Properties

Label 16.2.e.a.13.1
Level $16$
Weight $2$
Character 16.13
Analytic conductor $0.128$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 16 = 2^{4} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 16.e (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(0.127760643234\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(i)\)
Defining polynomial: \( x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 13.1
Root \(-1.00000i\) of defining polynomial
Character \(\chi\) \(=\) 16.13
Dual form 16.2.e.a.5.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.00000 + 1.00000i) q^{2} +(-1.00000 - 1.00000i) q^{3} -2.00000i q^{4} +(-1.00000 + 1.00000i) q^{5} +2.00000 q^{6} +2.00000i q^{7} +(2.00000 + 2.00000i) q^{8} -1.00000i q^{9} +O(q^{10})\) \(q+(-1.00000 + 1.00000i) q^{2} +(-1.00000 - 1.00000i) q^{3} -2.00000i q^{4} +(-1.00000 + 1.00000i) q^{5} +2.00000 q^{6} +2.00000i q^{7} +(2.00000 + 2.00000i) q^{8} -1.00000i q^{9} -2.00000i q^{10} +(1.00000 - 1.00000i) q^{11} +(-2.00000 + 2.00000i) q^{12} +(-1.00000 - 1.00000i) q^{13} +(-2.00000 - 2.00000i) q^{14} +2.00000 q^{15} -4.00000 q^{16} -2.00000 q^{17} +(1.00000 + 1.00000i) q^{18} +(3.00000 + 3.00000i) q^{19} +(2.00000 + 2.00000i) q^{20} +(2.00000 - 2.00000i) q^{21} +2.00000i q^{22} -6.00000i q^{23} -4.00000i q^{24} +3.00000i q^{25} +2.00000 q^{26} +(-4.00000 + 4.00000i) q^{27} +4.00000 q^{28} +(3.00000 + 3.00000i) q^{29} +(-2.00000 + 2.00000i) q^{30} -8.00000 q^{31} +(4.00000 - 4.00000i) q^{32} -2.00000 q^{33} +(2.00000 - 2.00000i) q^{34} +(-2.00000 - 2.00000i) q^{35} -2.00000 q^{36} +(3.00000 - 3.00000i) q^{37} -6.00000 q^{38} +2.00000i q^{39} -4.00000 q^{40} +4.00000i q^{42} +(5.00000 - 5.00000i) q^{43} +(-2.00000 - 2.00000i) q^{44} +(1.00000 + 1.00000i) q^{45} +(6.00000 + 6.00000i) q^{46} +8.00000 q^{47} +(4.00000 + 4.00000i) q^{48} +3.00000 q^{49} +(-3.00000 - 3.00000i) q^{50} +(2.00000 + 2.00000i) q^{51} +(-2.00000 + 2.00000i) q^{52} +(-5.00000 + 5.00000i) q^{53} -8.00000i q^{54} +2.00000i q^{55} +(-4.00000 + 4.00000i) q^{56} -6.00000i q^{57} -6.00000 q^{58} +(-3.00000 + 3.00000i) q^{59} -4.00000i q^{60} +(-9.00000 - 9.00000i) q^{61} +(8.00000 - 8.00000i) q^{62} +2.00000 q^{63} +8.00000i q^{64} +2.00000 q^{65} +(2.00000 - 2.00000i) q^{66} +(-5.00000 - 5.00000i) q^{67} +4.00000i q^{68} +(-6.00000 + 6.00000i) q^{69} +4.00000 q^{70} +10.0000i q^{71} +(2.00000 - 2.00000i) q^{72} +4.00000i q^{73} +6.00000i q^{74} +(3.00000 - 3.00000i) q^{75} +(6.00000 - 6.00000i) q^{76} +(2.00000 + 2.00000i) q^{77} +(-2.00000 - 2.00000i) q^{78} +(4.00000 - 4.00000i) q^{80} +5.00000 q^{81} +(-1.00000 - 1.00000i) q^{83} +(-4.00000 - 4.00000i) q^{84} +(2.00000 - 2.00000i) q^{85} +10.0000i q^{86} -6.00000i q^{87} +4.00000 q^{88} -4.00000i q^{89} -2.00000 q^{90} +(2.00000 - 2.00000i) q^{91} -12.0000 q^{92} +(8.00000 + 8.00000i) q^{93} +(-8.00000 + 8.00000i) q^{94} -6.00000 q^{95} -8.00000 q^{96} -2.00000 q^{97} +(-3.00000 + 3.00000i) q^{98} +(-1.00000 - 1.00000i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - 2 q^{2} - 2 q^{3} - 2 q^{5} + 4 q^{6} + 4 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 2 q - 2 q^{2} - 2 q^{3} - 2 q^{5} + 4 q^{6} + 4 q^{8} + 2 q^{11} - 4 q^{12} - 2 q^{13} - 4 q^{14} + 4 q^{15} - 8 q^{16} - 4 q^{17} + 2 q^{18} + 6 q^{19} + 4 q^{20} + 4 q^{21} + 4 q^{26} - 8 q^{27} + 8 q^{28} + 6 q^{29} - 4 q^{30} - 16 q^{31} + 8 q^{32} - 4 q^{33} + 4 q^{34} - 4 q^{35} - 4 q^{36} + 6 q^{37} - 12 q^{38} - 8 q^{40} + 10 q^{43} - 4 q^{44} + 2 q^{45} + 12 q^{46} + 16 q^{47} + 8 q^{48} + 6 q^{49} - 6 q^{50} + 4 q^{51} - 4 q^{52} - 10 q^{53} - 8 q^{56} - 12 q^{58} - 6 q^{59} - 18 q^{61} + 16 q^{62} + 4 q^{63} + 4 q^{65} + 4 q^{66} - 10 q^{67} - 12 q^{69} + 8 q^{70} + 4 q^{72} + 6 q^{75} + 12 q^{76} + 4 q^{77} - 4 q^{78} + 8 q^{80} + 10 q^{81} - 2 q^{83} - 8 q^{84} + 4 q^{85} + 8 q^{88} - 4 q^{90} + 4 q^{91} - 24 q^{92} + 16 q^{93} - 16 q^{94} - 12 q^{95} - 16 q^{96} - 4 q^{97} - 6 q^{98} - 2 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/16\mathbb{Z}\right)^\times\).

\(n\) \(5\) \(15\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 + 1.00000i −0.707107 + 0.707107i
\(3\) −1.00000 1.00000i −0.577350 0.577350i 0.356822 0.934172i \(-0.383860\pi\)
−0.934172 + 0.356822i \(0.883860\pi\)
\(4\) 2.00000i 1.00000i
\(5\) −1.00000 + 1.00000i −0.447214 + 0.447214i −0.894427 0.447214i \(-0.852416\pi\)
0.447214 + 0.894427i \(0.352416\pi\)
\(6\) 2.00000 0.816497
\(7\) 2.00000i 0.755929i 0.925820 + 0.377964i \(0.123376\pi\)
−0.925820 + 0.377964i \(0.876624\pi\)
\(8\) 2.00000 + 2.00000i 0.707107 + 0.707107i
\(9\) 1.00000i 0.333333i
\(10\) 2.00000i 0.632456i
\(11\) 1.00000 1.00000i 0.301511 0.301511i −0.540094 0.841605i \(-0.681611\pi\)
0.841605 + 0.540094i \(0.181611\pi\)
\(12\) −2.00000 + 2.00000i −0.577350 + 0.577350i
\(13\) −1.00000 1.00000i −0.277350 0.277350i 0.554700 0.832050i \(-0.312833\pi\)
−0.832050 + 0.554700i \(0.812833\pi\)
\(14\) −2.00000 2.00000i −0.534522 0.534522i
\(15\) 2.00000 0.516398
\(16\) −4.00000 −1.00000
\(17\) −2.00000 −0.485071 −0.242536 0.970143i \(-0.577979\pi\)
−0.242536 + 0.970143i \(0.577979\pi\)
\(18\) 1.00000 + 1.00000i 0.235702 + 0.235702i
\(19\) 3.00000 + 3.00000i 0.688247 + 0.688247i 0.961844 0.273597i \(-0.0882135\pi\)
−0.273597 + 0.961844i \(0.588214\pi\)
\(20\) 2.00000 + 2.00000i 0.447214 + 0.447214i
\(21\) 2.00000 2.00000i 0.436436 0.436436i
\(22\) 2.00000i 0.426401i
\(23\) 6.00000i 1.25109i −0.780189 0.625543i \(-0.784877\pi\)
0.780189 0.625543i \(-0.215123\pi\)
\(24\) 4.00000i 0.816497i
\(25\) 3.00000i 0.600000i
\(26\) 2.00000 0.392232
\(27\) −4.00000 + 4.00000i −0.769800 + 0.769800i
\(28\) 4.00000 0.755929
\(29\) 3.00000 + 3.00000i 0.557086 + 0.557086i 0.928477 0.371391i \(-0.121119\pi\)
−0.371391 + 0.928477i \(0.621119\pi\)
\(30\) −2.00000 + 2.00000i −0.365148 + 0.365148i
\(31\) −8.00000 −1.43684 −0.718421 0.695608i \(-0.755135\pi\)
−0.718421 + 0.695608i \(0.755135\pi\)
\(32\) 4.00000 4.00000i 0.707107 0.707107i
\(33\) −2.00000 −0.348155
\(34\) 2.00000 2.00000i 0.342997 0.342997i
\(35\) −2.00000 2.00000i −0.338062 0.338062i
\(36\) −2.00000 −0.333333
\(37\) 3.00000 3.00000i 0.493197 0.493197i −0.416115 0.909312i \(-0.636609\pi\)
0.909312 + 0.416115i \(0.136609\pi\)
\(38\) −6.00000 −0.973329
\(39\) 2.00000i 0.320256i
\(40\) −4.00000 −0.632456
\(41\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(42\) 4.00000i 0.617213i
\(43\) 5.00000 5.00000i 0.762493 0.762493i −0.214280 0.976772i \(-0.568740\pi\)
0.976772 + 0.214280i \(0.0687403\pi\)
\(44\) −2.00000 2.00000i −0.301511 0.301511i
\(45\) 1.00000 + 1.00000i 0.149071 + 0.149071i
\(46\) 6.00000 + 6.00000i 0.884652 + 0.884652i
\(47\) 8.00000 1.16692 0.583460 0.812142i \(-0.301699\pi\)
0.583460 + 0.812142i \(0.301699\pi\)
\(48\) 4.00000 + 4.00000i 0.577350 + 0.577350i
\(49\) 3.00000 0.428571
\(50\) −3.00000 3.00000i −0.424264 0.424264i
\(51\) 2.00000 + 2.00000i 0.280056 + 0.280056i
\(52\) −2.00000 + 2.00000i −0.277350 + 0.277350i
\(53\) −5.00000 + 5.00000i −0.686803 + 0.686803i −0.961524 0.274721i \(-0.911414\pi\)
0.274721 + 0.961524i \(0.411414\pi\)
\(54\) 8.00000i 1.08866i
\(55\) 2.00000i 0.269680i
\(56\) −4.00000 + 4.00000i −0.534522 + 0.534522i
\(57\) 6.00000i 0.794719i
\(58\) −6.00000 −0.787839
\(59\) −3.00000 + 3.00000i −0.390567 + 0.390567i −0.874889 0.484323i \(-0.839066\pi\)
0.484323 + 0.874889i \(0.339066\pi\)
\(60\) 4.00000i 0.516398i
\(61\) −9.00000 9.00000i −1.15233 1.15233i −0.986084 0.166248i \(-0.946835\pi\)
−0.166248 0.986084i \(-0.553165\pi\)
\(62\) 8.00000 8.00000i 1.01600 1.01600i
\(63\) 2.00000 0.251976
\(64\) 8.00000i 1.00000i
\(65\) 2.00000 0.248069
\(66\) 2.00000 2.00000i 0.246183 0.246183i
\(67\) −5.00000 5.00000i −0.610847 0.610847i 0.332320 0.943167i \(-0.392169\pi\)
−0.943167 + 0.332320i \(0.892169\pi\)
\(68\) 4.00000i 0.485071i
\(69\) −6.00000 + 6.00000i −0.722315 + 0.722315i
\(70\) 4.00000 0.478091
\(71\) 10.0000i 1.18678i 0.804914 + 0.593391i \(0.202211\pi\)
−0.804914 + 0.593391i \(0.797789\pi\)
\(72\) 2.00000 2.00000i 0.235702 0.235702i
\(73\) 4.00000i 0.468165i 0.972217 + 0.234082i \(0.0752085\pi\)
−0.972217 + 0.234082i \(0.924791\pi\)
\(74\) 6.00000i 0.697486i
\(75\) 3.00000 3.00000i 0.346410 0.346410i
\(76\) 6.00000 6.00000i 0.688247 0.688247i
\(77\) 2.00000 + 2.00000i 0.227921 + 0.227921i
\(78\) −2.00000 2.00000i −0.226455 0.226455i
\(79\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(80\) 4.00000 4.00000i 0.447214 0.447214i
\(81\) 5.00000 0.555556
\(82\) 0 0
\(83\) −1.00000 1.00000i −0.109764 0.109764i 0.650092 0.759856i \(-0.274731\pi\)
−0.759856 + 0.650092i \(0.774731\pi\)
\(84\) −4.00000 4.00000i −0.436436 0.436436i
\(85\) 2.00000 2.00000i 0.216930 0.216930i
\(86\) 10.0000i 1.07833i
\(87\) 6.00000i 0.643268i
\(88\) 4.00000 0.426401
\(89\) 4.00000i 0.423999i −0.977270 0.212000i \(-0.932002\pi\)
0.977270 0.212000i \(-0.0679975\pi\)
\(90\) −2.00000 −0.210819
\(91\) 2.00000 2.00000i 0.209657 0.209657i
\(92\) −12.0000 −1.25109
\(93\) 8.00000 + 8.00000i 0.829561 + 0.829561i
\(94\) −8.00000 + 8.00000i −0.825137 + 0.825137i
\(95\) −6.00000 −0.615587
\(96\) −8.00000 −0.816497
\(97\) −2.00000 −0.203069 −0.101535 0.994832i \(-0.532375\pi\)
−0.101535 + 0.994832i \(0.532375\pi\)
\(98\) −3.00000 + 3.00000i −0.303046 + 0.303046i
\(99\) −1.00000 1.00000i −0.100504 0.100504i
\(100\) 6.00000 0.600000
\(101\) 11.0000 11.0000i 1.09454 1.09454i 0.0995037 0.995037i \(-0.468274\pi\)
0.995037 0.0995037i \(-0.0317255\pi\)
\(102\) −4.00000 −0.396059
\(103\) 6.00000i 0.591198i −0.955312 0.295599i \(-0.904481\pi\)
0.955312 0.295599i \(-0.0955191\pi\)
\(104\) 4.00000i 0.392232i
\(105\) 4.00000i 0.390360i
\(106\) 10.0000i 0.971286i
\(107\) −7.00000 + 7.00000i −0.676716 + 0.676716i −0.959256 0.282540i \(-0.908823\pi\)
0.282540 + 0.959256i \(0.408823\pi\)
\(108\) 8.00000 + 8.00000i 0.769800 + 0.769800i
\(109\) 3.00000 + 3.00000i 0.287348 + 0.287348i 0.836031 0.548683i \(-0.184871\pi\)
−0.548683 + 0.836031i \(0.684871\pi\)
\(110\) −2.00000 2.00000i −0.190693 0.190693i
\(111\) −6.00000 −0.569495
\(112\) 8.00000i 0.755929i
\(113\) −6.00000 −0.564433 −0.282216 0.959351i \(-0.591070\pi\)
−0.282216 + 0.959351i \(0.591070\pi\)
\(114\) 6.00000 + 6.00000i 0.561951 + 0.561951i
\(115\) 6.00000 + 6.00000i 0.559503 + 0.559503i
\(116\) 6.00000 6.00000i 0.557086 0.557086i
\(117\) −1.00000 + 1.00000i −0.0924500 + 0.0924500i
\(118\) 6.00000i 0.552345i
\(119\) 4.00000i 0.366679i
\(120\) 4.00000 + 4.00000i 0.365148 + 0.365148i
\(121\) 9.00000i 0.818182i
\(122\) 18.0000 1.62964
\(123\) 0 0
\(124\) 16.0000i 1.43684i
\(125\) −8.00000 8.00000i −0.715542 0.715542i
\(126\) −2.00000 + 2.00000i −0.178174 + 0.178174i
\(127\) 8.00000 0.709885 0.354943 0.934888i \(-0.384500\pi\)
0.354943 + 0.934888i \(0.384500\pi\)
\(128\) −8.00000 8.00000i −0.707107 0.707107i
\(129\) −10.0000 −0.880451
\(130\) −2.00000 + 2.00000i −0.175412 + 0.175412i
\(131\) 11.0000 + 11.0000i 0.961074 + 0.961074i 0.999270 0.0381958i \(-0.0121611\pi\)
−0.0381958 + 0.999270i \(0.512161\pi\)
\(132\) 4.00000i 0.348155i
\(133\) −6.00000 + 6.00000i −0.520266 + 0.520266i
\(134\) 10.0000 0.863868
\(135\) 8.00000i 0.688530i
\(136\) −4.00000 4.00000i −0.342997 0.342997i
\(137\) 8.00000i 0.683486i −0.939793 0.341743i \(-0.888983\pi\)
0.939793 0.341743i \(-0.111017\pi\)
\(138\) 12.0000i 1.02151i
\(139\) −3.00000 + 3.00000i −0.254457 + 0.254457i −0.822795 0.568338i \(-0.807586\pi\)
0.568338 + 0.822795i \(0.307586\pi\)
\(140\) −4.00000 + 4.00000i −0.338062 + 0.338062i
\(141\) −8.00000 8.00000i −0.673722 0.673722i
\(142\) −10.0000 10.0000i −0.839181 0.839181i
\(143\) −2.00000 −0.167248
\(144\) 4.00000i 0.333333i
\(145\) −6.00000 −0.498273
\(146\) −4.00000 4.00000i −0.331042 0.331042i
\(147\) −3.00000 3.00000i −0.247436 0.247436i
\(148\) −6.00000 6.00000i −0.493197 0.493197i
\(149\) 7.00000 7.00000i 0.573462 0.573462i −0.359632 0.933094i \(-0.617098\pi\)
0.933094 + 0.359632i \(0.117098\pi\)
\(150\) 6.00000i 0.489898i
\(151\) 10.0000i 0.813788i 0.913475 + 0.406894i \(0.133388\pi\)
−0.913475 + 0.406894i \(0.866612\pi\)
\(152\) 12.0000i 0.973329i
\(153\) 2.00000i 0.161690i
\(154\) −4.00000 −0.322329
\(155\) 8.00000 8.00000i 0.642575 0.642575i
\(156\) 4.00000 0.320256
\(157\) 15.0000 + 15.0000i 1.19713 + 1.19713i 0.975022 + 0.222108i \(0.0712939\pi\)
0.222108 + 0.975022i \(0.428706\pi\)
\(158\) 0 0
\(159\) 10.0000 0.793052
\(160\) 8.00000i 0.632456i
\(161\) 12.0000 0.945732
\(162\) −5.00000 + 5.00000i −0.392837 + 0.392837i
\(163\) −1.00000 1.00000i −0.0783260 0.0783260i 0.666858 0.745184i \(-0.267639\pi\)
−0.745184 + 0.666858i \(0.767639\pi\)
\(164\) 0 0
\(165\) 2.00000 2.00000i 0.155700 0.155700i
\(166\) 2.00000 0.155230
\(167\) 2.00000i 0.154765i 0.997001 + 0.0773823i \(0.0246562\pi\)
−0.997001 + 0.0773823i \(0.975344\pi\)
\(168\) 8.00000 0.617213
\(169\) 11.0000i 0.846154i
\(170\) 4.00000i 0.306786i
\(171\) 3.00000 3.00000i 0.229416 0.229416i
\(172\) −10.0000 10.0000i −0.762493 0.762493i
\(173\) −1.00000 1.00000i −0.0760286 0.0760286i 0.668070 0.744099i \(-0.267121\pi\)
−0.744099 + 0.668070i \(0.767121\pi\)
\(174\) 6.00000 + 6.00000i 0.454859 + 0.454859i
\(175\) −6.00000 −0.453557
\(176\) −4.00000 + 4.00000i −0.301511 + 0.301511i
\(177\) 6.00000 0.450988
\(178\) 4.00000 + 4.00000i 0.299813 + 0.299813i
\(179\) −17.0000 17.0000i −1.27064 1.27064i −0.945753 0.324887i \(-0.894674\pi\)
−0.324887 0.945753i \(-0.605326\pi\)
\(180\) 2.00000 2.00000i 0.149071 0.149071i
\(181\) −9.00000 + 9.00000i −0.668965 + 0.668965i −0.957476 0.288512i \(-0.906840\pi\)
0.288512 + 0.957476i \(0.406840\pi\)
\(182\) 4.00000i 0.296500i
\(183\) 18.0000i 1.33060i
\(184\) 12.0000 12.0000i 0.884652 0.884652i
\(185\) 6.00000i 0.441129i
\(186\) −16.0000 −1.17318
\(187\) −2.00000 + 2.00000i −0.146254 + 0.146254i
\(188\) 16.0000i 1.16692i
\(189\) −8.00000 8.00000i −0.581914 0.581914i
\(190\) 6.00000 6.00000i 0.435286 0.435286i
\(191\) −8.00000 −0.578860 −0.289430 0.957199i \(-0.593466\pi\)
−0.289430 + 0.957199i \(0.593466\pi\)
\(192\) 8.00000 8.00000i 0.577350 0.577350i
\(193\) 14.0000 1.00774 0.503871 0.863779i \(-0.331909\pi\)
0.503871 + 0.863779i \(0.331909\pi\)
\(194\) 2.00000 2.00000i 0.143592 0.143592i
\(195\) −2.00000 2.00000i −0.143223 0.143223i
\(196\) 6.00000i 0.428571i
\(197\) −17.0000 + 17.0000i −1.21120 + 1.21120i −0.240567 + 0.970632i \(0.577334\pi\)
−0.970632 + 0.240567i \(0.922666\pi\)
\(198\) 2.00000 0.142134
\(199\) 14.0000i 0.992434i −0.868199 0.496217i \(-0.834722\pi\)
0.868199 0.496217i \(-0.165278\pi\)
\(200\) −6.00000 + 6.00000i −0.424264 + 0.424264i
\(201\) 10.0000i 0.705346i
\(202\) 22.0000i 1.54791i
\(203\) −6.00000 + 6.00000i −0.421117 + 0.421117i
\(204\) 4.00000 4.00000i 0.280056 0.280056i
\(205\) 0 0
\(206\) 6.00000 + 6.00000i 0.418040 + 0.418040i
\(207\) −6.00000 −0.417029
\(208\) 4.00000 + 4.00000i 0.277350 + 0.277350i
\(209\) 6.00000 0.415029
\(210\) −4.00000 4.00000i −0.276026 0.276026i
\(211\) −9.00000 9.00000i −0.619586 0.619586i 0.325840 0.945425i \(-0.394353\pi\)
−0.945425 + 0.325840i \(0.894353\pi\)
\(212\) 10.0000 + 10.0000i 0.686803 + 0.686803i
\(213\) 10.0000 10.0000i 0.685189 0.685189i
\(214\) 14.0000i 0.957020i
\(215\) 10.0000i 0.681994i
\(216\) −16.0000 −1.08866
\(217\) 16.0000i 1.08615i
\(218\) −6.00000 −0.406371
\(219\) 4.00000 4.00000i 0.270295 0.270295i
\(220\) 4.00000 0.269680
\(221\) 2.00000 + 2.00000i 0.134535 + 0.134535i
\(222\) 6.00000 6.00000i 0.402694 0.402694i
\(223\) 24.0000 1.60716 0.803579 0.595198i \(-0.202926\pi\)
0.803579 + 0.595198i \(0.202926\pi\)
\(224\) 8.00000 + 8.00000i 0.534522 + 0.534522i
\(225\) 3.00000 0.200000
\(226\) 6.00000 6.00000i 0.399114 0.399114i
\(227\) 15.0000 + 15.0000i 0.995585 + 0.995585i 0.999990 0.00440533i \(-0.00140226\pi\)
−0.00440533 + 0.999990i \(0.501402\pi\)
\(228\) −12.0000 −0.794719
\(229\) 7.00000 7.00000i 0.462573 0.462573i −0.436925 0.899498i \(-0.643932\pi\)
0.899498 + 0.436925i \(0.143932\pi\)
\(230\) −12.0000 −0.791257
\(231\) 4.00000i 0.263181i
\(232\) 12.0000i 0.787839i
\(233\) 4.00000i 0.262049i 0.991379 + 0.131024i \(0.0418266\pi\)
−0.991379 + 0.131024i \(0.958173\pi\)
\(234\) 2.00000i 0.130744i
\(235\) −8.00000 + 8.00000i −0.521862 + 0.521862i
\(236\) 6.00000 + 6.00000i 0.390567 + 0.390567i
\(237\) 0 0
\(238\) 4.00000 + 4.00000i 0.259281 + 0.259281i
\(239\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(240\) −8.00000 −0.516398
\(241\) −18.0000 −1.15948 −0.579741 0.814801i \(-0.696846\pi\)
−0.579741 + 0.814801i \(0.696846\pi\)
\(242\) −9.00000 9.00000i −0.578542 0.578542i
\(243\) 7.00000 + 7.00000i 0.449050 + 0.449050i
\(244\) −18.0000 + 18.0000i −1.15233 + 1.15233i
\(245\) −3.00000 + 3.00000i −0.191663 + 0.191663i
\(246\) 0 0
\(247\) 6.00000i 0.381771i
\(248\) −16.0000 16.0000i −1.01600 1.01600i
\(249\) 2.00000i 0.126745i
\(250\) 16.0000 1.01193
\(251\) 21.0000 21.0000i 1.32551 1.32551i 0.416265 0.909243i \(-0.363339\pi\)
0.909243 0.416265i \(-0.136661\pi\)
\(252\) 4.00000i 0.251976i
\(253\) −6.00000 6.00000i −0.377217 0.377217i
\(254\) −8.00000 + 8.00000i −0.501965 + 0.501965i
\(255\) −4.00000 −0.250490
\(256\) 16.0000 1.00000
\(257\) −22.0000 −1.37232 −0.686161 0.727450i \(-0.740706\pi\)
−0.686161 + 0.727450i \(0.740706\pi\)
\(258\) 10.0000 10.0000i 0.622573 0.622573i
\(259\) 6.00000 + 6.00000i 0.372822 + 0.372822i
\(260\) 4.00000i 0.248069i
\(261\) 3.00000 3.00000i 0.185695 0.185695i
\(262\) −22.0000 −1.35916
\(263\) 6.00000i 0.369976i −0.982741 0.184988i \(-0.940775\pi\)
0.982741 0.184988i \(-0.0592246\pi\)
\(264\) −4.00000 4.00000i −0.246183 0.246183i
\(265\) 10.0000i 0.614295i
\(266\) 12.0000i 0.735767i
\(267\) −4.00000 + 4.00000i −0.244796 + 0.244796i
\(268\) −10.0000 + 10.0000i −0.610847 + 0.610847i
\(269\) 3.00000 + 3.00000i 0.182913 + 0.182913i 0.792624 0.609711i \(-0.208714\pi\)
−0.609711 + 0.792624i \(0.708714\pi\)
\(270\) 8.00000 + 8.00000i 0.486864 + 0.486864i
\(271\) −8.00000 −0.485965 −0.242983 0.970031i \(-0.578126\pi\)
−0.242983 + 0.970031i \(0.578126\pi\)
\(272\) 8.00000 0.485071
\(273\) −4.00000 −0.242091
\(274\) 8.00000 + 8.00000i 0.483298 + 0.483298i
\(275\) 3.00000 + 3.00000i 0.180907 + 0.180907i
\(276\) 12.0000 + 12.0000i 0.722315 + 0.722315i
\(277\) 3.00000 3.00000i 0.180253 0.180253i −0.611213 0.791466i \(-0.709318\pi\)
0.791466 + 0.611213i \(0.209318\pi\)
\(278\) 6.00000i 0.359856i
\(279\) 8.00000i 0.478947i
\(280\) 8.00000i 0.478091i
\(281\) 20.0000i 1.19310i 0.802576 + 0.596550i \(0.203462\pi\)
−0.802576 + 0.596550i \(0.796538\pi\)
\(282\) 16.0000 0.952786
\(283\) −15.0000 + 15.0000i −0.891657 + 0.891657i −0.994679 0.103022i \(-0.967149\pi\)
0.103022 + 0.994679i \(0.467149\pi\)
\(284\) 20.0000 1.18678
\(285\) 6.00000 + 6.00000i 0.355409 + 0.355409i
\(286\) 2.00000 2.00000i 0.118262 0.118262i
\(287\) 0 0
\(288\) −4.00000 4.00000i −0.235702 0.235702i
\(289\) −13.0000 −0.764706
\(290\) 6.00000 6.00000i 0.352332 0.352332i
\(291\) 2.00000 + 2.00000i 0.117242 + 0.117242i
\(292\) 8.00000 0.468165
\(293\) 15.0000 15.0000i 0.876309 0.876309i −0.116841 0.993151i \(-0.537277\pi\)
0.993151 + 0.116841i \(0.0372769\pi\)
\(294\) 6.00000 0.349927
\(295\) 6.00000i 0.349334i
\(296\) 12.0000 0.697486
\(297\) 8.00000i 0.464207i
\(298\) 14.0000i 0.810998i
\(299\) −6.00000 + 6.00000i −0.346989 + 0.346989i
\(300\) −6.00000 6.00000i −0.346410 0.346410i
\(301\) 10.0000 + 10.0000i 0.576390 + 0.576390i
\(302\) −10.0000 10.0000i −0.575435 0.575435i
\(303\) −22.0000 −1.26387
\(304\) −12.0000 12.0000i −0.688247 0.688247i
\(305\) 18.0000 1.03068
\(306\) −2.00000 2.00000i −0.114332 0.114332i
\(307\) −5.00000 5.00000i −0.285365 0.285365i 0.549879 0.835244i \(-0.314674\pi\)
−0.835244 + 0.549879i \(0.814674\pi\)
\(308\) 4.00000 4.00000i 0.227921 0.227921i
\(309\) −6.00000 + 6.00000i −0.341328 + 0.341328i
\(310\) 16.0000i 0.908739i
\(311\) 30.0000i 1.70114i −0.525859 0.850572i \(-0.676256\pi\)
0.525859 0.850572i \(-0.323744\pi\)
\(312\) −4.00000 + 4.00000i −0.226455 + 0.226455i
\(313\) 16.0000i 0.904373i −0.891923 0.452187i \(-0.850644\pi\)
0.891923 0.452187i \(-0.149356\pi\)
\(314\) −30.0000 −1.69300
\(315\) −2.00000 + 2.00000i −0.112687 + 0.112687i
\(316\) 0 0
\(317\) −5.00000 5.00000i −0.280828 0.280828i 0.552611 0.833439i \(-0.313631\pi\)
−0.833439 + 0.552611i \(0.813631\pi\)
\(318\) −10.0000 + 10.0000i −0.560772 + 0.560772i
\(319\) 6.00000 0.335936
\(320\) −8.00000 8.00000i −0.447214 0.447214i
\(321\) 14.0000 0.781404
\(322\) −12.0000 + 12.0000i −0.668734 + 0.668734i
\(323\) −6.00000 6.00000i −0.333849 0.333849i
\(324\) 10.0000i 0.555556i
\(325\) 3.00000 3.00000i 0.166410 0.166410i
\(326\) 2.00000 0.110770
\(327\) 6.00000i 0.331801i
\(328\) 0 0
\(329\) 16.0000i 0.882109i
\(330\) 4.00000i 0.220193i
\(331\) 1.00000 1.00000i 0.0549650 0.0549650i −0.679090 0.734055i \(-0.737625\pi\)
0.734055 + 0.679090i \(0.237625\pi\)
\(332\) −2.00000 + 2.00000i −0.109764 + 0.109764i
\(333\) −3.00000 3.00000i −0.164399 0.164399i
\(334\) −2.00000 2.00000i −0.109435 0.109435i
\(335\) 10.0000 0.546358
\(336\) −8.00000 + 8.00000i −0.436436 + 0.436436i
\(337\) 18.0000 0.980522 0.490261 0.871576i \(-0.336901\pi\)
0.490261 + 0.871576i \(0.336901\pi\)
\(338\) 11.0000 + 11.0000i 0.598321 + 0.598321i
\(339\) 6.00000 + 6.00000i 0.325875 + 0.325875i
\(340\) −4.00000 4.00000i −0.216930 0.216930i
\(341\) −8.00000 + 8.00000i −0.433224 + 0.433224i
\(342\) 6.00000i 0.324443i
\(343\) 20.0000i 1.07990i
\(344\) 20.0000 1.07833
\(345\) 12.0000i 0.646058i
\(346\) 2.00000 0.107521
\(347\) 13.0000 13.0000i 0.697877 0.697877i −0.266076 0.963952i \(-0.585727\pi\)
0.963952 + 0.266076i \(0.0857271\pi\)
\(348\) −12.0000 −0.643268
\(349\) 3.00000 + 3.00000i 0.160586 + 0.160586i 0.782826 0.622240i \(-0.213777\pi\)
−0.622240 + 0.782826i \(0.713777\pi\)
\(350\) 6.00000 6.00000i 0.320713 0.320713i
\(351\) 8.00000 0.427008
\(352\) 8.00000i 0.426401i
\(353\) −6.00000 −0.319348 −0.159674 0.987170i \(-0.551044\pi\)
−0.159674 + 0.987170i \(0.551044\pi\)
\(354\) −6.00000 + 6.00000i −0.318896 + 0.318896i
\(355\) −10.0000 10.0000i −0.530745 0.530745i
\(356\) −8.00000 −0.423999
\(357\) −4.00000 + 4.00000i −0.211702 + 0.211702i
\(358\) 34.0000 1.79696
\(359\) 26.0000i 1.37223i 0.727494 + 0.686114i \(0.240685\pi\)
−0.727494 + 0.686114i \(0.759315\pi\)
\(360\) 4.00000i 0.210819i
\(361\) 1.00000i 0.0526316i
\(362\) 18.0000i 0.946059i
\(363\) 9.00000 9.00000i 0.472377 0.472377i
\(364\) −4.00000 4.00000i −0.209657 0.209657i
\(365\) −4.00000 4.00000i −0.209370 0.209370i
\(366\) −18.0000 18.0000i −0.940875 0.940875i
\(367\) 8.00000 0.417597 0.208798 0.977959i \(-0.433045\pi\)
0.208798 + 0.977959i \(0.433045\pi\)
\(368\) 24.0000i 1.25109i
\(369\) 0 0
\(370\) −6.00000 6.00000i −0.311925 0.311925i
\(371\) −10.0000 10.0000i −0.519174 0.519174i
\(372\) 16.0000 16.0000i 0.829561 0.829561i
\(373\) −5.00000 + 5.00000i −0.258890 + 0.258890i −0.824603 0.565712i \(-0.808601\pi\)
0.565712 + 0.824603i \(0.308601\pi\)
\(374\) 4.00000i 0.206835i
\(375\) 16.0000i 0.826236i
\(376\) 16.0000 + 16.0000i 0.825137 + 0.825137i
\(377\) 6.00000i 0.309016i
\(378\) 16.0000 0.822951
\(379\) −3.00000 + 3.00000i −0.154100 + 0.154100i −0.779946 0.625847i \(-0.784754\pi\)
0.625847 + 0.779946i \(0.284754\pi\)
\(380\) 12.0000i 0.615587i
\(381\) −8.00000 8.00000i −0.409852 0.409852i
\(382\) 8.00000 8.00000i 0.409316 0.409316i
\(383\) −16.0000 −0.817562 −0.408781 0.912633i \(-0.634046\pi\)
−0.408781 + 0.912633i \(0.634046\pi\)
\(384\) 16.0000i 0.816497i
\(385\) −4.00000 −0.203859
\(386\) −14.0000 + 14.0000i −0.712581 + 0.712581i
\(387\) −5.00000 5.00000i −0.254164 0.254164i
\(388\) 4.00000i 0.203069i
\(389\) −13.0000 + 13.0000i −0.659126 + 0.659126i −0.955173 0.296047i \(-0.904331\pi\)
0.296047 + 0.955173i \(0.404331\pi\)
\(390\) 4.00000 0.202548
\(391\) 12.0000i 0.606866i
\(392\) 6.00000 + 6.00000i 0.303046 + 0.303046i
\(393\) 22.0000i 1.10975i
\(394\) 34.0000i 1.71290i
\(395\) 0 0
\(396\) −2.00000 + 2.00000i −0.100504 + 0.100504i
\(397\) −5.00000 5.00000i −0.250943 0.250943i 0.570414 0.821357i \(-0.306783\pi\)
−0.821357 + 0.570414i \(0.806783\pi\)
\(398\) 14.0000 + 14.0000i 0.701757 + 0.701757i
\(399\) 12.0000 0.600751
\(400\) 12.0000i 0.600000i
\(401\) −18.0000 −0.898877 −0.449439 0.893311i \(-0.648376\pi\)
−0.449439 + 0.893311i \(0.648376\pi\)
\(402\) −10.0000 10.0000i −0.498755 0.498755i
\(403\) 8.00000 + 8.00000i 0.398508 + 0.398508i
\(404\) −22.0000 22.0000i −1.09454 1.09454i
\(405\) −5.00000 + 5.00000i −0.248452 + 0.248452i
\(406\) 12.0000i 0.595550i
\(407\) 6.00000i 0.297409i
\(408\) 8.00000i 0.396059i
\(409\) 16.0000i 0.791149i 0.918434 + 0.395575i \(0.129455\pi\)
−0.918434 + 0.395575i \(0.870545\pi\)
\(410\) 0 0
\(411\) −8.00000 + 8.00000i −0.394611 + 0.394611i
\(412\) −12.0000 −0.591198
\(413\) −6.00000 6.00000i −0.295241 0.295241i
\(414\) 6.00000 6.00000i 0.294884 0.294884i
\(415\) 2.00000 0.0981761
\(416\) −8.00000 −0.392232
\(417\) 6.00000 0.293821
\(418\) −6.00000 + 6.00000i −0.293470 + 0.293470i
\(419\) 3.00000 + 3.00000i 0.146560 + 0.146560i 0.776579 0.630020i \(-0.216953\pi\)
−0.630020 + 0.776579i \(0.716953\pi\)
\(420\) 8.00000 0.390360
\(421\) −9.00000 + 9.00000i −0.438633 + 0.438633i −0.891552 0.452919i \(-0.850383\pi\)
0.452919 + 0.891552i \(0.350383\pi\)
\(422\) 18.0000 0.876226
\(423\) 8.00000i 0.388973i
\(424\) −20.0000 −0.971286
\(425\) 6.00000i 0.291043i
\(426\) 20.0000i 0.969003i
\(427\) 18.0000 18.0000i 0.871081 0.871081i
\(428\) 14.0000 + 14.0000i 0.676716 + 0.676716i
\(429\) 2.00000 + 2.00000i 0.0965609 + 0.0965609i
\(430\) −10.0000 10.0000i −0.482243 0.482243i
\(431\) 32.0000 1.54139 0.770693 0.637207i \(-0.219910\pi\)
0.770693 + 0.637207i \(0.219910\pi\)
\(432\) 16.0000 16.0000i 0.769800 0.769800i
\(433\) 14.0000 0.672797 0.336399 0.941720i \(-0.390791\pi\)
0.336399 + 0.941720i \(0.390791\pi\)
\(434\) 16.0000 + 16.0000i 0.768025 + 0.768025i
\(435\) 6.00000 + 6.00000i 0.287678 + 0.287678i
\(436\) 6.00000 6.00000i 0.287348 0.287348i
\(437\) 18.0000 18.0000i 0.861057 0.861057i
\(438\) 8.00000i 0.382255i
\(439\) 14.0000i 0.668184i −0.942541 0.334092i \(-0.891570\pi\)
0.942541 0.334092i \(-0.108430\pi\)
\(440\) −4.00000 + 4.00000i −0.190693 + 0.190693i
\(441\) 3.00000i 0.142857i
\(442\) −4.00000 −0.190261
\(443\) −15.0000 + 15.0000i −0.712672 + 0.712672i −0.967093 0.254422i \(-0.918115\pi\)
0.254422 + 0.967093i \(0.418115\pi\)
\(444\) 12.0000i 0.569495i
\(445\) 4.00000 + 4.00000i 0.189618 + 0.189618i
\(446\) −24.0000 + 24.0000i −1.13643 + 1.13643i
\(447\) −14.0000 −0.662177
\(448\) −16.0000 −0.755929
\(449\) 30.0000 1.41579 0.707894 0.706319i \(-0.249646\pi\)
0.707894 + 0.706319i \(0.249646\pi\)
\(450\) −3.00000 + 3.00000i −0.141421 + 0.141421i
\(451\) 0 0
\(452\) 12.0000i 0.564433i
\(453\) 10.0000 10.0000i 0.469841 0.469841i
\(454\) −30.0000 −1.40797
\(455\) 4.00000i 0.187523i
\(456\) 12.0000 12.0000i 0.561951 0.561951i
\(457\) 32.0000i 1.49690i 0.663193 + 0.748448i \(0.269201\pi\)
−0.663193 + 0.748448i \(0.730799\pi\)
\(458\) 14.0000i 0.654177i
\(459\) 8.00000 8.00000i 0.373408 0.373408i
\(460\) 12.0000 12.0000i 0.559503 0.559503i
\(461\) 11.0000 + 11.0000i 0.512321 + 0.512321i 0.915237 0.402916i \(-0.132003\pi\)
−0.402916 + 0.915237i \(0.632003\pi\)
\(462\) 4.00000 + 4.00000i 0.186097 + 0.186097i
\(463\) −16.0000 −0.743583 −0.371792 0.928316i \(-0.621256\pi\)
−0.371792 + 0.928316i \(0.621256\pi\)
\(464\) −12.0000 12.0000i −0.557086 0.557086i
\(465\) −16.0000 −0.741982
\(466\) −4.00000 4.00000i −0.185296 0.185296i
\(467\) −5.00000 5.00000i −0.231372 0.231372i 0.581893 0.813265i \(-0.302312\pi\)
−0.813265 + 0.581893i \(0.802312\pi\)
\(468\) 2.00000 + 2.00000i 0.0924500 + 0.0924500i
\(469\) 10.0000 10.0000i 0.461757 0.461757i
\(470\) 16.0000i 0.738025i
\(471\) 30.0000i 1.38233i
\(472\) −12.0000 −0.552345
\(473\) 10.0000i 0.459800i
\(474\) 0 0
\(475\) −9.00000 + 9.00000i −0.412948 + 0.412948i
\(476\) −8.00000 −0.366679
\(477\) 5.00000 + 5.00000i 0.228934 + 0.228934i
\(478\) 0 0
\(479\) −40.0000 −1.82765 −0.913823 0.406112i \(-0.866884\pi\)
−0.913823 + 0.406112i \(0.866884\pi\)
\(480\) 8.00000 8.00000i 0.365148 0.365148i
\(481\) −6.00000 −0.273576
\(482\) 18.0000 18.0000i 0.819878 0.819878i
\(483\) −12.0000 12.0000i −0.546019 0.546019i
\(484\) 18.0000 0.818182
\(485\) 2.00000 2.00000i 0.0908153 0.0908153i
\(486\) −14.0000 −0.635053
\(487\) 2.00000i 0.0906287i 0.998973 + 0.0453143i \(0.0144289\pi\)
−0.998973 + 0.0453143i \(0.985571\pi\)
\(488\) 36.0000i 1.62964i
\(489\) 2.00000i 0.0904431i
\(490\) 6.00000i 0.271052i
\(491\) −19.0000 + 19.0000i −0.857458 + 0.857458i −0.991038 0.133580i \(-0.957353\pi\)
0.133580 + 0.991038i \(0.457353\pi\)
\(492\) 0 0
\(493\) −6.00000 6.00000i −0.270226 0.270226i
\(494\) 6.00000 + 6.00000i 0.269953 + 0.269953i
\(495\) 2.00000 0.0898933
\(496\) 32.0000 1.43684
\(497\) −20.0000 −0.897123
\(498\) −2.00000 2.00000i −0.0896221 0.0896221i
\(499\) 23.0000 + 23.0000i 1.02962 + 1.02962i 0.999548 + 0.0300737i \(0.00957421\pi\)
0.0300737 + 0.999548i \(0.490426\pi\)
\(500\) −16.0000 + 16.0000i −0.715542 + 0.715542i
\(501\) 2.00000 2.00000i 0.0893534 0.0893534i
\(502\) 42.0000i 1.87455i
\(503\) 6.00000i 0.267527i −0.991013 0.133763i \(-0.957294\pi\)
0.991013 0.133763i \(-0.0427062\pi\)
\(504\) 4.00000 + 4.00000i 0.178174 + 0.178174i
\(505\) 22.0000i 0.978987i
\(506\) 12.0000 0.533465
\(507\) −11.0000 + 11.0000i −0.488527 + 0.488527i
\(508\) 16.0000i 0.709885i
\(509\) 23.0000 + 23.0000i 1.01946 + 1.01946i 0.999807 + 0.0196502i \(0.00625524\pi\)
0.0196502 + 0.999807i \(0.493745\pi\)
\(510\) 4.00000 4.00000i 0.177123 0.177123i
\(511\) −8.00000 −0.353899
\(512\) −16.0000 + 16.0000i −0.707107 + 0.707107i
\(513\) −24.0000 −1.05963
\(514\) 22.0000 22.0000i 0.970378 0.970378i
\(515\) 6.00000 + 6.00000i 0.264392 + 0.264392i
\(516\) 20.0000i 0.880451i
\(517\) 8.00000 8.00000i 0.351840 0.351840i
\(518\) −12.0000 −0.527250
\(519\) 2.00000i 0.0877903i
\(520\) 4.00000 + 4.00000i 0.175412 + 0.175412i
\(521\) 40.0000i 1.75243i −0.481919 0.876216i \(-0.660060\pi\)
0.481919 0.876216i \(-0.339940\pi\)
\(522\) 6.00000i 0.262613i
\(523\) 25.0000 25.0000i 1.09317 1.09317i 0.0979859 0.995188i \(-0.468760\pi\)
0.995188 0.0979859i \(-0.0312400\pi\)
\(524\) 22.0000 22.0000i 0.961074 0.961074i
\(525\) 6.00000 + 6.00000i 0.261861 + 0.261861i
\(526\) 6.00000 + 6.00000i 0.261612 + 0.261612i
\(527\) 16.0000 0.696971
\(528\) 8.00000 0.348155
\(529\) −13.0000 −0.565217
\(530\) 10.0000 + 10.0000i 0.434372 + 0.434372i
\(531\) 3.00000 + 3.00000i 0.130189 + 0.130189i
\(532\) 12.0000 + 12.0000i 0.520266 + 0.520266i
\(533\) 0 0
\(534\) 8.00000i 0.346194i
\(535\) 14.0000i 0.605273i
\(536\) 20.0000i 0.863868i
\(537\) 34.0000i 1.46721i
\(538\) −6.00000 −0.258678
\(539\) 3.00000 3.00000i 0.129219 0.129219i
\(540\) −16.0000 −0.688530
\(541\) −9.00000 9.00000i −0.386940 0.386940i 0.486654 0.873595i \(-0.338217\pi\)
−0.873595 + 0.486654i \(0.838217\pi\)
\(542\) 8.00000 8.00000i 0.343629 0.343629i
\(543\) 18.0000 0.772454
\(544\) −8.00000 + 8.00000i −0.342997 + 0.342997i
\(545\) −6.00000 −0.257012
\(546\) 4.00000 4.00000i 0.171184 0.171184i
\(547\) −5.00000 5.00000i −0.213785 0.213785i 0.592088 0.805873i \(-0.298304\pi\)
−0.805873 + 0.592088i \(0.798304\pi\)
\(548\) −16.0000 −0.683486
\(549\) −9.00000 + 9.00000i −0.384111 + 0.384111i
\(550\) −6.00000 −0.255841
\(551\) 18.0000i 0.766826i
\(552\) −24.0000 −1.02151
\(553\) 0 0
\(554\) 6.00000i 0.254916i
\(555\) 6.00000 6.00000i 0.254686 0.254686i
\(556\) 6.00000 + 6.00000i 0.254457 + 0.254457i
\(557\) −25.0000 25.0000i −1.05928 1.05928i −0.998128 0.0611558i \(-0.980521\pi\)
−0.0611558 0.998128i \(-0.519479\pi\)
\(558\) −8.00000 8.00000i −0.338667 0.338667i
\(559\) −10.0000 −0.422955
\(560\) 8.00000 + 8.00000i 0.338062 + 0.338062i
\(561\) 4.00000 0.168880
\(562\) −20.0000 20.0000i −0.843649 0.843649i
\(563\) 19.0000 + 19.0000i 0.800755 + 0.800755i 0.983213 0.182459i \(-0.0584057\pi\)
−0.182459 + 0.983213i \(0.558406\pi\)
\(564\) −16.0000 + 16.0000i −0.673722 + 0.673722i
\(565\) 6.00000 6.00000i 0.252422 0.252422i
\(566\) 30.0000i 1.26099i
\(567\) 10.0000i 0.419961i
\(568\) −20.0000 + 20.0000i −0.839181 + 0.839181i
\(569\) 24.0000i 1.00613i −0.864248 0.503066i \(-0.832205\pi\)
0.864248 0.503066i \(-0.167795\pi\)
\(570\) −12.0000 −0.502625
\(571\) 1.00000 1.00000i 0.0418487 0.0418487i −0.685873 0.727721i \(-0.740579\pi\)
0.727721 + 0.685873i \(0.240579\pi\)
\(572\) 4.00000i 0.167248i
\(573\) 8.00000 + 8.00000i 0.334205 + 0.334205i
\(574\) 0 0
\(575\) 18.0000 0.750652
\(576\) 8.00000 0.333333
\(577\) 18.0000 0.749350 0.374675 0.927156i \(-0.377754\pi\)
0.374675 + 0.927156i \(0.377754\pi\)
\(578\) 13.0000 13.0000i 0.540729 0.540729i
\(579\) −14.0000 14.0000i −0.581820 0.581820i
\(580\) 12.0000i 0.498273i
\(581\) 2.00000 2.00000i 0.0829740 0.0829740i
\(582\) −4.00000 −0.165805
\(583\) 10.0000i 0.414158i
\(584\) −8.00000 + 8.00000i −0.331042 + 0.331042i
\(585\) 2.00000i 0.0826898i
\(586\) 30.0000i 1.23929i
\(587\) −7.00000 + 7.00000i −0.288921 + 0.288921i −0.836653 0.547733i \(-0.815491\pi\)
0.547733 + 0.836653i \(0.315491\pi\)
\(588\) −6.00000 + 6.00000i −0.247436 + 0.247436i
\(589\) −24.0000 24.0000i −0.988903 0.988903i
\(590\) 6.00000 + 6.00000i 0.247016 + 0.247016i
\(591\) 34.0000 1.39857
\(592\) −12.0000 + 12.0000i −0.493197 + 0.493197i
\(593\) 34.0000 1.39621 0.698106 0.715994i \(-0.254026\pi\)
0.698106 + 0.715994i \(0.254026\pi\)
\(594\) −8.00000 8.00000i −0.328244 0.328244i
\(595\) 4.00000 + 4.00000i 0.163984 + 0.163984i
\(596\) −14.0000 14.0000i −0.573462 0.573462i
\(597\) −14.0000 + 14.0000i −0.572982 + 0.572982i
\(598\) 12.0000i 0.490716i
\(599\) 14.0000i 0.572024i −0.958226 0.286012i \(-0.907670\pi\)
0.958226 0.286012i \(-0.0923298\pi\)
\(600\) 12.0000 0.489898
\(601\) 20.0000i 0.815817i −0.913023 0.407909i \(-0.866258\pi\)
0.913023 0.407909i \(-0.133742\pi\)
\(602\) −20.0000 −0.815139
\(603\) −5.00000 + 5.00000i −0.203616 + 0.203616i
\(604\) 20.0000 0.813788
\(605\) −9.00000 9.00000i −0.365902 0.365902i
\(606\) 22.0000 22.0000i 0.893689 0.893689i
\(607\) −32.0000 −1.29884 −0.649420 0.760430i \(-0.724988\pi\)
−0.649420 + 0.760430i \(0.724988\pi\)
\(608\) 24.0000 0.973329
\(609\) 12.0000 0.486265
\(610\) −18.0000 + 18.0000i −0.728799 + 0.728799i
\(611\) −8.00000 8.00000i −0.323645 0.323645i
\(612\) 4.00000 0.161690
\(613\) −25.0000 + 25.0000i −1.00974 + 1.00974i −0.00978840 + 0.999952i \(0.503116\pi\)
−0.999952 + 0.00978840i \(0.996884\pi\)
\(614\) 10.0000 0.403567
\(615\) 0 0
\(616\) 8.00000i 0.322329i
\(617\) 12.0000i 0.483102i 0.970388 + 0.241551i \(0.0776561\pi\)
−0.970388 + 0.241551i \(0.922344\pi\)
\(618\) 12.0000i 0.482711i
\(619\) 17.0000 17.0000i 0.683288 0.683288i −0.277452 0.960740i \(-0.589490\pi\)
0.960740 + 0.277452i \(0.0894899\pi\)
\(620\) −16.0000 16.0000i −0.642575 0.642575i
\(621\) 24.0000 + 24.0000i 0.963087 + 0.963087i
\(622\) 30.0000 + 30.0000i 1.20289 + 1.20289i
\(623\) 8.00000 0.320513
\(624\) 8.00000i 0.320256i
\(625\) 1.00000 0.0400000
\(626\) 16.0000 + 16.0000i 0.639489 + 0.639489i
\(627\) −6.00000 6.00000i −0.239617 0.239617i
\(628\) 30.0000 30.0000i 1.19713 1.19713i
\(629\) −6.00000 + 6.00000i −0.239236 + 0.239236i
\(630\) 4.00000i 0.159364i
\(631\) 10.0000i 0.398094i 0.979990 + 0.199047i \(0.0637846\pi\)
−0.979990 + 0.199047i \(0.936215\pi\)
\(632\) 0 0
\(633\) 18.0000i 0.715436i
\(634\) 10.0000 0.397151
\(635\) −8.00000 + 8.00000i −0.317470 + 0.317470i
\(636\) 20.0000i 0.793052i
\(637\) −3.00000 3.00000i −0.118864 0.118864i
\(638\) −6.00000 + 6.00000i −0.237542 + 0.237542i
\(639\) 10.0000 0.395594
\(640\) 16.0000 0.632456
\(641\) −18.0000 −0.710957 −0.355479 0.934684i \(-0.615682\pi\)
−0.355479 + 0.934684i \(0.615682\pi\)
\(642\) −14.0000 + 14.0000i −0.552536 + 0.552536i
\(643\) −21.0000 21.0000i −0.828159 0.828159i 0.159103 0.987262i \(-0.449140\pi\)
−0.987262 + 0.159103i \(0.949140\pi\)
\(644\) 24.0000i 0.945732i
\(645\) 10.0000 10.0000i 0.393750 0.393750i
\(646\) 12.0000 0.472134
\(647\) 42.0000i 1.65119i 0.564263 + 0.825595i \(0.309160\pi\)
−0.564263 + 0.825595i \(0.690840\pi\)
\(648\) 10.0000 + 10.0000i 0.392837 + 0.392837i
\(649\) 6.00000i 0.235521i
\(650\) 6.00000i 0.235339i
\(651\) −16.0000 + 16.0000i −0.627089 + 0.627089i
\(652\) −2.00000 + 2.00000i −0.0783260 + 0.0783260i
\(653\) 19.0000 + 19.0000i 0.743527 + 0.743527i 0.973255 0.229728i \(-0.0737835\pi\)
−0.229728 + 0.973255i \(0.573784\pi\)
\(654\) 6.00000 + 6.00000i 0.234619 + 0.234619i
\(655\) −22.0000 −0.859611
\(656\) 0 0
\(657\) 4.00000 0.156055
\(658\) −16.0000 16.0000i −0.623745 0.623745i
\(659\) −17.0000 17.0000i −0.662226 0.662226i 0.293678 0.955904i \(-0.405121\pi\)
−0.955904 + 0.293678i \(0.905121\pi\)
\(660\) −4.00000 4.00000i −0.155700 0.155700i
\(661\) −9.00000 + 9.00000i −0.350059 + 0.350059i −0.860132 0.510072i \(-0.829619\pi\)
0.510072 + 0.860132i \(0.329619\pi\)
\(662\) 2.00000i 0.0777322i
\(663\) 4.00000i 0.155347i
\(664\) 4.00000i 0.155230i
\(665\) 12.0000i 0.465340i
\(666\) 6.00000 0.232495
\(667\) 18.0000 18.0000i 0.696963 0.696963i
\(668\) 4.00000 0.154765
\(669\) −24.0000 24.0000i −0.927894 0.927894i
\(670\) −10.0000 + 10.0000i −0.386334 + 0.386334i
\(671\) −18.0000 −0.694882
\(672\) 16.0000i 0.617213i
\(673\) 14.0000 0.539660 0.269830 0.962908i \(-0.413032\pi\)
0.269830 + 0.962908i \(0.413032\pi\)
\(674\) −18.0000 + 18.0000i −0.693334 + 0.693334i
\(675\) −12.0000 12.0000i −0.461880 0.461880i
\(676\) −22.0000 −0.846154
\(677\) 3.00000 3.00000i 0.115299 0.115299i −0.647103 0.762402i \(-0.724020\pi\)
0.762402 + 0.647103i \(0.224020\pi\)
\(678\) −12.0000 −0.460857
\(679\) 4.00000i 0.153506i
\(680\) 8.00000 0.306786
\(681\) 30.0000i 1.14960i
\(682\) 16.0000i 0.612672i
\(683\) 5.00000 5.00000i 0.191320 0.191320i −0.604946 0.796266i \(-0.706805\pi\)
0.796266 + 0.604946i \(0.206805\pi\)
\(684\) −6.00000 6.00000i −0.229416 0.229416i
\(685\) 8.00000 + 8.00000i 0.305664 + 0.305664i
\(686\) −20.0000 20.0000i −0.763604 0.763604i
\(687\) −14.0000 −0.534133
\(688\) −20.0000 + 20.0000i −0.762493 + 0.762493i
\(689\) 10.0000 0.380970
\(690\) 12.0000 + 12.0000i 0.456832 + 0.456832i
\(691\) −9.00000 9.00000i −0.342376 0.342376i 0.514884 0.857260i \(-0.327835\pi\)
−0.857260 + 0.514884i \(0.827835\pi\)
\(692\) −2.00000 + 2.00000i −0.0760286 + 0.0760286i
\(693\) 2.00000 2.00000i 0.0759737 0.0759737i
\(694\) 26.0000i 0.986947i
\(695\) 6.00000i 0.227593i
\(696\) 12.0000 12.0000i 0.454859 0.454859i
\(697\) 0 0
\(698\) −6.00000 −0.227103
\(699\) 4.00000 4.00000i 0.151294 0.151294i
\(700\) 12.0000i 0.453557i
\(701\) 31.0000 + 31.0000i 1.17085 + 1.17085i 0.982006 + 0.188847i \(0.0604752\pi\)
0.188847 + 0.982006i \(0.439525\pi\)
\(702\) −8.00000 + 8.00000i −0.301941 + 0.301941i
\(703\) 18.0000 0.678883
\(704\) 8.00000 + 8.00000i 0.301511 + 0.301511i
\(705\) 16.0000 0.602595
\(706\) 6.00000 6.00000i 0.225813 0.225813i
\(707\) 22.0000 + 22.0000i 0.827395 + 0.827395i
\(708\) 12.0000i 0.450988i
\(709\) 27.0000 27.0000i 1.01401 1.01401i 0.0141058 0.999901i \(-0.495510\pi\)
0.999901 0.0141058i \(-0.00449016\pi\)
\(710\) 20.0000 0.750587
\(711\) 0 0
\(712\) 8.00000 8.00000i 0.299813 0.299813i
\(713\) 48.0000i 1.79761i
\(714\) 8.00000i 0.299392i
\(715\) 2.00000 2.00000i 0.0747958 0.0747958i
\(716\) −34.0000 + 34.0000i −1.27064 + 1.27064i
\(717\) 0 0
\(718\) −26.0000 26.0000i −0.970311 0.970311i
\(719\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(720\) −4.00000 4.00000i −0.149071 0.149071i
\(721\) 12.0000 0.446903
\(722\) 1.00000 + 1.00000i 0.0372161 + 0.0372161i
\(723\) 18.0000 + 18.0000i 0.669427 + 0.669427i
\(724\) 18.0000 + 18.0000i 0.668965 + 0.668965i
\(725\) −9.00000 + 9.00000i −0.334252 + 0.334252i
\(726\) 18.0000i 0.668043i
\(727\) 2.00000i 0.0741759i 0.999312 + 0.0370879i \(0.0118082\pi\)
−0.999312 + 0.0370879i \(0.988192\pi\)
\(728\) 8.00000 0.296500
\(729\) 29.0000i 1.07407i
\(730\) 8.00000 0.296093
\(731\) −10.0000 + 10.0000i −0.369863 + 0.369863i
\(732\) 36.0000 1.33060
\(733\) −21.0000 21.0000i −0.775653 0.775653i 0.203436 0.979088i \(-0.434789\pi\)
−0.979088 + 0.203436i \(0.934789\pi\)
\(734\) −8.00000 + 8.00000i −0.295285 + 0.295285i
\(735\) 6.00000 0.221313
\(736\) −24.0000 24.0000i −0.884652 0.884652i
\(737\) −10.0000 −0.368355
\(738\) 0 0
\(739\) 23.0000 + 23.0000i 0.846069 + 0.846069i 0.989640 0.143571i \(-0.0458586\pi\)
−0.143571 + 0.989640i \(0.545859\pi\)
\(740\) 12.0000 0.441129
\(741\) −6.00000 + 6.00000i −0.220416 + 0.220416i
\(742\) 20.0000 0.734223
\(743\) 46.0000i 1.68758i −0.536676 0.843788i \(-0.680320\pi\)
0.536676 0.843788i \(-0.319680\pi\)
\(744\) 32.0000i 1.17318i
\(745\) 14.0000i 0.512920i
\(746\) 10.0000i 0.366126i
\(747\) −1.00000 + 1.00000i −0.0365881 + 0.0365881i
\(748\) 4.00000 + 4.00000i 0.146254 + 0.146254i
\(749\) −14.0000 14.0000i −0.511549 0.511549i
\(750\) −16.0000 16.0000i −0.584237 0.584237i
\(751\) 32.0000 1.16770 0.583848 0.811863i \(-0.301546\pi\)
0.583848 + 0.811863i \(0.301546\pi\)
\(752\) −32.0000 −1.16692
\(753\) −42.0000 −1.53057
\(754\) 6.00000 + 6.00000i 0.218507 + 0.218507i
\(755\) −10.0000 10.0000i −0.363937 0.363937i
\(756\) −16.0000 + 16.0000i −0.581914 + 0.581914i
\(757\) 23.0000 23.0000i 0.835949 0.835949i −0.152374 0.988323i \(-0.548692\pi\)
0.988323 + 0.152374i \(0.0486917\pi\)
\(758\) 6.00000i 0.217930i
\(759\) 12.0000i 0.435572i
\(760\) −12.0000 12.0000i −0.435286 0.435286i
\(761\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(762\) 16.0000 0.579619
\(763\) −6.00000 + 6.00000i −0.217215 + 0.217215i
\(764\) 16.0000i 0.578860i
\(765\) −2.00000 2.00000i −0.0723102 0.0723102i
\(766\) 16.0000 16.0000i 0.578103 0.578103i
\(767\) 6.00000 0.216647
\(768\) −16.0000 16.0000i −0.577350 0.577350i
\(769\) −50.0000 −1.80305 −0.901523 0.432731i \(-0.857550\pi\)
−0.901523 + 0.432731i \(0.857550\pi\)
\(770\) 4.00000 4.00000i 0.144150 0.144150i
\(771\) 22.0000 + 22.0000i 0.792311 + 0.792311i
\(772\) 28.0000i 1.00774i
\(773\) −5.00000 + 5.00000i −0.179838 + 0.179838i −0.791285 0.611448i \(-0.790588\pi\)
0.611448 + 0.791285i \(0.290588\pi\)
\(774\) 10.0000 0.359443
\(775\) 24.0000i 0.862105i
\(776\) −4.00000 4.00000i −0.143592 0.143592i
\(777\) 12.0000i 0.430498i
\(778\) 26.0000i