Properties

Label 300.2.j.a.7.3
Level $300$
Weight $2$
Character 300.7
Analytic conductor $2.396$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 300 = 2^{2} \cdot 3 \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 300.j (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.39551206064\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(i)\)
Coefficient field: \(\Q(\zeta_{24})\)
Defining polynomial: \(x^{8} - x^{4} + 1\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 7.3
Root \(0.965926 + 0.258819i\) of defining polynomial
Character \(\chi\) \(=\) 300.7
Dual form 300.2.j.a.43.4

$q$-expansion

\(f(q)\) \(=\) \(q+(0.707107 - 1.22474i) q^{2} +(0.707107 + 0.707107i) q^{3} +(-1.00000 - 1.73205i) q^{4} +(1.36603 - 0.366025i) q^{6} +(1.74238 - 1.74238i) q^{7} -2.82843 q^{8} +1.00000i q^{9} +O(q^{10})\) \(q+(0.707107 - 1.22474i) q^{2} +(0.707107 + 0.707107i) q^{3} +(-1.00000 - 1.73205i) q^{4} +(1.36603 - 0.366025i) q^{6} +(1.74238 - 1.74238i) q^{7} -2.82843 q^{8} +1.00000i q^{9} -2.00000i q^{11} +(0.517638 - 1.93185i) q^{12} +(4.05317 - 4.05317i) q^{13} +(-0.901924 - 3.36603i) q^{14} +(-2.00000 + 3.46410i) q^{16} +(4.24264 + 4.24264i) q^{17} +(1.22474 + 0.707107i) q^{18} -7.19615 q^{19} +2.46410 q^{21} +(-2.44949 - 1.41421i) q^{22} +(0.378937 + 0.378937i) q^{23} +(-2.00000 - 2.00000i) q^{24} +(-2.09808 - 7.83013i) q^{26} +(-0.707107 + 0.707107i) q^{27} +(-4.76028 - 1.27551i) q^{28} +7.46410i q^{29} -0.267949i q^{31} +(2.82843 + 4.89898i) q^{32} +(1.41421 - 1.41421i) q^{33} +(8.19615 - 2.19615i) q^{34} +(1.73205 - 1.00000i) q^{36} +(2.07055 + 2.07055i) q^{37} +(-5.08845 + 8.81345i) q^{38} +5.73205 q^{39} -5.46410 q^{41} +(1.74238 - 3.01790i) q^{42} +(-1.74238 - 1.74238i) q^{43} +(-3.46410 + 2.00000i) q^{44} +(0.732051 - 0.196152i) q^{46} +(-9.14162 + 9.14162i) q^{47} +(-3.86370 + 1.03528i) q^{48} +0.928203i q^{49} +6.00000i q^{51} +(-11.0735 - 2.96713i) q^{52} +(1.03528 - 1.03528i) q^{53} +(0.366025 + 1.36603i) q^{54} +(-4.92820 + 4.92820i) q^{56} +(-5.08845 - 5.08845i) q^{57} +(9.14162 + 5.27792i) q^{58} +4.53590 q^{59} +3.00000 q^{61} +(-0.328169 - 0.189469i) q^{62} +(1.74238 + 1.74238i) q^{63} +8.00000 q^{64} +(-0.732051 - 2.73205i) q^{66} +(8.81345 - 8.81345i) q^{67} +(3.10583 - 11.5911i) q^{68} +0.535898i q^{69} +9.46410i q^{71} -2.82843i q^{72} +(-2.82843 + 2.82843i) q^{73} +(4.00000 - 1.07180i) q^{74} +(7.19615 + 12.4641i) q^{76} +(-3.48477 - 3.48477i) q^{77} +(4.05317 - 7.02030i) q^{78} -0.535898 q^{79} -1.00000 q^{81} +(-3.86370 + 6.69213i) q^{82} +(0.656339 + 0.656339i) q^{83} +(-2.46410 - 4.26795i) q^{84} +(-3.36603 + 0.901924i) q^{86} +(-5.27792 + 5.27792i) q^{87} +5.65685i q^{88} -6.92820i q^{89} -14.1244i q^{91} +(0.277401 - 1.03528i) q^{92} +(0.189469 - 0.189469i) q^{93} +(4.73205 + 17.6603i) q^{94} +(-1.46410 + 5.46410i) q^{96} +(-4.43211 - 4.43211i) q^{97} +(1.13681 + 0.656339i) q^{98} +2.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q - 8q^{4} + 4q^{6} + O(q^{10}) \) \( 8q - 8q^{4} + 4q^{6} - 28q^{14} - 16q^{16} - 16q^{19} - 8q^{21} - 16q^{24} + 4q^{26} + 24q^{34} + 32q^{39} - 16q^{41} - 8q^{46} - 4q^{54} + 16q^{56} + 64q^{59} + 24q^{61} + 64q^{64} + 8q^{66} + 32q^{74} + 16q^{76} - 32q^{79} - 8q^{81} + 8q^{84} - 20q^{86} + 24q^{94} + 16q^{96} + 16q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/300\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(151\) \(277\)
\(\chi(n)\) \(1\) \(-1\) \(e\left(\frac{1}{4}\right)\)

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 1.22474i 0.500000 0.866025i
\(3\) 0.707107 + 0.707107i 0.408248 + 0.408248i
\(4\) −1.00000 1.73205i −0.500000 0.866025i
\(5\) 0 0
\(6\) 1.36603 0.366025i 0.557678 0.149429i
\(7\) 1.74238 1.74238i 0.658559 0.658559i −0.296480 0.955039i \(-0.595813\pi\)
0.955039 + 0.296480i \(0.0958129\pi\)
\(8\) −2.82843 −1.00000
\(9\) 1.00000i 0.333333i
\(10\) 0 0
\(11\) 2.00000i 0.603023i −0.953463 0.301511i \(-0.902509\pi\)
0.953463 0.301511i \(-0.0974911\pi\)
\(12\) 0.517638 1.93185i 0.149429 0.557678i
\(13\) 4.05317 4.05317i 1.12415 1.12415i 0.133037 0.991111i \(-0.457527\pi\)
0.991111 0.133037i \(-0.0424728\pi\)
\(14\) −0.901924 3.36603i −0.241049 0.899608i
\(15\) 0 0
\(16\) −2.00000 + 3.46410i −0.500000 + 0.866025i
\(17\) 4.24264 + 4.24264i 1.02899 + 1.02899i 0.999567 + 0.0294245i \(0.00936746\pi\)
0.0294245 + 0.999567i \(0.490633\pi\)
\(18\) 1.22474 + 0.707107i 0.288675 + 0.166667i
\(19\) −7.19615 −1.65091 −0.825455 0.564467i \(-0.809082\pi\)
−0.825455 + 0.564467i \(0.809082\pi\)
\(20\) 0 0
\(21\) 2.46410 0.537711
\(22\) −2.44949 1.41421i −0.522233 0.301511i
\(23\) 0.378937 + 0.378937i 0.0790139 + 0.0790139i 0.745509 0.666495i \(-0.232206\pi\)
−0.666495 + 0.745509i \(0.732206\pi\)
\(24\) −2.00000 2.00000i −0.408248 0.408248i
\(25\) 0 0
\(26\) −2.09808 7.83013i −0.411467 1.53561i
\(27\) −0.707107 + 0.707107i −0.136083 + 0.136083i
\(28\) −4.76028 1.27551i −0.899608 0.241049i
\(29\) 7.46410i 1.38605i 0.720914 + 0.693024i \(0.243722\pi\)
−0.720914 + 0.693024i \(0.756278\pi\)
\(30\) 0 0
\(31\) 0.267949i 0.0481251i −0.999710 0.0240625i \(-0.992340\pi\)
0.999710 0.0240625i \(-0.00766009\pi\)
\(32\) 2.82843 + 4.89898i 0.500000 + 0.866025i
\(33\) 1.41421 1.41421i 0.246183 0.246183i
\(34\) 8.19615 2.19615i 1.40563 0.376637i
\(35\) 0 0
\(36\) 1.73205 1.00000i 0.288675 0.166667i
\(37\) 2.07055 + 2.07055i 0.340397 + 0.340397i 0.856516 0.516120i \(-0.172624\pi\)
−0.516120 + 0.856516i \(0.672624\pi\)
\(38\) −5.08845 + 8.81345i −0.825455 + 1.42973i
\(39\) 5.73205 0.917863
\(40\) 0 0
\(41\) −5.46410 −0.853349 −0.426675 0.904405i \(-0.640315\pi\)
−0.426675 + 0.904405i \(0.640315\pi\)
\(42\) 1.74238 3.01790i 0.268856 0.465671i
\(43\) −1.74238 1.74238i −0.265711 0.265711i 0.561658 0.827369i \(-0.310164\pi\)
−0.827369 + 0.561658i \(0.810164\pi\)
\(44\) −3.46410 + 2.00000i −0.522233 + 0.301511i
\(45\) 0 0
\(46\) 0.732051 0.196152i 0.107935 0.0289211i
\(47\) −9.14162 + 9.14162i −1.33344 + 1.33344i −0.431173 + 0.902269i \(0.641900\pi\)
−0.902269 + 0.431173i \(0.858100\pi\)
\(48\) −3.86370 + 1.03528i −0.557678 + 0.149429i
\(49\) 0.928203i 0.132600i
\(50\) 0 0
\(51\) 6.00000i 0.840168i
\(52\) −11.0735 2.96713i −1.53561 0.411467i
\(53\) 1.03528 1.03528i 0.142206 0.142206i −0.632420 0.774626i \(-0.717938\pi\)
0.774626 + 0.632420i \(0.217938\pi\)
\(54\) 0.366025 + 1.36603i 0.0498097 + 0.185893i
\(55\) 0 0
\(56\) −4.92820 + 4.92820i −0.658559 + 0.658559i
\(57\) −5.08845 5.08845i −0.673981 0.673981i
\(58\) 9.14162 + 5.27792i 1.20035 + 0.693024i
\(59\) 4.53590 0.590524 0.295262 0.955416i \(-0.404593\pi\)
0.295262 + 0.955416i \(0.404593\pi\)
\(60\) 0 0
\(61\) 3.00000 0.384111 0.192055 0.981384i \(-0.438485\pi\)
0.192055 + 0.981384i \(0.438485\pi\)
\(62\) −0.328169 0.189469i −0.0416776 0.0240625i
\(63\) 1.74238 + 1.74238i 0.219520 + 0.219520i
\(64\) 8.00000 1.00000
\(65\) 0 0
\(66\) −0.732051 2.73205i −0.0901092 0.336292i
\(67\) 8.81345 8.81345i 1.07673 1.07673i 0.0799342 0.996800i \(-0.474529\pi\)
0.996800 0.0799342i \(-0.0254710\pi\)
\(68\) 3.10583 11.5911i 0.376637 1.40563i
\(69\) 0.535898i 0.0645146i
\(70\) 0 0
\(71\) 9.46410i 1.12318i 0.827415 + 0.561591i \(0.189811\pi\)
−0.827415 + 0.561591i \(0.810189\pi\)
\(72\) 2.82843i 0.333333i
\(73\) −2.82843 + 2.82843i −0.331042 + 0.331042i −0.852982 0.521940i \(-0.825209\pi\)
0.521940 + 0.852982i \(0.325209\pi\)
\(74\) 4.00000 1.07180i 0.464991 0.124594i
\(75\) 0 0
\(76\) 7.19615 + 12.4641i 0.825455 + 1.42973i
\(77\) −3.48477 3.48477i −0.397126 0.397126i
\(78\) 4.05317 7.02030i 0.458931 0.794892i
\(79\) −0.535898 −0.0602933 −0.0301466 0.999545i \(-0.509597\pi\)
−0.0301466 + 0.999545i \(0.509597\pi\)
\(80\) 0 0
\(81\) −1.00000 −0.111111
\(82\) −3.86370 + 6.69213i −0.426675 + 0.739022i
\(83\) 0.656339 + 0.656339i 0.0720425 + 0.0720425i 0.742210 0.670167i \(-0.233778\pi\)
−0.670167 + 0.742210i \(0.733778\pi\)
\(84\) −2.46410 4.26795i −0.268856 0.465671i
\(85\) 0 0
\(86\) −3.36603 + 0.901924i −0.362968 + 0.0972569i
\(87\) −5.27792 + 5.27792i −0.565852 + 0.565852i
\(88\) 5.65685i 0.603023i
\(89\) 6.92820i 0.734388i −0.930144 0.367194i \(-0.880318\pi\)
0.930144 0.367194i \(-0.119682\pi\)
\(90\) 0 0
\(91\) 14.1244i 1.48063i
\(92\) 0.277401 1.03528i 0.0289211 0.107935i
\(93\) 0.189469 0.189469i 0.0196470 0.0196470i
\(94\) 4.73205 + 17.6603i 0.488074 + 1.82152i
\(95\) 0 0
\(96\) −1.46410 + 5.46410i −0.149429 + 0.557678i
\(97\) −4.43211 4.43211i −0.450013 0.450013i 0.445346 0.895359i \(-0.353081\pi\)
−0.895359 + 0.445346i \(0.853081\pi\)
\(98\) 1.13681 + 0.656339i 0.114835 + 0.0663002i
\(99\) 2.00000 0.201008
\(100\) 0 0
\(101\) −1.46410 −0.145684 −0.0728418 0.997344i \(-0.523207\pi\)
−0.0728418 + 0.997344i \(0.523207\pi\)
\(102\) 7.34847 + 4.24264i 0.727607 + 0.420084i
\(103\) 4.89898 + 4.89898i 0.482711 + 0.482711i 0.905996 0.423286i \(-0.139123\pi\)
−0.423286 + 0.905996i \(0.639123\pi\)
\(104\) −11.4641 + 11.4641i −1.12415 + 1.12415i
\(105\) 0 0
\(106\) −0.535898 2.00000i −0.0520511 0.194257i
\(107\) 4.62158 4.62158i 0.446785 0.446785i −0.447499 0.894284i \(-0.647685\pi\)
0.894284 + 0.447499i \(0.147685\pi\)
\(108\) 1.93185 + 0.517638i 0.185893 + 0.0498097i
\(109\) 7.00000i 0.670478i −0.942133 0.335239i \(-0.891183\pi\)
0.942133 0.335239i \(-0.108817\pi\)
\(110\) 0 0
\(111\) 2.92820i 0.277933i
\(112\) 2.55103 + 9.52056i 0.241049 + 0.899608i
\(113\) −9.79796 + 9.79796i −0.921714 + 0.921714i −0.997151 0.0754362i \(-0.975965\pi\)
0.0754362 + 0.997151i \(0.475965\pi\)
\(114\) −9.83013 + 2.63397i −0.920676 + 0.246694i
\(115\) 0 0
\(116\) 12.9282 7.46410i 1.20035 0.693024i
\(117\) 4.05317 + 4.05317i 0.374716 + 0.374716i
\(118\) 3.20736 5.55532i 0.295262 0.511409i
\(119\) 14.7846 1.35530
\(120\) 0 0
\(121\) 7.00000 0.636364
\(122\) 2.12132 3.67423i 0.192055 0.332650i
\(123\) −3.86370 3.86370i −0.348378 0.348378i
\(124\) −0.464102 + 0.267949i −0.0416776 + 0.0240625i
\(125\) 0 0
\(126\) 3.36603 0.901924i 0.299869 0.0803498i
\(127\) 2.07055 2.07055i 0.183732 0.183732i −0.609248 0.792980i \(-0.708529\pi\)
0.792980 + 0.609248i \(0.208529\pi\)
\(128\) 5.65685 9.79796i 0.500000 0.866025i
\(129\) 2.46410i 0.216952i
\(130\) 0 0
\(131\) 9.46410i 0.826882i −0.910531 0.413441i \(-0.864327\pi\)
0.910531 0.413441i \(-0.135673\pi\)
\(132\) −3.86370 1.03528i −0.336292 0.0901092i
\(133\) −12.5385 + 12.5385i −1.08722 + 1.08722i
\(134\) −4.56218 17.0263i −0.394112 1.47085i
\(135\) 0 0
\(136\) −12.0000 12.0000i −1.02899 1.02899i
\(137\) −6.03579 6.03579i −0.515672 0.515672i 0.400586 0.916259i \(-0.368806\pi\)
−0.916259 + 0.400586i \(0.868806\pi\)
\(138\) 0.656339 + 0.378937i 0.0558713 + 0.0322573i
\(139\) −19.4641 −1.65092 −0.825462 0.564458i \(-0.809085\pi\)
−0.825462 + 0.564458i \(0.809085\pi\)
\(140\) 0 0
\(141\) −12.9282 −1.08875
\(142\) 11.5911 + 6.69213i 0.972704 + 0.561591i
\(143\) −8.10634 8.10634i −0.677887 0.677887i
\(144\) −3.46410 2.00000i −0.288675 0.166667i
\(145\) 0 0
\(146\) 1.46410 + 5.46410i 0.121170 + 0.452212i
\(147\) −0.656339 + 0.656339i −0.0541339 + 0.0541339i
\(148\) 1.51575 5.65685i 0.124594 0.464991i
\(149\) 15.8564i 1.29901i −0.760358 0.649504i \(-0.774977\pi\)
0.760358 0.649504i \(-0.225023\pi\)
\(150\) 0 0
\(151\) 4.26795i 0.347321i −0.984806 0.173660i \(-0.944440\pi\)
0.984806 0.173660i \(-0.0555595\pi\)
\(152\) 20.3538 1.65091
\(153\) −4.24264 + 4.24264i −0.342997 + 0.342997i
\(154\) −6.73205 + 1.80385i −0.542484 + 0.145358i
\(155\) 0 0
\(156\) −5.73205 9.92820i −0.458931 0.794892i
\(157\) 6.88160 + 6.88160i 0.549211 + 0.549211i 0.926213 0.377001i \(-0.123045\pi\)
−0.377001 + 0.926213i \(0.623045\pi\)
\(158\) −0.378937 + 0.656339i −0.0301466 + 0.0522155i
\(159\) 1.46410 0.116111
\(160\) 0 0
\(161\) 1.32051 0.104071
\(162\) −0.707107 + 1.22474i −0.0555556 + 0.0962250i
\(163\) −10.2277 10.2277i −0.801092 0.801092i 0.182174 0.983266i \(-0.441687\pi\)
−0.983266 + 0.182174i \(0.941687\pi\)
\(164\) 5.46410 + 9.46410i 0.426675 + 0.739022i
\(165\) 0 0
\(166\) 1.26795 0.339746i 0.0984119 0.0263694i
\(167\) 3.10583 3.10583i 0.240336 0.240336i −0.576653 0.816989i \(-0.695642\pi\)
0.816989 + 0.576653i \(0.195642\pi\)
\(168\) −6.96953 −0.537711
\(169\) 19.8564i 1.52742i
\(170\) 0 0
\(171\) 7.19615i 0.550304i
\(172\) −1.27551 + 4.76028i −0.0972569 + 0.362968i
\(173\) 6.31319 6.31319i 0.479983 0.479983i −0.425143 0.905126i \(-0.639776\pi\)
0.905126 + 0.425143i \(0.139776\pi\)
\(174\) 2.73205 + 10.1962i 0.207116 + 0.772968i
\(175\) 0 0
\(176\) 6.92820 + 4.00000i 0.522233 + 0.301511i
\(177\) 3.20736 + 3.20736i 0.241080 + 0.241080i
\(178\) −8.48528 4.89898i −0.635999 0.367194i
\(179\) −25.3205 −1.89254 −0.946272 0.323372i \(-0.895183\pi\)
−0.946272 + 0.323372i \(0.895183\pi\)
\(180\) 0 0
\(181\) −13.9282 −1.03528 −0.517638 0.855600i \(-0.673188\pi\)
−0.517638 + 0.855600i \(0.673188\pi\)
\(182\) −17.2987 9.98743i −1.28227 0.740317i
\(183\) 2.12132 + 2.12132i 0.156813 + 0.156813i
\(184\) −1.07180 1.07180i −0.0790139 0.0790139i
\(185\) 0 0
\(186\) −0.0980762 0.366025i −0.00719130 0.0268383i
\(187\) 8.48528 8.48528i 0.620505 0.620505i
\(188\) 24.9754 + 6.69213i 1.82152 + 0.488074i
\(189\) 2.46410i 0.179237i
\(190\) 0 0
\(191\) 16.9282i 1.22488i 0.790516 + 0.612441i \(0.209812\pi\)
−0.790516 + 0.612441i \(0.790188\pi\)
\(192\) 5.65685 + 5.65685i 0.408248 + 0.408248i
\(193\) 9.71003 9.71003i 0.698943 0.698943i −0.265240 0.964183i \(-0.585451\pi\)
0.964183 + 0.265240i \(0.0854510\pi\)
\(194\) −8.56218 + 2.29423i −0.614729 + 0.164716i
\(195\) 0 0
\(196\) 1.60770 0.928203i 0.114835 0.0663002i
\(197\) −10.1769 10.1769i −0.725074 0.725074i 0.244560 0.969634i \(-0.421356\pi\)
−0.969634 + 0.244560i \(0.921356\pi\)
\(198\) 1.41421 2.44949i 0.100504 0.174078i
\(199\) 14.1244 1.00125 0.500625 0.865665i \(-0.333104\pi\)
0.500625 + 0.865665i \(0.333104\pi\)
\(200\) 0 0
\(201\) 12.4641 0.879150
\(202\) −1.03528 + 1.79315i −0.0728418 + 0.126166i
\(203\) 13.0053 + 13.0053i 0.912795 + 0.912795i
\(204\) 10.3923 6.00000i 0.727607 0.420084i
\(205\) 0 0
\(206\) 9.46410 2.53590i 0.659395 0.176684i
\(207\) −0.378937 + 0.378937i −0.0263380 + 0.0263380i
\(208\) 5.93426 + 22.1469i 0.411467 + 1.53561i
\(209\) 14.3923i 0.995537i
\(210\) 0 0
\(211\) 7.19615i 0.495404i 0.968836 + 0.247702i \(0.0796753\pi\)
−0.968836 + 0.247702i \(0.920325\pi\)
\(212\) −2.82843 0.757875i −0.194257 0.0520511i
\(213\) −6.69213 + 6.69213i −0.458537 + 0.458537i
\(214\) −2.39230 8.92820i −0.163535 0.610319i
\(215\) 0 0
\(216\) 2.00000 2.00000i 0.136083 0.136083i
\(217\) −0.466870 0.466870i −0.0316932 0.0316932i
\(218\) −8.57321 4.94975i −0.580651 0.335239i
\(219\) −4.00000 −0.270295
\(220\) 0 0
\(221\) 34.3923 2.31348
\(222\) 3.58630 + 2.07055i 0.240697 + 0.138966i
\(223\) −8.05558 8.05558i −0.539441 0.539441i 0.383924 0.923365i \(-0.374573\pi\)
−0.923365 + 0.383924i \(0.874573\pi\)
\(224\) 13.4641 + 3.60770i 0.899608 + 0.241049i
\(225\) 0 0
\(226\) 5.07180 + 18.9282i 0.337371 + 1.25909i
\(227\) 8.76268 8.76268i 0.581600 0.581600i −0.353743 0.935343i \(-0.615091\pi\)
0.935343 + 0.353743i \(0.115091\pi\)
\(228\) −3.72500 + 13.9019i −0.246694 + 0.920676i
\(229\) 24.8564i 1.64256i 0.570527 + 0.821279i \(0.306739\pi\)
−0.570527 + 0.821279i \(0.693261\pi\)
\(230\) 0 0
\(231\) 4.92820i 0.324252i
\(232\) 21.1117i 1.38605i
\(233\) 8.76268 8.76268i 0.574062 0.574062i −0.359199 0.933261i \(-0.616950\pi\)
0.933261 + 0.359199i \(0.116950\pi\)
\(234\) 7.83013 2.09808i 0.511871 0.137156i
\(235\) 0 0
\(236\) −4.53590 7.85641i −0.295262 0.511409i
\(237\) −0.378937 0.378937i −0.0246146 0.0246146i
\(238\) 10.4543 18.1074i 0.677651 1.17373i
\(239\) 17.4641 1.12966 0.564829 0.825208i \(-0.308942\pi\)
0.564829 + 0.825208i \(0.308942\pi\)
\(240\) 0 0
\(241\) −14.8564 −0.956985 −0.478493 0.878092i \(-0.658817\pi\)
−0.478493 + 0.878092i \(0.658817\pi\)
\(242\) 4.94975 8.57321i 0.318182 0.551107i
\(243\) −0.707107 0.707107i −0.0453609 0.0453609i
\(244\) −3.00000 5.19615i −0.192055 0.332650i
\(245\) 0 0
\(246\) −7.46410 + 2.00000i −0.475894 + 0.127515i
\(247\) −29.1672 + 29.1672i −1.85587 + 1.85587i
\(248\) 0.757875i 0.0481251i
\(249\) 0.928203i 0.0588225i
\(250\) 0 0
\(251\) 2.14359i 0.135302i 0.997709 + 0.0676512i \(0.0215505\pi\)
−0.997709 + 0.0676512i \(0.978449\pi\)
\(252\) 1.27551 4.76028i 0.0803498 0.299869i
\(253\) 0.757875 0.757875i 0.0476472 0.0476472i
\(254\) −1.07180 4.00000i −0.0672505 0.250982i
\(255\) 0 0
\(256\) −8.00000 13.8564i −0.500000 0.866025i
\(257\) 9.04008 + 9.04008i 0.563905 + 0.563905i 0.930414 0.366509i \(-0.119447\pi\)
−0.366509 + 0.930414i \(0.619447\pi\)
\(258\) −3.01790 1.74238i −0.187886 0.108476i
\(259\) 7.21539 0.448343
\(260\) 0 0
\(261\) −7.46410 −0.462016
\(262\) −11.5911 6.69213i −0.716101 0.413441i
\(263\) 15.1774 + 15.1774i 0.935879 + 0.935879i 0.998065 0.0621853i \(-0.0198070\pi\)
−0.0621853 + 0.998065i \(0.519807\pi\)
\(264\) −4.00000 + 4.00000i −0.246183 + 0.246183i
\(265\) 0 0
\(266\) 6.49038 + 24.2224i 0.397951 + 1.48517i
\(267\) 4.89898 4.89898i 0.299813 0.299813i
\(268\) −24.0788 6.45189i −1.47085 0.394112i
\(269\) 1.60770i 0.0980229i −0.998798 0.0490115i \(-0.984393\pi\)
0.998798 0.0490115i \(-0.0156071\pi\)
\(270\) 0 0
\(271\) 24.2487i 1.47300i 0.676435 + 0.736502i \(0.263524\pi\)
−0.676435 + 0.736502i \(0.736476\pi\)
\(272\) −23.1822 + 6.21166i −1.40563 + 0.376637i
\(273\) 9.98743 9.98743i 0.604467 0.604467i
\(274\) −11.6603 + 3.12436i −0.704422 + 0.188749i
\(275\) 0 0
\(276\) 0.928203 0.535898i 0.0558713 0.0322573i
\(277\) 0.845807 + 0.845807i 0.0508196 + 0.0508196i 0.732060 0.681240i \(-0.238559\pi\)
−0.681240 + 0.732060i \(0.738559\pi\)
\(278\) −13.7632 + 23.8386i −0.825462 + 1.42974i
\(279\) 0.267949 0.0160417
\(280\) 0 0
\(281\) −14.3923 −0.858573 −0.429286 0.903168i \(-0.641235\pi\)
−0.429286 + 0.903168i \(0.641235\pi\)
\(282\) −9.14162 + 15.8338i −0.544376 + 0.942886i
\(283\) 15.1266 + 15.1266i 0.899186 + 0.899186i 0.995364 0.0961785i \(-0.0306620\pi\)
−0.0961785 + 0.995364i \(0.530662\pi\)
\(284\) 16.3923 9.46410i 0.972704 0.561591i
\(285\) 0 0
\(286\) −15.6603 + 4.19615i −0.926010 + 0.248124i
\(287\) −9.52056 + 9.52056i −0.561981 + 0.561981i
\(288\) −4.89898 + 2.82843i −0.288675 + 0.166667i
\(289\) 19.0000i 1.11765i
\(290\) 0 0
\(291\) 6.26795i 0.367434i
\(292\) 7.72741 + 2.07055i 0.452212 + 0.121170i
\(293\) 8.86422 8.86422i 0.517853 0.517853i −0.399068 0.916921i \(-0.630666\pi\)
0.916921 + 0.399068i \(0.130666\pi\)
\(294\) 0.339746 + 1.26795i 0.0198144 + 0.0739483i
\(295\) 0 0
\(296\) −5.85641 5.85641i −0.340397 0.340397i
\(297\) 1.41421 + 1.41421i 0.0820610 + 0.0820610i
\(298\) −19.4201 11.2122i −1.12497 0.649504i
\(299\) 3.07180 0.177647
\(300\) 0 0
\(301\) −6.07180 −0.349973
\(302\) −5.22715 3.01790i −0.300789 0.173660i
\(303\) −1.03528 1.03528i −0.0594751 0.0594751i
\(304\) 14.3923 24.9282i 0.825455 1.42973i
\(305\) 0 0
\(306\) 2.19615 + 8.19615i 0.125546 + 0.468543i
\(307\) −9.46979 + 9.46979i −0.540469 + 0.540469i −0.923667 0.383197i \(-0.874823\pi\)
0.383197 + 0.923667i \(0.374823\pi\)
\(308\) −2.55103 + 9.52056i −0.145358 + 0.542484i
\(309\) 6.92820i 0.394132i
\(310\) 0 0
\(311\) 27.4641i 1.55735i −0.627430 0.778673i \(-0.715893\pi\)
0.627430 0.778673i \(-0.284107\pi\)
\(312\) −16.2127 −0.917863
\(313\) 5.74479 5.74479i 0.324715 0.324715i −0.525858 0.850572i \(-0.676256\pi\)
0.850572 + 0.525858i \(0.176256\pi\)
\(314\) 13.2942 3.56218i 0.750237 0.201025i
\(315\) 0 0
\(316\) 0.535898 + 0.928203i 0.0301466 + 0.0522155i
\(317\) −4.89898 4.89898i −0.275154 0.275154i 0.556017 0.831171i \(-0.312329\pi\)
−0.831171 + 0.556017i \(0.812329\pi\)
\(318\) 1.03528 1.79315i 0.0580554 0.100555i
\(319\) 14.9282 0.835819
\(320\) 0 0
\(321\) 6.53590 0.364798
\(322\) 0.933740 1.61729i 0.0520353 0.0901278i
\(323\) −30.5307 30.5307i −1.69877 1.69877i
\(324\) 1.00000 + 1.73205i 0.0555556 + 0.0962250i
\(325\) 0 0
\(326\) −19.7583 + 5.29423i −1.09431 + 0.293220i
\(327\) 4.94975 4.94975i 0.273722 0.273722i
\(328\) 15.4548 0.853349
\(329\) 31.8564i 1.75630i
\(330\) 0 0
\(331\) 2.39230i 0.131493i −0.997836 0.0657465i \(-0.979057\pi\)
0.997836 0.0657465i \(-0.0209429\pi\)
\(332\) 0.480473 1.79315i 0.0263694 0.0984119i
\(333\) −2.07055 + 2.07055i −0.113466 + 0.113466i
\(334\) −1.60770 6.00000i −0.0879692 0.328305i
\(335\) 0 0
\(336\) −4.92820 + 8.53590i −0.268856 + 0.465671i
\(337\) 8.01841 + 8.01841i 0.436791 + 0.436791i 0.890930 0.454140i \(-0.150053\pi\)
−0.454140 + 0.890930i \(0.650053\pi\)
\(338\) −24.3190 14.0406i −1.32278 0.763708i
\(339\) −13.8564 −0.752577
\(340\) 0 0
\(341\) −0.535898 −0.0290205
\(342\) −8.81345 5.08845i −0.476577 0.275152i
\(343\) 13.8140 + 13.8140i 0.745884 + 0.745884i
\(344\) 4.92820 + 4.92820i 0.265711 + 0.265711i
\(345\) 0 0
\(346\) −3.26795 12.1962i −0.175686 0.655669i
\(347\) 7.82894 7.82894i 0.420280 0.420280i −0.465020 0.885300i \(-0.653953\pi\)
0.885300 + 0.465020i \(0.153953\pi\)
\(348\) 14.4195 + 3.86370i 0.772968 + 0.207116i
\(349\) 3.85641i 0.206429i −0.994659 0.103214i \(-0.967087\pi\)
0.994659 0.103214i \(-0.0329128\pi\)
\(350\) 0 0
\(351\) 5.73205i 0.305954i
\(352\) 9.79796 5.65685i 0.522233 0.301511i
\(353\) −11.2122 + 11.2122i −0.596764 + 0.596764i −0.939450 0.342686i \(-0.888663\pi\)
0.342686 + 0.939450i \(0.388663\pi\)
\(354\) 6.19615 1.66025i 0.329322 0.0882415i
\(355\) 0 0
\(356\) −12.0000 + 6.92820i −0.635999 + 0.367194i
\(357\) 10.4543 + 10.4543i 0.553300 + 0.553300i
\(358\) −17.9043 + 31.0112i −0.946272 + 1.63899i
\(359\) −24.3923 −1.28738 −0.643688 0.765288i \(-0.722597\pi\)
−0.643688 + 0.765288i \(0.722597\pi\)
\(360\) 0 0
\(361\) 32.7846 1.72551
\(362\) −9.84873 + 17.0585i −0.517638 + 0.896575i
\(363\) 4.94975 + 4.94975i 0.259794 + 0.259794i
\(364\) −24.4641 + 14.1244i −1.28227 + 0.740317i
\(365\) 0 0
\(366\) 4.09808 1.09808i 0.214210 0.0573974i
\(367\) −7.50077 + 7.50077i −0.391537 + 0.391537i −0.875235 0.483698i \(-0.839293\pi\)
0.483698 + 0.875235i \(0.339293\pi\)
\(368\) −2.07055 + 0.554803i −0.107935 + 0.0289211i
\(369\) 5.46410i 0.284450i
\(370\) 0 0
\(371\) 3.60770i 0.187302i
\(372\) −0.517638 0.138701i −0.0268383 0.00719130i
\(373\) 13.6753 13.6753i 0.708078 0.708078i −0.258052 0.966131i \(-0.583081\pi\)
0.966131 + 0.258052i \(0.0830808\pi\)
\(374\) −4.39230 16.3923i −0.227121 0.847626i
\(375\) 0 0
\(376\) 25.8564 25.8564i 1.33344 1.33344i
\(377\) 30.2533 + 30.2533i 1.55812 + 1.55812i
\(378\) 3.01790 + 1.74238i 0.155224 + 0.0896185i
\(379\) 15.7321 0.808101 0.404051 0.914737i \(-0.367602\pi\)
0.404051 + 0.914737i \(0.367602\pi\)
\(380\) 0 0
\(381\) 2.92820 0.150016
\(382\) 20.7327 + 11.9700i 1.06078 + 0.612441i
\(383\) 11.8685 + 11.8685i 0.606453 + 0.606453i 0.942017 0.335565i \(-0.108927\pi\)
−0.335565 + 0.942017i \(0.608927\pi\)
\(384\) 10.9282 2.92820i 0.557678 0.149429i
\(385\) 0 0
\(386\) −5.02628 18.7583i −0.255831 0.954774i
\(387\) 1.74238 1.74238i 0.0885703 0.0885703i
\(388\) −3.24453 + 12.1087i −0.164716 + 0.614729i
\(389\) 14.5359i 0.736999i −0.929628 0.368500i \(-0.879872\pi\)
0.929628 0.368500i \(-0.120128\pi\)
\(390\) 0 0
\(391\) 3.21539i 0.162609i
\(392\) 2.62536i 0.132600i
\(393\) 6.69213 6.69213i 0.337573 0.337573i
\(394\) −19.6603 + 5.26795i −0.990469 + 0.265395i
\(395\) 0 0
\(396\) −2.00000 3.46410i −0.100504 0.174078i
\(397\) −13.8511 13.8511i −0.695168 0.695168i 0.268196 0.963364i \(-0.413573\pi\)
−0.963364 + 0.268196i \(0.913573\pi\)
\(398\) 9.98743 17.2987i 0.500625 0.867107i
\(399\) −17.7321 −0.887713
\(400\) 0 0
\(401\) −33.1769 −1.65678 −0.828388 0.560155i \(-0.810742\pi\)
−0.828388 + 0.560155i \(0.810742\pi\)
\(402\) 8.81345 15.2653i 0.439575 0.761366i
\(403\) −1.08604 1.08604i −0.0540997 0.0540997i
\(404\) 1.46410 + 2.53590i 0.0728418 + 0.126166i
\(405\) 0 0
\(406\) 25.1244 6.73205i 1.24690 0.334106i
\(407\) 4.14110 4.14110i 0.205267 0.205267i
\(408\) 16.9706i 0.840168i
\(409\) 27.7846i 1.37386i 0.726723 + 0.686930i \(0.241042\pi\)
−0.726723 + 0.686930i \(0.758958\pi\)
\(410\) 0 0
\(411\) 8.53590i 0.421045i
\(412\) 3.58630 13.3843i 0.176684 0.659395i
\(413\) 7.90327 7.90327i 0.388895 0.388895i
\(414\) 0.196152 + 0.732051i 0.00964037 + 0.0359783i
\(415\) 0 0
\(416\) 31.3205 + 8.39230i 1.53561 + 0.411467i
\(417\) −13.7632 13.7632i −0.673987 0.673987i
\(418\) 17.6269 + 10.1769i 0.862160 + 0.497768i
\(419\) −26.5359 −1.29636 −0.648182 0.761486i \(-0.724470\pi\)
−0.648182 + 0.761486i \(0.724470\pi\)
\(420\) 0 0
\(421\) 6.78461 0.330662 0.165331 0.986238i \(-0.447131\pi\)
0.165331 + 0.986238i \(0.447131\pi\)
\(422\) 8.81345 + 5.08845i 0.429032 + 0.247702i
\(423\) −9.14162 9.14162i −0.444481 0.444481i
\(424\) −2.92820 + 2.92820i −0.142206 + 0.142206i
\(425\) 0 0
\(426\) 3.46410 + 12.9282i 0.167836 + 0.626373i
\(427\) 5.22715 5.22715i 0.252959 0.252959i
\(428\) −12.6264 3.38323i −0.610319 0.163535i
\(429\) 11.4641i 0.553492i
\(430\) 0 0
\(431\) 25.7128i 1.23854i 0.785177 + 0.619271i \(0.212572\pi\)
−0.785177 + 0.619271i \(0.787428\pi\)
\(432\) −1.03528 3.86370i −0.0498097 0.185893i
\(433\) −3.11943 + 3.11943i −0.149910 + 0.149910i −0.778078 0.628168i \(-0.783805\pi\)
0.628168 + 0.778078i \(0.283805\pi\)
\(434\) −0.901924 + 0.241670i −0.0432937 + 0.0116005i
\(435\) 0 0
\(436\) −12.1244 + 7.00000i −0.580651 + 0.335239i
\(437\) −2.72689 2.72689i −0.130445 0.130445i
\(438\) −2.82843 + 4.89898i −0.135147 + 0.234082i
\(439\) 27.9808 1.33545 0.667724 0.744409i \(-0.267268\pi\)
0.667724 + 0.744409i \(0.267268\pi\)
\(440\) 0 0
\(441\) −0.928203 −0.0442002
\(442\) 24.3190 42.1218i 1.15674 2.00353i
\(443\) −9.04008 9.04008i −0.429507 0.429507i 0.458953 0.888460i \(-0.348225\pi\)
−0.888460 + 0.458953i \(0.848225\pi\)
\(444\) 5.07180 2.92820i 0.240697 0.138966i
\(445\) 0 0
\(446\) −15.5622 + 4.16987i −0.736890 + 0.197449i
\(447\) 11.2122 11.2122i 0.530318 0.530318i
\(448\) 13.9391 13.9391i 0.658559 0.658559i
\(449\) 33.8564i 1.59778i −0.601475 0.798891i \(-0.705420\pi\)
0.601475 0.798891i \(-0.294580\pi\)
\(450\) 0 0
\(451\) 10.9282i 0.514589i
\(452\) 26.7685 + 7.17260i 1.25909 + 0.337371i
\(453\) 3.01790 3.01790i 0.141793 0.141793i
\(454\) −4.53590 16.9282i −0.212880 0.794480i
\(455\) 0 0
\(456\) 14.3923 + 14.3923i 0.673981 + 0.673981i
\(457\) −25.2528 25.2528i −1.18127 1.18127i −0.979414 0.201861i \(-0.935301\pi\)
−0.201861 0.979414i \(-0.564699\pi\)
\(458\) 30.4428 + 17.5761i 1.42250 + 0.821279i
\(459\) −6.00000 −0.280056
\(460\) 0 0
\(461\) 15.6077 0.726923 0.363461 0.931609i \(-0.381595\pi\)
0.363461 + 0.931609i \(0.381595\pi\)
\(462\) −6.03579 3.48477i −0.280810 0.162126i
\(463\) −9.24316 9.24316i −0.429566 0.429566i 0.458915 0.888480i \(-0.348238\pi\)
−0.888480 + 0.458915i \(0.848238\pi\)
\(464\) −25.8564 14.9282i −1.20035 0.693024i
\(465\) 0 0
\(466\) −4.53590 16.9282i −0.210121 0.784184i
\(467\) 2.44949 2.44949i 0.113349 0.113349i −0.648157 0.761506i \(-0.724460\pi\)
0.761506 + 0.648157i \(0.224460\pi\)
\(468\) 2.96713 11.0735i 0.137156 0.511871i
\(469\) 30.7128i 1.41819i
\(470\) 0 0
\(471\) 9.73205i 0.448429i
\(472\) −12.8295 −0.590524
\(473\) −3.48477 + 3.48477i −0.160230 + 0.160230i
\(474\) −0.732051 + 0.196152i −0.0336242 + 0.00900958i
\(475\) 0 0
\(476\) −14.7846 25.6077i −0.677651 1.17373i
\(477\) 1.03528 + 1.03528i 0.0474020 + 0.0474020i
\(478\) 12.3490 21.3891i 0.564829 0.978313i
\(479\) −13.3205 −0.608630 −0.304315 0.952572i \(-0.598427\pi\)
−0.304315 + 0.952572i \(0.598427\pi\)
\(480\) 0 0
\(481\) 16.7846 0.765312
\(482\) −10.5051 + 18.1953i −0.478493 + 0.828774i
\(483\) 0.933740 + 0.933740i 0.0424867 + 0.0424867i
\(484\) −7.00000 12.1244i −0.318182 0.551107i
\(485\) 0 0
\(486\) −1.36603 + 0.366025i −0.0619642 + 0.0166032i
\(487\) 15.2282 15.2282i 0.690055 0.690055i −0.272189 0.962244i \(-0.587748\pi\)
0.962244 + 0.272189i \(0.0877476\pi\)
\(488\) −8.48528 −0.384111
\(489\) 14.4641i 0.654089i
\(490\) 0 0
\(491\) 34.6410i 1.56333i −0.623700 0.781664i \(-0.714371\pi\)
0.623700 0.781664i \(-0.285629\pi\)
\(492\) −2.82843 + 10.5558i −0.127515 + 0.475894i
\(493\) −31.6675 + 31.6675i −1.42623 + 1.42623i
\(494\) 15.0981 + 56.3468i 0.679295 + 2.53516i
\(495\) 0 0
\(496\) 0.928203 + 0.535898i 0.0416776 + 0.0240625i
\(497\) 16.4901 + 16.4901i 0.739682 + 0.739682i
\(498\) 1.13681 + 0.656339i 0.0509418 + 0.0294112i
\(499\) −5.87564 −0.263030 −0.131515 0.991314i \(-0.541984\pi\)
−0.131515 + 0.991314i \(0.541984\pi\)
\(500\) 0 0
\(501\) 4.39230 0.196234
\(502\) 2.62536 + 1.51575i 0.117175 + 0.0676512i
\(503\) −14.4195 14.4195i −0.642935 0.642935i 0.308341 0.951276i \(-0.400226\pi\)
−0.951276 + 0.308341i \(0.900226\pi\)
\(504\) −4.92820 4.92820i −0.219520 0.219520i
\(505\) 0 0
\(506\) −0.392305 1.46410i −0.0174401 0.0650873i
\(507\) 14.0406 14.0406i 0.623565 0.623565i
\(508\) −5.65685 1.51575i −0.250982 0.0672505i
\(509\) 11.0718i 0.490749i 0.969428 + 0.245374i \(0.0789109\pi\)
−0.969428 + 0.245374i \(0.921089\pi\)
\(510\) 0 0
\(511\) 9.85641i 0.436022i
\(512\) −22.6274 −1.00000
\(513\) 5.08845 5.08845i 0.224660 0.224660i
\(514\) 17.4641 4.67949i 0.770309 0.206404i
\(515\) 0 0
\(516\) −4.26795 + 2.46410i −0.187886 + 0.108476i
\(517\) 18.2832 + 18.2832i 0.804096 + 0.804096i
\(518\) 5.10205 8.83701i 0.224171 0.388276i
\(519\) 8.92820 0.391905
\(520\) 0 0
\(521\) −17.6077 −0.771407 −0.385704 0.922623i \(-0.626041\pi\)
−0.385704 + 0.922623i \(0.626041\pi\)
\(522\) −5.27792 + 9.14162i −0.231008 + 0.400118i
\(523\) 13.7124 + 13.7124i 0.599603 + 0.599603i 0.940207 0.340604i \(-0.110632\pi\)
−0.340604 + 0.940207i \(0.610632\pi\)
\(524\) −16.3923 + 9.46410i −0.716101 + 0.413441i
\(525\) 0 0
\(526\) 29.3205 7.85641i 1.27843 0.342556i
\(527\) 1.13681 1.13681i 0.0495203 0.0495203i
\(528\) 2.07055 + 7.72741i 0.0901092 + 0.336292i
\(529\) 22.7128i 0.987514i
\(530\) 0 0
\(531\) 4.53590i 0.196841i
\(532\) 34.2557 + 9.17878i 1.48517 + 0.397951i
\(533\) −22.1469 + 22.1469i −0.959291 + 0.959291i
\(534\) −2.53590 9.46410i −0.109739 0.409552i
\(535\) 0 0
\(536\) −24.9282 + 24.9282i −1.07673 + 1.07673i
\(537\) −17.9043 17.9043i −0.772628 0.772628i
\(538\) −1.96902 1.13681i −0.0848903 0.0490115i
\(539\) 1.85641 0.0799611
\(540\) 0 0
\(541\) −33.7846 −1.45251 −0.726257 0.687423i \(-0.758742\pi\)
−0.726257 + 0.687423i \(0.758742\pi\)
\(542\) 29.6985 + 17.1464i 1.27566 + 0.736502i
\(543\) −9.84873 9.84873i −0.422649 0.422649i
\(544\) −8.78461 + 32.7846i −0.376637 + 1.40563i
\(545\) 0 0
\(546\) −5.16987 19.2942i −0.221250 0.825717i
\(547\) −17.5254 + 17.5254i −0.749331 + 0.749331i −0.974353 0.225023i \(-0.927754\pi\)
0.225023 + 0.974353i \(0.427754\pi\)
\(548\) −4.41851 + 16.4901i −0.188749 + 0.704422i
\(549\) 3.00000i 0.128037i
\(550\) 0 0
\(551\) 53.7128i 2.28824i
\(552\) 1.51575i 0.0645146i
\(553\) −0.933740 + 0.933740i −0.0397067 + 0.0397067i
\(554\) 1.63397 0.437822i 0.0694209 0.0186013i
\(555\) 0 0
\(556\) 19.4641 + 33.7128i 0.825462 + 1.42974i
\(557\) −25.6317 25.6317i −1.08605 1.08605i −0.995931 0.0901194i \(-0.971275\pi\)
−0.0901194 0.995931i \(-0.528725\pi\)
\(558\) 0.189469 0.328169i 0.00802085 0.0138925i
\(559\) −14.1244 −0.597397
\(560\) 0 0
\(561\) 12.0000 0.506640
\(562\) −10.1769 + 17.6269i −0.429286 + 0.743546i
\(563\) 16.3886 + 16.3886i 0.690695 + 0.690695i 0.962385 0.271690i \(-0.0875824\pi\)
−0.271690 + 0.962385i \(0.587582\pi\)
\(564\) 12.9282 + 22.3923i 0.544376 + 0.942886i
\(565\) 0 0
\(566\) 29.2224 7.83013i 1.22831 0.329125i
\(567\) −1.74238 + 1.74238i −0.0731732 + 0.0731732i
\(568\) 26.7685i 1.12318i
\(569\) 17.3205i 0.726113i −0.931767 0.363057i \(-0.881733\pi\)
0.931767 0.363057i \(-0.118267\pi\)
\(570\) 0 0
\(571\) 16.8038i 0.703219i −0.936147 0.351610i \(-0.885634\pi\)
0.936147 0.351610i \(-0.114366\pi\)
\(572\) −5.93426 + 22.1469i −0.248124 + 0.926010i
\(573\) −11.9700 + 11.9700i −0.500056 + 0.500056i
\(574\) 4.92820 + 18.3923i 0.205699 + 0.767680i
\(575\) 0 0
\(576\) 8.00000i 0.333333i
\(577\) −10.8468 10.8468i −0.451560 0.451560i 0.444312 0.895872i \(-0.353448\pi\)
−0.895872 + 0.444312i \(0.853448\pi\)
\(578\) 23.2702 + 13.4350i 0.967911 + 0.558824i
\(579\) 13.7321 0.570685
\(580\) 0 0
\(581\) 2.28719 0.0948885
\(582\) −7.67664 4.43211i −0.318207 0.183717i
\(583\) −2.07055 2.07055i −0.0857535 0.0857535i
\(584\) 8.00000 8.00000i 0.331042 0.331042i
\(585\) 0 0
\(586\) −4.58846 17.1244i −0.189547 0.707401i
\(587\) −13.6617 + 13.6617i −0.563877 + 0.563877i −0.930406 0.366529i \(-0.880546\pi\)
0.366529 + 0.930406i \(0.380546\pi\)
\(588\) 1.79315 + 0.480473i 0.0739483 + 0.0198144i
\(589\) 1.92820i 0.0794502i
\(590\) 0 0
\(591\) 14.3923i 0.592020i
\(592\) −11.3137 + 3.03150i −0.464991 + 0.124594i
\(593\) −22.9048 + 22.9048i −0.940588 + 0.940588i −0.998331 0.0577433i \(-0.981610\pi\)
0.0577433 + 0.998331i \(0.481610\pi\)
\(594\) 2.73205 0.732051i 0.112097 0.0300364i
\(595\) 0 0
\(596\) −27.4641 + 15.8564i −1.12497 + 0.649504i
\(597\) 9.98743 + 9.98743i 0.408758 + 0.408758i
\(598\) 2.17209 3.76217i 0.0888233 0.153846i
\(599\) 46.6410 1.90570 0.952850 0.303441i \(-0.0981356\pi\)
0.952850 + 0.303441i \(0.0981356\pi\)
\(600\) 0 0
\(601\) −19.7846 −0.807031 −0.403516 0.914973i \(-0.632212\pi\)
−0.403516 + 0.914973i \(0.632212\pi\)
\(602\) −4.29341 + 7.43640i −0.174986 + 0.303085i
\(603\) 8.81345 + 8.81345i 0.358911 + 0.358911i
\(604\) −7.39230 + 4.26795i −0.300789 + 0.173660i
\(605\) 0 0
\(606\) −2.00000 + 0.535898i −0.0812444 + 0.0217694i
\(607\) −13.9391 + 13.9391i −0.565769 + 0.565769i −0.930940 0.365171i \(-0.881010\pi\)
0.365171 + 0.930940i \(0.381010\pi\)
\(608\) −20.3538 35.2538i −0.825455 1.42973i
\(609\) 18.3923i 0.745294i
\(610\) 0 0
\(611\) 74.1051i 2.99797i
\(612\) 11.5911 + 3.10583i 0.468543 + 0.125546i
\(613\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(614\) 4.90192 + 18.2942i 0.197826 + 0.738295i
\(615\) 0 0
\(616\) 9.85641 + 9.85641i 0.397126 + 0.397126i
\(617\) 10.0754 + 10.0754i 0.405619 + 0.405619i 0.880208 0.474589i \(-0.157403\pi\)
−0.474589 + 0.880208i \(0.657403\pi\)
\(618\) 8.48528 + 4.89898i 0.341328 + 0.197066i
\(619\) 35.9808 1.44619 0.723094 0.690749i \(-0.242719\pi\)
0.723094 + 0.690749i \(0.242719\pi\)
\(620\) 0 0
\(621\) −0.535898 −0.0215049
\(622\) −33.6365 19.4201i −1.34870 0.778673i
\(623\) −12.0716 12.0716i −0.483638 0.483638i
\(624\) −11.4641 + 19.8564i −0.458931 + 0.794892i
\(625\) 0 0
\(626\) −2.97372 11.0981i −0.118854 0.443568i
\(627\) −10.1769 + 10.1769i −0.406426 + 0.406426i
\(628\) 5.03768 18.8009i 0.201025 0.750237i
\(629\) 17.5692i 0.700531i
\(630\) 0 0
\(631\) 1.58846i 0.0632355i −0.999500 0.0316177i \(-0.989934\pi\)
0.999500 0.0316177i \(-0.0100659\pi\)
\(632\) 1.51575 0.0602933
\(633\) −5.08845 + 5.08845i −0.202248 + 0.202248i
\(634\) −9.46410 + 2.53590i −0.375867 + 0.100713i
\(635\) 0 0
\(636\) −1.46410 2.53590i −0.0580554 0.100555i
\(637\) 3.76217 + 3.76217i 0.149062 + 0.149062i
\(638\) 10.5558 18.2832i 0.417909 0.723840i
\(639\) −9.46410 −0.374394
\(640\) 0 0
\(641\) −3.21539 −0.127000 −0.0635001 0.997982i \(-0.520226\pi\)
−0.0635001 + 0.997982i \(0.520226\pi\)
\(642\) 4.62158 8.00481i 0.182399 0.315925i
\(643\) −12.0716 12.0716i −0.476057 0.476057i 0.427811 0.903868i \(-0.359285\pi\)
−0.903868 + 0.427811i \(0.859285\pi\)
\(644\) −1.32051 2.28719i −0.0520353 0.0901278i
\(645\) 0 0
\(646\) −58.9808 + 15.8038i −2.32057 + 0.621794i
\(647\) 3.58630 3.58630i 0.140992 0.140992i −0.633088 0.774080i \(-0.718213\pi\)
0.774080 + 0.633088i \(0.218213\pi\)
\(648\) 2.82843 0.111111
\(649\) 9.07180i 0.356099i
\(650\) 0 0
\(651\) 0.660254i 0.0258774i
\(652\) −7.48717 + 27.9425i −0.293220 + 1.09431i
\(653\) 7.34847 7.34847i 0.287568 0.287568i −0.548550 0.836118i \(-0.684820\pi\)
0.836118 + 0.548550i \(0.184820\pi\)
\(654\) −2.56218 9.56218i −0.100189 0.373911i
\(655\) 0 0
\(656\) 10.9282 18.9282i 0.426675 0.739022i
\(657\) −2.82843 2.82843i −0.110347 0.110347i
\(658\) 39.0160 + 22.5259i 1.52100 + 0.878150i
\(659\) 14.5359 0.566238 0.283119 0.959085i \(-0.408631\pi\)
0.283119 + 0.959085i \(0.408631\pi\)
\(660\) 0 0
\(661\) −7.85641 −0.305579 −0.152789 0.988259i \(-0.548826\pi\)
−0.152789 + 0.988259i \(0.548826\pi\)
\(662\) −2.92996 1.69161i −0.113876 0.0657465i
\(663\) 24.3190 + 24.3190i 0.944473 + 0.944473i
\(664\) −1.85641 1.85641i −0.0720425 0.0720425i
\(665\) 0 0
\(666\) 1.07180 + 4.00000i 0.0415313 + 0.154997i
\(667\) −2.82843 + 2.82843i −0.109517 + 0.109517i
\(668\) −8.48528 2.27362i −0.328305 0.0879692i
\(669\) 11.3923i 0.440452i
\(670\) 0 0
\(671\) 6.00000i 0.231627i
\(672\) 6.96953 + 12.0716i 0.268856 + 0.465671i
\(673\) 2.82843 2.82843i 0.109028 0.109028i −0.650488 0.759516i \(-0.725436\pi\)
0.759516 + 0.650488i \(0.225436\pi\)
\(674\) 15.4904 4.15064i 0.596667 0.159876i
\(675\) 0 0
\(676\) −34.3923 + 19.8564i −1.32278 + 0.763708i
\(677\) −25.9091 25.9091i −0.995768 0.995768i 0.00422306 0.999991i \(-0.498656\pi\)
−0.999991 + 0.00422306i \(0.998656\pi\)
\(678\) −9.79796 + 16.9706i −0.376288 + 0.651751i
\(679\) −15.4449 −0.592719
\(680\) 0 0
\(681\) 12.3923 0.474874
\(682\) −0.378937 + 0.656339i −0.0145103 + 0.0251325i
\(683\) 3.58630 + 3.58630i 0.137226 + 0.137226i 0.772383 0.635157i \(-0.219065\pi\)
−0.635157 + 0.772383i \(0.719065\pi\)
\(684\) −12.4641 + 7.19615i −0.476577 + 0.275152i
\(685\) 0 0
\(686\) 26.6865 7.15064i 1.01890 0.273013i
\(687\) −17.5761 + 17.5761i −0.670571 + 0.670571i
\(688\) 9.52056 2.55103i 0.362968 0.0972569i
\(689\) 8.39230i 0.319721i
\(690\) 0 0
\(691\) 25.3205i 0.963238i 0.876381 + 0.481619i \(0.159951\pi\)
−0.876381 + 0.481619i \(0.840049\pi\)
\(692\) −17.2480 4.62158i −0.655669 0.175686i
\(693\) 3.48477 3.48477i 0.132375 0.132375i
\(694\) −4.05256 15.1244i −0.153833 0.574113i
\(695\) 0 0
\(696\) 14.9282 14.9282i 0.565852 0.565852i
\(697\) −23.1822 23.1822i −0.878089 0.878089i
\(698\) −4.72311 2.72689i −0.178773 0.103214i
\(699\) 12.3923 0.468720
\(700\) 0 0
\(701\) −15.4641 −0.584071 −0.292036 0.956407i \(-0.594333\pi\)
−0.292036 + 0.956407i \(0.594333\pi\)
\(702\) 7.02030 + 4.05317i 0.264964 + 0.152977i
\(703\) −14.9000 14.9000i −0.561965 0.561965i
\(704\) 16.0000i 0.603023i
\(705\) 0 0
\(706\) 5.80385 + 21.6603i 0.218431 + 0.815194i
\(707\) −2.55103 + 2.55103i −0.0959412 + 0.0959412i
\(708\) 2.34795 8.76268i 0.0882415 0.329322i
\(709\) 24.8564i 0.933502i 0.884389 + 0.466751i \(0.154576\pi\)
−0.884389 + 0.466751i \(0.845424\pi\)
\(710\) 0 0
\(711\) 0.535898i 0.0200978i
\(712\) 19.5959i 0.734388i
\(713\) 0.101536 0.101536i 0.00380255 0.00380255i
\(714\) 20.1962 5.41154i 0.755822 0.202522i
\(715\) 0 0
\(716\) 25.3205 + 43.8564i 0.946272 + 1.63899i
\(717\) 12.3490 + 12.3490i 0.461181 + 0.461181i
\(718\) −17.2480 + 29.8744i −0.643688 + 1.11490i
\(719\) −12.9282 −0.482141 −0.241070 0.970508i \(-0.577498\pi\)
−0.241070 + 0.970508i \(0.577498\pi\)
\(720\) 0 0
\(721\) 17.0718 0.635787
\(722\) 23.1822 40.1528i 0.862753 1.49433i
\(723\) −10.5051 10.5051i −0.390688 0.390688i
\(724\) 13.9282 + 24.1244i 0.517638 + 0.896575i
\(725\) 0 0
\(726\) 9.56218 2.56218i 0.354886 0.0950913i
\(727\) 33.3083 33.3083i 1.23534 1.23534i 0.273453 0.961885i \(-0.411834\pi\)
0.961885 0.273453i \(-0.0881658\pi\)
\(728\) 39.9497i 1.48063i
\(729\) 1.00000i 0.0370370i
\(730\) 0 0
\(731\) 14.7846i 0.546829i
\(732\) 1.55291 5.79555i 0.0573974 0.214210i
\(733\) 13.9391 13.9391i 0.514851 0.514851i −0.401158 0.916009i \(-0.631392\pi\)
0.916009 + 0.401158i \(0.131392\pi\)
\(734\) 3.88269 + 14.4904i 0.143313 + 0.534850i
\(735\) 0 0
\(736\) −0.784610 + 2.92820i −0.0289211 + 0.107935i
\(737\) −17.6269 17.6269i −0.649295 0.649295i
\(738\) −6.69213 3.86370i −0.246341 0.142225i
\(739\) −14.3923 −0.529429 −0.264715 0.964327i \(-0.585278\pi\)
−0.264715 + 0.964327i \(0.585278\pi\)
\(740\) 0 0
\(741\) −41.2487 −1.51531
\(742\) −4.41851 2.55103i −0.162208 0.0936511i
\(743\) 21.8695 + 21.8695i 0.802316 + 0.802316i 0.983457 0.181141i \(-0.0579792\pi\)
−0.181141 + 0.983457i \(0.557979\pi\)
\(744\) −0.535898 + 0.535898i −0.0196470 + 0.0196470i
\(745\) 0 0
\(746\) −7.07884 26.4186i −0.259175 0.967253i
\(747\) −0.656339 + 0.656339i −0.0240142 + 0.0240142i
\(748\) −23.1822 6.21166i −0.847626 0.227121i
\(749\) 16.1051i 0.588468i
\(750\) 0 0
\(751\) 11.4641i 0.418331i 0.977880 + 0.209166i \(0.0670747\pi\)
−0.977880 + 0.209166i \(0.932925\pi\)
\(752\) −13.3843 49.9507i −0.488074 1.82152i
\(753\) −1.51575 + 1.51575i −0.0552370 + 0.0552370i
\(754\) 58.4449 15.6603i 2.12844 0.570313i
\(755\) 0 0
\(756\) 4.26795 2.46410i 0.155224 0.0896185i
\(757\) 20.6448 + 20.6448i 0.750348 + 0.750348i 0.974544 0.224196i \(-0.0719756\pi\)
−0.224196 + 0.974544i \(0.571976\pi\)
\(758\) 11.1242 19.2677i 0.404051 0.699836i
\(759\) 1.07180 0.0389038
\(760\) 0 0
\(761\) 46.6410 1.69074 0.845368 0.534185i \(-0.179381\pi\)
0.845368 + 0.534185i \(0.179381\pi\)
\(762\) 2.07055 3.58630i 0.0750082 0.129918i
\(763\) −12.1967 12.1967i −0.441549 0.441549i
\(764\) 29.3205 16.9282i 1.06078 0.612441i
\(765\) 0 0
\(766\) 22.9282 6.14359i 0.828430 0.221977i
\(767\) 18.3848 18.3848i 0.663836 0.663836i
\(768\) 4.14110 15.4548i 0.149429 0.557678i
\(769\) 29.9282i 1.07924i −0.841909 0.539619i \(-0.818568\pi\)
0.841909 0.539619i \(-0.181432\pi\)
\(770\) 0 0
\(771\) 12.7846i 0.460426i
\(772\) −26.5283 7.10823i −0.954774 0.255831i
\(773\) 23.4596 23.4596i 0.843784 0.843784i −0.145565 0.989349i \(-0.546500\pi\)
0.989349 + 0.145565i \(0.0464999\pi\)
\(774\) −0.901924 3.36603i −0.0324190 0.120989i
\(775\) 0 0
\(776\) 12.5359 + 12.5359i 0.450013 + 0.450013i
\(777\) 5.10205 + 5.10205i 0.183035 + 0.183035i
\(778\) −17.8028 10.2784i −0.638260 0.368500i
\(779\) 39.3205 1.40880
\(780\) 0 0
\(781\) 18.9282 0.677304
\(782\) 3.93803 + 2.27362i 0.140824 + 0.0813046i
\(783\) −5.27792 5.27792i −0.188617 0.188617i