Properties

Label 74.2.e.b.11.2
Level $74$
Weight $2$
Character 74.11
Analytic conductor $0.591$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 74 = 2 \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 74.e (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(0.590892974957\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\zeta_{12})\)
Defining polynomial: \( x^{4} - x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 11.2
Root \(0.866025 - 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 74.11
Dual form 74.2.e.b.27.2

$q$-expansion

\(f(q)\) \(=\) \(q+(0.866025 - 0.500000i) q^{2} +(-1.36603 + 2.36603i) q^{3} +(0.500000 - 0.866025i) q^{4} +(1.50000 + 0.866025i) q^{5} +2.73205i q^{6} +(1.00000 - 1.73205i) q^{7} -1.00000i q^{8} +(-2.23205 - 3.86603i) q^{9} +O(q^{10})\) \(q+(0.866025 - 0.500000i) q^{2} +(-1.36603 + 2.36603i) q^{3} +(0.500000 - 0.866025i) q^{4} +(1.50000 + 0.866025i) q^{5} +2.73205i q^{6} +(1.00000 - 1.73205i) q^{7} -1.00000i q^{8} +(-2.23205 - 3.86603i) q^{9} +1.73205 q^{10} -4.73205 q^{11} +(1.36603 + 2.36603i) q^{12} +(-3.00000 - 1.73205i) q^{13} -2.00000i q^{14} +(-4.09808 + 2.36603i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(6.69615 - 3.86603i) q^{17} +(-3.86603 - 2.23205i) q^{18} +(1.09808 + 0.633975i) q^{19} +(1.50000 - 0.866025i) q^{20} +(2.73205 + 4.73205i) q^{21} +(-4.09808 + 2.36603i) q^{22} +4.73205i q^{23} +(2.36603 + 1.36603i) q^{24} +(-1.00000 - 1.73205i) q^{25} -3.46410 q^{26} +4.00000 q^{27} +(-1.00000 - 1.73205i) q^{28} +8.66025i q^{29} +(-2.36603 + 4.09808i) q^{30} -1.26795i q^{31} +(-0.866025 - 0.500000i) q^{32} +(6.46410 - 11.1962i) q^{33} +(3.86603 - 6.69615i) q^{34} +(3.00000 - 1.73205i) q^{35} -4.46410 q^{36} +(-5.69615 - 2.13397i) q^{37} +1.26795 q^{38} +(8.19615 - 4.73205i) q^{39} +(0.866025 - 1.50000i) q^{40} +(-4.96410 + 8.59808i) q^{41} +(4.73205 + 2.73205i) q^{42} -0.928203i q^{43} +(-2.36603 + 4.09808i) q^{44} -7.73205i q^{45} +(2.36603 + 4.09808i) q^{46} +4.73205 q^{47} +2.73205 q^{48} +(1.50000 + 2.59808i) q^{49} +(-1.73205 - 1.00000i) q^{50} +21.1244i q^{51} +(-3.00000 + 1.73205i) q^{52} +(-1.26795 - 2.19615i) q^{53} +(3.46410 - 2.00000i) q^{54} +(-7.09808 - 4.09808i) q^{55} +(-1.73205 - 1.00000i) q^{56} +(-3.00000 + 1.73205i) q^{57} +(4.33013 + 7.50000i) q^{58} +(2.19615 - 1.26795i) q^{59} +4.73205i q^{60} +(1.50000 + 0.866025i) q^{61} +(-0.633975 - 1.09808i) q^{62} -8.92820 q^{63} -1.00000 q^{64} +(-3.00000 - 5.19615i) q^{65} -12.9282i q^{66} +(5.09808 - 8.83013i) q^{67} -7.73205i q^{68} +(-11.1962 - 6.46410i) q^{69} +(1.73205 - 3.00000i) q^{70} +(-1.73205 + 3.00000i) q^{71} +(-3.86603 + 2.23205i) q^{72} +4.00000 q^{73} +(-6.00000 + 1.00000i) q^{74} +5.46410 q^{75} +(1.09808 - 0.633975i) q^{76} +(-4.73205 + 8.19615i) q^{77} +(4.73205 - 8.19615i) q^{78} +(-11.4904 - 6.63397i) q^{79} -1.73205i q^{80} +(1.23205 - 2.13397i) q^{81} +9.92820i q^{82} +(2.83013 + 4.90192i) q^{83} +5.46410 q^{84} +13.3923 q^{85} +(-0.464102 - 0.803848i) q^{86} +(-20.4904 - 11.8301i) q^{87} +4.73205i q^{88} +(-5.89230 + 3.40192i) q^{89} +(-3.86603 - 6.69615i) q^{90} +(-6.00000 + 3.46410i) q^{91} +(4.09808 + 2.36603i) q^{92} +(3.00000 + 1.73205i) q^{93} +(4.09808 - 2.36603i) q^{94} +(1.09808 + 1.90192i) q^{95} +(2.36603 - 1.36603i) q^{96} +7.73205i q^{97} +(2.59808 + 1.50000i) q^{98} +(10.5622 + 18.2942i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 2 q^{3} + 2 q^{4} + 6 q^{5} + 4 q^{7} - 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - 2 q^{3} + 2 q^{4} + 6 q^{5} + 4 q^{7} - 2 q^{9} - 12 q^{11} + 2 q^{12} - 12 q^{13} - 6 q^{15} - 2 q^{16} + 6 q^{17} - 12 q^{18} - 6 q^{19} + 6 q^{20} + 4 q^{21} - 6 q^{22} + 6 q^{24} - 4 q^{25} + 16 q^{27} - 4 q^{28} - 6 q^{30} + 12 q^{33} + 12 q^{34} + 12 q^{35} - 4 q^{36} - 2 q^{37} + 12 q^{38} + 12 q^{39} - 6 q^{41} + 12 q^{42} - 6 q^{44} + 6 q^{46} + 12 q^{47} + 4 q^{48} + 6 q^{49} - 12 q^{52} - 12 q^{53} - 18 q^{55} - 12 q^{57} - 12 q^{59} + 6 q^{61} - 6 q^{62} - 8 q^{63} - 4 q^{64} - 12 q^{65} + 10 q^{67} - 24 q^{69} - 12 q^{72} + 16 q^{73} - 24 q^{74} + 8 q^{75} - 6 q^{76} - 12 q^{77} + 12 q^{78} + 6 q^{79} - 2 q^{81} - 6 q^{83} + 8 q^{84} + 12 q^{85} + 12 q^{86} - 30 q^{87} + 18 q^{89} - 12 q^{90} - 24 q^{91} + 6 q^{92} + 12 q^{93} + 6 q^{94} - 6 q^{95} + 6 q^{96} + 18 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/74\mathbb{Z}\right)^\times\).

\(n\) \(39\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.866025 0.500000i 0.612372 0.353553i
\(3\) −1.36603 + 2.36603i −0.788675 + 1.36603i 0.138104 + 0.990418i \(0.455899\pi\)
−0.926779 + 0.375608i \(0.877434\pi\)
\(4\) 0.500000 0.866025i 0.250000 0.433013i
\(5\) 1.50000 + 0.866025i 0.670820 + 0.387298i 0.796387 0.604787i \(-0.206742\pi\)
−0.125567 + 0.992085i \(0.540075\pi\)
\(6\) 2.73205i 1.11536i
\(7\) 1.00000 1.73205i 0.377964 0.654654i −0.612801 0.790237i \(-0.709957\pi\)
0.990766 + 0.135583i \(0.0432908\pi\)
\(8\) 1.00000i 0.353553i
\(9\) −2.23205 3.86603i −0.744017 1.28868i
\(10\) 1.73205 0.547723
\(11\) −4.73205 −1.42677 −0.713384 0.700774i \(-0.752838\pi\)
−0.713384 + 0.700774i \(0.752838\pi\)
\(12\) 1.36603 + 2.36603i 0.394338 + 0.683013i
\(13\) −3.00000 1.73205i −0.832050 0.480384i 0.0225039 0.999747i \(-0.492836\pi\)
−0.854554 + 0.519362i \(0.826170\pi\)
\(14\) 2.00000i 0.534522i
\(15\) −4.09808 + 2.36603i −1.05812 + 0.610905i
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) 6.69615 3.86603i 1.62406 0.937649i 0.638236 0.769841i \(-0.279664\pi\)
0.985820 0.167808i \(-0.0536689\pi\)
\(18\) −3.86603 2.23205i −0.911231 0.526099i
\(19\) 1.09808 + 0.633975i 0.251916 + 0.145444i 0.620641 0.784095i \(-0.286872\pi\)
−0.368725 + 0.929538i \(0.620206\pi\)
\(20\) 1.50000 0.866025i 0.335410 0.193649i
\(21\) 2.73205 + 4.73205i 0.596182 + 1.03262i
\(22\) −4.09808 + 2.36603i −0.873713 + 0.504438i
\(23\) 4.73205i 0.986701i 0.869831 + 0.493350i \(0.164228\pi\)
−0.869831 + 0.493350i \(0.835772\pi\)
\(24\) 2.36603 + 1.36603i 0.482963 + 0.278839i
\(25\) −1.00000 1.73205i −0.200000 0.346410i
\(26\) −3.46410 −0.679366
\(27\) 4.00000 0.769800
\(28\) −1.00000 1.73205i −0.188982 0.327327i
\(29\) 8.66025i 1.60817i 0.594515 + 0.804084i \(0.297344\pi\)
−0.594515 + 0.804084i \(0.702656\pi\)
\(30\) −2.36603 + 4.09808i −0.431975 + 0.748203i
\(31\) 1.26795i 0.227730i −0.993496 0.113865i \(-0.963677\pi\)
0.993496 0.113865i \(-0.0363232\pi\)
\(32\) −0.866025 0.500000i −0.153093 0.0883883i
\(33\) 6.46410 11.1962i 1.12526 1.94900i
\(34\) 3.86603 6.69615i 0.663018 1.14838i
\(35\) 3.00000 1.73205i 0.507093 0.292770i
\(36\) −4.46410 −0.744017
\(37\) −5.69615 2.13397i −0.936442 0.350823i
\(38\) 1.26795 0.205689
\(39\) 8.19615 4.73205i 1.31243 0.757735i
\(40\) 0.866025 1.50000i 0.136931 0.237171i
\(41\) −4.96410 + 8.59808i −0.775262 + 1.34279i 0.159384 + 0.987217i \(0.449049\pi\)
−0.934647 + 0.355577i \(0.884284\pi\)
\(42\) 4.73205 + 2.73205i 0.730171 + 0.421565i
\(43\) 0.928203i 0.141550i −0.997492 0.0707748i \(-0.977453\pi\)
0.997492 0.0707748i \(-0.0225472\pi\)
\(44\) −2.36603 + 4.09808i −0.356692 + 0.617808i
\(45\) 7.73205i 1.15263i
\(46\) 2.36603 + 4.09808i 0.348851 + 0.604228i
\(47\) 4.73205 0.690241 0.345120 0.938558i \(-0.387838\pi\)
0.345120 + 0.938558i \(0.387838\pi\)
\(48\) 2.73205 0.394338
\(49\) 1.50000 + 2.59808i 0.214286 + 0.371154i
\(50\) −1.73205 1.00000i −0.244949 0.141421i
\(51\) 21.1244i 2.95800i
\(52\) −3.00000 + 1.73205i −0.416025 + 0.240192i
\(53\) −1.26795 2.19615i −0.174166 0.301665i 0.765706 0.643191i \(-0.222390\pi\)
−0.939872 + 0.341526i \(0.889056\pi\)
\(54\) 3.46410 2.00000i 0.471405 0.272166i
\(55\) −7.09808 4.09808i −0.957104 0.552584i
\(56\) −1.73205 1.00000i −0.231455 0.133631i
\(57\) −3.00000 + 1.73205i −0.397360 + 0.229416i
\(58\) 4.33013 + 7.50000i 0.568574 + 0.984798i
\(59\) 2.19615 1.26795i 0.285915 0.165073i −0.350183 0.936681i \(-0.613881\pi\)
0.636098 + 0.771608i \(0.280547\pi\)
\(60\) 4.73205i 0.610905i
\(61\) 1.50000 + 0.866025i 0.192055 + 0.110883i 0.592944 0.805243i \(-0.297965\pi\)
−0.400889 + 0.916127i \(0.631299\pi\)
\(62\) −0.633975 1.09808i −0.0805149 0.139456i
\(63\) −8.92820 −1.12485
\(64\) −1.00000 −0.125000
\(65\) −3.00000 5.19615i −0.372104 0.644503i
\(66\) 12.9282i 1.59135i
\(67\) 5.09808 8.83013i 0.622829 1.07877i −0.366127 0.930565i \(-0.619317\pi\)
0.988956 0.148207i \(-0.0473502\pi\)
\(68\) 7.73205i 0.937649i
\(69\) −11.1962 6.46410i −1.34786 0.778186i
\(70\) 1.73205 3.00000i 0.207020 0.358569i
\(71\) −1.73205 + 3.00000i −0.205557 + 0.356034i −0.950310 0.311305i \(-0.899234\pi\)
0.744753 + 0.667340i \(0.232567\pi\)
\(72\) −3.86603 + 2.23205i −0.455615 + 0.263050i
\(73\) 4.00000 0.468165 0.234082 0.972217i \(-0.424791\pi\)
0.234082 + 0.972217i \(0.424791\pi\)
\(74\) −6.00000 + 1.00000i −0.697486 + 0.116248i
\(75\) 5.46410 0.630940
\(76\) 1.09808 0.633975i 0.125958 0.0727219i
\(77\) −4.73205 + 8.19615i −0.539267 + 0.934038i
\(78\) 4.73205 8.19615i 0.535799 0.928032i
\(79\) −11.4904 6.63397i −1.29277 0.746380i −0.313625 0.949547i \(-0.601543\pi\)
−0.979144 + 0.203167i \(0.934877\pi\)
\(80\) 1.73205i 0.193649i
\(81\) 1.23205 2.13397i 0.136895 0.237108i
\(82\) 9.92820i 1.09639i
\(83\) 2.83013 + 4.90192i 0.310647 + 0.538056i 0.978503 0.206235i \(-0.0661210\pi\)
−0.667856 + 0.744291i \(0.732788\pi\)
\(84\) 5.46410 0.596182
\(85\) 13.3923 1.45260
\(86\) −0.464102 0.803848i −0.0500454 0.0866811i
\(87\) −20.4904 11.8301i −2.19680 1.26832i
\(88\) 4.73205i 0.504438i
\(89\) −5.89230 + 3.40192i −0.624583 + 0.360603i −0.778651 0.627457i \(-0.784096\pi\)
0.154068 + 0.988060i \(0.450762\pi\)
\(90\) −3.86603 6.69615i −0.407515 0.705836i
\(91\) −6.00000 + 3.46410i −0.628971 + 0.363137i
\(92\) 4.09808 + 2.36603i 0.427254 + 0.246675i
\(93\) 3.00000 + 1.73205i 0.311086 + 0.179605i
\(94\) 4.09808 2.36603i 0.422684 0.244037i
\(95\) 1.09808 + 1.90192i 0.112660 + 0.195133i
\(96\) 2.36603 1.36603i 0.241481 0.139419i
\(97\) 7.73205i 0.785071i 0.919737 + 0.392535i \(0.128402\pi\)
−0.919737 + 0.392535i \(0.871598\pi\)
\(98\) 2.59808 + 1.50000i 0.262445 + 0.151523i
\(99\) 10.5622 + 18.2942i 1.06154 + 1.83864i
\(100\) −2.00000 −0.200000
\(101\) 12.4641 1.24022 0.620112 0.784513i \(-0.287087\pi\)
0.620112 + 0.784513i \(0.287087\pi\)
\(102\) 10.5622 + 18.2942i 1.04581 + 1.81140i
\(103\) 8.53590i 0.841067i −0.907277 0.420534i \(-0.861843\pi\)
0.907277 0.420534i \(-0.138157\pi\)
\(104\) −1.73205 + 3.00000i −0.169842 + 0.294174i
\(105\) 9.46410i 0.923602i
\(106\) −2.19615 1.26795i −0.213309 0.123154i
\(107\) 5.19615 9.00000i 0.502331 0.870063i −0.497665 0.867369i \(-0.665809\pi\)
0.999996 0.00269372i \(-0.000857438\pi\)
\(108\) 2.00000 3.46410i 0.192450 0.333333i
\(109\) 2.30385 1.33013i 0.220669 0.127403i −0.385591 0.922670i \(-0.626002\pi\)
0.606260 + 0.795267i \(0.292669\pi\)
\(110\) −8.19615 −0.781472
\(111\) 12.8301 10.5622i 1.21778 1.00252i
\(112\) −2.00000 −0.188982
\(113\) −3.00000 + 1.73205i −0.282216 + 0.162938i −0.634426 0.772983i \(-0.718764\pi\)
0.352210 + 0.935921i \(0.385430\pi\)
\(114\) −1.73205 + 3.00000i −0.162221 + 0.280976i
\(115\) −4.09808 + 7.09808i −0.382148 + 0.661899i
\(116\) 7.50000 + 4.33013i 0.696358 + 0.402042i
\(117\) 15.4641i 1.42966i
\(118\) 1.26795 2.19615i 0.116724 0.202172i
\(119\) 15.4641i 1.41759i
\(120\) 2.36603 + 4.09808i 0.215988 + 0.374101i
\(121\) 11.3923 1.03566
\(122\) 1.73205 0.156813
\(123\) −13.5622 23.4904i −1.22286 2.11806i
\(124\) −1.09808 0.633975i −0.0986102 0.0569326i
\(125\) 12.1244i 1.08444i
\(126\) −7.73205 + 4.46410i −0.688826 + 0.397694i
\(127\) 3.90192 + 6.75833i 0.346240 + 0.599705i 0.985578 0.169221i \(-0.0541250\pi\)
−0.639338 + 0.768925i \(0.720792\pi\)
\(128\) −0.866025 + 0.500000i −0.0765466 + 0.0441942i
\(129\) 2.19615 + 1.26795i 0.193360 + 0.111637i
\(130\) −5.19615 3.00000i −0.455733 0.263117i
\(131\) 8.49038 4.90192i 0.741808 0.428283i −0.0809183 0.996721i \(-0.525785\pi\)
0.822726 + 0.568438i \(0.192452\pi\)
\(132\) −6.46410 11.1962i −0.562628 0.974500i
\(133\) 2.19615 1.26795i 0.190431 0.109945i
\(134\) 10.1962i 0.880813i
\(135\) 6.00000 + 3.46410i 0.516398 + 0.298142i
\(136\) −3.86603 6.69615i −0.331509 0.574190i
\(137\) −1.39230 −0.118953 −0.0594763 0.998230i \(-0.518943\pi\)
−0.0594763 + 0.998230i \(0.518943\pi\)
\(138\) −12.9282 −1.10052
\(139\) 10.2942 + 17.8301i 0.873145 + 1.51233i 0.858726 + 0.512436i \(0.171257\pi\)
0.0144194 + 0.999896i \(0.495410\pi\)
\(140\) 3.46410i 0.292770i
\(141\) −6.46410 + 11.1962i −0.544376 + 0.942886i
\(142\) 3.46410i 0.290701i
\(143\) 14.1962 + 8.19615i 1.18714 + 0.685397i
\(144\) −2.23205 + 3.86603i −0.186004 + 0.322169i
\(145\) −7.50000 + 12.9904i −0.622841 + 1.07879i
\(146\) 3.46410 2.00000i 0.286691 0.165521i
\(147\) −8.19615 −0.676007
\(148\) −4.69615 + 3.86603i −0.386021 + 0.317785i
\(149\) −15.9282 −1.30489 −0.652445 0.757836i \(-0.726257\pi\)
−0.652445 + 0.757836i \(0.726257\pi\)
\(150\) 4.73205 2.73205i 0.386370 0.223071i
\(151\) −2.09808 + 3.63397i −0.170739 + 0.295729i −0.938678 0.344794i \(-0.887949\pi\)
0.767939 + 0.640522i \(0.221282\pi\)
\(152\) 0.633975 1.09808i 0.0514221 0.0890657i
\(153\) −29.8923 17.2583i −2.41665 1.39525i
\(154\) 9.46410i 0.762639i
\(155\) 1.09808 1.90192i 0.0881996 0.152766i
\(156\) 9.46410i 0.757735i
\(157\) −0.500000 0.866025i −0.0399043 0.0691164i 0.845383 0.534160i \(-0.179372\pi\)
−0.885288 + 0.465044i \(0.846039\pi\)
\(158\) −13.2679 −1.05554
\(159\) 6.92820 0.549442
\(160\) −0.866025 1.50000i −0.0684653 0.118585i
\(161\) 8.19615 + 4.73205i 0.645947 + 0.372938i
\(162\) 2.46410i 0.193598i
\(163\) 11.1962 6.46410i 0.876950 0.506308i 0.00729867 0.999973i \(-0.497677\pi\)
0.869652 + 0.493666i \(0.164343\pi\)
\(164\) 4.96410 + 8.59808i 0.387631 + 0.671397i
\(165\) 19.3923 11.1962i 1.50969 0.871619i
\(166\) 4.90192 + 2.83013i 0.380463 + 0.219660i
\(167\) −12.0000 6.92820i −0.928588 0.536120i −0.0422232 0.999108i \(-0.513444\pi\)
−0.886365 + 0.462988i \(0.846777\pi\)
\(168\) 4.73205 2.73205i 0.365086 0.210782i
\(169\) −0.500000 0.866025i −0.0384615 0.0666173i
\(170\) 11.5981 6.69615i 0.889532 0.513571i
\(171\) 5.66025i 0.432850i
\(172\) −0.803848 0.464102i −0.0612928 0.0353874i
\(173\) −2.76795 4.79423i −0.210443 0.364498i 0.741410 0.671052i \(-0.234157\pi\)
−0.951853 + 0.306554i \(0.900824\pi\)
\(174\) −23.6603 −1.79368
\(175\) −4.00000 −0.302372
\(176\) 2.36603 + 4.09808i 0.178346 + 0.308904i
\(177\) 6.92820i 0.520756i
\(178\) −3.40192 + 5.89230i −0.254985 + 0.441647i
\(179\) 9.46410i 0.707380i −0.935363 0.353690i \(-0.884927\pi\)
0.935363 0.353690i \(-0.115073\pi\)
\(180\) −6.69615 3.86603i −0.499102 0.288157i
\(181\) 4.69615 8.13397i 0.349062 0.604594i −0.637021 0.770847i \(-0.719834\pi\)
0.986083 + 0.166253i \(0.0531668\pi\)
\(182\) −3.46410 + 6.00000i −0.256776 + 0.444750i
\(183\) −4.09808 + 2.36603i −0.302939 + 0.174902i
\(184\) 4.73205 0.348851
\(185\) −6.69615 8.13397i −0.492311 0.598022i
\(186\) 3.46410 0.254000
\(187\) −31.6865 + 18.2942i −2.31715 + 1.33781i
\(188\) 2.36603 4.09808i 0.172560 0.298883i
\(189\) 4.00000 6.92820i 0.290957 0.503953i
\(190\) 1.90192 + 1.09808i 0.137980 + 0.0796628i
\(191\) 2.19615i 0.158908i 0.996839 + 0.0794540i \(0.0253177\pi\)
−0.996839 + 0.0794540i \(0.974682\pi\)
\(192\) 1.36603 2.36603i 0.0985844 0.170753i
\(193\) 11.1962i 0.805917i 0.915218 + 0.402958i \(0.132018\pi\)
−0.915218 + 0.402958i \(0.867982\pi\)
\(194\) 3.86603 + 6.69615i 0.277564 + 0.480756i
\(195\) 16.3923 1.17388
\(196\) 3.00000 0.214286
\(197\) −3.23205 5.59808i −0.230274 0.398846i 0.727615 0.685986i \(-0.240629\pi\)
−0.957889 + 0.287140i \(0.907296\pi\)
\(198\) 18.2942 + 10.5622i 1.30011 + 0.750621i
\(199\) 10.3923i 0.736691i −0.929689 0.368345i \(-0.879924\pi\)
0.929689 0.368345i \(-0.120076\pi\)
\(200\) −1.73205 + 1.00000i −0.122474 + 0.0707107i
\(201\) 13.9282 + 24.1244i 0.982420 + 1.70160i
\(202\) 10.7942 6.23205i 0.759479 0.438486i
\(203\) 15.0000 + 8.66025i 1.05279 + 0.607831i
\(204\) 18.2942 + 10.5622i 1.28085 + 0.739500i
\(205\) −14.8923 + 8.59808i −1.04012 + 0.600516i
\(206\) −4.26795 7.39230i −0.297362 0.515046i
\(207\) 18.2942 10.5622i 1.27154 0.734122i
\(208\) 3.46410i 0.240192i
\(209\) −5.19615 3.00000i −0.359425 0.207514i
\(210\) 4.73205 + 8.19615i 0.326543 + 0.565588i
\(211\) −2.39230 −0.164693 −0.0823465 0.996604i \(-0.526241\pi\)
−0.0823465 + 0.996604i \(0.526241\pi\)
\(212\) −2.53590 −0.174166
\(213\) −4.73205 8.19615i −0.324235 0.561591i
\(214\) 10.3923i 0.710403i
\(215\) 0.803848 1.39230i 0.0548219 0.0949544i
\(216\) 4.00000i 0.272166i
\(217\) −2.19615 1.26795i −0.149085 0.0860740i
\(218\) 1.33013 2.30385i 0.0900876 0.156036i
\(219\) −5.46410 + 9.46410i −0.369230 + 0.639525i
\(220\) −7.09808 + 4.09808i −0.478552 + 0.276292i
\(221\) −26.7846 −1.80173
\(222\) 5.83013 15.5622i 0.391293 1.04446i
\(223\) 16.1962 1.08457 0.542287 0.840193i \(-0.317558\pi\)
0.542287 + 0.840193i \(0.317558\pi\)
\(224\) −1.73205 + 1.00000i −0.115728 + 0.0668153i
\(225\) −4.46410 + 7.73205i −0.297607 + 0.515470i
\(226\) −1.73205 + 3.00000i −0.115214 + 0.199557i
\(227\) 1.09808 + 0.633975i 0.0728819 + 0.0420784i 0.535998 0.844219i \(-0.319935\pi\)
−0.463116 + 0.886298i \(0.653269\pi\)
\(228\) 3.46410i 0.229416i
\(229\) −13.6962 + 23.7224i −0.905067 + 1.56762i −0.0842403 + 0.996445i \(0.526846\pi\)
−0.820827 + 0.571177i \(0.806487\pi\)
\(230\) 8.19615i 0.540438i
\(231\) −12.9282 22.3923i −0.850613 1.47331i
\(232\) 8.66025 0.568574
\(233\) 15.0000 0.982683 0.491341 0.870967i \(-0.336507\pi\)
0.491341 + 0.870967i \(0.336507\pi\)
\(234\) 7.73205 + 13.3923i 0.505460 + 0.875482i
\(235\) 7.09808 + 4.09808i 0.463027 + 0.267329i
\(236\) 2.53590i 0.165073i
\(237\) 31.3923 18.1244i 2.03915 1.17730i
\(238\) −7.73205 13.3923i −0.501194 0.868094i
\(239\) −15.0000 + 8.66025i −0.970269 + 0.560185i −0.899318 0.437295i \(-0.855937\pi\)
−0.0709510 + 0.997480i \(0.522603\pi\)
\(240\) 4.09808 + 2.36603i 0.264530 + 0.152726i
\(241\) 13.3923 + 7.73205i 0.862674 + 0.498065i 0.864907 0.501932i \(-0.167377\pi\)
−0.00223270 + 0.999998i \(0.500711\pi\)
\(242\) 9.86603 5.69615i 0.634212 0.366163i
\(243\) 9.36603 + 16.2224i 0.600831 + 1.04067i
\(244\) 1.50000 0.866025i 0.0960277 0.0554416i
\(245\) 5.19615i 0.331970i
\(246\) −23.4904 13.5622i −1.49769 0.864693i
\(247\) −2.19615 3.80385i −0.139738 0.242033i
\(248\) −1.26795 −0.0805149
\(249\) −15.4641 −0.979998
\(250\) −6.06218 10.5000i −0.383406 0.664078i
\(251\) 17.3205i 1.09326i −0.837374 0.546630i \(-0.815910\pi\)
0.837374 0.546630i \(-0.184090\pi\)
\(252\) −4.46410 + 7.73205i −0.281212 + 0.487073i
\(253\) 22.3923i 1.40779i
\(254\) 6.75833 + 3.90192i 0.424055 + 0.244828i
\(255\) −18.2942 + 31.6865i −1.14563 + 1.98429i
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) 5.89230 3.40192i 0.367552 0.212206i −0.304837 0.952405i \(-0.598602\pi\)
0.672388 + 0.740199i \(0.265268\pi\)
\(258\) 2.53590 0.157878
\(259\) −9.39230 + 7.73205i −0.583609 + 0.480446i
\(260\) −6.00000 −0.372104
\(261\) 33.4808 19.3301i 2.07241 1.19650i
\(262\) 4.90192 8.49038i 0.302842 0.524537i
\(263\) −10.7321 + 18.5885i −0.661767 + 1.14621i 0.318385 + 0.947962i \(0.396860\pi\)
−0.980151 + 0.198252i \(0.936474\pi\)
\(264\) −11.1962 6.46410i −0.689076 0.397838i
\(265\) 4.39230i 0.269817i
\(266\) 1.26795 2.19615i 0.0777430 0.134655i
\(267\) 18.5885i 1.13760i
\(268\) −5.09808 8.83013i −0.311415 0.539386i
\(269\) −4.39230 −0.267804 −0.133902 0.990995i \(-0.542751\pi\)
−0.133902 + 0.990995i \(0.542751\pi\)
\(270\) 6.92820 0.421637
\(271\) 1.29423 + 2.24167i 0.0786188 + 0.136172i 0.902654 0.430367i \(-0.141616\pi\)
−0.824035 + 0.566538i \(0.808282\pi\)
\(272\) −6.69615 3.86603i −0.406014 0.234412i
\(273\) 18.9282i 1.14559i
\(274\) −1.20577 + 0.696152i −0.0728433 + 0.0420561i
\(275\) 4.73205 + 8.19615i 0.285353 + 0.494247i
\(276\) −11.1962 + 6.46410i −0.673929 + 0.389093i
\(277\) 9.69615 + 5.59808i 0.582585 + 0.336356i 0.762160 0.647389i \(-0.224139\pi\)
−0.179575 + 0.983744i \(0.557472\pi\)
\(278\) 17.8301 + 10.2942i 1.06938 + 0.617407i
\(279\) −4.90192 + 2.83013i −0.293471 + 0.169435i
\(280\) −1.73205 3.00000i −0.103510 0.179284i
\(281\) −23.8923 + 13.7942i −1.42530 + 0.822895i −0.996745 0.0806230i \(-0.974309\pi\)
−0.428551 + 0.903518i \(0.640976\pi\)
\(282\) 12.9282i 0.769863i
\(283\) −6.80385 3.92820i −0.404447 0.233507i 0.283954 0.958838i \(-0.408354\pi\)
−0.688401 + 0.725330i \(0.741687\pi\)
\(284\) 1.73205 + 3.00000i 0.102778 + 0.178017i
\(285\) −6.00000 −0.355409
\(286\) 16.3923 0.969297
\(287\) 9.92820 + 17.1962i 0.586043 + 1.01506i
\(288\) 4.46410i 0.263050i
\(289\) 21.3923 37.0526i 1.25837 2.17956i
\(290\) 15.0000i 0.880830i
\(291\) −18.2942 10.5622i −1.07243 0.619166i
\(292\) 2.00000 3.46410i 0.117041 0.202721i
\(293\) 0.696152 1.20577i 0.0406697 0.0704419i −0.844974 0.534807i \(-0.820384\pi\)
0.885644 + 0.464365i \(0.153718\pi\)
\(294\) −7.09808 + 4.09808i −0.413968 + 0.239005i
\(295\) 4.39230 0.255730
\(296\) −2.13397 + 5.69615i −0.124035 + 0.331082i
\(297\) −18.9282 −1.09833
\(298\) −13.7942 + 7.96410i −0.799078 + 0.461348i
\(299\) 8.19615 14.1962i 0.473996 0.820985i
\(300\) 2.73205 4.73205i 0.157735 0.273205i
\(301\) −1.60770 0.928203i −0.0926660 0.0535007i
\(302\) 4.19615i 0.241461i
\(303\) −17.0263 + 29.4904i −0.978134 + 1.69418i
\(304\) 1.26795i 0.0727219i
\(305\) 1.50000 + 2.59808i 0.0858898 + 0.148765i
\(306\) −34.5167 −1.97319
\(307\) −22.0000 −1.25561 −0.627803 0.778372i \(-0.716046\pi\)
−0.627803 + 0.778372i \(0.716046\pi\)
\(308\) 4.73205 + 8.19615i 0.269634 + 0.467019i
\(309\) 20.1962 + 11.6603i 1.14892 + 0.663329i
\(310\) 2.19615i 0.124733i
\(311\) −15.5885 + 9.00000i −0.883940 + 0.510343i −0.871956 0.489585i \(-0.837148\pi\)
−0.0119847 + 0.999928i \(0.503815\pi\)
\(312\) −4.73205 8.19615i −0.267900 0.464016i
\(313\) 20.8923 12.0622i 1.18090 0.681795i 0.224680 0.974433i \(-0.427866\pi\)
0.956223 + 0.292638i \(0.0945331\pi\)
\(314\) −0.866025 0.500000i −0.0488726 0.0282166i
\(315\) −13.3923 7.73205i −0.754571 0.435652i
\(316\) −11.4904 + 6.63397i −0.646384 + 0.373190i
\(317\) −3.69615 6.40192i −0.207597 0.359568i 0.743360 0.668891i \(-0.233231\pi\)
−0.950957 + 0.309323i \(0.899897\pi\)
\(318\) 6.00000 3.46410i 0.336463 0.194257i
\(319\) 40.9808i 2.29448i
\(320\) −1.50000 0.866025i −0.0838525 0.0484123i
\(321\) 14.1962 + 24.5885i 0.792352 + 1.37239i
\(322\) 9.46410 0.527414
\(323\) 9.80385 0.545501
\(324\) −1.23205 2.13397i −0.0684473 0.118554i
\(325\) 6.92820i 0.384308i
\(326\) 6.46410 11.1962i 0.358013 0.620098i
\(327\) 7.26795i 0.401919i
\(328\) 8.59808 + 4.96410i 0.474749 + 0.274097i
\(329\) 4.73205 8.19615i 0.260886 0.451869i
\(330\) 11.1962 19.3923i 0.616328 1.06751i
\(331\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(332\) 5.66025 0.310647
\(333\) 4.46410 + 26.7846i 0.244631 + 1.46779i
\(334\) −13.8564 −0.758189
\(335\) 15.2942 8.83013i 0.835613 0.482441i
\(336\) 2.73205 4.73205i 0.149046 0.258155i
\(337\) 16.0885 27.8660i 0.876394 1.51796i 0.0211239 0.999777i \(-0.493276\pi\)
0.855270 0.518182i \(-0.173391\pi\)
\(338\) −0.866025 0.500000i −0.0471056 0.0271964i
\(339\) 9.46410i 0.514019i
\(340\) 6.69615 11.5981i 0.363150 0.628994i
\(341\) 6.00000i 0.324918i
\(342\) −2.83013 4.90192i −0.153036 0.265066i
\(343\) 20.0000 1.07990
\(344\) −0.928203 −0.0500454
\(345\) −11.1962 19.3923i −0.602781 1.04405i
\(346\) −4.79423 2.76795i −0.257739 0.148806i
\(347\) 9.12436i 0.489821i 0.969546 + 0.244911i \(0.0787586\pi\)
−0.969546 + 0.244911i \(0.921241\pi\)
\(348\) −20.4904 + 11.8301i −1.09840 + 0.634161i
\(349\) −5.69615 9.86603i −0.304908 0.528116i 0.672333 0.740249i \(-0.265292\pi\)
−0.977241 + 0.212133i \(0.931959\pi\)
\(350\) −3.46410 + 2.00000i −0.185164 + 0.106904i
\(351\) −12.0000 6.92820i −0.640513 0.369800i
\(352\) 4.09808 + 2.36603i 0.218428 + 0.126110i
\(353\) −17.0885 + 9.86603i −0.909527 + 0.525116i −0.880279 0.474457i \(-0.842645\pi\)
−0.0292479 + 0.999572i \(0.509311\pi\)
\(354\) 3.46410 + 6.00000i 0.184115 + 0.318896i
\(355\) −5.19615 + 3.00000i −0.275783 + 0.159223i
\(356\) 6.80385i 0.360603i
\(357\) 36.5885 + 21.1244i 1.93647 + 1.11802i
\(358\) −4.73205 8.19615i −0.250097 0.433180i
\(359\) 35.3205 1.86415 0.932073 0.362272i \(-0.117999\pi\)
0.932073 + 0.362272i \(0.117999\pi\)
\(360\) −7.73205 −0.407515
\(361\) −8.69615 15.0622i −0.457692 0.792746i
\(362\) 9.39230i 0.493649i
\(363\) −15.5622 + 26.9545i −0.816803 + 1.41474i
\(364\) 6.92820i 0.363137i
\(365\) 6.00000 + 3.46410i 0.314054 + 0.181319i
\(366\) −2.36603 + 4.09808i −0.123674 + 0.214210i
\(367\) −6.19615 + 10.7321i −0.323437 + 0.560208i −0.981195 0.193021i \(-0.938172\pi\)
0.657758 + 0.753229i \(0.271505\pi\)
\(368\) 4.09808 2.36603i 0.213627 0.123338i
\(369\) 44.3205 2.30723
\(370\) −9.86603 3.69615i −0.512910 0.192154i
\(371\) −5.07180 −0.263315
\(372\) 3.00000 1.73205i 0.155543 0.0898027i
\(373\) −3.50000 + 6.06218i −0.181223 + 0.313888i −0.942297 0.334777i \(-0.891339\pi\)
0.761074 + 0.648665i \(0.224672\pi\)
\(374\) −18.2942 + 31.6865i −0.945972 + 1.63847i
\(375\) 28.6865 + 16.5622i 1.48137 + 0.855267i
\(376\) 4.73205i 0.244037i
\(377\) 15.0000 25.9808i 0.772539 1.33808i
\(378\) 8.00000i 0.411476i
\(379\) 17.3923 + 30.1244i 0.893383 + 1.54738i 0.835794 + 0.549044i \(0.185008\pi\)
0.0575891 + 0.998340i \(0.481659\pi\)
\(380\) 2.19615 0.112660
\(381\) −21.3205 −1.09228
\(382\) 1.09808 + 1.90192i 0.0561825 + 0.0973109i
\(383\) −3.00000 1.73205i −0.153293 0.0885037i 0.421392 0.906879i \(-0.361542\pi\)
−0.574684 + 0.818375i \(0.694875\pi\)
\(384\) 2.73205i 0.139419i
\(385\) −14.1962 + 8.19615i −0.723503 + 0.417715i
\(386\) 5.59808 + 9.69615i 0.284935 + 0.493521i
\(387\) −3.58846 + 2.07180i −0.182412 + 0.105315i
\(388\) 6.69615 + 3.86603i 0.339946 + 0.196268i
\(389\) −22.5000 12.9904i −1.14080 0.658638i −0.194168 0.980968i \(-0.562201\pi\)
−0.946627 + 0.322330i \(0.895534\pi\)
\(390\) 14.1962 8.19615i 0.718850 0.415028i
\(391\) 18.2942 + 31.6865i 0.925179 + 1.60246i
\(392\) 2.59808 1.50000i 0.131223 0.0757614i
\(393\) 26.7846i 1.35110i
\(394\) −5.59808 3.23205i −0.282027 0.162828i
\(395\) −11.4904 19.9019i −0.578144 1.00137i
\(396\) 21.1244 1.06154
\(397\) −23.0000 −1.15434 −0.577168 0.816625i \(-0.695842\pi\)
−0.577168 + 0.816625i \(0.695842\pi\)
\(398\) −5.19615 9.00000i −0.260460 0.451129i
\(399\) 6.92820i 0.346844i
\(400\) −1.00000 + 1.73205i −0.0500000 + 0.0866025i
\(401\) 10.3923i 0.518967i −0.965748 0.259483i \(-0.916448\pi\)
0.965748 0.259483i \(-0.0835523\pi\)
\(402\) 24.1244 + 13.9282i 1.20321 + 0.694676i
\(403\) −2.19615 + 3.80385i −0.109398 + 0.189483i
\(404\) 6.23205 10.7942i 0.310056 0.537033i
\(405\) 3.69615 2.13397i 0.183663 0.106038i
\(406\) 17.3205 0.859602
\(407\) 26.9545 + 10.0981i 1.33608 + 0.500543i
\(408\) 21.1244 1.04581
\(409\) 9.10770 5.25833i 0.450347 0.260008i −0.257630 0.966244i \(-0.582942\pi\)
0.707977 + 0.706236i \(0.249608\pi\)
\(410\) −8.59808 + 14.8923i −0.424629 + 0.735479i
\(411\) 1.90192 3.29423i 0.0938150 0.162492i
\(412\) −7.39230 4.26795i −0.364193 0.210267i
\(413\) 5.07180i 0.249567i
\(414\) 10.5622 18.2942i 0.519103 0.899112i
\(415\) 9.80385i 0.481252i
\(416\) 1.73205 + 3.00000i 0.0849208 + 0.147087i
\(417\) −56.2487 −2.75451
\(418\) −6.00000 −0.293470
\(419\) 2.07180 + 3.58846i 0.101214 + 0.175308i 0.912185 0.409779i \(-0.134394\pi\)
−0.810971 + 0.585086i \(0.801061\pi\)
\(420\) 8.19615 + 4.73205i 0.399931 + 0.230900i
\(421\) 12.1244i 0.590905i −0.955357 0.295452i \(-0.904530\pi\)
0.955357 0.295452i \(-0.0954704\pi\)
\(422\) −2.07180 + 1.19615i −0.100853 + 0.0582278i
\(423\) −10.5622 18.2942i −0.513551 0.889496i
\(424\) −2.19615 + 1.26795i −0.106655 + 0.0615771i
\(425\) −13.3923 7.73205i −0.649622 0.375060i
\(426\) −8.19615 4.73205i −0.397105 0.229269i
\(427\) 3.00000 1.73205i 0.145180 0.0838198i
\(428\) −5.19615 9.00000i −0.251166 0.435031i
\(429\) −38.7846 + 22.3923i −1.87254 + 1.08111i
\(430\) 1.60770i 0.0775299i
\(431\) −15.2942 8.83013i −0.736697 0.425332i 0.0841701 0.996451i \(-0.473176\pi\)
−0.820867 + 0.571119i \(0.806509\pi\)
\(432\) −2.00000 3.46410i −0.0962250 0.166667i
\(433\) 15.7846 0.758560 0.379280 0.925282i \(-0.376172\pi\)
0.379280 + 0.925282i \(0.376172\pi\)
\(434\) −2.53590 −0.121727
\(435\) −20.4904 35.4904i −0.982439 1.70163i
\(436\) 2.66025i 0.127403i
\(437\) −3.00000 + 5.19615i −0.143509 + 0.248566i
\(438\) 10.9282i 0.522170i
\(439\) −15.8038 9.12436i −0.754276 0.435482i 0.0729605 0.997335i \(-0.476755\pi\)
−0.827237 + 0.561853i \(0.810089\pi\)
\(440\) −4.09808 + 7.09808i −0.195368 + 0.338388i
\(441\) 6.69615 11.5981i 0.318864 0.552289i
\(442\) −23.1962 + 13.3923i −1.10333 + 0.637007i
\(443\) −14.5359 −0.690621 −0.345311 0.938488i \(-0.612226\pi\)
−0.345311 + 0.938488i \(0.612226\pi\)
\(444\) −2.73205 16.3923i −0.129657 0.777944i
\(445\) −11.7846 −0.558644
\(446\) 14.0263 8.09808i 0.664164 0.383455i
\(447\) 21.7583 37.6865i 1.02913 1.78251i
\(448\) −1.00000 + 1.73205i −0.0472456 + 0.0818317i
\(449\) 17.7846 + 10.2679i 0.839308 + 0.484574i 0.857029 0.515268i \(-0.172308\pi\)
−0.0177212 + 0.999843i \(0.505641\pi\)
\(450\) 8.92820i 0.420880i
\(451\) 23.4904 40.6865i 1.10612 1.91585i
\(452\) 3.46410i 0.162938i
\(453\) −5.73205 9.92820i −0.269315 0.466468i
\(454\) 1.26795 0.0595078
\(455\) −12.0000 −0.562569
\(456\) 1.73205 + 3.00000i 0.0811107 + 0.140488i
\(457\) −32.8923 18.9904i −1.53864 0.888333i −0.998919 0.0464868i \(-0.985197\pi\)
−0.539718 0.841846i \(-0.681469\pi\)
\(458\) 27.3923i 1.27996i
\(459\) 26.7846 15.4641i 1.25020 0.721802i
\(460\) 4.09808 + 7.09808i 0.191074 + 0.330950i
\(461\) −34.1769 + 19.7321i −1.59178 + 0.919013i −0.598775 + 0.800917i \(0.704346\pi\)
−0.993002 + 0.118096i \(0.962321\pi\)
\(462\) −22.3923 12.9282i −1.04178 0.601474i
\(463\) −25.9808 15.0000i −1.20743 0.697109i −0.245232 0.969465i \(-0.578864\pi\)
−0.962197 + 0.272355i \(0.912197\pi\)
\(464\) 7.50000 4.33013i 0.348179 0.201021i
\(465\) 3.00000 + 5.19615i 0.139122 + 0.240966i
\(466\) 12.9904 7.50000i 0.601768 0.347431i
\(467\) 2.53590i 0.117347i −0.998277 0.0586737i \(-0.981313\pi\)
0.998277 0.0586737i \(-0.0186871\pi\)
\(468\) 13.3923 + 7.73205i 0.619060 + 0.357414i
\(469\) −10.1962 17.6603i −0.470815 0.815475i
\(470\) 8.19615 0.378060
\(471\) 2.73205 0.125886
\(472\) −1.26795 2.19615i −0.0583621 0.101086i
\(473\) 4.39230i 0.201958i
\(474\) 18.1244 31.3923i 0.832479 1.44190i
\(475\) 2.53590i 0.116355i
\(476\) −13.3923 7.73205i −0.613835 0.354398i
\(477\) −5.66025 + 9.80385i −0.259165 + 0.448887i
\(478\) −8.66025 + 15.0000i −0.396111 + 0.686084i
\(479\) 8.19615 4.73205i 0.374492 0.216213i −0.300927 0.953647i \(-0.597296\pi\)
0.675419 + 0.737434i \(0.263963\pi\)
\(480\) 4.73205 0.215988
\(481\) 13.3923 + 16.2679i 0.610637 + 0.741755i
\(482\) 15.4641 0.704371
\(483\) −22.3923 + 12.9282i −1.01889 + 0.588254i
\(484\) 5.69615 9.86603i 0.258916 0.448456i
\(485\) −6.69615 + 11.5981i −0.304057 + 0.526642i
\(486\) 16.2224 + 9.36603i 0.735864 + 0.424852i
\(487\) 16.0526i 0.727411i 0.931514 + 0.363705i \(0.118489\pi\)
−0.931514 + 0.363705i \(0.881511\pi\)
\(488\) 0.866025 1.50000i 0.0392031 0.0679018i
\(489\) 35.3205i 1.59725i
\(490\) 2.59808 + 4.50000i 0.117369 + 0.203289i
\(491\) 26.1962 1.18222 0.591108 0.806592i \(-0.298691\pi\)
0.591108 + 0.806592i \(0.298691\pi\)
\(492\) −27.1244 −1.22286
\(493\) 33.4808 + 57.9904i 1.50790 + 2.61176i
\(494\) −3.80385 2.19615i −0.171143 0.0988096i
\(495\) 36.5885i 1.64453i
\(496\) −1.09808 + 0.633975i −0.0493051 + 0.0284663i
\(497\) 3.46410 + 6.00000i 0.155386 + 0.269137i
\(498\) −13.3923 + 7.73205i −0.600124 + 0.346481i
\(499\) −17.4904 10.0981i −0.782977 0.452052i 0.0545073 0.998513i \(-0.482641\pi\)
−0.837484 + 0.546461i \(0.815975\pi\)
\(500\) −10.5000 6.06218i −0.469574 0.271109i
\(501\) 32.7846 18.9282i 1.46471 0.845650i
\(502\) −8.66025 15.0000i −0.386526 0.669483i
\(503\) −17.4904 + 10.0981i −0.779858 + 0.450251i −0.836380 0.548150i \(-0.815332\pi\)
0.0565223 + 0.998401i \(0.481999\pi\)
\(504\) 8.92820i 0.397694i
\(505\) 18.6962 + 10.7942i 0.831968 + 0.480337i
\(506\) −11.1962 19.3923i −0.497730 0.862093i
\(507\) 2.73205 0.121335
\(508\) 7.80385 0.346240
\(509\) 3.23205 + 5.59808i 0.143258 + 0.248130i 0.928722 0.370777i \(-0.120909\pi\)
−0.785464 + 0.618908i \(0.787575\pi\)
\(510\) 36.5885i 1.62016i
\(511\) 4.00000 6.92820i 0.176950 0.306486i
\(512\) 1.00000i 0.0441942i
\(513\) 4.39230 + 2.53590i 0.193925 + 0.111963i
\(514\) 3.40192 5.89230i 0.150052 0.259898i
\(515\) 7.39230 12.8038i 0.325744 0.564205i
\(516\) 2.19615 1.26795i 0.0966802 0.0558184i
\(517\) −22.3923 −0.984812
\(518\) −4.26795 + 11.3923i −0.187523 + 0.500549i
\(519\) 15.1244 0.663886
\(520\) −5.19615 + 3.00000i −0.227866 + 0.131559i
\(521\) −2.53590 + 4.39230i −0.111100 + 0.192430i −0.916214 0.400689i \(-0.868771\pi\)
0.805114 + 0.593120i \(0.202104\pi\)
\(522\) 19.3301 33.4808i 0.846057 1.46541i
\(523\) 17.7058 + 10.2224i 0.774219 + 0.446996i 0.834378 0.551193i \(-0.185827\pi\)
−0.0601584 + 0.998189i \(0.519161\pi\)
\(524\) 9.80385i 0.428283i
\(525\) 5.46410 9.46410i 0.238473 0.413047i
\(526\) 21.4641i 0.935879i
\(527\) −4.90192 8.49038i −0.213531 0.369847i
\(528\) −12.9282 −0.562628
\(529\) 0.607695 0.0264215
\(530\) −2.19615 3.80385i −0.0953948 0.165229i
\(531\) −9.80385 5.66025i −0.425451 0.245634i
\(532\) 2.53590i 0.109945i
\(533\) 29.7846 17.1962i 1.29011 0.744848i
\(534\) −9.29423 16.0981i −0.402201 0.696632i
\(535\) 15.5885 9.00000i 0.673948 0.389104i
\(536\) −8.83013 5.09808i −0.381403 0.220203i
\(537\) 22.3923 + 12.9282i 0.966299 + 0.557893i
\(538\) −3.80385 + 2.19615i −0.163996 + 0.0946829i
\(539\) −7.09808 12.2942i −0.305736 0.529550i
\(540\) 6.00000 3.46410i 0.258199 0.149071i
\(541\) 19.0526i 0.819133i 0.912280 + 0.409567i \(0.134320\pi\)
−0.912280 + 0.409567i \(0.865680\pi\)
\(542\) 2.24167 + 1.29423i 0.0962880 + 0.0555919i
\(543\) 12.8301 + 22.2224i 0.550593 + 0.953656i
\(544\) −7.73205 −0.331509
\(545\) 4.60770 0.197372
\(546\) −9.46410 16.3923i −0.405026 0.701526i
\(547\) 41.6603i 1.78126i 0.454725 + 0.890632i \(0.349738\pi\)
−0.454725 + 0.890632i \(0.650262\pi\)
\(548\) −0.696152 + 1.20577i −0.0297382 + 0.0515080i
\(549\) 7.73205i 0.329996i
\(550\) 8.19615 + 4.73205i 0.349485 + 0.201775i
\(551\) −5.49038 + 9.50962i −0.233898 + 0.405123i
\(552\) −6.46410 + 11.1962i −0.275130 + 0.476540i
\(553\) −22.9808 + 13.2679i −0.977241 + 0.564211i
\(554\) 11.1962 0.475679
\(555\) 28.3923 4.73205i 1.20519 0.200864i
\(556\) 20.5885 0.873145
\(557\) 20.3038 11.7224i 0.860302 0.496695i −0.00381165 0.999993i \(-0.501213\pi\)
0.864113 + 0.503297i \(0.167880\pi\)
\(558\) −2.83013 + 4.90192i −0.119809 + 0.207515i
\(559\) −1.60770 + 2.78461i −0.0679983 + 0.117776i
\(560\) −3.00000 1.73205i −0.126773 0.0731925i
\(561\) 99.9615i 4.22038i
\(562\) −13.7942 + 23.8923i −0.581874 + 1.00784i
\(563\) 18.5885i 0.783410i −0.920091 0.391705i \(-0.871885\pi\)
0.920091 0.391705i \(-0.128115\pi\)
\(564\) 6.46410 + 11.1962i 0.272188 + 0.471443i
\(565\) −6.00000 −0.252422
\(566\) −7.85641 −0.330229
\(567\) −2.46410 4.26795i −0.103483 0.179237i
\(568\) 3.00000 + 1.73205i 0.125877 + 0.0726752i
\(569\) 5.87564i 0.246320i −0.992387 0.123160i \(-0.960697\pi\)
0.992387 0.123160i \(-0.0393028\pi\)
\(570\) −5.19615 + 3.00000i −0.217643 + 0.125656i
\(571\) −18.6865 32.3660i −0.782007 1.35448i −0.930771 0.365603i \(-0.880863\pi\)
0.148764 0.988873i \(-0.452471\pi\)
\(572\) 14.1962 8.19615i 0.593571 0.342698i
\(573\) −5.19615 3.00000i −0.217072 0.125327i
\(574\) 17.1962 + 9.92820i 0.717754 + 0.414395i
\(575\) 8.19615 4.73205i 0.341803 0.197340i
\(576\) 2.23205 + 3.86603i 0.0930021 + 0.161084i
\(577\) −0.803848 + 0.464102i −0.0334646 + 0.0193208i −0.516639 0.856203i \(-0.672817\pi\)
0.483174 + 0.875524i \(0.339484\pi\)
\(578\) 42.7846i 1.77961i
\(579\) −26.4904 15.2942i −1.10090 0.635606i
\(580\) 7.50000 + 12.9904i 0.311421 + 0.539396i
\(581\) 11.3205 0.469654
\(582\) −21.1244 −0.875633
\(583\) 6.00000 + 10.3923i 0.248495 + 0.430405i
\(584\) 4.00000i 0.165521i
\(585\) −13.3923 + 23.1962i −0.553704 + 0.959043i
\(586\) 1.39230i 0.0575156i
\(587\) 28.6865 + 16.5622i 1.18402 + 0.683594i 0.956941 0.290282i \(-0.0937492\pi\)
0.227079 + 0.973876i \(0.427082\pi\)
\(588\) −4.09808 + 7.09808i −0.169002 + 0.292720i
\(589\) 0.803848 1.39230i 0.0331220 0.0573689i
\(590\) 3.80385 2.19615i 0.156602 0.0904142i
\(591\) 17.6603 0.726446
\(592\) 1.00000 + 6.00000i 0.0410997 + 0.246598i
\(593\) 43.6410 1.79212 0.896061 0.443931i \(-0.146417\pi\)
0.896061 + 0.443931i \(0.146417\pi\)
\(594\) −16.3923 + 9.46410i −0.672584 + 0.388317i
\(595\) 13.3923 23.1962i 0.549031 0.950950i
\(596\) −7.96410 + 13.7942i −0.326222 + 0.565034i
\(597\) 24.5885 + 14.1962i 1.00634 + 0.581010i
\(598\) 16.3923i 0.670331i
\(599\) −23.8301 + 41.2750i −0.973673 + 1.68645i −0.289425 + 0.957201i \(0.593464\pi\)
−0.684248 + 0.729250i \(0.739869\pi\)
\(600\) 5.46410i 0.223071i
\(601\) 6.30385 + 10.9186i 0.257139 + 0.445378i 0.965474 0.260498i \(-0.0838867\pi\)
−0.708335 + 0.705876i \(0.750553\pi\)
\(602\) −1.85641 −0.0756615
\(603\) −45.5167 −1.85358
\(604\) 2.09808 + 3.63397i 0.0853695 + 0.147864i
\(605\) 17.0885 + 9.86603i 0.694745 + 0.401111i
\(606\) 34.0526i 1.38329i
\(607\) −20.7058 + 11.9545i −0.840421 + 0.485217i −0.857407 0.514638i \(-0.827926\pi\)
0.0169861 + 0.999856i \(0.494593\pi\)
\(608\) −0.633975 1.09808i −0.0257111 0.0445329i
\(609\) −40.9808 + 23.6603i −1.66062 + 0.958762i
\(610\) 2.59808 + 1.50000i 0.105193 + 0.0607332i
\(611\) −14.1962 8.19615i −0.574315 0.331581i
\(612\) −29.8923 + 17.2583i −1.20832 + 0.697627i
\(613\) −3.89230 6.74167i −0.157209 0.272293i 0.776652 0.629929i \(-0.216916\pi\)
−0.933861 + 0.357636i \(0.883583\pi\)
\(614\) −19.0526 + 11.0000i −0.768899 + 0.443924i
\(615\) 46.9808i 1.89445i
\(616\) 8.19615 + 4.73205i 0.330232 + 0.190660i
\(617\) −6.33975 10.9808i −0.255229 0.442069i 0.709729 0.704475i \(-0.248817\pi\)
−0.964958 + 0.262406i \(0.915484\pi\)
\(618\) 23.3205 0.938088
\(619\) 30.3923 1.22157 0.610785 0.791797i \(-0.290854\pi\)
0.610785 + 0.791797i \(0.290854\pi\)
\(620\) −1.09808 1.90192i −0.0440998 0.0763831i
\(621\) 18.9282i 0.759563i
\(622\) −9.00000 + 15.5885i −0.360867 + 0.625040i
\(623\) 13.6077i 0.545181i
\(624\) −8.19615 4.73205i −0.328109 0.189434i
\(625\) 5.50000 9.52628i 0.220000 0.381051i
\(626\) 12.0622 20.8923i 0.482102 0.835024i
\(627\) 14.1962 8.19615i 0.566940 0.327323i
\(628\) −1.00000 −0.0399043
\(629\) −46.3923 + 7.73205i −1.84978 + 0.308297i
\(630\) −15.4641 −0.616105
\(631\) −30.2942 + 17.4904i −1.20599 + 0.696281i −0.961882 0.273466i \(-0.911830\pi\)
−0.244112 + 0.969747i \(0.578497\pi\)
\(632\) −6.63397 + 11.4904i −0.263885 + 0.457063i
\(633\) 3.26795 5.66025i 0.129889 0.224975i
\(634\) −6.40192 3.69615i −0.254253 0.146793i
\(635\) 13.5167i 0.536392i
\(636\) 3.46410 6.00000i 0.137361 0.237915i
\(637\) 10.3923i 0.411758i
\(638\) −20.4904 35.4904i −0.811222 1.40508i
\(639\) 15.4641 0.611750
\(640\) −1.73205 −0.0684653
\(641\) −0.571797 0.990381i −0.0225846 0.0391177i 0.854512 0.519431i \(-0.173856\pi\)
−0.877097 + 0.480314i \(0.840523\pi\)
\(642\) 24.5885 + 14.1962i 0.970429 + 0.560277i
\(643\) 13.2679i 0.523237i −0.965171 0.261618i \(-0.915744\pi\)
0.965171 0.261618i \(-0.0842562\pi\)
\(644\) 8.19615 4.73205i 0.322974 0.186469i
\(645\) 2.19615 + 3.80385i 0.0864734 + 0.149776i
\(646\) 8.49038 4.90192i 0.334050 0.192864i
\(647\) 19.9808 + 11.5359i 0.785525 + 0.453523i 0.838385 0.545079i \(-0.183500\pi\)
−0.0528599 + 0.998602i \(0.516834\pi\)
\(648\) −2.13397 1.23205i −0.0838304 0.0483995i
\(649\) −10.3923 + 6.00000i −0.407934 + 0.235521i
\(650\) 3.46410 + 6.00000i 0.135873 + 0.235339i
\(651\) 6.00000 3.46410i 0.235159 0.135769i
\(652\) 12.9282i 0.506308i
\(653\) −38.0885 21.9904i −1.49052 0.860550i −0.490575 0.871399i \(-0.663213\pi\)
−0.999941 + 0.0108487i \(0.996547\pi\)
\(654\) 3.63397 + 6.29423i 0.142100 + 0.246124i
\(655\) 16.9808 0.663493
\(656\) 9.92820 0.387631
\(657\) −8.92820 15.4641i −0.348322 0.603312i
\(658\) 9.46410i 0.368949i
\(659\) 4.73205 8.19615i 0.184335 0.319277i −0.759018 0.651070i \(-0.774320\pi\)
0.943352 + 0.331793i \(0.107654\pi\)
\(660\) 22.3923i 0.871619i
\(661\) 1.50000 + 0.866025i 0.0583432 + 0.0336845i 0.528888 0.848692i \(-0.322609\pi\)
−0.470545 + 0.882376i \(0.655943\pi\)
\(662\) 0 0
\(663\) 36.5885 63.3731i 1.42098 2.46121i
\(664\) 4.90192 2.83013i 0.190232 0.109830i
\(665\) 4.39230 0.170326
\(666\) 17.2583 + 20.9641i 0.668747 + 0.812342i
\(667\) −40.9808 −1.58678
\(668\) −12.0000 + 6.92820i −0.464294 + 0.268060i
\(669\) −22.1244 + 38.3205i −0.855377 + 1.48156i
\(670\) 8.83013 15.2942i 0.341138 0.590868i
\(671\) −7.09808 4.09808i −0.274018 0.158204i
\(672\) 5.46410i 0.210782i
\(673\) −8.00000 + 13.8564i −0.308377 + 0.534125i −0.978008 0.208569i \(-0.933119\pi\)
0.669630 + 0.742695i \(0.266453\pi\)
\(674\) 32.1769i 1.23941i
\(675\) −4.00000 6.92820i −0.153960 0.266667i
\(676\) −1.00000 −0.0384615
\(677\) 33.9282 1.30397 0.651983 0.758233i \(-0.273937\pi\)
0.651983 + 0.758233i \(0.273937\pi\)
\(678\) −4.73205 8.19615i −0.181733 0.314771i
\(679\) 13.3923 + 7.73205i 0.513949 + 0.296729i
\(680\) 13.3923i 0.513571i
\(681\) −3.00000 + 1.73205i −0.114960 + 0.0663723i
\(682\) 3.00000 + 5.19615i 0.114876 + 0.198971i
\(683\) −17.7846 + 10.2679i −0.680509 + 0.392892i −0.800047 0.599938i \(-0.795192\pi\)
0.119538 + 0.992830i \(0.461859\pi\)
\(684\) −4.90192 2.83013i −0.187430 0.108213i
\(685\) −2.08846 1.20577i −0.0797959 0.0460702i
\(686\) 17.3205 10.0000i 0.661300 0.381802i
\(687\) −37.4186 64.8109i −1.42761 2.47269i
\(688\) −0.803848 + 0.464102i −0.0306464 + 0.0176937i
\(689\) 8.78461i 0.334667i
\(690\) −19.3923 11.1962i −0.738252 0.426230i
\(691\) −13.4904 23.3660i −0.513198 0.888885i −0.999883 0.0153077i \(-0.995127\pi\)
0.486685 0.873578i \(-0.338206\pi\)
\(692\) −5.53590 −0.210443
\(693\) 42.2487 1.60490
\(694\) 4.56218 + 7.90192i 0.173178 + 0.299953i
\(695\) 35.6603i 1.35267i
\(696\) −11.8301 + 20.4904i −0.448420 + 0.776686i
\(697\) 76.7654i 2.90770i
\(698\) −9.86603 5.69615i −0.373435 0.215603i
\(699\) −20.4904 + 35.4904i −0.775017 + 1.34237i
\(700\) −2.00000 + 3.46410i −0.0755929 + 0.130931i
\(701\) 16.3923 9.46410i 0.619129 0.357454i −0.157401 0.987535i \(-0.550311\pi\)
0.776530 + 0.630081i \(0.216978\pi\)
\(702\) −13.8564 −0.522976
\(703\) −4.90192 5.95448i −0.184880 0.224578i
\(704\) 4.73205 0.178346
\(705\) −19.3923 + 11.1962i −0.730356 + 0.421671i
\(706\) −9.86603 + 17.0885i −0.371313 + 0.643133i
\(707\) 12.4641 21.5885i 0.468761 0.811917i
\(708\) 6.00000 + 3.46410i 0.225494 + 0.130189i
\(709\) 9.71281i 0.364772i −0.983227 0.182386i \(-0.941618\pi\)
0.983227 0.182386i \(-0.0583821\pi\)
\(710\) −3.00000 + 5.19615i −0.112588 + 0.195008i
\(711\) 59.2295i 2.22128i
\(712\) 3.40192 + 5.89230i 0.127492 + 0.220823i
\(713\) 6.00000 0.224702
\(714\) 42.2487 1.58112
\(715\) 14.1962 + 24.5885i 0.530906 + 0.919556i
\(716\) −8.19615 4.73205i −0.306305 0.176845i
\(717\) 47.3205i 1.76722i
\(718\) 30.5885 17.6603i 1.14155 0.659075i
\(719\) −18.6340 32.2750i −0.694930 1.20365i −0.970204 0.242288i \(-0.922102\pi\)
0.275274 0.961366i \(-0.411231\pi\)
\(720\) −6.69615 + 3.86603i −0.249551 + 0.144078i
\(721\) −14.7846 8.53590i −0.550608 0.317893i
\(722\) −15.0622 8.69615i −0.560556 0.323637i
\(723\) −36.5885 + 21.1244i −1.36074 + 0.785623i
\(724\) −4.69615 8.13397i −0.174531 0.302297i
\(725\) 15.0000 8.66025i 0.557086 0.321634i
\(726\) 31.1244i 1.15513i
\(727\) 34.3923 + 19.8564i 1.27554 + 0.736433i 0.976025 0.217658i \(-0.0698418\pi\)
0.299515 + 0.954092i \(0.403175\pi\)
\(728\) 3.46410 + 6.00000i 0.128388 + 0.222375i
\(729\) −43.7846 −1.62165
\(730\) 6.92820 0.256424
\(731\) −3.58846 6.21539i −0.132724 0.229885i
\(732\) 4.73205i 0.174902i
\(733\) 16.7846 29.0718i 0.619954 1.07379i −0.369540 0.929215i \(-0.620485\pi\)
0.989494 0.144576i \(-0.0461820\pi\)
\(734\) 12.3923i 0.457408i
\(735\) −12.2942 7.09808i −0.453479 0.261816i
\(736\) 2.36603 4.09808i 0.0872129 0.151057i
\(737\) −24.1244 + 41.7846i −0.888632 + 1.53916i
\(738\) 38.3827 22.1603i 1.41289 0.815730i
\(739\) 32.5885 1.19879 0.599393 0.800455i \(-0.295409\pi\)
0.599393 + 0.800455i \(0.295409\pi\)
\(740\) −10.3923 + 1.73205i −0.382029 + 0.0636715i
\(741\) 12.0000 0.440831
\(742\) −4.39230 + 2.53590i −0.161247 + 0.0930958i
\(743\) −0.758330 + 1.31347i −0.0278204 + 0.0481864i −0.879600 0.475713i \(-0.842190\pi\)
0.851780 + 0.523900i \(0.175523\pi\)
\(744\) 1.73205 3.00000i 0.0635001 0.109985i
\(745\) −23.8923 13.7942i −0.875346 0.505381i
\(746\) 7.00000i 0.256288i
\(747\) 12.6340 21.8827i 0.462253 0.800646i
\(748\) 36.5885i 1.33781i
\(749\) −10.3923 18.0000i −0.379727 0.657706i
\(750\) 33.1244 1.20953
\(751\) 29.6077 1.08040 0.540200 0.841537i \(-0.318349\pi\)
0.540200 + 0.841537i \(0.318349\pi\)
\(752\) −2.36603 4.09808i −0.0862801 0.149441i
\(753\) 40.9808 + 23.6603i 1.49342 + 0.862228i
\(754\) 30.0000i 1.09254i
\(755\) −6.29423 + 3.63397i −0.229070 + 0.132254i
\(756\) −4.00000 6.92820i −0.145479 0.251976i
\(757\) 14.8923 8.59808i 0.541270 0.312502i −0.204323 0.978903i \(-0.565499\pi\)
0.745593 + 0.666401i \(0.232166\pi\)
\(758\) 30.1244 + 17.3923i 1.09417 + 0.631717i
\(759\) 52.9808 + 30.5885i 1.92308 + 1.11029i
\(760\) 1.90192 1.09808i 0.0689900 0.0398314i
\(761\) 1.16025 + 2.00962i 0.0420592 + 0.0728486i 0.886289 0.463133i \(-0.153275\pi\)
−0.844229 + 0.535982i \(0.819942\pi\)
\(762\) −18.4641 + 10.6603i −0.668884 + 0.386180i
\(763\) 5.32051i 0.192615i
\(764\) 1.90192 + 1.09808i 0.0688092 + 0.0397270i
\(765\) −29.8923 51.7750i −1.08076 1.87193i
\(766\) −3.46410 −0.125163
\(767\) −8.78461 −0.317194
\(768\) −1.36603 2.36603i −0.0492922 0.0853766i
\(769\) 13.6077i 0.490706i 0.969434 + 0.245353i \(0.0789039\pi\)
−0.969434 + 0.245353i \(0.921096\pi\)
\(770\) −8.19615 + 14.1962i −0.295369 + 0.511594i
\(771\) 18.5885i 0.669447i
\(772\) 9.69615 + 5.59808i 0.348972 + 0.201479i
\(773\) −16.9641 + 29.3827i −0.610156 + 1.05682i 0.381057 + 0.924551i \(0.375560\pi\)
−0.991214