Properties

Label 300.2.j.a.43.2
Level $300$
Weight $2$
Character 300.43
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 43.2
Root \(0.258819 - 0.965926i\) of defining polynomial
Character \(\chi\) \(=\) 300.43
Dual form 300.2.j.a.7.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.707107 + 1.22474i) q^{2} +(-0.707107 + 0.707107i) q^{3} +(-1.00000 - 1.73205i) q^{4} +(-0.366025 - 1.36603i) q^{6} +(3.15660 + 3.15660i) q^{7} +2.82843 q^{8} -1.00000i q^{9} +O(q^{10})\) \(q+(-0.707107 + 1.22474i) q^{2} +(-0.707107 + 0.707107i) q^{3} +(-1.00000 - 1.73205i) q^{4} +(-0.366025 - 1.36603i) q^{6} +(3.15660 + 3.15660i) q^{7} +2.82843 q^{8} -1.00000i q^{9} +2.00000i q^{11} +(1.93185 + 0.517638i) q^{12} +(-1.60368 - 1.60368i) q^{13} +(-6.09808 + 1.63397i) q^{14} +(-2.00000 + 3.46410i) q^{16} +(-4.24264 + 4.24264i) q^{17} +(1.22474 + 0.707107i) q^{18} +3.19615 q^{19} -4.46410 q^{21} +(-2.44949 - 1.41421i) q^{22} +(-5.27792 + 5.27792i) q^{23} +(-2.00000 + 2.00000i) q^{24} +(3.09808 - 0.830127i) q^{26} +(0.707107 + 0.707107i) q^{27} +(2.31079 - 8.62398i) q^{28} -0.535898i q^{29} +3.73205i q^{31} +(-2.82843 - 4.89898i) q^{32} +(-1.41421 - 1.41421i) q^{33} +(-2.19615 - 8.19615i) q^{34} +(-1.73205 + 1.00000i) q^{36} +(7.72741 - 7.72741i) q^{37} +(-2.26002 + 3.91447i) q^{38} +2.26795 q^{39} +1.46410 q^{41} +(3.15660 - 5.46739i) q^{42} +(-3.15660 + 3.15660i) q^{43} +(3.46410 - 2.00000i) q^{44} +(-2.73205 - 10.1962i) q^{46} +(-0.656339 - 0.656339i) q^{47} +(-1.03528 - 3.86370i) q^{48} +12.9282i q^{49} -6.00000i q^{51} +(-1.17398 + 4.38134i) q^{52} +(3.86370 + 3.86370i) q^{53} +(-1.36603 + 0.366025i) q^{54} +(8.92820 + 8.92820i) q^{56} +(-2.26002 + 2.26002i) q^{57} +(0.656339 + 0.378937i) q^{58} +11.4641 q^{59} +3.00000 q^{61} +(-4.57081 - 2.63896i) q^{62} +(3.15660 - 3.15660i) q^{63} +8.00000 q^{64} +(2.73205 - 0.732051i) q^{66} +(-3.91447 - 3.91447i) q^{67} +(11.5911 + 3.10583i) q^{68} -7.46410i q^{69} -2.53590i q^{71} -2.82843i q^{72} +(2.82843 + 2.82843i) q^{73} +(4.00000 + 14.9282i) q^{74} +(-3.19615 - 5.53590i) q^{76} +(-6.31319 + 6.31319i) q^{77} +(-1.60368 + 2.77766i) q^{78} -7.46410 q^{79} -1.00000 q^{81} +(-1.03528 + 1.79315i) q^{82} +(9.14162 - 9.14162i) q^{83} +(4.46410 + 7.73205i) q^{84} +(-1.63397 - 6.09808i) q^{86} +(0.378937 + 0.378937i) q^{87} +5.65685i q^{88} -6.92820i q^{89} -10.1244i q^{91} +(14.4195 + 3.86370i) q^{92} +(-2.63896 - 2.63896i) q^{93} +(1.26795 - 0.339746i) q^{94} +(5.46410 + 1.46410i) q^{96} +(6.88160 - 6.88160i) q^{97} +(-15.8338 - 9.14162i) 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 \(\left(\mathbb{Z}/300\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(151\) \(277\)
\(\chi(n)\) \(1\) \(-1\) \(e\left(\frac{3}{4}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.707107 + 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
\(6\) −0.366025 1.36603i −0.149429 0.557678i
\(7\) 3.15660 + 3.15660i 1.19308 + 1.19308i 0.976197 + 0.216884i \(0.0695893\pi\)
0.216884 + 0.976197i \(0.430411\pi\)
\(8\) 2.82843 1.00000
\(9\) 1.00000i 0.333333i
\(10\) 0 0
\(11\) 2.00000i 0.603023i 0.953463 + 0.301511i \(0.0974911\pi\)
−0.953463 + 0.301511i \(0.902509\pi\)
\(12\) 1.93185 + 0.517638i 0.557678 + 0.149429i
\(13\) −1.60368 1.60368i −0.444781 0.444781i 0.448834 0.893615i \(-0.351840\pi\)
−0.893615 + 0.448834i \(0.851840\pi\)
\(14\) −6.09808 + 1.63397i −1.62978 + 0.436698i
\(15\) 0 0
\(16\) −2.00000 + 3.46410i −0.500000 + 0.866025i
\(17\) −4.24264 + 4.24264i −1.02899 + 1.02899i −0.0294245 + 0.999567i \(0.509367\pi\)
−0.999567 + 0.0294245i \(0.990633\pi\)
\(18\) 1.22474 + 0.707107i 0.288675 + 0.166667i
\(19\) 3.19615 0.733248 0.366624 0.930369i \(-0.380514\pi\)
0.366624 + 0.930369i \(0.380514\pi\)
\(20\) 0 0
\(21\) −4.46410 −0.974147
\(22\) −2.44949 1.41421i −0.522233 0.301511i
\(23\) −5.27792 + 5.27792i −1.10052 + 1.10052i −0.106174 + 0.994348i \(0.533860\pi\)
−0.994348 + 0.106174i \(0.966140\pi\)
\(24\) −2.00000 + 2.00000i −0.408248 + 0.408248i
\(25\) 0 0
\(26\) 3.09808 0.830127i 0.607583 0.162801i
\(27\) 0.707107 + 0.707107i 0.136083 + 0.136083i
\(28\) 2.31079 8.62398i 0.436698 1.62978i
\(29\) 0.535898i 0.0995138i −0.998761 0.0497569i \(-0.984155\pi\)
0.998761 0.0497569i \(-0.0158447\pi\)
\(30\) 0 0
\(31\) 3.73205i 0.670296i 0.942165 + 0.335148i \(0.108786\pi\)
−0.942165 + 0.335148i \(0.891214\pi\)
\(32\) −2.82843 4.89898i −0.500000 0.866025i
\(33\) −1.41421 1.41421i −0.246183 0.246183i
\(34\) −2.19615 8.19615i −0.376637 1.40563i
\(35\) 0 0
\(36\) −1.73205 + 1.00000i −0.288675 + 0.166667i
\(37\) 7.72741 7.72741i 1.27038 1.27038i 0.324488 0.945890i \(-0.394808\pi\)
0.945890 0.324488i \(-0.105192\pi\)
\(38\) −2.26002 + 3.91447i −0.366624 + 0.635011i
\(39\) 2.26795 0.363163
\(40\) 0 0
\(41\) 1.46410 0.228654 0.114327 0.993443i \(-0.463529\pi\)
0.114327 + 0.993443i \(0.463529\pi\)
\(42\) 3.15660 5.46739i 0.487073 0.843636i
\(43\) −3.15660 + 3.15660i −0.481376 + 0.481376i −0.905571 0.424195i \(-0.860557\pi\)
0.424195 + 0.905571i \(0.360557\pi\)
\(44\) 3.46410 2.00000i 0.522233 0.301511i
\(45\) 0 0
\(46\) −2.73205 10.1962i −0.402819 1.50334i
\(47\) −0.656339 0.656339i −0.0957369 0.0957369i 0.657616 0.753353i \(-0.271565\pi\)
−0.753353 + 0.657616i \(0.771565\pi\)
\(48\) −1.03528 3.86370i −0.149429 0.557678i
\(49\) 12.9282i 1.84689i
\(50\) 0 0
\(51\) 6.00000i 0.840168i
\(52\) −1.17398 + 4.38134i −0.162801 + 0.607583i
\(53\) 3.86370 + 3.86370i 0.530720 + 0.530720i 0.920787 0.390066i \(-0.127548\pi\)
−0.390066 + 0.920787i \(0.627548\pi\)
\(54\) −1.36603 + 0.366025i −0.185893 + 0.0498097i
\(55\) 0 0
\(56\) 8.92820 + 8.92820i 1.19308 + 1.19308i
\(57\) −2.26002 + 2.26002i −0.299347 + 0.299347i
\(58\) 0.656339 + 0.378937i 0.0861815 + 0.0497569i
\(59\) 11.4641 1.49250 0.746249 0.665666i \(-0.231853\pi\)
0.746249 + 0.665666i \(0.231853\pi\)
\(60\) 0 0
\(61\) 3.00000 0.384111 0.192055 0.981384i \(-0.438485\pi\)
0.192055 + 0.981384i \(0.438485\pi\)
\(62\) −4.57081 2.63896i −0.580493 0.335148i
\(63\) 3.15660 3.15660i 0.397694 0.397694i
\(64\) 8.00000 1.00000
\(65\) 0 0
\(66\) 2.73205 0.732051i 0.336292 0.0901092i
\(67\) −3.91447 3.91447i −0.478229 0.478229i 0.426336 0.904565i \(-0.359804\pi\)
−0.904565 + 0.426336i \(0.859804\pi\)
\(68\) 11.5911 + 3.10583i 1.40563 + 0.376637i
\(69\) 7.46410i 0.898572i
\(70\) 0 0
\(71\) 2.53590i 0.300956i −0.988613 0.150478i \(-0.951919\pi\)
0.988613 0.150478i \(-0.0480812\pi\)
\(72\) 2.82843i 0.333333i
\(73\) 2.82843 + 2.82843i 0.331042 + 0.331042i 0.852982 0.521940i \(-0.174791\pi\)
−0.521940 + 0.852982i \(0.674791\pi\)
\(74\) 4.00000 + 14.9282i 0.464991 + 1.73537i
\(75\) 0 0
\(76\) −3.19615 5.53590i −0.366624 0.635011i
\(77\) −6.31319 + 6.31319i −0.719455 + 0.719455i
\(78\) −1.60368 + 2.77766i −0.181581 + 0.314508i
\(79\) −7.46410 −0.839777 −0.419889 0.907576i \(-0.637931\pi\)
−0.419889 + 0.907576i \(0.637931\pi\)
\(80\) 0 0
\(81\) −1.00000 −0.111111
\(82\) −1.03528 + 1.79315i −0.114327 + 0.198020i
\(83\) 9.14162 9.14162i 1.00342 1.00342i 0.00342905 0.999994i \(-0.498908\pi\)
0.999994 0.00342905i \(-0.00109150\pi\)
\(84\) 4.46410 + 7.73205i 0.487073 + 0.843636i
\(85\) 0 0
\(86\) −1.63397 6.09808i −0.176196 0.657572i
\(87\) 0.378937 + 0.378937i 0.0406264 + 0.0406264i
\(88\) 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
\(91\) 10.1244i 1.06132i
\(92\) 14.4195 + 3.86370i 1.50334 + 0.402819i
\(93\) −2.63896 2.63896i −0.273647 0.273647i
\(94\) 1.26795 0.339746i 0.130779 0.0350421i
\(95\) 0 0
\(96\) 5.46410 + 1.46410i 0.557678 + 0.149429i
\(97\) 6.88160 6.88160i 0.698721 0.698721i −0.265414 0.964135i \(-0.585509\pi\)
0.964135 + 0.265414i \(0.0855086\pi\)
\(98\) −15.8338 9.14162i −1.59945 0.923443i
\(99\) 2.00000 0.201008
\(100\) 0 0
\(101\) 5.46410 0.543698 0.271849 0.962340i \(-0.412365\pi\)
0.271849 + 0.962340i \(0.412365\pi\)
\(102\) 7.34847 + 4.24264i 0.727607 + 0.420084i
\(103\) 4.89898 4.89898i 0.482711 0.482711i −0.423286 0.905996i \(-0.639123\pi\)
0.905996 + 0.423286i \(0.139123\pi\)
\(104\) −4.53590 4.53590i −0.444781 0.444781i
\(105\) 0 0
\(106\) −7.46410 + 2.00000i −0.724978 + 0.194257i
\(107\) −9.52056 9.52056i −0.920387 0.920387i 0.0766695 0.997057i \(-0.475571\pi\)
−0.997057 + 0.0766695i \(0.975571\pi\)
\(108\) 0.517638 1.93185i 0.0498097 0.185893i
\(109\) 7.00000i 0.670478i 0.942133 + 0.335239i \(0.108817\pi\)
−0.942133 + 0.335239i \(0.891183\pi\)
\(110\) 0 0
\(111\) 10.9282i 1.03726i
\(112\) −17.2480 + 4.62158i −1.62978 + 0.436698i
\(113\) −9.79796 9.79796i −0.921714 0.921714i 0.0754362 0.997151i \(-0.475965\pi\)
−0.997151 + 0.0754362i \(0.975965\pi\)
\(114\) −1.16987 4.36603i −0.109569 0.408916i
\(115\) 0 0
\(116\) −0.928203 + 0.535898i −0.0861815 + 0.0497569i
\(117\) −1.60368 + 1.60368i −0.148260 + 0.148260i
\(118\) −8.10634 + 14.0406i −0.746249 + 1.29254i
\(119\) −26.7846 −2.45534
\(120\) 0 0
\(121\) 7.00000 0.636364
\(122\) −2.12132 + 3.67423i −0.192055 + 0.332650i
\(123\) −1.03528 + 1.03528i −0.0933477 + 0.0933477i
\(124\) 6.46410 3.73205i 0.580493 0.335148i
\(125\) 0 0
\(126\) 1.63397 + 6.09808i 0.145566 + 0.543260i
\(127\) 7.72741 + 7.72741i 0.685696 + 0.685696i 0.961278 0.275581i \(-0.0888703\pi\)
−0.275581 + 0.961278i \(0.588870\pi\)
\(128\) −5.65685 + 9.79796i −0.500000 + 0.866025i
\(129\) 4.46410i 0.393042i
\(130\) 0 0
\(131\) 2.53590i 0.221562i 0.993845 + 0.110781i \(0.0353353\pi\)
−0.993845 + 0.110781i \(0.964665\pi\)
\(132\) −1.03528 + 3.86370i −0.0901092 + 0.336292i
\(133\) 10.0890 + 10.0890i 0.874824 + 0.874824i
\(134\) 7.56218 2.02628i 0.653273 0.175044i
\(135\) 0 0
\(136\) −12.0000 + 12.0000i −1.02899 + 1.02899i
\(137\) 10.9348 10.9348i 0.934221 0.934221i −0.0637456 0.997966i \(-0.520305\pi\)
0.997966 + 0.0637456i \(0.0203046\pi\)
\(138\) 9.14162 + 5.27792i 0.778186 + 0.449286i
\(139\) −12.5359 −1.06328 −0.531641 0.846970i \(-0.678424\pi\)
−0.531641 + 0.846970i \(0.678424\pi\)
\(140\) 0 0
\(141\) 0.928203 0.0781688
\(142\) 3.10583 + 1.79315i 0.260635 + 0.150478i
\(143\) 3.20736 3.20736i 0.268213 0.268213i
\(144\) 3.46410 + 2.00000i 0.288675 + 0.166667i
\(145\) 0 0
\(146\) −5.46410 + 1.46410i −0.452212 + 0.121170i
\(147\) −9.14162 9.14162i −0.753988 0.753988i
\(148\) −21.1117 5.65685i −1.73537 0.464991i
\(149\) 11.8564i 0.971315i −0.874149 0.485657i \(-0.838580\pi\)
0.874149 0.485657i \(-0.161420\pi\)
\(150\) 0 0
\(151\) 7.73205i 0.629225i 0.949220 + 0.314613i \(0.101875\pi\)
−0.949220 + 0.314613i \(0.898125\pi\)
\(152\) 9.04008 0.733248
\(153\) 4.24264 + 4.24264i 0.342997 + 0.342997i
\(154\) −3.26795 12.1962i −0.263339 0.982794i
\(155\) 0 0
\(156\) −2.26795 3.92820i −0.181581 0.314508i
\(157\) −4.43211 + 4.43211i −0.353721 + 0.353721i −0.861492 0.507771i \(-0.830470\pi\)
0.507771 + 0.861492i \(0.330470\pi\)
\(158\) 5.27792 9.14162i 0.419889 0.727268i
\(159\) −5.46410 −0.433331
\(160\) 0 0
\(161\) −33.3205 −2.62602
\(162\) 0.707107 1.22474i 0.0555556 0.0962250i
\(163\) 5.32868 5.32868i 0.417375 0.417375i −0.466923 0.884298i \(-0.654638\pi\)
0.884298 + 0.466923i \(0.154638\pi\)
\(164\) −1.46410 2.53590i −0.114327 0.198020i
\(165\) 0 0
\(166\) 4.73205 + 17.6603i 0.367278 + 1.37070i
\(167\) 11.5911 + 11.5911i 0.896947 + 0.896947i 0.995165 0.0982179i \(-0.0313142\pi\)
−0.0982179 + 0.995165i \(0.531314\pi\)
\(168\) −12.6264 −0.974147
\(169\) 7.85641i 0.604339i
\(170\) 0 0
\(171\) 3.19615i 0.244416i
\(172\) 8.62398 + 2.31079i 0.657572 + 0.176196i
\(173\) 3.48477 + 3.48477i 0.264942 + 0.264942i 0.827058 0.562116i \(-0.190013\pi\)
−0.562116 + 0.827058i \(0.690013\pi\)
\(174\) −0.732051 + 0.196152i −0.0554966 + 0.0148703i
\(175\) 0 0
\(176\) −6.92820 4.00000i −0.522233 0.301511i
\(177\) −8.10634 + 8.10634i −0.609310 + 0.609310i
\(178\) 8.48528 + 4.89898i 0.635999 + 0.367194i
\(179\) 9.32051 0.696647 0.348324 0.937374i \(-0.386751\pi\)
0.348324 + 0.937374i \(0.386751\pi\)
\(180\) 0 0
\(181\) −0.0717968 −0.00533661 −0.00266831 0.999996i \(-0.500849\pi\)
−0.00266831 + 0.999996i \(0.500849\pi\)
\(182\) 12.3998 + 7.15900i 0.919131 + 0.530660i
\(183\) −2.12132 + 2.12132i −0.156813 + 0.156813i
\(184\) −14.9282 + 14.9282i −1.10052 + 1.10052i
\(185\) 0 0
\(186\) 5.09808 1.36603i 0.373809 0.100162i
\(187\) −8.48528 8.48528i −0.620505 0.620505i
\(188\) −0.480473 + 1.79315i −0.0350421 + 0.130779i
\(189\) 4.46410i 0.324716i
\(190\) 0 0
\(191\) 3.07180i 0.222267i −0.993805 0.111134i \(-0.964552\pi\)
0.993805 0.111134i \(-0.0354482\pi\)
\(192\) −5.65685 + 5.65685i −0.408248 + 0.408248i
\(193\) −7.26054 7.26054i −0.522625 0.522625i 0.395738 0.918363i \(-0.370489\pi\)
−0.918363 + 0.395738i \(0.870489\pi\)
\(194\) 3.56218 + 13.2942i 0.255749 + 0.954470i
\(195\) 0 0
\(196\) 22.3923 12.9282i 1.59945 0.923443i
\(197\) −4.52004 + 4.52004i −0.322040 + 0.322040i −0.849549 0.527509i \(-0.823126\pi\)
0.527509 + 0.849549i \(0.323126\pi\)
\(198\) −1.41421 + 2.44949i −0.100504 + 0.174078i
\(199\) −10.1244 −0.717697 −0.358848 0.933396i \(-0.616830\pi\)
−0.358848 + 0.933396i \(0.616830\pi\)
\(200\) 0 0
\(201\) 5.53590 0.390472
\(202\) −3.86370 + 6.69213i −0.271849 + 0.470857i
\(203\) 1.69161 1.69161i 0.118728 0.118728i
\(204\) −10.3923 + 6.00000i −0.727607 + 0.420084i
\(205\) 0 0
\(206\) 2.53590 + 9.46410i 0.176684 + 0.659395i
\(207\) 5.27792 + 5.27792i 0.366841 + 0.366841i
\(208\) 8.76268 2.34795i 0.607583 0.162801i
\(209\) 6.39230i 0.442165i
\(210\) 0 0
\(211\) 3.19615i 0.220032i 0.993930 + 0.110016i \(0.0350902\pi\)
−0.993930 + 0.110016i \(0.964910\pi\)
\(212\) 2.82843 10.5558i 0.194257 0.724978i
\(213\) 1.79315 + 1.79315i 0.122865 + 0.122865i
\(214\) 18.3923 4.92820i 1.25727 0.336885i
\(215\) 0 0
\(216\) 2.00000 + 2.00000i 0.136083 + 0.136083i
\(217\) −11.7806 + 11.7806i −0.799718 + 0.799718i
\(218\) −8.57321 4.94975i −0.580651 0.335239i
\(219\) −4.00000 −0.270295
\(220\) 0 0
\(221\) 13.6077 0.915353
\(222\) −13.3843 7.72741i −0.898293 0.518630i
\(223\) −6.64136 + 6.64136i −0.444739 + 0.444739i −0.893601 0.448862i \(-0.851829\pi\)
0.448862 + 0.893601i \(0.351829\pi\)
\(224\) 6.53590 24.3923i 0.436698 1.62978i
\(225\) 0 0
\(226\) 18.9282 5.07180i 1.25909 0.337371i
\(227\) 5.93426 + 5.93426i 0.393870 + 0.393870i 0.876064 0.482194i \(-0.160160\pi\)
−0.482194 + 0.876064i \(0.660160\pi\)
\(228\) 6.17449 + 1.65445i 0.408916 + 0.109569i
\(229\) 2.85641i 0.188757i 0.995536 + 0.0943783i \(0.0300863\pi\)
−0.995536 + 0.0943783i \(0.969914\pi\)
\(230\) 0 0
\(231\) 8.92820i 0.587433i
\(232\) 1.51575i 0.0995138i
\(233\) 5.93426 + 5.93426i 0.388766 + 0.388766i 0.874247 0.485481i \(-0.161356\pi\)
−0.485481 + 0.874247i \(0.661356\pi\)
\(234\) −0.830127 3.09808i −0.0542671 0.202528i
\(235\) 0 0
\(236\) −11.4641 19.8564i −0.746249 1.29254i
\(237\) 5.27792 5.27792i 0.342838 0.342838i
\(238\) 18.9396 32.8043i 1.22767 2.12639i
\(239\) 10.5359 0.681511 0.340755 0.940152i \(-0.389317\pi\)
0.340755 + 0.940152i \(0.389317\pi\)
\(240\) 0 0
\(241\) 12.8564 0.828154 0.414077 0.910242i \(-0.364104\pi\)
0.414077 + 0.910242i \(0.364104\pi\)
\(242\) −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
\(246\) −0.535898 2.00000i −0.0341676 0.127515i
\(247\) −5.12561 5.12561i −0.326135 0.326135i
\(248\) 10.5558i 0.670296i
\(249\) 12.9282i 0.819292i
\(250\) 0 0
\(251\) 29.8564i 1.88452i −0.334883 0.942260i \(-0.608697\pi\)
0.334883 0.942260i \(-0.391303\pi\)
\(252\) −8.62398 2.31079i −0.543260 0.145566i
\(253\) −10.5558 10.5558i −0.663640 0.663640i
\(254\) −14.9282 + 4.00000i −0.936679 + 0.250982i
\(255\) 0 0
\(256\) −8.00000 13.8564i −0.500000 0.866025i
\(257\) 20.3538 20.3538i 1.26963 1.26963i 0.323358 0.946277i \(-0.395188\pi\)
0.946277 0.323358i \(-0.104812\pi\)
\(258\) 5.46739 + 3.15660i 0.340385 + 0.196521i
\(259\) 48.7846 3.03133
\(260\) 0 0
\(261\) −0.535898 −0.0331713
\(262\) −3.10583 1.79315i −0.191879 0.110781i
\(263\) −10.2784 + 10.2784i −0.633795 + 0.633795i −0.949018 0.315223i \(-0.897921\pi\)
0.315223 + 0.949018i \(0.397921\pi\)
\(264\) −4.00000 4.00000i −0.246183 0.246183i
\(265\) 0 0
\(266\) −19.4904 + 5.22243i −1.19503 + 0.320208i
\(267\) 4.89898 + 4.89898i 0.299813 + 0.299813i
\(268\) −2.86559 + 10.6945i −0.175044 + 0.653273i
\(269\) 22.3923i 1.36528i 0.730753 + 0.682641i \(0.239169\pi\)
−0.730753 + 0.682641i \(0.760831\pi\)
\(270\) 0 0
\(271\) 24.2487i 1.47300i 0.676435 + 0.736502i \(0.263524\pi\)
−0.676435 + 0.736502i \(0.736476\pi\)
\(272\) −6.21166 23.1822i −0.376637 1.40563i
\(273\) 7.15900 + 7.15900i 0.433282 + 0.433282i
\(274\) 5.66025 + 21.1244i 0.341948 + 1.27617i
\(275\) 0 0
\(276\) −12.9282 + 7.46410i −0.778186 + 0.449286i
\(277\) 6.50266 6.50266i 0.390707 0.390707i −0.484232 0.874939i \(-0.660901\pi\)
0.874939 + 0.484232i \(0.160901\pi\)
\(278\) 8.86422 15.3533i 0.531641 0.920828i
\(279\) 3.73205 0.223432
\(280\) 0 0
\(281\) 6.39230 0.381333 0.190666 0.981655i \(-0.438935\pi\)
0.190666 + 0.981655i \(0.438935\pi\)
\(282\) −0.656339 + 1.13681i −0.0390844 + 0.0676962i
\(283\) −0.429705 + 0.429705i −0.0255433 + 0.0255433i −0.719763 0.694220i \(-0.755750\pi\)
0.694220 + 0.719763i \(0.255750\pi\)
\(284\) −4.39230 + 2.53590i −0.260635 + 0.150478i
\(285\) 0 0
\(286\) 1.66025 + 6.19615i 0.0981729 + 0.366386i
\(287\) 4.62158 + 4.62158i 0.272803 + 0.272803i
\(288\) −4.89898 + 2.82843i −0.288675 + 0.166667i
\(289\) 19.0000i 1.11765i
\(290\) 0 0
\(291\) 9.73205i 0.570503i
\(292\) 2.07055 7.72741i 0.121170 0.452212i
\(293\) −13.7632 13.7632i −0.804055 0.804055i 0.179672 0.983727i \(-0.442496\pi\)
−0.983727 + 0.179672i \(0.942496\pi\)
\(294\) 17.6603 4.73205i 1.02997 0.275979i
\(295\) 0 0
\(296\) 21.8564 21.8564i 1.27038 1.27038i
\(297\) −1.41421 + 1.41421i −0.0820610 + 0.0820610i
\(298\) 14.5211 + 8.38375i 0.841183 + 0.485657i
\(299\) 16.9282 0.978983
\(300\) 0 0
\(301\) −19.9282 −1.14864
\(302\) −9.46979 5.46739i −0.544925 0.314613i
\(303\) −3.86370 + 3.86370i −0.221964 + 0.221964i
\(304\) −6.39230 + 11.0718i −0.366624 + 0.635011i
\(305\) 0 0
\(306\) −8.19615 + 2.19615i −0.468543 + 0.125546i
\(307\) −5.22715 5.22715i −0.298329 0.298329i 0.542030 0.840359i \(-0.317656\pi\)
−0.840359 + 0.542030i \(0.817656\pi\)
\(308\) 17.2480 + 4.62158i 0.982794 + 0.263339i
\(309\) 6.92820i 0.394132i
\(310\) 0 0
\(311\) 20.5359i 1.16448i 0.813016 + 0.582242i \(0.197824\pi\)
−0.813016 + 0.582242i \(0.802176\pi\)
\(312\) 6.41473 0.363163
\(313\) 11.4016 + 11.4016i 0.644459 + 0.644459i 0.951648 0.307190i \(-0.0993885\pi\)
−0.307190 + 0.951648i \(0.599389\pi\)
\(314\) −2.29423 8.56218i −0.129471 0.483192i
\(315\) 0 0
\(316\) 7.46410 + 12.9282i 0.419889 + 0.727268i
\(317\) −4.89898 + 4.89898i −0.275154 + 0.275154i −0.831171 0.556017i \(-0.812329\pi\)
0.556017 + 0.831171i \(0.312329\pi\)
\(318\) 3.86370 6.69213i 0.216666 0.375276i
\(319\) 1.07180 0.0600091
\(320\) 0 0
\(321\) 13.4641 0.751493
\(322\) 23.5612 40.8091i 1.31301 2.27420i
\(323\) −13.5601 + 13.5601i −0.754506 + 0.754506i
\(324\) 1.00000 + 1.73205i 0.0555556 + 0.0962250i
\(325\) 0 0
\(326\) 2.75833 + 10.2942i 0.152770 + 0.570145i
\(327\) −4.94975 4.94975i −0.273722 0.273722i
\(328\) 4.14110 0.228654
\(329\) 4.14359i 0.228444i
\(330\) 0 0
\(331\) 18.3923i 1.01093i −0.862846 0.505466i \(-0.831321\pi\)
0.862846 0.505466i \(-0.168679\pi\)
\(332\) −24.9754 6.69213i −1.37070 0.367278i
\(333\) −7.72741 7.72741i −0.423459 0.423459i
\(334\) −22.3923 + 6.00000i −1.22525 + 0.328305i
\(335\) 0 0
\(336\) 8.92820 15.4641i 0.487073 0.843636i
\(337\) −20.2659 + 20.2659i −1.10395 + 1.10395i −0.110023 + 0.993929i \(0.535092\pi\)
−0.993929 + 0.110023i \(0.964908\pi\)
\(338\) 9.62209 + 5.55532i 0.523373 + 0.302169i
\(339\) 13.8564 0.752577
\(340\) 0 0
\(341\) −7.46410 −0.404204
\(342\) 3.91447 + 2.26002i 0.211670 + 0.122208i
\(343\) −18.7129 + 18.7129i −1.01040 + 1.01040i
\(344\) −8.92820 + 8.92820i −0.481376 + 0.481376i
\(345\) 0 0
\(346\) −6.73205 + 1.80385i −0.361917 + 0.0969754i
\(347\) −17.6269 17.6269i −0.946262 0.946262i 0.0523663 0.998628i \(-0.483324\pi\)
−0.998628 + 0.0523663i \(0.983324\pi\)
\(348\) 0.277401 1.03528i 0.0148703 0.0554966i
\(349\) 23.8564i 1.27700i −0.769620 0.638502i \(-0.779554\pi\)
0.769620 0.638502i \(-0.220446\pi\)
\(350\) 0 0
\(351\) 2.26795i 0.121054i
\(352\) 9.79796 5.65685i 0.522233 0.301511i
\(353\) −8.38375 8.38375i −0.446222 0.446222i 0.447875 0.894096i \(-0.352181\pi\)
−0.894096 + 0.447875i \(0.852181\pi\)
\(354\) −4.19615 15.6603i −0.223023 0.832333i
\(355\) 0 0
\(356\) −12.0000 + 6.92820i −0.635999 + 0.367194i
\(357\) 18.9396 18.9396i 1.00239 1.00239i
\(358\) −6.59059 + 11.4152i −0.348324 + 0.603314i
\(359\) −3.60770 −0.190407 −0.0952034 0.995458i \(-0.530350\pi\)
−0.0952034 + 0.995458i \(0.530350\pi\)
\(360\) 0 0
\(361\) −8.78461 −0.462348
\(362\) 0.0507680 0.0879327i 0.00266831 0.00462164i
\(363\) −4.94975 + 4.94975i −0.259794 + 0.259794i
\(364\) −17.5359 + 10.1244i −0.919131 + 0.530660i
\(365\) 0 0
\(366\) −1.09808 4.09808i −0.0573974 0.214210i
\(367\) 22.1977 + 22.1977i 1.15871 + 1.15871i 0.984753 + 0.173958i \(0.0556557\pi\)
0.173958 + 0.984753i \(0.444344\pi\)
\(368\) −7.72741 28.8391i −0.402819 1.50334i
\(369\) 1.46410i 0.0762181i
\(370\) 0 0
\(371\) 24.3923i 1.26639i
\(372\) −1.93185 + 7.20977i −0.100162 + 0.373809i
\(373\) −25.9227 25.9227i −1.34223 1.34223i −0.893839 0.448388i \(-0.851998\pi\)
−0.448388 0.893839i \(-0.648002\pi\)
\(374\) 16.3923 4.39230i 0.847626 0.227121i
\(375\) 0 0
\(376\) −1.85641 1.85641i −0.0957369 0.0957369i
\(377\) −0.859411 + 0.859411i −0.0442619 + 0.0442619i
\(378\) −5.46739 3.15660i −0.281212 0.162358i
\(379\) 12.2679 0.630162 0.315081 0.949065i \(-0.397968\pi\)
0.315081 + 0.949065i \(0.397968\pi\)
\(380\) 0 0
\(381\) −10.9282 −0.559869
\(382\) 3.76217 + 2.17209i 0.192489 + 0.111134i
\(383\) 17.5254 17.5254i 0.895504 0.895504i −0.0995302 0.995035i \(-0.531734\pi\)
0.995035 + 0.0995302i \(0.0317340\pi\)
\(384\) −2.92820 10.9282i −0.149429 0.557678i
\(385\) 0 0
\(386\) 14.0263 3.75833i 0.713919 0.191294i
\(387\) 3.15660 + 3.15660i 0.160459 + 0.160459i
\(388\) −18.8009 5.03768i −0.954470 0.255749i
\(389\) 21.4641i 1.08827i 0.838997 + 0.544137i \(0.183143\pi\)
−0.838997 + 0.544137i \(0.816857\pi\)
\(390\) 0 0
\(391\) 44.7846i 2.26486i
\(392\) 36.5665i 1.84689i
\(393\) −1.79315 1.79315i −0.0904525 0.0904525i
\(394\) −2.33975 8.73205i −0.117875 0.439914i
\(395\) 0 0
\(396\) −2.00000 3.46410i −0.100504 0.174078i
\(397\) −8.19428 + 8.19428i −0.411259 + 0.411259i −0.882177 0.470918i \(-0.843923\pi\)
0.470918 + 0.882177i \(0.343923\pi\)
\(398\) 7.15900 12.3998i 0.358848 0.621543i
\(399\) −14.2679 −0.714291
\(400\) 0 0
\(401\) 29.1769 1.45703 0.728513 0.685032i \(-0.240212\pi\)
0.728513 + 0.685032i \(0.240212\pi\)
\(402\) −3.91447 + 6.78006i −0.195236 + 0.338159i
\(403\) 5.98502 5.98502i 0.298135 0.298135i
\(404\) −5.46410 9.46410i −0.271849 0.470857i
\(405\) 0 0
\(406\) 0.875644 + 3.26795i 0.0434575 + 0.162186i
\(407\) 15.4548 + 15.4548i 0.766067 + 0.766067i
\(408\) 16.9706i 0.840168i
\(409\) 13.7846i 0.681605i 0.940135 + 0.340803i \(0.110699\pi\)
−0.940135 + 0.340803i \(0.889301\pi\)
\(410\) 0 0
\(411\) 15.4641i 0.762788i
\(412\) −13.3843 3.58630i −0.659395 0.176684i
\(413\) 36.1875 + 36.1875i 1.78067 + 1.78067i
\(414\) −10.1962 + 2.73205i −0.501114 + 0.134273i
\(415\) 0 0
\(416\) −3.32051 + 12.3923i −0.162801 + 0.607583i
\(417\) 8.86422 8.86422i 0.434083 0.434083i
\(418\) −7.82894 4.52004i −0.382926 0.221082i
\(419\) −33.4641 −1.63483 −0.817414 0.576050i \(-0.804593\pi\)
−0.817414 + 0.576050i \(0.804593\pi\)
\(420\) 0 0
\(421\) −34.7846 −1.69530 −0.847649 0.530557i \(-0.821983\pi\)
−0.847649 + 0.530557i \(0.821983\pi\)
\(422\) −3.91447 2.26002i −0.190553 0.110016i
\(423\) −0.656339 + 0.656339i −0.0319123 + 0.0319123i
\(424\) 10.9282 + 10.9282i 0.530720 + 0.530720i
\(425\) 0 0
\(426\) −3.46410 + 0.928203i −0.167836 + 0.0449716i
\(427\) 9.46979 + 9.46979i 0.458275 + 0.458275i
\(428\) −6.96953 + 26.0106i −0.336885 + 1.25727i
\(429\) 4.53590i 0.218995i
\(430\) 0 0
\(431\) 29.7128i 1.43122i 0.698502 + 0.715608i \(0.253850\pi\)
−0.698502 + 0.715608i \(0.746150\pi\)
\(432\) −3.86370 + 1.03528i −0.185893 + 0.0498097i
\(433\) 25.1648 + 25.1648i 1.20935 + 1.20935i 0.971239 + 0.238106i \(0.0765265\pi\)
0.238106 + 0.971239i \(0.423474\pi\)
\(434\) −6.09808 22.7583i −0.292717 1.09243i
\(435\) 0 0
\(436\) 12.1244 7.00000i 0.580651 0.335239i
\(437\) −16.8690 + 16.8690i −0.806955 + 0.806955i
\(438\) 2.82843 4.89898i 0.135147 0.234082i
\(439\) −23.9808 −1.14454 −0.572270 0.820066i \(-0.693937\pi\)
−0.572270 + 0.820066i \(0.693937\pi\)
\(440\) 0 0
\(441\) 12.9282 0.615629
\(442\) −9.62209 + 16.6660i −0.457676 + 0.792719i
\(443\) −20.3538 + 20.3538i −0.967038 + 0.967038i −0.999474 0.0324359i \(-0.989674\pi\)
0.0324359 + 0.999474i \(0.489674\pi\)
\(444\) 18.9282 10.9282i 0.898293 0.518630i
\(445\) 0 0
\(446\) −3.43782 12.8301i −0.162786 0.607524i
\(447\) 8.38375 + 8.38375i 0.396538 + 0.396538i
\(448\) 25.2528 + 25.2528i 1.19308 + 1.19308i
\(449\) 6.14359i 0.289934i 0.989436 + 0.144967i \(0.0463076\pi\)
−0.989436 + 0.144967i \(0.953692\pi\)
\(450\) 0 0
\(451\) 2.92820i 0.137884i
\(452\) −7.17260 + 26.7685i −0.337371 + 1.25909i
\(453\) −5.46739 5.46739i −0.256880 0.256880i
\(454\) −11.4641 + 3.07180i −0.538037 + 0.144167i
\(455\) 0 0
\(456\) −6.39230 + 6.39230i −0.299347 + 0.299347i
\(457\) −13.9391 + 13.9391i −0.652042 + 0.652042i −0.953484 0.301442i \(-0.902532\pi\)
0.301442 + 0.953484i \(0.402532\pi\)
\(458\) −3.49837 2.01978i −0.163468 0.0943783i
\(459\) −6.00000 −0.280056
\(460\) 0 0
\(461\) 36.3923 1.69496 0.847479 0.530828i \(-0.178119\pi\)
0.847479 + 0.530828i \(0.178119\pi\)
\(462\) 10.9348 + 6.31319i 0.508732 + 0.293716i
\(463\) 19.0411 19.0411i 0.884916 0.884916i −0.109114 0.994029i \(-0.534801\pi\)
0.994029 + 0.109114i \(0.0348012\pi\)
\(464\) 1.85641 + 1.07180i 0.0861815 + 0.0497569i
\(465\) 0 0
\(466\) −11.4641 + 3.07180i −0.531064 + 0.142298i
\(467\) 2.44949 + 2.44949i 0.113349 + 0.113349i 0.761506 0.648157i \(-0.224460\pi\)
−0.648157 + 0.761506i \(0.724460\pi\)
\(468\) 4.38134 + 1.17398i 0.202528 + 0.0542671i
\(469\) 24.7128i 1.14113i
\(470\) 0 0
\(471\) 6.26795i 0.288812i
\(472\) 32.4254 1.49250
\(473\) −6.31319 6.31319i −0.290281 0.290281i
\(474\) 2.73205 + 10.1962i 0.125487 + 0.468325i
\(475\) 0 0
\(476\) 26.7846 + 46.3923i 1.22767 + 2.12639i
\(477\) 3.86370 3.86370i 0.176907 0.176907i
\(478\) −7.45001 + 12.9038i −0.340755 + 0.590206i
\(479\) 21.3205 0.974159 0.487079 0.873358i \(-0.338062\pi\)
0.487079 + 0.873358i \(0.338062\pi\)
\(480\) 0 0
\(481\) −24.7846 −1.13008
\(482\) −9.09085 + 15.7458i −0.414077 + 0.717202i
\(483\) 23.5612 23.5612i 1.07207 1.07207i
\(484\) −7.00000 12.1244i −0.318182 0.551107i
\(485\) 0 0
\(486\) 0.366025 + 1.36603i 0.0166032 + 0.0619642i
\(487\) −20.1272 20.1272i −0.912049 0.912049i 0.0843846 0.996433i \(-0.473108\pi\)
−0.996433 + 0.0843846i \(0.973108\pi\)
\(488\) 8.48528 0.384111
\(489\) 7.53590i 0.340785i
\(490\) 0 0
\(491\) 34.6410i 1.56333i −0.623700 0.781664i \(-0.714371\pi\)
0.623700 0.781664i \(-0.285629\pi\)
\(492\) 2.82843 + 0.757875i 0.127515 + 0.0341676i
\(493\) 2.27362 + 2.27362i 0.102399 + 0.102399i
\(494\) 9.90192 2.65321i 0.445509 0.119374i
\(495\) 0 0
\(496\) −12.9282 7.46410i −0.580493 0.335148i
\(497\) 8.00481 8.00481i 0.359065 0.359065i
\(498\) −15.8338 9.14162i −0.709527 0.409646i
\(499\) −30.1244 −1.34855 −0.674276 0.738480i \(-0.735544\pi\)
−0.674276 + 0.738480i \(0.735544\pi\)
\(500\) 0 0
\(501\) −16.3923 −0.732354
\(502\) 36.5665 + 21.1117i 1.63204 + 0.942260i
\(503\) −0.277401 + 0.277401i −0.0123687 + 0.0123687i −0.713264 0.700895i \(-0.752784\pi\)
0.700895 + 0.713264i \(0.252784\pi\)
\(504\) 8.92820 8.92820i 0.397694 0.397694i
\(505\) 0 0
\(506\) 20.3923 5.46410i 0.906549 0.242909i
\(507\) 5.55532 + 5.55532i 0.246720 + 0.246720i
\(508\) 5.65685 21.1117i 0.250982 0.936679i
\(509\) 24.9282i 1.10492i −0.833538 0.552462i \(-0.813689\pi\)
0.833538 0.552462i \(-0.186311\pi\)
\(510\) 0 0
\(511\) 17.8564i 0.789921i
\(512\) 22.6274 1.00000
\(513\) 2.26002 + 2.26002i 0.0997824 + 0.0997824i
\(514\) 10.5359 + 39.3205i 0.464719 + 1.73435i
\(515\) 0 0
\(516\) −7.73205 + 4.46410i −0.340385 + 0.196521i
\(517\) 1.31268 1.31268i 0.0577315 0.0577315i
\(518\) −34.4959 + 59.7487i −1.51566 + 2.62521i
\(519\) −4.92820 −0.216324
\(520\) 0 0
\(521\) −38.3923 −1.68200 −0.840999 0.541037i \(-0.818032\pi\)
−0.840999 + 0.541037i \(0.818032\pi\)
\(522\) 0.378937 0.656339i 0.0165856 0.0287272i
\(523\) 0.984508 0.984508i 0.0430495 0.0430495i −0.685254 0.728304i \(-0.740309\pi\)
0.728304 + 0.685254i \(0.240309\pi\)
\(524\) 4.39230 2.53590i 0.191879 0.110781i
\(525\) 0 0
\(526\) −5.32051 19.8564i −0.231985 0.865780i
\(527\) −15.8338 15.8338i −0.689729 0.689729i
\(528\) 7.72741 2.07055i 0.336292 0.0901092i
\(529\) 32.7128i 1.42230i
\(530\) 0 0
\(531\) 11.4641i 0.497500i
\(532\) 7.38563 27.5636i 0.320208 1.19503i
\(533\) −2.34795 2.34795i −0.101701 0.101701i
\(534\) −9.46410 + 2.53590i −0.409552 + 0.109739i
\(535\) 0 0
\(536\) −11.0718 11.0718i −0.478229 0.478229i
\(537\) −6.59059 + 6.59059i −0.284405 + 0.284405i
\(538\) −27.4249 15.8338i −1.18237 0.682641i
\(539\) −25.8564 −1.11371
\(540\) 0 0
\(541\) 7.78461 0.334687 0.167343 0.985899i \(-0.446481\pi\)
0.167343 + 0.985899i \(0.446481\pi\)
\(542\) −29.6985 17.1464i −1.27566 0.736502i
\(543\) 0.0507680 0.0507680i 0.00217866 0.00217866i
\(544\) 32.7846 + 8.78461i 1.40563 + 0.376637i
\(545\) 0 0
\(546\) −13.8301 + 3.70577i −0.591875 + 0.158592i
\(547\) −11.8685 11.8685i −0.507461 0.507461i 0.406285 0.913746i \(-0.366824\pi\)
−0.913746 + 0.406285i \(0.866824\pi\)
\(548\) −29.8744 8.00481i −1.27617 0.341948i
\(549\) 3.00000i 0.128037i
\(550\) 0 0
\(551\) 1.71281i 0.0729683i
\(552\) 21.1117i 0.898572i
\(553\) −23.5612 23.5612i −1.00192 1.00192i
\(554\) 3.36603 + 12.5622i 0.143009 + 0.533716i
\(555\) 0 0
\(556\) 12.5359 + 21.7128i 0.531641 + 0.920828i
\(557\) −8.66115 + 8.66115i −0.366985 + 0.366985i −0.866376 0.499392i \(-0.833557\pi\)
0.499392 + 0.866376i \(0.333557\pi\)
\(558\) −2.63896 + 4.57081i −0.111716 + 0.193498i
\(559\) 10.1244 0.428215
\(560\) 0 0
\(561\) 12.0000 0.506640
\(562\) −4.52004 + 7.82894i −0.190666 + 0.330244i
\(563\) 27.7023 27.7023i 1.16751 1.16751i 0.184720 0.982791i \(-0.440862\pi\)
0.982791 0.184720i \(-0.0591378\pi\)
\(564\) −0.928203 1.60770i −0.0390844 0.0676962i
\(565\) 0 0
\(566\) −0.222432 0.830127i −0.00934951 0.0348928i
\(567\) −3.15660 3.15660i −0.132565 0.132565i
\(568\) 7.17260i 0.300956i
\(569\) 17.3205i 0.726113i −0.931767 0.363057i \(-0.881733\pi\)
0.931767 0.363057i \(-0.118267\pi\)
\(570\) 0 0
\(571\) 27.1962i 1.13812i 0.822295 + 0.569062i \(0.192693\pi\)
−0.822295 + 0.569062i \(0.807307\pi\)
\(572\) −8.76268 2.34795i −0.366386 0.0981729i
\(573\) 2.17209 + 2.17209i 0.0907403 + 0.0907403i
\(574\) −8.92820 + 2.39230i −0.372656 + 0.0998529i
\(575\) 0 0
\(576\) 8.00000i 0.333333i
\(577\) 23.0943 23.0943i 0.961428 0.961428i −0.0378555 0.999283i \(-0.512053\pi\)
0.999283 + 0.0378555i \(0.0120527\pi\)
\(578\) 23.2702 + 13.4350i 0.967911 + 0.558824i
\(579\) 10.2679 0.426721
\(580\) 0 0
\(581\) 57.7128 2.39433
\(582\) −11.9193 6.88160i −0.494070 0.285251i
\(583\) −7.72741 + 7.72741i −0.320036 + 0.320036i
\(584\) 8.00000 + 8.00000i 0.331042 + 0.331042i
\(585\) 0 0
\(586\) 26.5885 7.12436i 1.09836 0.294304i
\(587\) −10.8332 10.8332i −0.447135 0.447135i 0.447266 0.894401i \(-0.352398\pi\)
−0.894401 + 0.447266i \(0.852398\pi\)
\(588\) −6.69213 + 24.9754i −0.275979 + 1.02997i
\(589\) 11.9282i 0.491493i
\(590\) 0 0
\(591\) 6.39230i 0.262944i
\(592\) 11.3137 + 42.2233i 0.464991 + 1.73537i
\(593\) 8.20788 + 8.20788i 0.337057 + 0.337057i 0.855259 0.518201i \(-0.173398\pi\)
−0.518201 + 0.855259i \(0.673398\pi\)
\(594\) −0.732051 2.73205i −0.0300364 0.112097i
\(595\) 0 0
\(596\) −20.5359 + 11.8564i −0.841183 + 0.485657i
\(597\) 7.15900 7.15900i 0.292998 0.292998i
\(598\) −11.9700 + 20.7327i −0.489492 + 0.847824i
\(599\) −22.6410 −0.925087 −0.462543 0.886597i \(-0.653063\pi\)
−0.462543 + 0.886597i \(0.653063\pi\)
\(600\) 0 0
\(601\) 21.7846 0.888613 0.444306 0.895875i \(-0.353450\pi\)
0.444306 + 0.895875i \(0.353450\pi\)
\(602\) 14.0914 24.4070i 0.574321 0.994754i
\(603\) −3.91447 + 3.91447i −0.159410 + 0.159410i
\(604\) 13.3923 7.73205i 0.544925 0.314613i
\(605\) 0 0
\(606\) −2.00000 7.46410i −0.0812444 0.303208i
\(607\) −25.2528 25.2528i −1.02498 1.02498i −0.999680 0.0252985i \(-0.991946\pi\)
−0.0252985 0.999680i \(-0.508054\pi\)
\(608\) −9.04008 15.6579i −0.366624 0.635011i
\(609\) 2.39230i 0.0969411i
\(610\) 0 0
\(611\) 2.10512i 0.0851639i
\(612\) 3.10583 11.5911i 0.125546 0.468543i
\(613\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(614\) 10.0981 2.70577i 0.407525 0.109196i
\(615\) 0 0
\(616\) −17.8564 + 17.8564i −0.719455 + 0.719455i
\(617\) 24.2175 24.2175i 0.974960 0.974960i −0.0247344 0.999694i \(-0.507874\pi\)
0.999694 + 0.0247344i \(0.00787400\pi\)
\(618\) −8.48528 4.89898i −0.341328 0.197066i
\(619\) −15.9808 −0.642321 −0.321161 0.947025i \(-0.604073\pi\)
−0.321161 + 0.947025i \(0.604073\pi\)
\(620\) 0 0
\(621\) −7.46410 −0.299524
\(622\) −25.1512 14.5211i −1.00847 0.582242i
\(623\) 21.8695 21.8695i 0.876185 0.876185i
\(624\) −4.53590 + 7.85641i −0.181581 + 0.314508i
\(625\) 0 0
\(626\) −22.0263 + 5.90192i −0.880347 + 0.235888i
\(627\) −4.52004 4.52004i −0.180513 0.180513i
\(628\) 12.1087 + 3.24453i 0.483192 + 0.129471i
\(629\) 65.5692i 2.61442i
\(630\) 0 0
\(631\) 29.5885i 1.17790i −0.808170 0.588949i \(-0.799542\pi\)
0.808170 0.588949i \(-0.200458\pi\)
\(632\) −21.1117 −0.839777
\(633\) −2.26002 2.26002i −0.0898278 0.0898278i
\(634\) −2.53590 9.46410i −0.100713 0.375867i
\(635\) 0 0
\(636\) 5.46410 + 9.46410i 0.216666 + 0.375276i
\(637\) 20.7327 20.7327i 0.821461 0.821461i
\(638\) −0.757875 + 1.31268i −0.0300045 + 0.0519694i
\(639\) −2.53590 −0.100319
\(640\) 0 0
\(641\) −44.7846 −1.76889 −0.884443 0.466648i \(-0.845461\pi\)
−0.884443 + 0.466648i \(0.845461\pi\)
\(642\) −9.52056 + 16.4901i −0.375746 + 0.650812i
\(643\) 21.8695 21.8695i 0.862451 0.862451i −0.129172 0.991622i \(-0.541232\pi\)
0.991622 + 0.129172i \(0.0412318\pi\)
\(644\) 33.3205 + 57.7128i 1.31301 + 2.27420i
\(645\) 0 0
\(646\) −7.01924 26.1962i −0.276168 1.03067i
\(647\) −13.3843 13.3843i −0.526190 0.526190i 0.393244 0.919434i \(-0.371353\pi\)
−0.919434 + 0.393244i \(0.871353\pi\)
\(648\) −2.82843 −0.111111
\(649\) 22.9282i 0.900011i
\(650\) 0 0
\(651\) 16.6603i 0.652967i
\(652\) −14.5582 3.90087i −0.570145 0.152770i
\(653\) 7.34847 + 7.34847i 0.287568 + 0.287568i 0.836118 0.548550i \(-0.184820\pi\)
−0.548550 + 0.836118i \(0.684820\pi\)
\(654\) 9.56218 2.56218i 0.373911 0.100189i
\(655\) 0 0
\(656\) −2.92820 + 5.07180i −0.114327 + 0.198020i
\(657\) 2.82843 2.82843i 0.110347 0.110347i
\(658\) 5.07484 + 2.92996i 0.197838 + 0.114222i
\(659\) 21.4641 0.836123 0.418061 0.908419i \(-0.362710\pi\)
0.418061 + 0.908419i \(0.362710\pi\)
\(660\) 0 0
\(661\) 19.8564 0.772325 0.386162 0.922431i \(-0.373800\pi\)
0.386162 + 0.922431i \(0.373800\pi\)
\(662\) 22.5259 + 13.0053i 0.875493 + 0.505466i
\(663\) −9.62209 + 9.62209i −0.373691 + 0.373691i
\(664\) 25.8564 25.8564i 1.00342 1.00342i
\(665\) 0 0
\(666\) 14.9282 4.00000i 0.578456 0.154997i
\(667\) 2.82843 + 2.82843i 0.109517 + 0.109517i
\(668\) 8.48528 31.6675i 0.328305 1.22525i
\(669\) 9.39230i 0.363127i
\(670\) 0 0
\(671\) 6.00000i 0.231627i
\(672\) 12.6264 + 21.8695i 0.487073 + 0.843636i
\(673\) −2.82843 2.82843i −0.109028 0.109028i 0.650488 0.759516i \(-0.274564\pi\)
−0.759516 + 0.650488i \(0.774564\pi\)
\(674\) −10.4904 39.1506i −0.404074 1.50803i
\(675\) 0 0
\(676\) −13.6077 + 7.85641i −0.523373 + 0.302169i
\(677\) −23.0807 + 23.0807i −0.887063 + 0.887063i −0.994240 0.107177i \(-0.965819\pi\)
0.107177 + 0.994240i \(0.465819\pi\)
\(678\) −9.79796 + 16.9706i −0.376288 + 0.651751i
\(679\) 43.4449 1.66726
\(680\) 0 0
\(681\) −8.39230 −0.321594
\(682\) 5.27792 9.14162i 0.202102 0.350051i
\(683\) −13.3843 + 13.3843i −0.512135 + 0.512135i −0.915180 0.403045i \(-0.867952\pi\)
0.403045 + 0.915180i \(0.367952\pi\)
\(684\) −5.53590 + 3.19615i −0.211670 + 0.122208i
\(685\) 0 0
\(686\) −9.68653 36.1506i −0.369834 1.38024i
\(687\) −2.01978 2.01978i −0.0770596 0.0770596i
\(688\) −4.62158 17.2480i −0.176196 0.657572i
\(689\) 12.3923i 0.472109i
\(690\) 0 0
\(691\) 9.32051i 0.354569i 0.984160 + 0.177284i \(0.0567312\pi\)
−0.984160 + 0.177284i \(0.943269\pi\)
\(692\) 2.55103 9.52056i 0.0969754 0.361917i
\(693\) 6.31319 + 6.31319i 0.239818 + 0.239818i
\(694\) 34.0526 9.12436i 1.29262 0.346356i
\(695\) 0 0
\(696\) 1.07180 + 1.07180i 0.0406264 + 0.0406264i
\(697\) −6.21166 + 6.21166i −0.235283 + 0.235283i
\(698\) 29.2180 + 16.8690i 1.10592 + 0.638502i
\(699\) −8.39230 −0.317426
\(700\) 0 0
\(701\) −8.53590 −0.322396 −0.161198 0.986922i \(-0.551536\pi\)
−0.161198 + 0.986922i \(0.551536\pi\)
\(702\) 2.77766 + 1.60368i 0.104836 + 0.0605271i
\(703\) 24.6980 24.6980i 0.931502 0.931502i
\(704\) 16.0000i 0.603023i
\(705\) 0 0
\(706\) 16.1962 4.33975i 0.609550 0.163328i
\(707\) 17.2480 + 17.2480i 0.648676 + 0.648676i
\(708\) 22.1469 + 5.93426i 0.832333 + 0.223023i
\(709\) 2.85641i 0.107275i 0.998560 + 0.0536373i \(0.0170815\pi\)
−0.998560 + 0.0536373i \(0.982919\pi\)
\(710\) 0 0
\(711\) 7.46410i 0.279926i
\(712\) 19.5959i 0.734388i
\(713\) −19.6975 19.6975i −0.737675 0.737675i
\(714\) 9.80385 + 36.5885i 0.366900 + 1.36929i
\(715\) 0 0
\(716\) −9.32051 16.1436i −0.348324 0.603314i
\(717\) −7.45001 + 7.45001i −0.278226 + 0.278226i
\(718\) 2.55103 4.41851i 0.0952034 0.164897i
\(719\) 0.928203 0.0346161 0.0173081 0.999850i \(-0.494490\pi\)
0.0173081 + 0.999850i \(0.494490\pi\)
\(720\) 0 0
\(721\) 30.9282 1.15183
\(722\) 6.21166 10.7589i 0.231174 0.400405i
\(723\) −9.09085 + 9.09085i −0.338092 + 0.338092i
\(724\) 0.0717968 + 0.124356i 0.00266831 + 0.00462164i
\(725\) 0 0
\(726\) −2.56218 9.56218i −0.0950913 0.354886i
\(727\) 20.5804 + 20.5804i 0.763286 + 0.763286i 0.976915 0.213629i \(-0.0685284\pi\)
−0.213629 + 0.976915i \(0.568528\pi\)
\(728\) 28.6360i 1.06132i
\(729\) 1.00000i 0.0370370i
\(730\) 0 0
\(731\) 26.7846i 0.990665i
\(732\) 5.79555 + 1.55291i 0.214210 + 0.0573974i
\(733\) 25.2528 + 25.2528i 0.932732 + 0.932732i 0.997876 0.0651435i \(-0.0207505\pi\)
−0.0651435 + 0.997876i \(0.520751\pi\)
\(734\) −42.8827 + 11.4904i −1.58283 + 0.424118i
\(735\) 0 0
\(736\) 40.7846 + 10.9282i 1.50334 + 0.402819i
\(737\) 7.82894 7.82894i 0.288383 0.288383i
\(738\) 1.79315 + 1.03528i 0.0660068 + 0.0381090i
\(739\) 6.39230 0.235145 0.117572 0.993064i \(-0.462489\pi\)
0.117572 + 0.993064i \(0.462489\pi\)
\(740\) 0 0
\(741\) 7.24871 0.266288
\(742\) −29.8744 17.2480i −1.09672 0.633193i
\(743\) −12.0716 + 12.0716i −0.442863 + 0.442863i −0.892973 0.450110i \(-0.851385\pi\)
0.450110 + 0.892973i \(0.351385\pi\)
\(744\) −7.46410 7.46410i −0.273647 0.273647i
\(745\) 0 0
\(746\) 50.0788 13.4186i 1.83352 0.491289i
\(747\) −9.14162 9.14162i −0.334474 0.334474i
\(748\) −6.21166 + 23.1822i −0.227121 + 0.847626i
\(749\) 60.1051i 2.19619i
\(750\) 0 0
\(751\) 4.53590i 0.165517i −0.996570 0.0827586i \(-0.973627\pi\)
0.996570 0.0827586i \(-0.0263731\pi\)
\(752\) 3.58630 0.960947i 0.130779 0.0350421i
\(753\) 21.1117 + 21.1117i 0.769352 + 0.769352i
\(754\) −0.444864 1.66025i −0.0162010 0.0604629i
\(755\) 0 0
\(756\) 7.73205 4.46410i 0.281212 0.162358i
\(757\) −13.2963 + 13.2963i −0.483263 + 0.483263i −0.906172 0.422909i \(-0.861009\pi\)
0.422909 + 0.906172i \(0.361009\pi\)
\(758\) −8.67475 + 15.0251i −0.315081 + 0.545736i
\(759\) 14.9282 0.541859
\(760\) 0 0
\(761\) −22.6410 −0.820736 −0.410368 0.911920i \(-0.634600\pi\)
−0.410368 + 0.911920i \(0.634600\pi\)
\(762\) 7.72741 13.3843i 0.279934 0.484861i
\(763\) −22.0962 + 22.0962i −0.799935 + 0.799935i
\(764\) −5.32051 + 3.07180i −0.192489 + 0.111134i
\(765\) 0 0
\(766\) 9.07180 + 33.8564i 0.327777 + 1.22328i
\(767\) −18.3848 18.3848i −0.663836 0.663836i
\(768\) 15.4548 + 4.14110i 0.557678 + 0.149429i
\(769\) 16.0718i 0.579564i 0.957093 + 0.289782i \(0.0935828\pi\)
−0.957093 + 0.289782i \(0.906417\pi\)
\(770\) 0 0
\(771\) 28.7846i 1.03665i
\(772\) −5.31508 + 19.8362i −0.191294 + 0.713919i
\(773\) 20.6312 + 20.6312i 0.742052 + 0.742052i 0.972973 0.230920i \(-0.0741736\pi\)
−0.230920 + 0.972973i \(0.574174\pi\)
\(774\) −6.09808 + 1.63397i −0.219191 + 0.0587320i
\(775\) 0 0
\(776\) 19.4641 19.4641i 0.698721 0.698721i
\(777\) −34.4959 + 34.4959i −1.23753 + 1.23753i
\(778\) −26.2880 15.1774i −0.942472 0.544137i
\(779\) 4.67949 0.167660
\(780\) 0 0
\(781\) 5.07180 0.181483
\(782\) 54.8497 + 31.6675i 1.96142 + 1.13243i
\(783\) 0.378937 0.378937i 0.0135421 0.0135421i
\(784\) −44.7846 25.8564i