Properties

Label 105.2.g.a.104.4
Level 105
Weight 2
Character 105.104
Analytic conductor 0.838
Analytic rank 0
Dimension 4
CM no
Inner twists 4

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Newspace parameters

Level: \( N \) = \( 105 = 3 \cdot 5 \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 105.g (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(0.838429221223\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\Q(\sqrt{-2}, \sqrt{3})\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 104.4
Root \(1.93185i\)
Character \(\chi\) = 105.104
Dual form 105.2.g.a.104.3

$q$-expansion

\(f(q)\) \(=\) \(q+1.73205 q^{2} +(-1.00000 + 1.41421i) q^{3} +1.00000 q^{4} +(1.73205 - 1.41421i) q^{5} +(-1.73205 + 2.44949i) q^{6} +(1.00000 + 2.44949i) q^{7} -1.73205 q^{8} +(-1.00000 - 2.82843i) q^{9} +O(q^{10})\) \(q+1.73205 q^{2} +(-1.00000 + 1.41421i) q^{3} +1.00000 q^{4} +(1.73205 - 1.41421i) q^{5} +(-1.73205 + 2.44949i) q^{6} +(1.00000 + 2.44949i) q^{7} -1.73205 q^{8} +(-1.00000 - 2.82843i) q^{9} +(3.00000 - 2.44949i) q^{10} -2.82843i q^{11} +(-1.00000 + 1.41421i) q^{12} -4.00000 q^{13} +(1.73205 + 4.24264i) q^{14} +(0.267949 + 3.86370i) q^{15} -5.00000 q^{16} -2.82843i q^{17} +(-1.73205 - 4.89898i) q^{18} +(1.73205 - 1.41421i) q^{20} +(-4.46410 - 1.03528i) q^{21} -4.89898i q^{22} +3.46410 q^{23} +(1.73205 - 2.44949i) q^{24} +(1.00000 - 4.89898i) q^{25} -6.92820 q^{26} +(5.00000 + 1.41421i) q^{27} +(1.00000 + 2.44949i) q^{28} +5.65685i q^{29} +(0.464102 + 6.69213i) q^{30} +9.79796i q^{31} -5.19615 q^{32} +(4.00000 + 2.82843i) q^{33} -4.89898i q^{34} +(5.19615 + 2.82843i) q^{35} +(-1.00000 - 2.82843i) q^{36} +(4.00000 - 5.65685i) q^{39} +(-3.00000 + 2.44949i) q^{40} +3.46410 q^{41} +(-7.73205 - 1.79315i) q^{42} +4.89898i q^{43} -2.82843i q^{44} +(-5.73205 - 3.48477i) q^{45} +6.00000 q^{46} -2.82843i q^{47} +(5.00000 - 7.07107i) q^{48} +(-5.00000 + 4.89898i) q^{49} +(1.73205 - 8.48528i) q^{50} +(4.00000 + 2.82843i) q^{51} -4.00000 q^{52} +(8.66025 + 2.44949i) q^{54} +(-4.00000 - 4.89898i) q^{55} +(-1.73205 - 4.24264i) q^{56} +9.79796i q^{58} -6.92820 q^{59} +(0.267949 + 3.86370i) q^{60} -9.79796i q^{61} +16.9706i q^{62} +(5.92820 - 5.27792i) q^{63} +1.00000 q^{64} +(-6.92820 + 5.65685i) q^{65} +(6.92820 + 4.89898i) q^{66} -4.89898i q^{67} -2.82843i q^{68} +(-3.46410 + 4.89898i) q^{69} +(9.00000 + 4.89898i) q^{70} -2.82843i q^{71} +(1.73205 + 4.89898i) q^{72} +8.00000 q^{73} +(5.92820 + 6.31319i) q^{75} +(6.92820 - 2.82843i) q^{77} +(6.92820 - 9.79796i) q^{78} +8.00000 q^{79} +(-8.66025 + 7.07107i) q^{80} +(-7.00000 + 5.65685i) q^{81} +6.00000 q^{82} -2.82843i q^{83} +(-4.46410 - 1.03528i) q^{84} +(-4.00000 - 4.89898i) q^{85} +8.48528i q^{86} +(-8.00000 - 5.65685i) q^{87} +4.89898i q^{88} -10.3923 q^{89} +(-9.92820 - 6.03579i) q^{90} +(-4.00000 - 9.79796i) q^{91} +3.46410 q^{92} +(-13.8564 - 9.79796i) q^{93} -4.89898i q^{94} +(5.19615 - 7.34847i) q^{96} +8.00000 q^{97} +(-8.66025 + 8.48528i) q^{98} +(-8.00000 + 2.82843i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q - 4q^{3} + 4q^{4} + 4q^{7} - 4q^{9} + O(q^{10}) \) \( 4q - 4q^{3} + 4q^{4} + 4q^{7} - 4q^{9} + 12q^{10} - 4q^{12} - 16q^{13} + 8q^{15} - 20q^{16} - 4q^{21} + 4q^{25} + 20q^{27} + 4q^{28} - 12q^{30} + 16q^{33} - 4q^{36} + 16q^{39} - 12q^{40} - 24q^{42} - 16q^{45} + 24q^{46} + 20q^{48} - 20q^{49} + 16q^{51} - 16q^{52} - 16q^{55} + 8q^{60} - 4q^{63} + 4q^{64} + 36q^{70} + 32q^{73} - 4q^{75} + 32q^{79} - 28q^{81} + 24q^{82} - 4q^{84} - 16q^{85} - 32q^{87} - 12q^{90} - 16q^{91} + 32q^{97} - 32q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/105\mathbb{Z}\right)^\times\).

\(n\) \(22\) \(31\) \(71\)
\(\chi(n)\) \(-1\) \(-1\) \(-1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.73205 1.22474 0.612372 0.790569i \(-0.290215\pi\)
0.612372 + 0.790569i \(0.290215\pi\)
\(3\) −1.00000 + 1.41421i −0.577350 + 0.816497i
\(4\) 1.00000 0.500000
\(5\) 1.73205 1.41421i 0.774597 0.632456i
\(6\) −1.73205 + 2.44949i −0.707107 + 1.00000i
\(7\) 1.00000 + 2.44949i 0.377964 + 0.925820i
\(8\) −1.73205 −0.612372
\(9\) −1.00000 2.82843i −0.333333 0.942809i
\(10\) 3.00000 2.44949i 0.948683 0.774597i
\(11\) 2.82843i 0.852803i −0.904534 0.426401i \(-0.859781\pi\)
0.904534 0.426401i \(-0.140219\pi\)
\(12\) −1.00000 + 1.41421i −0.288675 + 0.408248i
\(13\) −4.00000 −1.10940 −0.554700 0.832050i \(-0.687167\pi\)
−0.554700 + 0.832050i \(0.687167\pi\)
\(14\) 1.73205 + 4.24264i 0.462910 + 1.13389i
\(15\) 0.267949 + 3.86370i 0.0691842 + 0.997604i
\(16\) −5.00000 −1.25000
\(17\) 2.82843i 0.685994i −0.939336 0.342997i \(-0.888558\pi\)
0.939336 0.342997i \(-0.111442\pi\)
\(18\) −1.73205 4.89898i −0.408248 1.15470i
\(19\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(20\) 1.73205 1.41421i 0.387298 0.316228i
\(21\) −4.46410 1.03528i −0.974147 0.225916i
\(22\) 4.89898i 1.04447i
\(23\) 3.46410 0.722315 0.361158 0.932505i \(-0.382382\pi\)
0.361158 + 0.932505i \(0.382382\pi\)
\(24\) 1.73205 2.44949i 0.353553 0.500000i
\(25\) 1.00000 4.89898i 0.200000 0.979796i
\(26\) −6.92820 −1.35873
\(27\) 5.00000 + 1.41421i 0.962250 + 0.272166i
\(28\) 1.00000 + 2.44949i 0.188982 + 0.462910i
\(29\) 5.65685i 1.05045i 0.850963 + 0.525226i \(0.176019\pi\)
−0.850963 + 0.525226i \(0.823981\pi\)
\(30\) 0.464102 + 6.69213i 0.0847330 + 1.22181i
\(31\) 9.79796i 1.75977i 0.475191 + 0.879883i \(0.342379\pi\)
−0.475191 + 0.879883i \(0.657621\pi\)
\(32\) −5.19615 −0.918559
\(33\) 4.00000 + 2.82843i 0.696311 + 0.492366i
\(34\) 4.89898i 0.840168i
\(35\) 5.19615 + 2.82843i 0.878310 + 0.478091i
\(36\) −1.00000 2.82843i −0.166667 0.471405i
\(37\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(38\) 0 0
\(39\) 4.00000 5.65685i 0.640513 0.905822i
\(40\) −3.00000 + 2.44949i −0.474342 + 0.387298i
\(41\) 3.46410 0.541002 0.270501 0.962720i \(-0.412811\pi\)
0.270501 + 0.962720i \(0.412811\pi\)
\(42\) −7.73205 1.79315i −1.19308 0.276689i
\(43\) 4.89898i 0.747087i 0.927613 + 0.373544i \(0.121857\pi\)
−0.927613 + 0.373544i \(0.878143\pi\)
\(44\) 2.82843i 0.426401i
\(45\) −5.73205 3.48477i −0.854484 0.519478i
\(46\) 6.00000 0.884652
\(47\) 2.82843i 0.412568i −0.978492 0.206284i \(-0.933863\pi\)
0.978492 0.206284i \(-0.0661372\pi\)
\(48\) 5.00000 7.07107i 0.721688 1.02062i
\(49\) −5.00000 + 4.89898i −0.714286 + 0.699854i
\(50\) 1.73205 8.48528i 0.244949 1.20000i
\(51\) 4.00000 + 2.82843i 0.560112 + 0.396059i
\(52\) −4.00000 −0.554700
\(53\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(54\) 8.66025 + 2.44949i 1.17851 + 0.333333i
\(55\) −4.00000 4.89898i −0.539360 0.660578i
\(56\) −1.73205 4.24264i −0.231455 0.566947i
\(57\) 0 0
\(58\) 9.79796i 1.28654i
\(59\) −6.92820 −0.901975 −0.450988 0.892530i \(-0.648928\pi\)
−0.450988 + 0.892530i \(0.648928\pi\)
\(60\) 0.267949 + 3.86370i 0.0345921 + 0.498802i
\(61\) 9.79796i 1.25450i −0.778818 0.627250i \(-0.784180\pi\)
0.778818 0.627250i \(-0.215820\pi\)
\(62\) 16.9706i 2.15526i
\(63\) 5.92820 5.27792i 0.746883 0.664955i
\(64\) 1.00000 0.125000
\(65\) −6.92820 + 5.65685i −0.859338 + 0.701646i
\(66\) 6.92820 + 4.89898i 0.852803 + 0.603023i
\(67\) 4.89898i 0.598506i −0.954174 0.299253i \(-0.903263\pi\)
0.954174 0.299253i \(-0.0967374\pi\)
\(68\) 2.82843i 0.342997i
\(69\) −3.46410 + 4.89898i −0.417029 + 0.589768i
\(70\) 9.00000 + 4.89898i 1.07571 + 0.585540i
\(71\) 2.82843i 0.335673i −0.985815 0.167836i \(-0.946322\pi\)
0.985815 0.167836i \(-0.0536780\pi\)
\(72\) 1.73205 + 4.89898i 0.204124 + 0.577350i
\(73\) 8.00000 0.936329 0.468165 0.883641i \(-0.344915\pi\)
0.468165 + 0.883641i \(0.344915\pi\)
\(74\) 0 0
\(75\) 5.92820 + 6.31319i 0.684530 + 0.728985i
\(76\) 0 0
\(77\) 6.92820 2.82843i 0.789542 0.322329i
\(78\) 6.92820 9.79796i 0.784465 1.10940i
\(79\) 8.00000 0.900070 0.450035 0.893011i \(-0.351411\pi\)
0.450035 + 0.893011i \(0.351411\pi\)
\(80\) −8.66025 + 7.07107i −0.968246 + 0.790569i
\(81\) −7.00000 + 5.65685i −0.777778 + 0.628539i
\(82\) 6.00000 0.662589
\(83\) 2.82843i 0.310460i −0.987878 0.155230i \(-0.950388\pi\)
0.987878 0.155230i \(-0.0496119\pi\)
\(84\) −4.46410 1.03528i −0.487073 0.112958i
\(85\) −4.00000 4.89898i −0.433861 0.531369i
\(86\) 8.48528i 0.914991i
\(87\) −8.00000 5.65685i −0.857690 0.606478i
\(88\) 4.89898i 0.522233i
\(89\) −10.3923 −1.10158 −0.550791 0.834643i \(-0.685674\pi\)
−0.550791 + 0.834643i \(0.685674\pi\)
\(90\) −9.92820 6.03579i −1.04652 0.636228i
\(91\) −4.00000 9.79796i −0.419314 1.02711i
\(92\) 3.46410 0.361158
\(93\) −13.8564 9.79796i −1.43684 1.01600i
\(94\) 4.89898i 0.505291i
\(95\) 0 0
\(96\) 5.19615 7.34847i 0.530330 0.750000i
\(97\) 8.00000 0.812277 0.406138 0.913812i \(-0.366875\pi\)
0.406138 + 0.913812i \(0.366875\pi\)
\(98\) −8.66025 + 8.48528i −0.874818 + 0.857143i
\(99\) −8.00000 + 2.82843i −0.804030 + 0.284268i
\(100\) 1.00000 4.89898i 0.100000 0.489898i
\(101\) 17.3205 1.72345 0.861727 0.507371i \(-0.169383\pi\)
0.861727 + 0.507371i \(0.169383\pi\)
\(102\) 6.92820 + 4.89898i 0.685994 + 0.485071i
\(103\) −10.0000 −0.985329 −0.492665 0.870219i \(-0.663977\pi\)
−0.492665 + 0.870219i \(0.663977\pi\)
\(104\) 6.92820 0.679366
\(105\) −9.19615 + 4.52004i −0.897453 + 0.441111i
\(106\) 0 0
\(107\) −10.3923 −1.00466 −0.502331 0.864675i \(-0.667524\pi\)
−0.502331 + 0.864675i \(0.667524\pi\)
\(108\) 5.00000 + 1.41421i 0.481125 + 0.136083i
\(109\) −10.0000 −0.957826 −0.478913 0.877862i \(-0.658969\pi\)
−0.478913 + 0.877862i \(0.658969\pi\)
\(110\) −6.92820 8.48528i −0.660578 0.809040i
\(111\) 0 0
\(112\) −5.00000 12.2474i −0.472456 1.15728i
\(113\) −6.92820 −0.651751 −0.325875 0.945413i \(-0.605659\pi\)
−0.325875 + 0.945413i \(0.605659\pi\)
\(114\) 0 0
\(115\) 6.00000 4.89898i 0.559503 0.456832i
\(116\) 5.65685i 0.525226i
\(117\) 4.00000 + 11.3137i 0.369800 + 1.04595i
\(118\) −12.0000 −1.10469
\(119\) 6.92820 2.82843i 0.635107 0.259281i
\(120\) −0.464102 6.69213i −0.0423665 0.610905i
\(121\) 3.00000 0.272727
\(122\) 16.9706i 1.53644i
\(123\) −3.46410 + 4.89898i −0.312348 + 0.441726i
\(124\) 9.79796i 0.879883i
\(125\) −5.19615 9.89949i −0.464758 0.885438i
\(126\) 10.2679 9.14162i 0.914742 0.814400i
\(127\) 14.6969i 1.30414i 0.758158 + 0.652071i \(0.226100\pi\)
−0.758158 + 0.652071i \(0.773900\pi\)
\(128\) 12.1244 1.07165
\(129\) −6.92820 4.89898i −0.609994 0.431331i
\(130\) −12.0000 + 9.79796i −1.05247 + 0.859338i
\(131\) −6.92820 −0.605320 −0.302660 0.953099i \(-0.597875\pi\)
−0.302660 + 0.953099i \(0.597875\pi\)
\(132\) 4.00000 + 2.82843i 0.348155 + 0.246183i
\(133\) 0 0
\(134\) 8.48528i 0.733017i
\(135\) 10.6603 4.62158i 0.917489 0.397762i
\(136\) 4.89898i 0.420084i
\(137\) 6.92820 0.591916 0.295958 0.955201i \(-0.404361\pi\)
0.295958 + 0.955201i \(0.404361\pi\)
\(138\) −6.00000 + 8.48528i −0.510754 + 0.722315i
\(139\) 9.79796i 0.831052i 0.909581 + 0.415526i \(0.136402\pi\)
−0.909581 + 0.415526i \(0.863598\pi\)
\(140\) 5.19615 + 2.82843i 0.439155 + 0.239046i
\(141\) 4.00000 + 2.82843i 0.336861 + 0.238197i
\(142\) 4.89898i 0.411113i
\(143\) 11.3137i 0.946100i
\(144\) 5.00000 + 14.1421i 0.416667 + 1.17851i
\(145\) 8.00000 + 9.79796i 0.664364 + 0.813676i
\(146\) 13.8564 1.14676
\(147\) −1.92820 11.9700i −0.159036 0.987273i
\(148\) 0 0
\(149\) 11.3137i 0.926855i −0.886135 0.463428i \(-0.846619\pi\)
0.886135 0.463428i \(-0.153381\pi\)
\(150\) 10.2679 + 10.9348i 0.838375 + 0.892820i
\(151\) 8.00000 0.651031 0.325515 0.945537i \(-0.394462\pi\)
0.325515 + 0.945537i \(0.394462\pi\)
\(152\) 0 0
\(153\) −8.00000 + 2.82843i −0.646762 + 0.228665i
\(154\) 12.0000 4.89898i 0.966988 0.394771i
\(155\) 13.8564 + 16.9706i 1.11297 + 1.36311i
\(156\) 4.00000 5.65685i 0.320256 0.452911i
\(157\) −4.00000 −0.319235 −0.159617 0.987179i \(-0.551026\pi\)
−0.159617 + 0.987179i \(0.551026\pi\)
\(158\) 13.8564 1.10236
\(159\) 0 0
\(160\) −9.00000 + 7.34847i −0.711512 + 0.580948i
\(161\) 3.46410 + 8.48528i 0.273009 + 0.668734i
\(162\) −12.1244 + 9.79796i −0.952579 + 0.769800i
\(163\) 14.6969i 1.15115i −0.817748 0.575577i \(-0.804778\pi\)
0.817748 0.575577i \(-0.195222\pi\)
\(164\) 3.46410 0.270501
\(165\) 10.9282 0.757875i 0.850759 0.0590005i
\(166\) 4.89898i 0.380235i
\(167\) 14.1421i 1.09435i 0.837018 + 0.547176i \(0.184297\pi\)
−0.837018 + 0.547176i \(0.815703\pi\)
\(168\) 7.73205 + 1.79315i 0.596541 + 0.138345i
\(169\) 3.00000 0.230769
\(170\) −6.92820 8.48528i −0.531369 0.650791i
\(171\) 0 0
\(172\) 4.89898i 0.373544i
\(173\) 19.7990i 1.50529i −0.658427 0.752645i \(-0.728778\pi\)
0.658427 0.752645i \(-0.271222\pi\)
\(174\) −13.8564 9.79796i −1.05045 0.742781i
\(175\) 13.0000 2.44949i 0.982708 0.185164i
\(176\) 14.1421i 1.06600i
\(177\) 6.92820 9.79796i 0.520756 0.736460i
\(178\) −18.0000 −1.34916
\(179\) 2.82843i 0.211407i −0.994398 0.105703i \(-0.966291\pi\)
0.994398 0.105703i \(-0.0337094\pi\)
\(180\) −5.73205 3.48477i −0.427242 0.259739i
\(181\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(182\) −6.92820 16.9706i −0.513553 1.25794i
\(183\) 13.8564 + 9.79796i 1.02430 + 0.724286i
\(184\) −6.00000 −0.442326
\(185\) 0 0
\(186\) −24.0000 16.9706i −1.75977 1.24434i
\(187\) −8.00000 −0.585018
\(188\) 2.82843i 0.206284i
\(189\) 1.53590 + 13.6617i 0.111720 + 0.993740i
\(190\) 0 0
\(191\) 19.7990i 1.43260i −0.697790 0.716302i \(-0.745833\pi\)
0.697790 0.716302i \(-0.254167\pi\)
\(192\) −1.00000 + 1.41421i −0.0721688 + 0.102062i
\(193\) 9.79796i 0.705273i 0.935760 + 0.352636i \(0.114715\pi\)
−0.935760 + 0.352636i \(0.885285\pi\)
\(194\) 13.8564 0.994832
\(195\) −1.07180 15.4548i −0.0767530 1.10674i
\(196\) −5.00000 + 4.89898i −0.357143 + 0.349927i
\(197\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(198\) −13.8564 + 4.89898i −0.984732 + 0.348155i
\(199\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(200\) −1.73205 + 8.48528i −0.122474 + 0.600000i
\(201\) 6.92820 + 4.89898i 0.488678 + 0.345547i
\(202\) 30.0000 2.11079
\(203\) −13.8564 + 5.65685i −0.972529 + 0.397033i
\(204\) 4.00000 + 2.82843i 0.280056 + 0.198030i
\(205\) 6.00000 4.89898i 0.419058 0.342160i
\(206\) −17.3205 −1.20678
\(207\) −3.46410 9.79796i −0.240772 0.681005i
\(208\) 20.0000 1.38675
\(209\) 0 0
\(210\) −15.9282 + 7.82894i −1.09915 + 0.540248i
\(211\) −4.00000 −0.275371 −0.137686 0.990476i \(-0.543966\pi\)
−0.137686 + 0.990476i \(0.543966\pi\)
\(212\) 0 0
\(213\) 4.00000 + 2.82843i 0.274075 + 0.193801i
\(214\) −18.0000 −1.23045
\(215\) 6.92820 + 8.48528i 0.472500 + 0.578691i
\(216\) −8.66025 2.44949i −0.589256 0.166667i
\(217\) −24.0000 + 9.79796i −1.62923 + 0.665129i
\(218\) −17.3205 −1.17309
\(219\) −8.00000 + 11.3137i −0.540590 + 0.764510i
\(220\) −4.00000 4.89898i −0.269680 0.330289i
\(221\) 11.3137i 0.761042i
\(222\) 0 0
\(223\) 26.0000 1.74109 0.870544 0.492090i \(-0.163767\pi\)
0.870544 + 0.492090i \(0.163767\pi\)
\(224\) −5.19615 12.7279i −0.347183 0.850420i
\(225\) −14.8564 + 2.07055i −0.990427 + 0.138037i
\(226\) −12.0000 −0.798228
\(227\) 2.82843i 0.187729i −0.995585 0.0938647i \(-0.970078\pi\)
0.995585 0.0938647i \(-0.0299221\pi\)
\(228\) 0 0
\(229\) 19.5959i 1.29493i −0.762093 0.647467i \(-0.775828\pi\)
0.762093 0.647467i \(-0.224172\pi\)
\(230\) 10.3923 8.48528i 0.685248 0.559503i
\(231\) −2.92820 + 12.6264i −0.192662 + 0.830755i
\(232\) 9.79796i 0.643268i
\(233\) 20.7846 1.36165 0.680823 0.732448i \(-0.261622\pi\)
0.680823 + 0.732448i \(0.261622\pi\)
\(234\) 6.92820 + 19.5959i 0.452911 + 1.28103i
\(235\) −4.00000 4.89898i −0.260931 0.319574i
\(236\) −6.92820 −0.450988
\(237\) −8.00000 + 11.3137i −0.519656 + 0.734904i
\(238\) 12.0000 4.89898i 0.777844 0.317554i
\(239\) 2.82843i 0.182956i −0.995807 0.0914779i \(-0.970841\pi\)
0.995807 0.0914779i \(-0.0291591\pi\)
\(240\) −1.33975 19.3185i −0.0864802 1.24700i
\(241\) 9.79796i 0.631142i −0.948902 0.315571i \(-0.897804\pi\)
0.948902 0.315571i \(-0.102196\pi\)
\(242\) 5.19615 0.334021
\(243\) −1.00000 15.5563i −0.0641500 0.997940i
\(244\) 9.79796i 0.627250i
\(245\) −1.73205 + 15.5563i −0.110657 + 0.993859i
\(246\) −6.00000 + 8.48528i −0.382546 + 0.541002i
\(247\) 0 0
\(248\) 16.9706i 1.07763i
\(249\) 4.00000 + 2.82843i 0.253490 + 0.179244i
\(250\) −9.00000 17.1464i −0.569210 1.08444i
\(251\) −20.7846 −1.31191 −0.655956 0.754799i \(-0.727735\pi\)
−0.655956 + 0.754799i \(0.727735\pi\)
\(252\) 5.92820 5.27792i 0.373442 0.332478i
\(253\) 9.79796i 0.615992i
\(254\) 25.4558i 1.59724i
\(255\) 10.9282 0.757875i 0.684351 0.0474600i
\(256\) 19.0000 1.18750
\(257\) 14.1421i 0.882162i 0.897467 + 0.441081i \(0.145405\pi\)
−0.897467 + 0.441081i \(0.854595\pi\)
\(258\) −12.0000 8.48528i −0.747087 0.528271i
\(259\) 0 0
\(260\) −6.92820 + 5.65685i −0.429669 + 0.350823i
\(261\) 16.0000 5.65685i 0.990375 0.350150i
\(262\) −12.0000 −0.741362
\(263\) −3.46410 −0.213606 −0.106803 0.994280i \(-0.534061\pi\)
−0.106803 + 0.994280i \(0.534061\pi\)
\(264\) −6.92820 4.89898i −0.426401 0.301511i
\(265\) 0 0
\(266\) 0 0
\(267\) 10.3923 14.6969i 0.635999 0.899438i
\(268\) 4.89898i 0.299253i
\(269\) 10.3923 0.633630 0.316815 0.948487i \(-0.397387\pi\)
0.316815 + 0.948487i \(0.397387\pi\)
\(270\) 18.4641 8.00481i 1.12369 0.487157i
\(271\) 29.3939i 1.78555i 0.450502 + 0.892775i \(0.351245\pi\)
−0.450502 + 0.892775i \(0.648755\pi\)
\(272\) 14.1421i 0.857493i
\(273\) 17.8564 + 4.14110i 1.08072 + 0.250631i
\(274\) 12.0000 0.724947
\(275\) −13.8564 2.82843i −0.835573 0.170561i
\(276\) −3.46410 + 4.89898i −0.208514 + 0.294884i
\(277\) 19.5959i 1.17740i 0.808350 + 0.588702i \(0.200361\pi\)
−0.808350 + 0.588702i \(0.799639\pi\)
\(278\) 16.9706i 1.01783i
\(279\) 27.7128 9.79796i 1.65912 0.586588i
\(280\) −9.00000 4.89898i −0.537853 0.292770i
\(281\) 28.2843i 1.68730i −0.536895 0.843649i \(-0.680403\pi\)
0.536895 0.843649i \(-0.319597\pi\)
\(282\) 6.92820 + 4.89898i 0.412568 + 0.291730i
\(283\) 14.0000 0.832214 0.416107 0.909316i \(-0.363394\pi\)
0.416107 + 0.909316i \(0.363394\pi\)
\(284\) 2.82843i 0.167836i
\(285\) 0 0
\(286\) 19.5959i 1.15873i
\(287\) 3.46410 + 8.48528i 0.204479 + 0.500870i
\(288\) 5.19615 + 14.6969i 0.306186 + 0.866025i
\(289\) 9.00000 0.529412
\(290\) 13.8564 + 16.9706i 0.813676 + 0.996546i
\(291\) −8.00000 + 11.3137i −0.468968 + 0.663221i
\(292\) 8.00000 0.468165
\(293\) 2.82843i 0.165238i −0.996581 0.0826192i \(-0.973671\pi\)
0.996581 0.0826192i \(-0.0263285\pi\)
\(294\) −3.33975 20.7327i −0.194778 1.20916i
\(295\) −12.0000 + 9.79796i −0.698667 + 0.570459i
\(296\) 0 0
\(297\) 4.00000 14.1421i 0.232104 0.820610i
\(298\) 19.5959i 1.13516i
\(299\) −13.8564 −0.801337
\(300\) 5.92820 + 6.31319i 0.342265 + 0.364492i
\(301\) −12.0000 + 4.89898i −0.691669 + 0.282372i
\(302\) 13.8564 0.797347
\(303\) −17.3205 + 24.4949i −0.995037 + 1.40720i
\(304\) 0 0
\(305\) −13.8564 16.9706i −0.793416 0.971732i
\(306\) −13.8564 + 4.89898i −0.792118 + 0.280056i
\(307\) −10.0000 −0.570730 −0.285365 0.958419i \(-0.592115\pi\)
−0.285365 + 0.958419i \(0.592115\pi\)
\(308\) 6.92820 2.82843i 0.394771 0.161165i
\(309\) 10.0000 14.1421i 0.568880 0.804518i
\(310\) 24.0000 + 29.3939i 1.36311 + 1.66946i
\(311\) −27.7128 −1.57145 −0.785725 0.618576i \(-0.787710\pi\)
−0.785725 + 0.618576i \(0.787710\pi\)
\(312\) −6.92820 + 9.79796i −0.392232 + 0.554700i
\(313\) −16.0000 −0.904373 −0.452187 0.891923i \(-0.649356\pi\)
−0.452187 + 0.891923i \(0.649356\pi\)
\(314\) −6.92820 −0.390981
\(315\) 2.80385 17.5254i 0.157979 0.987442i
\(316\) 8.00000 0.450035
\(317\) −13.8564 −0.778253 −0.389127 0.921184i \(-0.627223\pi\)
−0.389127 + 0.921184i \(0.627223\pi\)
\(318\) 0 0
\(319\) 16.0000 0.895828
\(320\) 1.73205 1.41421i 0.0968246 0.0790569i
\(321\) 10.3923 14.6969i 0.580042 0.820303i
\(322\) 6.00000 + 14.6969i 0.334367 + 0.819028i
\(323\) 0 0
\(324\) −7.00000 + 5.65685i −0.388889 + 0.314270i
\(325\) −4.00000 + 19.5959i −0.221880 + 1.08699i
\(326\) 25.4558i 1.40987i
\(327\) 10.0000 14.1421i 0.553001 0.782062i
\(328\) −6.00000 −0.331295
\(329\) 6.92820 2.82843i 0.381964 0.155936i
\(330\) 18.9282 1.31268i 1.04196 0.0722605i
\(331\) −28.0000 −1.53902 −0.769510 0.638635i \(-0.779499\pi\)
−0.769510 + 0.638635i \(0.779499\pi\)
\(332\) 2.82843i 0.155230i
\(333\) 0 0
\(334\) 24.4949i 1.34030i
\(335\) −6.92820 8.48528i −0.378528 0.463600i
\(336\) 22.3205 + 5.17638i 1.21768 + 0.282395i
\(337\) 19.5959i 1.06746i −0.845656 0.533729i \(-0.820790\pi\)
0.845656 0.533729i \(-0.179210\pi\)
\(338\) 5.19615 0.282633
\(339\) 6.92820 9.79796i 0.376288 0.532152i
\(340\) −4.00000 4.89898i −0.216930 0.265684i
\(341\) 27.7128 1.50073
\(342\) 0 0
\(343\) −17.0000 7.34847i −0.917914 0.396780i
\(344\) 8.48528i 0.457496i
\(345\) 0.928203 + 13.3843i 0.0499728 + 0.720584i
\(346\) 34.2929i 1.84360i
\(347\) −17.3205 −0.929814 −0.464907 0.885360i \(-0.653912\pi\)
−0.464907 + 0.885360i \(0.653912\pi\)
\(348\) −8.00000 5.65685i −0.428845 0.303239i
\(349\) 19.5959i 1.04895i 0.851427 + 0.524473i \(0.175738\pi\)
−0.851427 + 0.524473i \(0.824262\pi\)
\(350\) 22.5167 4.24264i 1.20357 0.226779i
\(351\) −20.0000 5.65685i −1.06752 0.301941i
\(352\) 14.6969i 0.783349i
\(353\) 31.1127i 1.65596i 0.560756 + 0.827981i \(0.310510\pi\)
−0.560756 + 0.827981i \(0.689490\pi\)
\(354\) 12.0000 16.9706i 0.637793 0.901975i
\(355\) −4.00000 4.89898i −0.212298 0.260011i
\(356\) −10.3923 −0.550791
\(357\) −2.92820 + 12.6264i −0.154977 + 0.668259i
\(358\) 4.89898i 0.258919i
\(359\) 31.1127i 1.64207i 0.570881 + 0.821033i \(0.306602\pi\)
−0.570881 + 0.821033i \(0.693398\pi\)
\(360\) 9.92820 + 6.03579i 0.523262 + 0.318114i
\(361\) 19.0000 1.00000
\(362\) 0 0
\(363\) −3.00000 + 4.24264i −0.157459 + 0.222681i
\(364\) −4.00000 9.79796i −0.209657 0.513553i
\(365\) 13.8564 11.3137i 0.725277 0.592187i
\(366\) 24.0000 + 16.9706i 1.25450 + 0.887066i
\(367\) −10.0000 −0.521996 −0.260998 0.965339i \(-0.584052\pi\)
−0.260998 + 0.965339i \(0.584052\pi\)
\(368\) −17.3205 −0.902894
\(369\) −3.46410 9.79796i −0.180334 0.510061i
\(370\) 0 0
\(371\) 0 0
\(372\) −13.8564 9.79796i −0.718421 0.508001i
\(373\) 9.79796i 0.507319i 0.967294 + 0.253660i \(0.0816343\pi\)
−0.967294 + 0.253660i \(0.918366\pi\)
\(374\) −13.8564 −0.716498
\(375\) 19.1962 + 2.55103i 0.991285 + 0.131734i
\(376\) 4.89898i 0.252646i
\(377\) 22.6274i 1.16537i
\(378\) 2.66025 + 23.6627i 0.136829 + 1.21708i
\(379\) −28.0000 −1.43826 −0.719132 0.694874i \(-0.755460\pi\)
−0.719132 + 0.694874i \(0.755460\pi\)
\(380\) 0 0
\(381\) −20.7846 14.6969i −1.06483 0.752947i
\(382\) 34.2929i 1.75458i
\(383\) 14.1421i 0.722629i 0.932444 + 0.361315i \(0.117672\pi\)
−0.932444 + 0.361315i \(0.882328\pi\)
\(384\) −12.1244 + 17.1464i −0.618718 + 0.875000i
\(385\) 8.00000 14.6969i 0.407718 0.749025i
\(386\) 16.9706i 0.863779i
\(387\) 13.8564 4.89898i 0.704361 0.249029i
\(388\) 8.00000 0.406138
\(389\) 22.6274i 1.14726i 0.819116 + 0.573628i \(0.194464\pi\)
−0.819116 + 0.573628i \(0.805536\pi\)
\(390\) −1.85641 26.7685i −0.0940028 1.35548i
\(391\) 9.79796i 0.495504i
\(392\) 8.66025 8.48528i 0.437409 0.428571i
\(393\) 6.92820 9.79796i 0.349482 0.494242i
\(394\) 0 0
\(395\) 13.8564 11.3137i 0.697191 0.569254i
\(396\) −8.00000 + 2.82843i −0.402015 + 0.142134i
\(397\) 20.0000 1.00377 0.501886 0.864934i \(-0.332640\pi\)
0.501886 + 0.864934i \(0.332640\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) −5.00000 + 24.4949i −0.250000 + 1.22474i
\(401\) 22.6274i 1.12996i 0.825105 + 0.564980i \(0.191116\pi\)
−0.825105 + 0.564980i \(0.808884\pi\)
\(402\) 12.0000 + 8.48528i 0.598506 + 0.423207i
\(403\) 39.1918i 1.95228i
\(404\) 17.3205 0.861727
\(405\) −4.12436 + 19.6975i −0.204941 + 0.978774i
\(406\) −24.0000 + 9.79796i −1.19110 + 0.486265i
\(407\) 0 0
\(408\) −6.92820 4.89898i −0.342997 0.242536i
\(409\) 9.79796i 0.484478i 0.970217 + 0.242239i \(0.0778818\pi\)
−0.970217 + 0.242239i \(0.922118\pi\)
\(410\) 10.3923 8.48528i 0.513239 0.419058i
\(411\) −6.92820 + 9.79796i −0.341743 + 0.483298i
\(412\) −10.0000 −0.492665
\(413\) −6.92820 16.9706i −0.340915 0.835067i
\(414\) −6.00000 16.9706i −0.294884 0.834058i
\(415\) −4.00000 4.89898i −0.196352 0.240481i
\(416\) 20.7846 1.01905
\(417\) −13.8564 9.79796i −0.678551 0.479808i
\(418\) 0 0
\(419\) −6.92820 −0.338465 −0.169232 0.985576i \(-0.554129\pi\)
−0.169232 + 0.985576i \(0.554129\pi\)
\(420\) −9.19615 + 4.52004i −0.448726 + 0.220555i
\(421\) 26.0000 1.26716 0.633581 0.773676i \(-0.281584\pi\)
0.633581 + 0.773676i \(0.281584\pi\)
\(422\) −6.92820 −0.337260
\(423\) −8.00000 + 2.82843i −0.388973 + 0.137523i
\(424\) 0 0
\(425\) −13.8564 2.82843i −0.672134 0.137199i
\(426\) 6.92820 + 4.89898i 0.335673 + 0.237356i
\(427\) 24.0000 9.79796i 1.16144 0.474156i
\(428\) −10.3923 −0.502331
\(429\) −16.0000 11.3137i −0.772487 0.546231i
\(430\) 12.0000 + 14.6969i 0.578691 + 0.708749i
\(431\) 2.82843i 0.136241i −0.997677 0.0681203i \(-0.978300\pi\)
0.997677 0.0681203i \(-0.0217002\pi\)
\(432\) −25.0000 7.07107i −1.20281 0.340207i
\(433\) −16.0000 −0.768911 −0.384455 0.923144i \(-0.625611\pi\)
−0.384455 + 0.923144i \(0.625611\pi\)
\(434\) −41.5692 + 16.9706i −1.99539 + 0.814613i
\(435\) −21.8564 + 1.51575i −1.04793 + 0.0726746i
\(436\) −10.0000 −0.478913
\(437\) 0 0
\(438\) −13.8564 + 19.5959i −0.662085 + 0.936329i
\(439\) 39.1918i 1.87052i −0.353956 0.935262i \(-0.615164\pi\)
0.353956 0.935262i \(-0.384836\pi\)
\(440\) 6.92820 + 8.48528i 0.330289 + 0.404520i
\(441\) 18.8564 + 9.24316i 0.897924 + 0.440150i
\(442\) 19.5959i 0.932083i
\(443\) 17.3205 0.822922 0.411461 0.911427i \(-0.365019\pi\)
0.411461 + 0.911427i \(0.365019\pi\)
\(444\) 0 0
\(445\) −18.0000 + 14.6969i −0.853282 + 0.696702i
\(446\) 45.0333 2.13239
\(447\) 16.0000 + 11.3137i 0.756774 + 0.535120i
\(448\) 1.00000 + 2.44949i 0.0472456 + 0.115728i
\(449\) 5.65685i 0.266963i 0.991051 + 0.133482i \(0.0426157\pi\)
−0.991051 + 0.133482i \(0.957384\pi\)
\(450\) −25.7321 + 3.58630i −1.21302 + 0.169060i
\(451\) 9.79796i 0.461368i
\(452\) −6.92820 −0.325875
\(453\) −8.00000 + 11.3137i −0.375873 + 0.531564i
\(454\) 4.89898i 0.229920i
\(455\) −20.7846 11.3137i −0.974398 0.530395i
\(456\) 0 0
\(457\) 19.5959i 0.916658i 0.888783 + 0.458329i \(0.151552\pi\)
−0.888783 + 0.458329i \(0.848448\pi\)
\(458\) 33.9411i 1.58596i
\(459\) 4.00000 14.1421i 0.186704 0.660098i
\(460\) 6.00000 4.89898i 0.279751 0.228416i
\(461\) −3.46410 −0.161339 −0.0806696 0.996741i \(-0.525706\pi\)
−0.0806696 + 0.996741i \(0.525706\pi\)
\(462\) −5.07180 + 21.8695i −0.235961 + 1.01746i
\(463\) 4.89898i 0.227675i −0.993499 0.113837i \(-0.963686\pi\)
0.993499 0.113837i \(-0.0363143\pi\)
\(464\) 28.2843i 1.31306i
\(465\) −37.8564 + 2.62536i −1.75555 + 0.121748i
\(466\) 36.0000 1.66767
\(467\) 2.82843i 0.130884i −0.997856 0.0654420i \(-0.979154\pi\)
0.997856 0.0654420i \(-0.0208457\pi\)
\(468\) 4.00000 + 11.3137i 0.184900 + 0.522976i
\(469\) 12.0000 4.89898i 0.554109 0.226214i
\(470\) −6.92820 8.48528i −0.319574 0.391397i
\(471\) 4.00000 5.65685i 0.184310 0.260654i
\(472\) 12.0000 0.552345
\(473\) 13.8564 0.637118
\(474\) −13.8564 + 19.5959i −0.636446 + 0.900070i
\(475\) 0 0
\(476\) 6.92820 2.82843i 0.317554 0.129641i
\(477\) 0 0
\(478\) 4.89898i 0.224074i
\(479\) 27.7128 1.26623 0.633115 0.774057i \(-0.281776\pi\)
0.633115 + 0.774057i \(0.281776\pi\)
\(480\) −1.39230 20.0764i −0.0635497 0.916358i
\(481\) 0 0
\(482\) 16.9706i 0.772988i
\(483\) −15.4641 3.58630i −0.703641 0.163182i
\(484\) 3.00000 0.136364
\(485\) 13.8564 11.3137i 0.629187 0.513729i
\(486\) −1.73205 26.9444i −0.0785674 1.22222i
\(487\) 14.6969i 0.665982i 0.942930 + 0.332991i \(0.108058\pi\)
−0.942930 + 0.332991i \(0.891942\pi\)
\(488\) 16.9706i 0.768221i
\(489\) 20.7846 + 14.6969i 0.939913 + 0.664619i
\(490\) −3.00000 + 26.9444i −0.135526 + 1.21722i
\(491\) 14.1421i 0.638226i 0.947717 + 0.319113i \(0.103385\pi\)
−0.947717 + 0.319113i \(0.896615\pi\)
\(492\) −3.46410 + 4.89898i −0.156174 + 0.220863i
\(493\) 16.0000 0.720604
\(494\) 0 0
\(495\) −9.85641 + 16.2127i −0.443013 + 0.728706i
\(496\) 48.9898i 2.19971i
\(497\) 6.92820 2.82843i 0.310772 0.126872i
\(498\) 6.92820 + 4.89898i 0.310460 + 0.219529i
\(499\) −4.00000 −0.179065 −0.0895323 0.995984i \(-0.528537\pi\)
−0.0895323 + 0.995984i \(0.528537\pi\)
\(500\) −5.19615 9.89949i −0.232379 0.442719i
\(501\) −20.0000 14.1421i −0.893534 0.631824i
\(502\) −36.0000 −1.60676
\(503\) 19.7990i 0.882793i −0.897312 0.441397i \(-0.854483\pi\)
0.897312 0.441397i \(-0.145517\pi\)
\(504\) −10.2679 + 9.14162i −0.457371 + 0.407200i
\(505\) 30.0000 24.4949i 1.33498 1.09001i
\(506\) 16.9706i 0.754434i
\(507\) −3.00000 + 4.24264i −0.133235 + 0.188422i
\(508\) 14.6969i 0.652071i
\(509\) 3.46410 0.153544 0.0767718 0.997049i \(-0.475539\pi\)
0.0767718 + 0.997049i \(0.475539\pi\)
\(510\) 18.9282 1.31268i 0.838155 0.0581263i
\(511\) 8.00000 + 19.5959i 0.353899 + 0.866872i
\(512\) 8.66025 0.382733
\(513\) 0 0
\(514\) 24.4949i 1.08042i
\(515\) −17.3205 + 14.1421i −0.763233 + 0.623177i
\(516\) −6.92820 4.89898i −0.304997 0.215666i
\(517\) −8.00000 −0.351840
\(518\) 0 0
\(519\) 28.0000 + 19.7990i 1.22906 + 0.869079i
\(520\) 12.0000 9.79796i 0.526235 0.429669i
\(521\) 10.3923 0.455295 0.227648 0.973744i \(-0.426897\pi\)
0.227648 + 0.973744i \(0.426897\pi\)
\(522\) 27.7128 9.79796i 1.21296 0.428845i
\(523\) 26.0000 1.13690 0.568450 0.822718i \(-0.307543\pi\)
0.568450 + 0.822718i \(0.307543\pi\)
\(524\) −6.92820 −0.302660
\(525\) −9.53590 + 20.8343i −0.416181 + 0.909282i
\(526\) −6.00000 −0.261612
\(527\) 27.7128 1.20719
\(528\) −20.0000 14.1421i −0.870388 0.615457i
\(529\) −11.0000 −0.478261
\(530\) 0 0
\(531\) 6.92820 + 19.5959i 0.300658 + 0.850390i
\(532\) 0 0
\(533\) −13.8564 −0.600188
\(534\) 18.0000 25.4558i 0.778936 1.10158i
\(535\) −18.0000 + 14.6969i −0.778208 + 0.635404i
\(536\) 8.48528i 0.366508i
\(537\) 4.00000 + 2.82843i 0.172613 + 0.122056i
\(538\) 18.0000 0.776035
\(539\) 13.8564 + 14.1421i 0.596838 + 0.609145i
\(540\) 10.6603 4.62158i 0.458744 0.198881i
\(541\) −10.0000 −0.429934 −0.214967 0.976621i \(-0.568964\pi\)
−0.214967 + 0.976621i \(0.568964\pi\)
\(542\) 50.9117i 2.18684i
\(543\) 0 0
\(544\) 14.6969i 0.630126i
\(545\) −17.3205 + 14.1421i −0.741929 + 0.605783i
\(546\) 30.9282 + 7.17260i 1.32360 + 0.306959i
\(547\) 34.2929i 1.46626i 0.680090 + 0.733128i \(0.261941\pi\)
−0.680090 + 0.733128i \(0.738059\pi\)
\(548\) 6.92820 0.295958
\(549\) −27.7128 + 9.79796i −1.18275 + 0.418167i
\(550\) −24.0000 4.89898i −1.02336 0.208893i
\(551\) 0 0
\(552\) 6.00000 8.48528i 0.255377 0.361158i
\(553\) 8.00000 + 19.5959i 0.340195 + 0.833303i
\(554\) 33.9411i 1.44202i
\(555\) 0 0
\(556\) 9.79796i 0.415526i
\(557\) 41.5692 1.76134 0.880672 0.473726i \(-0.157091\pi\)
0.880672 + 0.473726i \(0.157091\pi\)
\(558\) 48.0000 16.9706i 2.03200 0.718421i
\(559\) 19.5959i 0.828819i
\(560\) −25.9808 14.1421i −1.09789 0.597614i
\(561\) 8.00000 11.3137i 0.337760 0.477665i
\(562\) 48.9898i 2.06651i
\(563\) 14.1421i 0.596020i 0.954563 + 0.298010i \(0.0963229\pi\)
−0.954563 + 0.298010i \(0.903677\pi\)
\(564\) 4.00000 + 2.82843i 0.168430 + 0.119098i
\(565\) −12.0000 + 9.79796i −0.504844 + 0.412203i
\(566\) 24.2487 1.01925
\(567\) −20.8564 11.4896i −0.875887 0.482517i
\(568\) 4.89898i 0.205557i
\(569\) 28.2843i 1.18574i −0.805299 0.592869i \(-0.797995\pi\)
0.805299 0.592869i \(-0.202005\pi\)
\(570\) 0 0
\(571\) −4.00000 −0.167395 −0.0836974 0.996491i \(-0.526673\pi\)
−0.0836974 + 0.996491i \(0.526673\pi\)
\(572\) 11.3137i 0.473050i
\(573\) 28.0000 + 19.7990i 1.16972 + 0.827115i
\(574\) 6.00000 + 14.6969i 0.250435 + 0.613438i
\(575\) 3.46410 16.9706i 0.144463 0.707721i
\(576\) −1.00000 2.82843i −0.0416667 0.117851i
\(577\) 8.00000 0.333044 0.166522 0.986038i \(-0.446746\pi\)
0.166522 + 0.986038i \(0.446746\pi\)
\(578\) 15.5885 0.648394
\(579\) −13.8564 9.79796i −0.575853 0.407189i
\(580\) 8.00000 + 9.79796i 0.332182 + 0.406838i
\(581\) 6.92820 2.82843i 0.287430 0.117343i
\(582\) −13.8564 + 19.5959i −0.574367 + 0.812277i
\(583\) 0 0
\(584\) −13.8564 −0.573382
\(585\) 22.9282 + 13.9391i 0.947965 + 0.576309i
\(586\) 4.89898i 0.202375i
\(587\) 19.7990i 0.817192i −0.912715 0.408596i \(-0.866019\pi\)
0.912715 0.408596i \(-0.133981\pi\)
\(588\) −1.92820 11.9700i −0.0795178 0.493636i
\(589\) 0 0
\(590\) −20.7846 + 16.9706i −0.855689 + 0.698667i
\(591\) 0 0
\(592\) 0 0
\(593\) 19.7990i 0.813047i −0.913640 0.406524i \(-0.866741\pi\)
0.913640 0.406524i \(-0.133259\pi\)
\(594\) 6.92820 24.4949i 0.284268 1.00504i
\(595\) 8.00000 14.6969i 0.327968 0.602516i
\(596\) 11.3137i 0.463428i
\(597\) 0 0
\(598\) −24.0000 −0.981433
\(599\) 36.7696i 1.50236i −0.660096 0.751182i \(-0.729484\pi\)
0.660096 0.751182i \(-0.270516\pi\)
\(600\) −10.2679 10.9348i −0.419187 0.446410i
\(601\) 9.79796i 0.399667i −0.979830 0.199834i \(-0.935960\pi\)
0.979830 0.199834i \(-0.0640401\pi\)
\(602\) −20.7846 + 8.48528i −0.847117 + 0.345834i
\(603\) −13.8564 + 4.89898i −0.564276 + 0.199502i
\(604\) 8.00000 0.325515
\(605\) 5.19615 4.24264i 0.211254 0.172488i
\(606\) −30.0000 + 42.4264i −1.21867 + 1.72345i
\(607\) −10.0000 −0.405887 −0.202944 0.979190i \(-0.565051\pi\)
−0.202944 + 0.979190i \(0.565051\pi\)
\(608\) 0 0
\(609\) 5.85641 25.2528i 0.237314 1.02329i
\(610\) −24.0000 29.3939i −0.971732 1.19012i
\(611\) 11.3137i 0.457704i
\(612\) −8.00000 + 2.82843i −0.323381 + 0.114332i
\(613\) 29.3939i 1.18721i 0.804757 + 0.593604i \(0.202295\pi\)
−0.804757 + 0.593604i \(0.797705\pi\)
\(614\) −17.3205 −0.698999
\(615\) 0.928203 + 13.3843i 0.0374288 + 0.539705i
\(616\) −12.0000 + 4.89898i −0.483494 + 0.197386i
\(617\) −48.4974 −1.95243 −0.976216 0.216799i \(-0.930439\pi\)
−0.976216 + 0.216799i \(0.930439\pi\)
\(618\) 17.3205 24.4949i 0.696733 0.985329i
\(619\) 9.79796i 0.393813i −0.980422 0.196907i \(-0.936910\pi\)
0.980422 0.196907i \(-0.0630896\pi\)
\(620\) 13.8564 + 16.9706i 0.556487 + 0.681554i
\(621\) 17.3205 + 4.89898i 0.695048 + 0.196589i
\(622\) −48.0000 −1.92462
\(623\) −10.3923 25.4558i −0.416359 1.01987i
\(624\) −20.0000 + 28.2843i −0.800641 + 1.13228i
\(625\) −23.0000 9.79796i −0.920000 0.391918i
\(626\) −27.7128 −1.10763
\(627\) 0 0
\(628\) −4.00000 −0.159617
\(629\) 0 0
\(630\) 4.85641 30.3548i 0.193484 1.20937i
\(631\) 8.00000 0.318475 0.159237 0.987240i \(-0.449096\pi\)
0.159237 + 0.987240i \(0.449096\pi\)
\(632\) −13.8564 −0.551178
\(633\) 4.00000 5.65685i 0.158986 0.224840i
\(634\) −24.0000 −0.953162
\(635\) 20.7846 + 25.4558i 0.824812 + 1.01018i
\(636\) 0 0
\(637\) 20.0000 19.5959i 0.792429 0.776419i
\(638\) 27.7128 1.09716
\(639\) −8.00000 + 2.82843i −0.316475 + 0.111891i
\(640\) 21.0000 17.1464i 0.830098 0.677772i
\(641\) 5.65685i 0.223432i 0.993740 + 0.111716i \(0.0356347\pi\)
−0.993740 + 0.111716i \(0.964365\pi\)
\(642\) 18.0000 25.4558i 0.710403 1.00466i
\(643\) −22.0000 −0.867595 −0.433798 0.901010i \(-0.642827\pi\)
−0.433798 + 0.901010i \(0.642827\pi\)
\(644\) 3.46410 + 8.48528i 0.136505 + 0.334367i
\(645\) −18.9282 + 1.31268i −0.745297 + 0.0516866i
\(646\) 0 0
\(647\) 19.7990i 0.778379i −0.921158 0.389189i \(-0.872755\pi\)
0.921158 0.389189i \(-0.127245\pi\)
\(648\) 12.1244 9.79796i 0.476290 0.384900i
\(649\) 19.5959i 0.769207i
\(650\) −6.92820 + 33.9411i −0.271746 + 1.33128i
\(651\) 10.1436 43.7391i 0.397559 1.71427i
\(652\) 14.6969i 0.575577i
\(653\) −27.7128 −1.08449 −0.542243 0.840222i \(-0.682425\pi\)
−0.542243 + 0.840222i \(0.682425\pi\)
\(654\) 17.3205 24.4949i 0.677285 0.957826i
\(655\) −12.0000 + 9.79796i −0.468879 + 0.382838i
\(656\) −17.3205 −0.676252
\(657\) −8.00000 22.6274i −0.312110 0.882780i
\(658\) 12.0000 4.89898i 0.467809 0.190982i
\(659\) 2.82843i 0.110180i −0.998481 0.0550899i \(-0.982455\pi\)
0.998481 0.0550899i \(-0.0175446\pi\)
\(660\) 10.9282 0.757875i 0.425380 0.0295002i
\(661\) 9.79796i 0.381096i 0.981678 + 0.190548i \(0.0610266\pi\)
−0.981678 + 0.190548i \(0.938973\pi\)
\(662\) −48.4974 −1.88491
\(663\) −16.0000 11.3137i −0.621389 0.439388i
\(664\) 4.89898i 0.190117i
\(665\) 0 0
\(666\) 0 0
\(667\) 19.5959i 0.758757i
\(668\) 14.1421i 0.547176i
\(669\) −26.0000 + 36.7696i −1.00522 + 1.42159i
\(670\) −12.0000 14.6969i −0.463600 0.567792i
\(671\) −27.7128 −1.06984
\(672\) 23.1962 + 5.37945i 0.894811 + 0.207517i
\(673\) 9.79796i 0.377684i −0.982008 0.188842i \(-0.939527\pi\)
0.982008 0.188842i \(-0.0604733\pi\)
\(674\) 33.9411i 1.30736i
\(675\) 11.9282 23.0807i 0.459117 0.888376i
\(676\) 3.00000 0.115385
\(677\) 2.82843i 0.108705i −0.998522 0.0543526i \(-0.982690\pi\)
0.998522 0.0543526i \(-0.0173095\pi\)
\(678\) 12.0000 16.9706i 0.460857 0.651751i
\(679\) 8.00000 + 19.5959i 0.307012 + 0.752022i
\(680\) 6.92820 + 8.48528i 0.265684 + 0.325396i
\(681\) 4.00000 + 2.82843i 0.153280 + 0.108386i
\(682\) 48.0000 1.83801
\(683\) −10.3923 −0.397650 −0.198825 0.980035i \(-0.563713\pi\)
−0.198825 + 0.980035i \(0.563713\pi\)
\(684\) 0 0
\(685\) 12.0000 9.79796i 0.458496 0.374361i
\(686\) −29.4449 12.7279i −1.12421 0.485954i
\(687\) 27.7128 + 19.5959i 1.05731 + 0.747631i
\(688\) 24.4949i 0.933859i
\(689\) 0 0
\(690\) 1.60770 + 23.1822i 0.0612039 + 0.882532i
\(691\) 9.79796i 0.372732i −0.982480 0.186366i \(-0.940329\pi\)
0.982480 0.186366i \(-0.0596710\pi\)
\(692\) 19.7990i 0.752645i
\(693\) −14.9282 16.7675i −0.567076 0.636944i
\(694\) −30.0000 −1.13878
\(695\) 13.8564 + 16.9706i 0.525603 + 0.643730i
\(696\) 13.8564 + 9.79796i 0.525226 + 0.371391i
\(697\) 9.79796i 0.371124i
\(698\) 33.9411i 1.28469i
\(699\) −20.7846 + 29.3939i −0.786146 + 1.11178i
\(700\) 13.0000 2.44949i 0.491354 0.0925820i
\(701\) 22.6274i 0.854626i 0.904104 + 0.427313i \(0.140540\pi\)
−0.904104 + 0.427313i \(0.859460\pi\)
\(702\) −34.6410 9.79796i −1.30744 0.369800i
\(703\) 0 0
\(704\) 2.82843i 0.106600i
\(705\) 10.9282 0.757875i 0.411580 0.0285432i
\(706\) 53.8888i 2.02813i
\(707\) 17.3205 + 42.4264i 0.651405 + 1.59561i
\(708\) 6.92820 9.79796i 0.260378 0.368230i
\(709\) 38.0000 1.42712 0.713560 0.700594i \(-0.247082\pi\)
0.713560 + 0.700594i \(0.247082\pi\)
\(710\) −6.92820 8.48528i −0.260011 0.318447i
\(711\) −8.00000 22.6274i −0.300023 0.848594i
\(712\) 18.0000 0.674579
\(713\) 33.9411i 1.27111i
\(714\) −5.07180 + 21.8695i −0.189807 + 0.818447i
\(715\) 16.0000 + 19.5959i 0.598366 + 0.732846i
\(716\) 2.82843i 0.105703i
\(717\) 4.00000 + 2.82843i 0.149383 + 0.105630i
\(718\) 53.8888i 2.01111i
\(719\) 41.5692 1.55027 0.775135 0.631795i \(-0.217682\pi\)
0.775135 + 0.631795i \(0.217682\pi\)
\(720\) 28.6603 + 17.4238i 1.06810 + 0.649348i
\(721\) −10.0000 24.4949i −0.372419 0.912238i
\(722\) 32.9090 1.22474
\(723\) 13.8564 + 9.79796i 0.515325 + 0.364390i
\(724\) 0 0
\(725\) 27.7128 + 5.65685i 1.02923 + 0.210090i
\(726\) −5.19615 + 7.34847i −0.192847 + 0.272727i
\(727\) −10.0000 −0.370879 −0.185440 0.982656i \(-0.559371\pi\)
−0.185440 + 0.982656i \(0.559371\pi\)
\(728\) 6.92820 + 16.9706i 0.256776 + 0.628971i
\(729\) 23.0000 + 14.1421i 0.851852 + 0.523783i
\(730\) 24.0000 19.5959i 0.888280 0.725277i
\(731\) 13.8564 0.512498
\(732\) 13.8564 + 9.79796i 0.512148 + 0.362143i
\(733\) −28.0000 −1.03420 −0.517102 0.855924i \(-0.672989\pi\)
−0.517102 + 0.855924i \(0.672989\pi\)
\(734\) −17.3205 −0.639312
\(735\) −20.2679 18.0058i −0.747595 0.664155i
\(736\) −18.0000 −0.663489
\(737\) −13.8564 −0.510407
\(738\) −6.00000 16.9706i −0.220863 0.624695i
\(739\) 20.0000 0.735712 0.367856 0.929883i \(-0.380092\pi\)
0.367856 + 0.929883i \(0.380092\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 24.2487 0.889599 0.444799 0.895630i \(-0.353275\pi\)
0.444799 + 0.895630i \(0.353275\pi\)
\(744\) 24.0000 + 16.9706i 0.879883 + 0.622171i
\(745\) −16.0000 19.5959i −0.586195 0.717939i
\(746\) 16.9706i 0.621336i
\(747\) −8.00000 + 2.82843i −0.292705 + 0.103487i
\(748\) −8.00000 −0.292509
\(749\) −10.3923 25.4558i −0.379727 0.930136i
\(750\) 33.2487 + 4.41851i 1.21407 + 0.161341i
\(751\) 8.00000 0.291924 0.145962 0.989290i \(-0.453372\pi\)
0.145962 + 0.989290i \(0.453372\pi\)
\(752\) 14.1421i 0.515711i
\(753\) 20.7846 29.3939i 0.757433 1.07117i
\(754\) 39.1918i 1.42728i
\(755\) 13.8564 11.3137i 0.504286 0.411748i
\(756\) 1.53590 + 13.6617i 0.0558601 + 0.496870i
\(757\) 29.3939i 1.06834i −0.845378 0.534169i \(-0.820624\pi\)
0.845378 0.534169i \(-0.179376\pi\)
\(758\) −48.4974 −1.76151
\(759\) 13.8564 + 9.79796i 0.502956 + 0.355643i
\(760\) 0 0
\(761\) −38.1051 −1.38131 −0.690655 0.723185i \(-0.742678\pi\)
−0.690655 + 0.723185i \(0.742678\pi\)
\(762\) −36.0000 25.4558i −1.30414 0.922168i
\(763\) −10.0000 24.4949i −0.362024 0.886775i
\(764\) 19.7990i 0.716302i
\(765\) −9.85641 + 16.2127i −0.356359 + 0.586171i
\(766\) 24.4949i 0.885037i
\(767\) 27.7128 1.00065
\(768\) −19.0000 + 26.8701i −0.685603 + 0.969590i
\(769\) 19.5959i 0.706647i −0.935501 0.353323i \(-0.885052\pi\)
0.935501 0.353323i \(-0.114948\pi\)
\(770\) 13.8564 25.4558i 0.499350 0.917365i
\(771\) −20.0000 14.1421i −0.720282 0.509317i
\(772\) 9.79796i 0.352636i
\(773\) 2.82843i 0.101731i −0.998706 0.0508657i \(-0.983802\pi\)
0.998706 0.0508657i \(-0.0161981\pi\)
\(774\) 24.0000 8.48528i 0.862662 0.304997i
\(775\) 48.0000 + 9.79796i 1.72421 + 0.351953i
\(776\) −13.8564 −0.497416
\(777\) 0 0
\(778\) 39.1918i 1.40510i
\(779\) 0 0
\(780\) −1.07180 15.4548i −0.0383765 0.553371i
\(781\) −8.00000 −0.286263
\(782\) 16.9706i 0.606866i
\(783\) −8.00000 + 28.2843i −0.285897 + 1.01080i
\(784\) 25.0000 24.4949i 0.892857 0.874818i
\(785\) −6.92820 + 5.65685i −0.247278 + 0.201902i
\(786\) 12.0000 16.9706i 0.428026 0.605320i
\(787\) 14.0000 0.499046 0.249523 0.968369i \(-0.419726\pi\)
0.249523 + 0.968369i \(0.419726\pi\)
\(788\) 0 0
\(789\) 3.46410 4.89898i 0.123325 0.174408i
\(790\) 24.0000 19.5959i 0.853882 0.697191i