i
\(243\) 0.500000 0.866025i 0.0320750 0.0555556i
\(244\) 4.37526 0.280097
\(245\) −16.5090 + 5.64480i −1.05472 + 0.360633i
\(246\) 4.64383 0.296080
\(247\) 2.49248 4.31710i 0.158593 0.274690i
\(248\) −3.64204 6.30819i −0.231270 0.400571i
\(249\) −2.79912 4.84821i −0.177387 0.307243i
\(250\) −4.72020 + 8.17562i −0.298532 + 0.517072i
\(251\) 6.59917 0.416536 0.208268 0.978072i \(-0.433217\pi\)
0.208268 + 0.978072i \(0.433217\pi\)
\(252\) 2.47720 + 0.929227i 0.156049 + 0.0585358i
\(253\) −20.7856 −1.30678
\(254\) 3.04784 5.27902i 0.191239 0.331235i
\(255\) 2.79531 + 4.84161i 0.175049 + 0.303194i
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) 1.32562 2.29605i 0.0826902 0.143224i −0.821714 0.569899i \(-0.806982\pi\)
0.904405 + 0.426676i \(0.140315\pi\)
\(258\) 9.54211 0.594066
\(259\) 18.7310 15.4068i 1.16389 0.957332i
\(260\) −12.4249 −0.770559
\(261\) 2.75578 4.77315i 0.170579 0.295451i
\(262\) 4.65708 + 8.06630i 0.287715 + 0.498338i
\(263\) 0.727720 + 1.26045i 0.0448731 + 0.0777225i 0.887590 0.460635i \(-0.152378\pi\)
−0.842716 + 0.538358i \(0.819045\pi\)
\(264\) 1.73096 2.99812i 0.106534 0.184521i
\(265\) −14.6414 −0.899413
\(266\) 0.433868 + 2.60993i 0.0266022 + 0.160025i
\(267\) −7.52952 −0.460799
\(268\) −7.57915 + 13.1275i −0.462970 + 0.801888i
\(269\) −7.16159 12.4042i −0.436650 0.756299i 0.560779 0.827966i \(-0.310502\pi\)
−0.997429 + 0.0716661i \(0.977168\pi\)
\(270\) −1.24624 2.15855i −0.0758437 0.131365i
\(271\) −10.3329 + 17.8971i −0.627680 + 1.08717i 0.360337 + 0.932822i \(0.382662\pi\)
−0.988016 + 0.154351i \(0.950671\pi\)
\(272\) 2.24299 0.136001
\(273\) −2.16281 13.0104i −0.130899 0.787426i
\(274\) 7.78510 0.470315
\(275\) 2.09870 3.63506i 0.126556 0.219202i
\(276\) 3.00202 + 5.19965i 0.180700 + 0.312982i
\(277\) 14.2710 + 24.7182i 0.857464 + 1.48517i 0.874340 + 0.485314i \(0.161295\pi\)
−0.0168758 + 0.999858i \(0.505372\pi\)
\(278\) 6.29408 10.9017i 0.377494 0.653839i
\(279\) −7.28407 −0.436086
\(280\) 5.09297 4.18913i 0.304363 0.250348i
\(281\) −13.6443 −0.813950 −0.406975 0.913439i \(-0.633416\pi\)
−0.406975 + 0.913439i \(0.633416\pi\)
\(282\) −2.68011 + 4.64208i −0.159598 + 0.276432i
\(283\) 0.767015 + 1.32851i 0.0455943 + 0.0789717i 0.887922 0.459994i \(-0.152149\pi\)
−0.842328 + 0.538966i \(0.818815\pi\)
\(284\) −6.04536 10.4709i −0.358726 0.621331i
\(285\) 1.24624 2.15855i 0.0738208 0.127861i
\(286\) −17.2576 −1.02046
\(287\) 11.5037 + 4.31517i 0.679042 + 0.254716i
\(288\) −1.00000 −0.0589256
\(289\) 5.98449 10.3654i 0.352029 0.609732i
\(290\) −6.86872 11.8970i −0.403345 0.698615i
\(291\) 3.50202 + 6.06568i 0.205292 + 0.355576i
\(292\) −7.21019 + 12.4884i −0.421944 + 0.730829i
\(293\) −33.3773 −1.94992 −0.974962 0.222373i \(-0.928620\pi\)
−0.974962 + 0.222373i \(0.928620\pi\)
\(294\) 5.27308 + 4.60377i 0.307532 + 0.268497i
\(295\) −21.6308 −1.25939
\(296\) −4.58343 + 7.93873i −0.266406 + 0.461429i
\(297\) −1.73096 2.99812i −0.100441 0.173969i
\(298\) 8.14608 + 14.1094i 0.471890 + 0.817337i
\(299\) 14.9649 25.9200i 0.865445 1.49899i
\(300\) −1.21245 −0.0700006
\(301\) 23.6378 + 8.86678i 1.36246 + 0.511073i
\(302\) −19.9735 −1.14935
\(303\) 3.54784 6.14504i 0.203818 0.353024i
\(304\) −0.500000 0.866025i −0.0286770 0.0496700i
\(305\) −5.45262 9.44421i −0.312216 0.540774i
\(306\) 1.12150 1.94249i 0.0641117 0.111045i
\(307\) 9.52952 0.543878 0.271939 0.962314i \(-0.412335\pi\)
0.271939 + 0.962314i \(0.412335\pi\)
\(308\) 7.07388 5.81849i 0.403072 0.331539i
\(309\) −7.15135 −0.406826
\(310\) −9.07769 + 15.7230i −0.515578 + 0.893008i
\(311\) −8.22020 14.2378i −0.466125 0.807352i 0.533127 0.846035i \(-0.321017\pi\)
−0.999252 + 0.0386837i \(0.987684\pi\)
\(312\) 2.49248 + 4.31710i 0.141109 + 0.244408i
\(313\) −5.49698 + 9.52106i −0.310708 + 0.538162i −0.978516 0.206172i \(-0.933899\pi\)
0.667808 + 0.744334i \(0.267233\pi\)
\(314\) 0.739053 0.0417072
\(315\) −1.08141 6.50520i −0.0609303 0.366527i
\(316\) −7.08667 −0.398656
\(317\) −3.33146 + 5.77025i −0.187113 + 0.324090i −0.944287 0.329124i \(-0.893246\pi\)
0.757173 + 0.653214i \(0.226580\pi\)
\(318\) 2.93711 + 5.08723i 0.164705 + 0.285278i
\(319\) −9.54032 16.5243i −0.534155 0.925184i
\(320\) −1.24624 + 2.15855i −0.0696669 + 0.120667i
\(321\) 15.7305 0.877991
\(322\) 2.60496 + 15.6702i 0.145169 + 0.873263i
\(323\) 2.24299 0.124804
\(324\) −0.500000 + 0.866025i −0.0277778 + 0.0481125i
\(325\) 3.02199 + 5.23425i 0.167630 + 0.290344i
\(326\) −2.89904 5.02129i −0.160563 0.278103i
\(327\) 4.15854 7.20279i 0.229968 0.398315i
\(328\) −4.64383 −0.256412
\(329\) −10.9527 + 9.00895i −0.603843 + 0.496680i
\(330\) −8.62878 −0.474999
\(331\) −12.9051 + 22.3523i −0.709329 + 1.22859i 0.255778 + 0.966736i \(0.417668\pi\)
−0.965107 + 0.261858i \(0.915665\pi\)
\(332\) 2.79912 + 4.84821i 0.153622 + 0.266080i
\(333\) 4.58343 + 7.93873i 0.251170 + 0.435040i
\(334\) 8.55288 14.8140i 0.467993 0.810587i
\(335\) 37.7817 2.06424
\(336\) −2.47720 0.929227i −0.135143 0.0506935i
\(337\) 10.0932 0.549810 0.274905 0.961471i \(-0.411354\pi\)
0.274905 + 0.961471i \(0.411354\pi\)
\(338\) 5.92489 10.2622i 0.322272 0.558191i
\(339\) 6.68213 + 11.5738i 0.362923 + 0.628602i
\(340\) −2.79531 4.84161i −0.151597 0.262573i
\(341\) −12.6085 + 21.8385i −0.682787 + 1.18262i
\(342\) −1.00000 −0.0540738
\(343\) 8.78454 + 16.3044i 0.474321 + 0.880352i
\(344\) −9.54211 −0.514476
\(345\) 7.48247 12.9600i 0.402843 0.697744i
\(346\) −1.29206 2.23792i −0.0694617 0.120311i
\(347\) 0.184614 + 0.319761i 0.00991059 + 0.0171657i 0.870938 0.491393i \(-0.163512\pi\)
−0.861028 + 0.508558i \(0.830179\pi\)
\(348\) −2.75578 + 4.77315i −0.147725 + 0.255868i
\(349\) 31.3643 1.67889 0.839445 0.543445i \(-0.182880\pi\)
0.839445 + 0.543445i \(0.182880\pi\)
\(350\) −3.00347 1.12664i −0.160542 0.0602213i
\(351\) 4.98496 0.266077
\(352\) −1.73096 + 2.99812i −0.0922607 + 0.159800i
\(353\) 11.4096 + 19.7620i 0.607272 + 1.05183i 0.991688 + 0.128666i \(0.0410696\pi\)
−0.384416 + 0.923160i \(0.625597\pi\)
\(354\) 4.33921 + 7.51573i 0.230626 + 0.399456i
\(355\) −15.0679 + 26.0984i −0.799722 + 1.38516i
\(356\) 7.52952 0.399064
\(357\) 4.58319 3.76982i 0.242568 0.199520i
\(358\) 3.24948 0.171741
\(359\) −12.0138 + 20.8085i −0.634065 + 1.09823i 0.352648 + 0.935756i \(0.385281\pi\)
−0.986712 + 0.162476i \(0.948052\pi\)
\(360\) 1.24624 + 2.15855i 0.0656826 + 0.113766i
\(361\) −0.500000 0.866025i −0.0263158 0.0455803i
\(362\) 6.22795 10.7871i 0.327334 0.566959i
\(363\) −0.984956 −0.0516968
\(364\) 2.16281 + 13.0104i 0.113362 + 0.681931i
\(365\) 35.9425 1.88131
\(366\) −2.18763 + 3.78908i −0.114349 + 0.198059i
\(367\) −7.90481 13.6915i −0.412628 0.714692i 0.582548 0.812796i \(-0.302056\pi\)
−0.995176 + 0.0981037i \(0.968722\pi\)
\(368\) −3.00202 5.19965i −0.156491 0.271051i
\(369\) −2.32191 + 4.02167i −0.120874 + 0.209360i
\(370\) 22.8482 1.18782
\(371\) 2.54864 + 15.3313i 0.132319 + 0.795964i
\(372\) 7.28407 0.377662
\(373\) −15.4254 + 26.7175i −0.798694 + 1.38338i 0.121772 + 0.992558i \(0.461142\pi\)
−0.920467 + 0.390821i \(0.872191\pi\)
\(374\) −3.88254 6.72476i −0.200762 0.347729i
\(375\) −4.72020 8.17562i −0.243750 0.422187i
\(376\) 2.68011 4.64208i 0.138216 0.239397i
\(377\) 27.4749 1.41503
\(378\) −2.04334 + 1.68071i −0.105098 + 0.0864463i
\(379\) 23.5450 1.20943 0.604713 0.796443i \(-0.293288\pi\)
0.604713 + 0.796443i \(0.293288\pi\)
\(380\) −1.24624 + 2.15855i −0.0639307 + 0.110731i
\(381\) 3.04784 + 5.27902i 0.156146 + 0.270452i
\(382\) −8.22222 14.2413i −0.420685 0.728648i
\(383\) −2.43635 + 4.21989i −0.124492 + 0.215626i −0.921534 0.388297i \(-0.873063\pi\)
0.797042 + 0.603923i \(0.206397\pi\)
\(384\) 1.00000 0.0510310
\(385\) −21.3753 8.01809i −1.08938 0.408640i
\(386\) 18.6854 0.951060
\(387\) −4.77106 + 8.26371i −0.242526 + 0.420068i
\(388\) −3.50202 6.06568i −0.177788 0.307938i
\(389\) 14.1428 + 24.4960i 0.717068 + 1.24200i 0.962156 + 0.272498i \(0.0878497\pi\)
−0.245088 + 0.969501i \(0.578817\pi\)
\(390\) 6.21245 10.7603i 0.314579 0.544868i
\(391\) 13.4670 0.681057
\(392\) −5.27308 4.60377i −0.266331 0.232525i
\(393\) −9.31416 −0.469837
\(394\) −7.74826 + 13.4204i −0.390352 + 0.676109i
\(395\) 8.83169 + 15.2969i 0.444370 + 0.769672i
\(396\) 1.73096 + 2.99812i 0.0869843 + 0.150661i
\(397\) −1.32562 + 2.29605i −0.0665312 + 0.115235i −0.897372 0.441274i \(-0.854527\pi\)
0.830841 + 0.556510i \(0.187860\pi\)
\(398\) 1.45948 0.0731571
\(399\) −2.47720 0.929227i −0.124015 0.0465195i
\(400\) 1.21245 0.0606223
\(401\) 3.72646 6.45441i 0.186090 0.322318i −0.757853 0.652425i \(-0.773752\pi\)
0.943943 + 0.330107i \(0.107085\pi\)
\(402\) −7.57915 13.1275i −0.378014 0.654739i
\(403\) −18.1554 31.4461i −0.904384 1.56644i
\(404\) −3.54784 + 6.14504i −0.176512 + 0.305727i
\(405\) 2.49248 0.123852
\(406\) −11.2620 + 9.26333i −0.558922 + 0.459731i
\(407\) 31.7350 1.57305
\(408\) −1.12150 + 1.94249i −0.0555224 + 0.0961676i
\(409\) −8.70187 15.0721i −0.430280 0.745267i 0.566617 0.823981i \(-0.308252\pi\)
−0.996897 + 0.0787145i \(0.974918\pi\)
\(410\) 5.78732 + 10.0239i 0.285815 + 0.495047i
\(411\) −3.89255 + 6.74210i −0.192005 + 0.332563i
\(412\) 7.15135 0.352322
\(413\) 3.76529 + 22.6501i 0.185278 + 1.11454i
\(414\) −6.00404 −0.295082
\(415\) 6.97674 12.0841i 0.342475 0.593183i
\(416\) −2.49248 4.31710i −0.122204 0.211663i
\(417\) 6.29408 + 10.9017i 0.308223 + 0.533857i
\(418\) −1.73096 + 2.99812i −0.0846643 + 0.146643i
\(419\) −3.76105 −0.183739 −0.0918696 0.995771i \(-0.529284\pi\)
−0.0918696 + 0.995771i \(0.529284\pi\)
\(420\) 1.08141 + 6.50520i 0.0527672 + 0.317421i
\(421\) 31.6343 1.54176 0.770882 0.636978i \(-0.219816\pi\)
0.770882 + 0.636978i \(0.219816\pi\)
\(422\) −11.6976 + 20.2609i −0.569432 + 0.986285i
\(423\) −2.68011 4.64208i −0.130311 0.225706i
\(424\) −2.93711 5.08723i −0.142639 0.247058i
\(425\) −1.35975 + 2.35516i −0.0659578 + 0.114242i
\(426\) 12.0907 0.585797
\(427\) −8.94012 + 7.35353i −0.432643 + 0.355862i
\(428\) −15.7305 −0.760362
\(429\) 8.62878 14.9455i 0.416602 0.721575i
\(430\) 11.8917 + 20.5971i 0.573471 + 0.993281i
\(431\) 0.832910 + 1.44264i 0.0401199 + 0.0694897i 0.885388 0.464853i \(-0.153893\pi\)
−0.845268 + 0.534342i \(0.820559\pi\)
\(432\) 0.500000 0.866025i 0.0240563 0.0416667i
\(433\) 16.1062 0.774015 0.387008 0.922076i \(-0.373509\pi\)
0.387008 + 0.922076i \(0.373509\pi\)
\(434\) 18.0441 + 6.76855i 0.866146 + 0.324901i
\(435\) 13.7374 0.658660
\(436\) −4.15854 + 7.20279i −0.199158 + 0.344951i
\(437\) −3.00202 5.19965i −0.143606 0.248733i
\(438\) −7.21019 12.4884i −0.344516 0.596719i
\(439\) −10.5433 + 18.2616i −0.503206 + 0.871578i 0.496787 + 0.867872i \(0.334513\pi\)
−0.999993 + 0.00370589i \(0.998820\pi\)
\(440\) 8.62878 0.411361
\(441\) −6.62352 + 2.26473i −0.315406 + 0.107844i
\(442\) 11.1812 0.531837
\(443\) 9.29789 16.1044i 0.441756 0.765144i −0.556064 0.831140i \(-0.687689\pi\)
0.997820 + 0.0659955i \(0.0210223\pi\)
\(444\) −4.58343 7.93873i −0.217520 0.376755i
\(445\) −9.38358 16.2528i −0.444824 0.770458i
\(446\) 7.41107 12.8364i 0.350924 0.607819i
\(447\) −16.2922 −0.770592
\(448\) 2.47720 + 0.929227i 0.117037 + 0.0439018i
\(449\) 19.7410 0.931637 0.465818 0.884880i \(-0.345760\pi\)
0.465818 + 0.884880i \(0.345760\pi\)
\(450\) 0.606223 1.05001i 0.0285776 0.0494979i
\(451\) 8.03830 + 13.9227i 0.378509 + 0.655596i
\(452\) −6.68213 11.5738i −0.314301 0.544385i
\(453\) 9.98675 17.2976i 0.469218 0.812710i
\(454\) −16.2295 −0.761687
\(455\) 25.3882 20.8826i 1.19022 0.978992i
\(456\) 1.00000 0.0468293
\(457\) −0.234446 + 0.406073i −0.0109669 + 0.0189953i −0.871457 0.490472i \(-0.836824\pi\)
0.860490 + 0.509468i \(0.170158\pi\)
\(458\) −3.19740 5.53806i −0.149405 0.258777i
\(459\) 1.12150 + 1.94249i 0.0523470 + 0.0906677i
\(460\) −7.48247 + 12.9600i −0.348872 + 0.604264i
\(461\) −19.0556 −0.887510 −0.443755 0.896148i \(-0.646354\pi\)
−0.443755 + 0.896148i \(0.646354\pi\)
\(462\) 1.50202 + 9.03541i 0.0698803 + 0.420365i
\(463\) −9.65575 −0.448741 −0.224370 0.974504i \(-0.572033\pi\)
−0.224370 + 0.974504i \(0.572033\pi\)
\(464\) 2.75578 4.77315i 0.127934 0.221588i
\(465\) −9.07769 15.7230i −0.420968 0.729138i
\(466\) −10.6899 18.5154i −0.495199 0.857710i
\(467\) 4.58141 7.93523i 0.212002 0.367199i −0.740339 0.672234i \(-0.765335\pi\)
0.952341 + 0.305035i \(0.0986683\pi\)
\(468\) −4.98496 −0.230430
\(469\) −6.57670 39.5622i −0.303684 1.82681i
\(470\) −13.3602 −0.616261
\(471\) −0.369526 + 0.640038i −0.0170269 + 0.0294914i
\(472\) −4.33921 7.51573i −0.199728 0.345939i
\(473\) 16.5171 + 28.6084i 0.759455 + 1.31541i
\(474\) 3.54334 6.13724i 0.162751 0.281893i
\(475\) 1.21245 0.0556308
\(476\) −4.58319 + 3.76982i −0.210070 + 0.172789i
\(477\) −5.87423 −0.268962
\(478\) 9.44689 16.3625i 0.432090 0.748403i
\(479\) −21.4106 37.0843i −0.978276 1.69442i −0.668673 0.743557i \(-0.733137\pi\)
−0.309603 0.950866i \(-0.600196\pi\)
\(480\) −1.24624 2.15855i −0.0568828 0.0985238i
\(481\) −22.8482 + 39.5742i −1.04179 + 1.80443i
\(482\) −4.05009 −0.184477
\(483\) −14.8732 5.57911i −0.676755 0.253858i
\(484\) 0.984956 0.0447707
\(485\) −8.72871 + 15.1186i −0.396350 + 0.686499i
\(486\) −0.500000 0.866025i −0.0226805 0.0392837i
\(487\) 13.1576 + 22.7897i 0.596230 + 1.03270i 0.993372 + 0.114943i \(0.0366685\pi\)
−0.397143 + 0.917757i \(0.629998\pi\)
\(488\) 2.18763 3.78908i 0.0990293 0.171524i
\(489\) 5.79808 0.262198
\(490\) −3.36595 + 17.1196i −0.152058 + 0.773384i
\(491\) −14.2064 −0.641127 −0.320563 0.947227i \(-0.603872\pi\)
−0.320563 + 0.947227i \(0.603872\pi\)
\(492\) 2.32191 4.02167i 0.104680 0.181311i
\(493\) 6.18120 + 10.7062i 0.278387 + 0.482181i
\(494\) −2.49248 4.31710i −0.112142 0.194235i
\(495\) 4.31439 7.47274i 0.193917 0.335875i
\(496\) −7.28407 −0.327065
\(497\) 29.9512 + 11.2350i 1.34349 + 0.503959i
\(498\) −5.59823 −0.250863
\(499\) −17.0163 + 29.4730i −0.761753 + 1.31939i 0.180194 + 0.983631i \(0.442327\pi\)
−0.941947 + 0.335763i \(0.891006\pi\)
\(500\) 4.72020 + 8.17562i 0.211094 + 0.365625i
\(501\) 8.55288 + 14.8140i 0.382114 + 0.661842i
\(502\) 3.29958 5.71505i 0.147268 0.255075i
\(503\) 18.2003 0.811512 0.405756 0.913981i \(-0.367008\pi\)
0.405756 + 0.913981i \(0.367008\pi\)
\(504\) 2.04334 1.68071i 0.0910174 0.0748647i
\(505\) 17.6858 0.787009
\(506\) −10.3928 + 18.0008i −0.462016 + 0.800234i
\(507\) 5.92489 + 10.2622i 0.263134 + 0.455761i
\(508\) −3.04784 5.27902i −0.135226 0.234219i
\(509\) 2.28239 3.95321i 0.101165 0.175223i −0.811000 0.585046i \(-0.801076\pi\)
0.912165 + 0.409823i \(0.134410\pi\)
\(510\) 5.59061 0.247556
\(511\) −6.25654 37.6362i −0.276773 1.66493i
\(512\) −1.00000 −0.0441942
\(513\) 0.500000 0.866025i 0.0220755 0.0382360i
\(514\) −1.32562 2.29605i −0.0584708 0.101274i
\(515\) −8.91229 15.4365i −0.392722 0.680215i
\(516\) 4.77106 8.26371i 0.210034 0.363790i
\(517\) −18.5567 −0.816122
\(518\) −3.97720 23.9249i −0.174748 1.05120i
\(519\) 2.58412 0.113430
\(520\) −6.21245 + 10.7603i −0.272434 + 0.471869i
\(521\) 20.2580 + 35.0879i 0.887520 + 1.53723i 0.842798 + 0.538231i \(0.180907\pi\)
0.0447225 + 0.998999i \(0.485760\pi\)
\(522\) −2.75578 4.77315i −0.120617 0.208915i
\(523\) 14.7322 25.5170i 0.644195 1.11578i −0.340292 0.940320i \(-0.610526\pi\)
0.984487 0.175459i \(-0.0561408\pi\)
\(524\) 9.31416 0.406891
\(525\) 2.47743 2.03777i 0.108124 0.0889354i
\(526\) 1.45544 0.0634602
\(527\) 8.16907 14.1492i 0.355850 0.616350i
\(528\) −1.73096 2.99812i −0.0753306 0.130476i
\(529\) −6.52425 11.3003i −0.283663 0.491319i
\(530\) −7.32069 + 12.6798i −0.317990 + 0.550776i
\(531\) −8.67842 −0.376611
\(532\) 2.47720 + 0.929227i 0.107400 + 0.0402871i
\(533\) −23.1493 −1.00271
\(534\) −3.76476 + 6.52075i −0.162917 + 0.282181i
\(535\) 19.6040 + 33.9551i 0.847553 + 1.46800i
\(536\) 7.57915 + 13.1275i 0.327369 + 0.567020i
\(537\) −1.62474 + 2.81414i −0.0701128 + 0.121439i
\(538\) −14.3232 −0.617516
\(539\) −4.67513 + 23.7783i −0.201372 + 1.02420i
\(540\) −2.49248 −0.107259
\(541\) 2.76400 4.78739i 0.118834 0.205826i −0.800472 0.599370i \(-0.795418\pi\)
0.919306 + 0.393544i \(0.128751\pi\)
\(542\) 10.3329 + 17.8971i 0.443837 + 0.768747i
\(543\) 6.22795 + 10.7871i 0.267267 + 0.462920i
\(544\) 1.12150 1.94249i 0.0480838 0.0832836i
\(545\) 20.7301 0.887980
\(546\) −12.3488 4.63215i −0.528478 0.198238i
\(547\) −13.7329 −0.587178 −0.293589 0.955932i \(-0.594850\pi\)
−0.293589 + 0.955932i \(0.594850\pi\)
\(548\) 3.89255 6.74210i 0.166282 0.288008i
\(549\) −2.18763 3.78908i −0.0933657 0.161714i
\(550\) −2.09870 3.63506i −0.0894889 0.154999i
\(551\) 2.75578 4.77315i 0.117400 0.203343i
\(552\) 6.00404 0.255549
\(553\) 14.4804 11.9106i 0.615771 0.506491i
\(554\) 28.5421 1.21264
\(555\) −11.4241 + 19.7871i −0.484926 + 0.839916i
\(556\) −6.29408 10.9017i −0.266929 0.462334i
\(557\) 0.199621 + 0.345753i 0.00845821 + 0.0146500i 0.870224 0.492657i \(-0.163974\pi\)
−0.861765 + 0.507307i \(0.830641\pi\)
\(558\) −3.64204 + 6.30819i −0.154180 + 0.267047i
\(559\) −47.5670 −2.01187
\(560\) −1.08141 6.50520i −0.0456978 0.274895i
\(561\) 7.76509 0.327842
\(562\) −6.82214 + 11.8163i −0.287775 + 0.498440i
\(563\) −13.0621 22.6242i −0.550501 0.953496i −0.998238 0.0593309i \(-0.981103\pi\)
0.447737 0.894165i \(-0.352230\pi\)
\(564\) 2.68011 + 4.64208i 0.112853 + 0.195467i
\(565\) −16.6551 + 28.8474i −0.700683 + 1.21362i
\(566\) 1.53403 0.0644801
\(567\) −0.433868 2.60993i −0.0182207 0.109607i
\(568\) −12.0907 −0.507315
\(569\) −1.53158 + 2.65278i −0.0642072 + 0.111210i −0.896342 0.443363i \(-0.853785\pi\)
0.832135 + 0.554573i \(0.187119\pi\)
\(570\) −1.24624 2.15855i −0.0521992 0.0904117i
\(571\) −2.94533 5.10146i −0.123258 0.213490i 0.797792 0.602932i \(-0.206001\pi\)
−0.921051 + 0.389443i \(0.872668\pi\)
\(572\) −8.62878 + 14.9455i −0.360788 + 0.624902i
\(573\) 16.4444 0.686976
\(574\) 9.48890 7.80492i 0.396059 0.325771i
\(575\) 7.27957 0.303579
\(576\) −0.500000 + 0.866025i −0.0208333 + 0.0360844i
\(577\) 12.8948 + 22.3345i 0.536818 + 0.929795i 0.999073 + 0.0430486i \(0.0137070\pi\)
−0.462255 + 0.886747i \(0.652960\pi\)
\(578\) −5.98449 10.3654i −0.248922 0.431145i
\(579\) −9.34268 + 16.1820i −0.388269 + 0.672501i
\(580\) −13.7374 −0.570416
\(581\) −13.8680 5.20203i −0.575340 0.215816i
\(582\) 7.00404 0.290327
\(583\) −10.1681 + 17.6116i −0.421119 + 0.729399i
\(584\) 7.21019 + 12.4884i 0.298360 + 0.516774i
\(585\) 6.21245 + 10.7603i 0.256853 + 0.444882i
\(586\) −16.6887 + 28.9056i −0.689402 + 1.19408i
\(587\) 0.822143 0.0339335 0.0169667 0.999856i \(-0.494599\pi\)
0.0169667 + 0.999856i \(0.494599\pi\)
\(588\) 6.62352 2.26473i 0.273149 0.0933961i
\(589\) −7.28407 −0.300135
\(590\) −10.8154 + 18.7328i −0.445262 + 0.771217i
\(591\) −7.74826 13.4204i −0.318721 0.552041i
\(592\) 4.58343 + 7.93873i 0.188378 + 0.326280i
\(593\) 8.32035 14.4113i 0.341676 0.591800i −0.643068 0.765809i \(-0.722339\pi\)
0.984744 + 0.174009i \(0.0556721\pi\)
\(594\) −3.46193 −0.142045
\(595\) 13.8491 + 5.19495i 0.567757 + 0.212972i
\(596\) 16.2922 0.667353
\(597\) −0.729740 + 1.26395i −0.0298663 + 0.0517299i
\(598\) −14.9649 25.9200i −0.611962 1.05995i
\(599\) −4.28835 7.42764i −0.175217 0.303485i 0.765019 0.644007i \(-0.222729\pi\)
−0.940236 + 0.340522i \(0.889396\pi\)
\(600\) −0.606223 + 1.05001i −0.0247489 + 0.0428664i
\(601\) 13.6993 0.558805 0.279403 0.960174i \(-0.409864\pi\)
0.279403 + 0.960174i \(0.409864\pi\)
\(602\) 19.4977 16.0375i 0.794668 0.653640i
\(603\) 15.1583 0.617294
\(604\) −9.98675 + 17.2976i −0.406355 + 0.703827i
\(605\) −1.22749 2.12608i −0.0499046 0.0864372i
\(606\) −3.54784 6.14504i −0.144121 0.249625i
\(607\) −21.2703 + 36.8412i −0.863333 + 1.49534i 0.00536006 + 0.999986i \(0.498294\pi\)
−0.868693 + 0.495351i \(0.835040\pi\)
\(608\) −1.00000 −0.0405554
\(609\) −2.39129 14.3848i −0.0969000 0.582902i
\(610\) −10.9052 −0.441540
\(611\) 13.3602 23.1406i 0.540496 0.936167i
\(612\) −1.12150 1.94249i −0.0453338 0.0785205i
\(613\) −7.25479 12.5657i −0.293018 0.507522i 0.681504 0.731815i \(-0.261326\pi\)
−0.974522 + 0.224292i \(0.927993\pi\)
\(614\) 4.76476 8.25280i 0.192290 0.333056i
\(615\) −11.5746 −0.466734
\(616\) −1.50202 9.03541i −0.0605181 0.364047i
\(617\) −25.3468 −1.02042 −0.510211 0.860049i \(-0.670433\pi\)
−0.510211 + 0.860049i \(0.670433\pi\)
\(618\) −3.57567 + 6.19325i −0.143835 + 0.249129i
\(619\) 7.99718 + 13.8515i 0.321434 + 0.556739i 0.980784 0.195096i \(-0.0625019\pi\)
−0.659350 + 0.751836i \(0.729169\pi\)
\(620\) 9.07769 + 15.7230i 0.364569 + 0.631452i
\(621\) 3.00202 5.19965i 0.120467 0.208655i
\(622\) −16.4404 −0.659200
\(623\) −15.3853 + 12.6549i −0.616400 + 0.507009i
\(624\) 4.98496 0.199558
\(625\) 14.7961 25.6276i 0.591844 1.02510i
\(626\) 5.49698 + 9.52106i 0.219704 + 0.380538i
\(627\) −1.73096 2.99812i −0.0691281 0.119733i
\(628\) 0.369526 0.640038i 0.0147457 0.0255403i
\(629\) −20.5612 −0.819829
\(630\) −6.17438 2.31608i −0.245993 0.0922747i
\(631\) −25.6970 −1.02298 −0.511491 0.859288i \(-0.670907\pi\)
−0.511491 + 0.859288i \(0.670907\pi\)
\(632\) −3.54334 + 6.13724i −0.140946 + 0.244126i
\(633\) −11.6976 20.2609i −0.464939 0.805298i
\(634\) 3.33146 + 5.77025i 0.132309 + 0.229166i
\(635\) −7.59668 + 13.1578i −0.301465 + 0.522153i
\(636\) 5.87423 0.232928
\(637\) −26.2860 22.9496i −1.04149 0.909295i
\(638\) −19.0806 −0.755410
\(639\) −6.04536 + 10.4709i −0.239151 + 0.414221i
\(640\) 1.24624 + 2.15855i 0.0492619 + 0.0853241i
\(641\) −22.0374 38.1698i −0.870424 1.50762i −0.861559 0.507657i \(-0.830512\pi\)
−0.00886458 0.999961i \(-0.502822\pi\)
\(642\) 7.86525 13.6230i 0.310417 0.537657i
\(643\) 22.7730 0.898078 0.449039 0.893512i \(-0.351766\pi\)
0.449039 + 0.893512i \(0.351766\pi\)
\(644\) 14.8732 + 5.57911i 0.586087 + 0.219848i
\(645\) −23.7835 −0.936474
\(646\) 1.12150 1.94249i 0.0441247 0.0764262i
\(647\) −15.1839 26.2993i −0.596941 1.03393i −0.993270 0.115824i \(-0.963049\pi\)
0.396328 0.918109i \(-0.370284\pi\)
\(648\) 0.500000 + 0.866025i 0.0196419 + 0.0340207i
\(649\) −15.0220 + 26.0189i −0.589666 + 1.02133i
\(650\) 6.04399 0.237065
\(651\) −14.8838 + 12.2424i −0.583342 + 0.479817i
\(652\) −5.79808 −0.227071
\(653\) 2.31767 4.01433i 0.0906976 0.157093i −0.817107 0.576486i \(-0.804424\pi\)
0.907805 + 0.419393i \(0.137757\pi\)
\(654\) −4.15854 7.20279i −0.162612 0.281652i
\(655\) −11.6077 20.1051i −0.453549 0.785570i
\(656\) −2.32191 + 4.02167i −0.0906555 + 0.157020i
\(657\) 14.4204 0.562592
\(658\) 2.32562 + 13.9898i 0.0906623 + 0.545379i
\(659\) −18.8998 −0.736232 −0.368116 0.929780i \(-0.619997\pi\)
−0.368116 + 0.929780i \(0.619997\pi\)
\(660\) −4.31439 + 7.47274i −0.167937 + 0.290876i
\(661\) −12.9021 22.3471i −0.501833 0.869200i −0.999998 0.00211793i \(-0.999326\pi\)
0.498165 0.867082i \(-0.334007\pi\)
\(662\) 12.9051 + 22.3523i 0.501571 + 0.868747i
\(663\) −5.59061 + 9.68323i −0.217121 + 0.376065i
\(664\) 5.59823 0.217254
\(665\) −1.08141 6.50520i −0.0419351 0.252261i
\(666\) 9.16685 0.355208
\(667\) 16.5458 28.6582i 0.640657 1.10965i
\(668\) −8.55288 14.8140i −0.330921 0.573172i
\(669\) 7.41107 + 12.8364i 0.286529 + 0.496282i
\(670\) 18.8909 32.7199i 0.729818 1.26408i
\(671\) −15.1468 −0.584737
\(672\) −2.04334 + 1.68071i −0.0788234 + 0.0648347i
\(673\) 15.7844 0.608445 0.304223 0.952601i \(-0.401603\pi\)
0.304223 + 0.952601i \(0.401603\pi\)
\(674\) 5.04658 8.74093i 0.194387 0.336688i
\(675\) 0.606223 + 1.05001i 0.0233335 + 0.0404149i
\(676\) −5.92489 10.2622i −0.227880 0.394700i
\(677\) 12.0393 20.8527i 0.462707 0.801433i −0.536387 0.843972i \(-0.680211\pi\)
0.999095 + 0.0425391i \(0.0135447\pi\)
\(678\) 13.3643 0.513251
\(679\) 17.3504 + 6.50834i 0.665849 + 0.249767i
\(680\) −5.59061 −0.214390
\(681\) 8.11473 14.0551i 0.310957 0.538594i
\(682\) 12.6085 + 21.8385i 0.482803 + 0.836240i
\(683\) −7.42531 12.8610i −0.284122 0.492113i 0.688274 0.725451i \(-0.258369\pi\)
−0.972396 + 0.233337i \(0.925035\pi\)
\(684\) −0.500000 + 0.866025i −0.0191180 + 0.0331133i
\(685\) −19.4042 −0.741396
\(686\) 18.5123 + 0.544542i 0.706801 + 0.0207907i
\(687\) 6.39480 0.243977
\(688\) −4.77106 + 8.26371i −0.181895 + 0.315051i
\(689\) −14.6414 25.3596i −0.557792 0.966124i
\(690\) −7.48247 12.9600i −0.284853 0.493379i
\(691\) −19.1471 + 33.1637i −0.728389 + 1.26161i 0.229175 + 0.973385i \(0.426397\pi\)
−0.957564 + 0.288221i \(0.906936\pi\)
\(692\) −2.58412 −0.0982336
\(693\) −8.57590 3.21692i −0.325772 0.122201i
\(694\) 0.369228 0.0140157
\(695\) −15.6879 + 27.1722i −0.595074 + 1.03070i
\(696\) 2.75578 + 4.77315i 0.104458 + 0.180926i
\(697\) −5.20804 9.02059i −0.197268 0.341679i
\(698\) 15.6821 27.1622i 0.593577 1.02811i
\(699\) 21.3798 0.808657
\(700\) −2.47743 + 2.03777i −0.0936382 + 0.0770204i
\(701\) −24.6068 −0.929385 −0.464693 0.885472i \(-0.653835\pi\)
−0.464693 + 0.885472i \(0.653835\pi\)
\(702\) 2.49248 4.31710i 0.0940725 0.162938i
\(703\) 4.58343 + 7.93873i 0.172867 + 0.299415i
\(704\) 1.73096 + 2.99812i 0.0652382 + 0.112996i
\(705\) 6.68011 11.5703i 0.251587 0.435762i
\(706\) 22.8192 0.858813
\(707\) −3.07859 18.5193i −0.115782 0.696489i
\(708\) 8.67842 0.326155
\(709\) −8.63325 + 14.9532i −0.324229 + 0.561580i −0.981356 0.192199i \(-0.938438\pi\)
0.657127 + 0.753780i \(0.271771\pi\)
\(710\) 15.0679 + 26.0984i 0.565489 + 0.979455i
\(711\) 3.54334 + 6.13724i 0.132885 + 0.230164i
\(712\) 3.76476 6.52075i 0.141090 0.244376i
\(713\) −43.7339 −1.63785
\(714\) −0.973163 5.85407i −0.0364197 0.219083i
\(715\) 43.0141 1.60864
\(716\) 1.62474 2.81414i 0.0607195 0.105169i
\(717\) 9.44689 + 16.3625i 0.352800 + 0.611068i
\(718\) 12.0138 + 20.8085i 0.448352 + 0.776568i
\(719\) −21.6263 + 37.4579i −0.806526 + 1.39694i 0.108730 + 0.994071i \(0.465322\pi\)
−0.915256 + 0.402873i \(0.868012\pi\)
\(720\) 2.49248 0.0928892
\(721\) −14.6126 + 12.0193i −0.544202 + 0.447623i
\(722\) −1.00000 −0.0372161
\(723\) 2.02505 3.50748i 0.0753123 0.130445i
\(724\) −6.22795 10.7871i −0.231460 0.400900i
\(725\) 3.34124 + 5.78719i 0.124090 + 0.214931i
\(726\) −0.492478 + 0.852997i −0.0182776 + 0.0316577i
\(727\) −26.0766 −0.967127 −0.483564 0.875309i \(-0.660658\pi\)
−0.483564 + 0.875309i \(0.660658\pi\)
\(728\) 12.3488 + 4.63215i 0.457675 + 0.171679i
\(729\) 1.00000 0.0370370
\(730\) 17.9712 31.1271i 0.665145 1.15207i
\(731\) −10.7014 18.5355i −0.395807 0.685558i
\(732\) 2.18763 + 3.78908i 0.0808571 + 0.140049i
\(733\) 4.10947 7.11781i 0.151787 0.262902i −0.780098 0.625658i \(-0.784831\pi\)
0.931884 + 0.362756i \(0.118164\pi\)
\(734\) −15.8096 −0.583544
\(735\) −13.1430 11.4748i −0.484788 0.423254i
\(736\) −6.00404 −0.221312
\(737\) 26.2385 45.4464i 0.966507 1.67404i
\(738\) 2.32191 + 4.02167i 0.0854708 + 0.148040i
\(739\) −19.2989 33.4266i −0.709921 1.22962i −0.964886 0.262669i \(-0.915397\pi\)
0.254965 0.966950i \(-0.417936\pi\)
\(740\) 11.4241 19.7871i 0.419958 0.727388i
\(741\) 4.98496 0.183127
\(742\) 14.5517 + 5.45849i 0.534208 + 0.200387i
\(743\) −5.51309 −0.202256 −0.101128 0.994873i \(-0.532245\pi\)
−0.101128 + 0.994873i \(0.532245\pi\)
\(744\) 3.64204 6.30819i 0.133524 0.231270i
\(745\) −20.3039 35.1674i −0.743878 1.28843i
\(746\) 15.4254 + 26.7175i 0.564762 + 0.978197i
\(747\) 2.79912 4.84821i 0.102414 0.177387i
\(748\) −7.76509 −0.283920
\(749\) 32.1427 26.4384i 1.17447 0.966037i
\(750\) −9.44040 −0.344714
\(751\) −9.63001 + 16.6797i −0.351404 + 0.608649i −0.986496 0.163787i \(-0.947629\pi\)
0.635092 + 0.772437i \(0.280962\pi\)
\(752\) −2.68011 4.64208i −0.0977334 0.169279i
\(753\) 3.29958 + 5.71505i 0.120244 + 0.208268i
\(754\) 13.7374 23.7940i 0.500288 0.866525i
\(755\) 49.7835 1.81181
\(756\) 0.433868 + 2.60993i 0.0157796 + 0.0949224i
\(757\) −0.556024 −0.0202090 −0.0101045 0.999949i \(-0.503216\pi\)
−0.0101045 + 0.999949i \(0.503216\pi\)
\(758\) 11.7725 20.3906i 0.427597 0.740619i
\(759\) −10.3928 18.0008i −0.377234 0.653389i
\(760\) 1.24624 + 2.15855i 0.0452058 + 0.0782988i
\(761\) −4.58846 + 7.94745i −0.166332 + 0.288095i −0.937127 0.348988i \(-0.886526\pi\)
0.770796 + 0.637082i \(0.219859\pi\)
\(762\) 6.09569 0.220823
\(763\) −3.60851 21.7070i −0.130637 0.785847i
\(764\) −16.4444 −0.594939
\(765\) −2.79531 + 4.84161i −0.101065 + 0.175049i
\(766\) 2.43635 + 4.21989i 0.0880291 + 0.152471i
\(767\) −21.6308 37.4656i −0.781041 1.35280i
\(768\) 0.500000 0.866025i 0.0180422 0.0312500i
\(769\) 10.2515 0.369680 0.184840 0.982769i \(-0.440823\pi\)
0.184840 + 0.982769i \(0.440823\pi\)
\(770\) −17.6315 + 14.5025i −0.635395 + 0.522632i
\(771\) 2.65125 0.0954824
\(772\) 9.34268 16.1820i 0.336251 0.582403i
\(773\) 12.6864 + 21.9735i 0.456298 + 0.790332i 0.998762 0.0497476i \(-0.0158417\pi\)
−0.542464 + 0.840079i \(0.682508\pi\)
\(774\) 4.77106 + 8.26371i 0.171492 + 0.297033i
\(775\) 4.41577 7.64834i 0.158619 0.274736i
\(776\) −7.00404 −0.251430
\(777\) 22.7082 + 8.51808i 0.814651 + 0.305585i