Properties

Label 105.2.g.a.104.2
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 104.2
Root \(-0.517638i\)
Character \(\chi\) = 105.104
Dual form 105.2.g.a.104.1

$q$-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} +(3.73205 - 1.03528i) q^{15} -5.00000 q^{16} -2.82843i q^{17} +(1.73205 + 4.89898i) q^{18} +(-1.73205 - 1.41421i) q^{20} +(2.46410 + 3.86370i) 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} +(-6.46410 + 1.79315i) 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} +(-4.26795 - 6.69213i) q^{42} -4.89898i q^{43} -2.82843i q^{44} +(-2.26795 + 6.31319i) 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} +(3.73205 - 1.03528i) q^{60} +9.79796i q^{61} +16.9706i q^{62} +(-7.92820 - 0.378937i) 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} +(-7.92820 - 3.48477i) 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} +(2.46410 + 3.86370i) 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} +(3.92820 - 10.9348i) 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 \(-0.709785\pi\)
−0.612372 + 0.790569i \(0.709785\pi\)
\(3\) −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
\(15\) 3.73205 1.03528i 0.963611 0.267307i
\(16\) −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
\(21\) 2.46410 + 3.86370i 0.537711 + 0.843129i
\(22\) 4.89898i 1.04447i
\(23\) −3.46410 −0.722315 −0.361158 0.932505i \(-0.617618\pi\)
−0.361158 + 0.932505i \(0.617618\pi\)
\(24\) −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 \(0.823981\pi\)
\(30\) −6.46410 + 1.79315i −1.18018 + 0.327383i
\(31\) 9.79796i 1.75977i −0.475191 0.879883i \(-0.657621\pi\)
0.475191 0.879883i \(-0.342379\pi\)
\(32\) 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 \(-0.587189\pi\)
−0.270501 + 0.962720i \(0.587189\pi\)
\(42\) −4.26795 6.69213i −0.658559 1.03262i
\(43\) 4.89898i 0.747087i −0.927613 0.373544i \(-0.878143\pi\)
0.927613 0.373544i \(-0.121857\pi\)
\(44\) 2.82843i 0.426401i
\(45\) −2.26795 + 6.31319i −0.338086 + 0.941115i
\(46\) 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 \(-0.351072\pi\)
0.450988 + 0.892530i \(0.351072\pi\)
\(60\) 3.73205 1.03528i 0.481806 0.133654i
\(61\) 9.79796i 1.25450i 0.778818 + 0.627250i \(0.215820\pi\)
−0.778818 + 0.627250i \(0.784180\pi\)
\(62\) 16.9706i 2.15526i
\(63\) −7.92820 0.378937i −0.998860 0.0477416i
\(64\) 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 \(0.0967374\pi\)
−0.954174 + 0.299253i \(0.903263\pi\)
\(68\) 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
\(75\) −7.92820 3.48477i −0.915470 0.402386i
\(76\) 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 \(-0.0496119\pi\)
\(84\) 2.46410 + 3.86370i 0.268856 + 0.421565i
\(85\) −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 \(-0.314326\pi\)
0.550791 + 0.834643i \(0.314326\pi\)
\(90\) 3.92820 10.9348i 0.414069 1.15263i
\(91\) −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 \(-0.830617\pi\)
−0.861727 + 0.507371i \(0.830617\pi\)
\(102\) −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
\(105\) 1.19615 10.1769i 0.116733 0.993163i
\(106\) 0 0
\(107\) 10.3923 1.00466 0.502331 0.864675i \(-0.332476\pi\)
0.502331 + 0.864675i \(0.332476\pi\)
\(108\) 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 \(-0.394341\pi\)
0.325875 + 0.945413i \(0.394341\pi\)
\(114\) 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
\(120\) 6.46410 1.79315i 0.590089 0.163692i
\(121\) 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
\(126\) 13.7321 + 0.656339i 1.22335 + 0.0584713i
\(127\) 14.6969i 1.30414i −0.758158 0.652071i \(-0.773900\pi\)
0.758158 0.652071i \(-0.226100\pi\)
\(128\) −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 \(-0.402125\pi\)
0.302660 + 0.953099i \(0.402125\pi\)
\(132\) 4.00000 + 2.82843i 0.348155 + 0.246183i
\(133\) 0 0
\(134\) 8.48528i 0.733017i
\(135\) −6.66025 9.52056i −0.573223 0.819399i
\(136\) 4.89898i 0.420084i
\(137\) −6.92820 −0.591916 −0.295958 0.955201i \(-0.595639\pi\)
−0.295958 + 0.955201i \(0.595639\pi\)
\(138\) −6.00000 + 8.48528i −0.510754 + 0.722315i
\(139\) 9.79796i 0.831052i −0.909581 0.415526i \(-0.863598\pi\)
0.909581 0.415526i \(-0.136402\pi\)
\(140\) −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
\(147\) 11.9282 2.17209i 0.983822 0.179151i
\(148\) 0 0
\(149\) 11.3137i 0.926855i −0.886135 0.463428i \(-0.846619\pi\)
0.886135 0.463428i \(-0.153381\pi\)
\(150\) 13.7321 + 6.03579i 1.12122 + 0.492820i
\(151\) 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 \(0.195222\pi\)
−0.817748 + 0.575577i \(0.804778\pi\)
\(164\) −3.46410 −0.270501
\(165\) −2.92820 10.5558i −0.227960 0.821771i
\(166\) 4.89898i 0.380235i
\(167\) 14.1421i 1.09435i 0.837018 + 0.547176i \(0.184297\pi\)
−0.837018 + 0.547176i \(0.815703\pi\)
\(168\) 4.26795 + 6.69213i 0.329279 + 0.516309i
\(169\) 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 \(-0.0337094\pi\)
\(180\) −2.26795 + 6.31319i −0.169043 + 0.470558i
\(181\) 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
\(189\) 8.46410 10.8332i 0.615673 0.788002i
\(190\) 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 \(-0.885285\pi\)
0.935760 0.352636i \(-0.114715\pi\)
\(194\) −13.8564 −0.994832
\(195\) −14.9282 + 4.14110i −1.06903 + 0.296551i
\(196\) −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
\(210\) −2.07180 + 17.6269i −0.142968 + 1.21637i
\(211\) −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
\(225\) 12.8564 7.72741i 0.857094 0.515160i
\(226\) −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 \(0.224172\pi\)
−0.762093 + 0.647467i \(0.775828\pi\)
\(230\) −10.3923 8.48528i −0.685248 0.559503i
\(231\) 10.9282 6.96953i 0.719023 0.458562i
\(232\) 9.79796i 0.643268i
\(233\) −20.7846 −1.36165 −0.680823 0.732448i \(-0.738378\pi\)
−0.680823 + 0.732448i \(0.738378\pi\)
\(234\) −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 \(-0.0291591\pi\)
\(240\) −18.6603 + 5.17638i −1.20451 + 0.334134i
\(241\) 9.79796i 0.631142i 0.948902 + 0.315571i \(0.102196\pi\)
−0.948902 + 0.315571i \(0.897804\pi\)
\(242\) −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 \(-0.272265\pi\)
0.655956 + 0.754799i \(0.272265\pi\)
\(252\) −7.92820 0.378937i −0.499430 0.0238708i
\(253\) 9.79796i 0.615992i
\(254\) 25.4558i 1.59724i
\(255\) −2.92820 10.5558i −0.183371 0.661032i
\(256\) 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 \(-0.465939\pi\)
0.106803 + 0.994280i \(0.465939\pi\)
\(264\) 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 \(-0.602613\pi\)
−0.316815 + 0.948487i \(0.602613\pi\)
\(270\) 11.5359 + 16.4901i 0.702052 + 1.00355i
\(271\) 29.3939i 1.78555i −0.450502 0.892775i \(-0.648755\pi\)
0.450502 0.892775i \(-0.351245\pi\)
\(272\) 14.1421i 0.857493i
\(273\) −9.85641 15.4548i −0.596537 0.935368i
\(274\) 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 \(-0.799639\pi\)
0.808350 0.588702i \(-0.200361\pi\)
\(278\) 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 \(-0.0263285\pi\)
\(294\) −20.6603 + 3.76217i −1.20493 + 0.219414i
\(295\) −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
\(300\) −7.92820 3.48477i −0.457735 0.201193i
\(301\) −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 \(-0.212290\pi\)
0.785725 + 0.618576i \(0.212290\pi\)
\(312\) 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
\(315\) 13.1962 + 11.8685i 0.743519 + 0.668715i
\(316\) 8.00000 0.450035
\(317\) 13.8564 0.778253 0.389127 0.921184i \(-0.372777\pi\)
0.389127 + 0.921184i \(0.372777\pi\)
\(318\) 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
\(330\) 5.07180 + 18.2832i 0.279193 + 1.00646i
\(331\) −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
\(336\) −12.3205 19.3185i −0.672139 1.05391i
\(337\) 19.5959i 1.06746i 0.845656 + 0.533729i \(0.179210\pi\)
−0.845656 + 0.533729i \(0.820790\pi\)
\(338\) −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
\(345\) −12.9282 + 3.58630i −0.696031 + 0.193080i
\(346\) 34.2929i 1.84360i
\(347\) 17.3205 0.929814 0.464907 0.885360i \(-0.346088\pi\)
0.464907 + 0.885360i \(0.346088\pi\)
\(348\) −8.00000 5.65685i −0.428845 0.303239i
\(349\) 19.5959i 1.04895i −0.851427 0.524473i \(-0.824262\pi\)
0.851427 0.524473i \(-0.175738\pi\)
\(350\) −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
\(357\) 10.9282 6.96953i 0.578382 0.368867i
\(358\) 4.89898i 0.258919i
\(359\) 31.1127i 1.64207i 0.570881 + 0.821033i \(0.306602\pi\)
−0.570881 + 0.821033i \(0.693398\pi\)
\(360\) −3.92820 + 10.9348i −0.207034 + 0.576313i
\(361\) 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 \(-0.918366\pi\)
0.967294 0.253660i \(-0.0816343\pi\)
\(374\) 13.8564 0.716498
\(375\) 8.80385 + 17.2480i 0.454629 + 0.890681i
\(376\) 4.89898i 0.252646i
\(377\) 22.6274i 1.16537i
\(378\) −14.6603 + 18.7637i −0.754042 + 0.965101i
\(379\) −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 \(0.805536\pi\)
\(390\) 25.8564 7.17260i 1.30929 0.363199i
\(391\) 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
\(405\) 20.1244 + 0.101536i 0.999987 + 0.00504536i
\(406\) −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 \(-0.922118\pi\)
0.970217 0.242239i \(-0.0778818\pi\)
\(410\) −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 \(-0.445871\pi\)
0.169232 + 0.985576i \(0.445871\pi\)
\(420\) 1.19615 10.1769i 0.0583663 0.496582i
\(421\) 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
\(435\) 5.85641 + 21.1117i 0.280793 + 1.01223i
\(436\) −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 \(0.384836\pi\)
−0.353956 + 0.935262i \(0.615164\pi\)
\(440\) −6.92820 + 8.48528i −0.330289 + 0.404520i
\(441\) −8.85641 + 19.0411i −0.421734 + 0.906720i
\(442\) 19.5959i 0.932083i
\(443\) −17.3205 −0.822922 −0.411461 0.911427i \(-0.634981\pi\)
−0.411461 + 0.911427i \(0.634981\pi\)
\(444\) 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 \(0.957384\pi\)
\(450\) −22.2679 + 13.3843i −1.04972 + 0.630940i
\(451\) 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 \(-0.848448\pi\)
0.888783 0.458329i \(-0.151552\pi\)
\(458\) 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 \(-0.474294\pi\)
0.0806696 + 0.996741i \(0.474294\pi\)
\(462\) −18.9282 + 12.0716i −0.880620 + 0.561621i
\(463\) 4.89898i 0.227675i 0.993499 + 0.113837i \(0.0363143\pi\)
−0.993499 + 0.113837i \(0.963686\pi\)
\(464\) 28.2843i 1.31306i
\(465\) −10.1436 36.5665i −0.470398 1.69573i
\(466\) 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 \(-0.718224\pi\)
−0.633115 + 0.774057i \(0.718224\pi\)
\(480\) 19.3923 5.37945i 0.885134 0.245537i
\(481\) 0 0
\(482\) 16.9706i 0.772988i
\(483\) −8.53590 13.3843i −0.388397 0.609005i
\(484\) 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 \(-0.891942\pi\)
0.942930 0.332991i \(-0.108058\pi\)
\(488\) 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
\(495\) 17.8564 + 6.41473i 0.802586 + 0.288321i
\(496\) 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 \(-0.145517\pi\)
\(504\) −13.7321 0.656339i −0.611674 0.0292357i
\(505\) 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 \(-0.524461\pi\)
−0.0767718 + 0.997049i \(0.524461\pi\)
\(510\) 5.07180 + 18.2832i 0.224583 + 0.809595i
\(511\) 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 \(-0.573103\pi\)
−0.227648 + 0.973744i \(0.573103\pi\)
\(522\) −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
\(525\) −16.4641 + 15.9353i −0.718552 + 0.695473i
\(526\) −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
\(540\) −6.66025 9.52056i −0.286612 0.409700i
\(541\) −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
\(546\) 17.0718 + 26.7685i 0.730605 + 1.14559i
\(547\) 34.2929i 1.46626i −0.680090 0.733128i \(-0.738059\pi\)
0.680090 0.733128i \(-0.261941\pi\)
\(548\) −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 \(-0.842909\pi\)
−0.880672 + 0.473726i \(0.842909\pi\)
\(558\) 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
\(567\) 6.85641 + 22.8033i 0.287942 + 0.957648i
\(568\) 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
\(585\) 9.07180 25.2528i 0.375073 1.04407i
\(586\) 4.89898i 0.202375i
\(587\) 19.7990i 0.817192i −0.912715 0.408596i \(-0.866019\pi\)
0.912715 0.408596i \(-0.133981\pi\)
\(588\) 11.9282 2.17209i 0.491911 0.0895754i
\(589\) 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 \(-0.270516\pi\)
\(600\) −13.7321 6.03579i −0.560609 0.246410i
\(601\) 9.79796i 0.399667i 0.979830 + 0.199834i \(0.0640401\pi\)
−0.979830 + 0.199834i \(0.935960\pi\)
\(602\) 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
\(609\) −21.8564 + 13.9391i −0.885666 + 0.564839i
\(610\) −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 \(-0.797705\pi\)
0.804757 0.593604i \(-0.202295\pi\)
\(614\) 17.3205 0.698999
\(615\) −12.9282 + 3.58630i −0.521315 + 0.144614i
\(616\) −12.0000 4.89898i −0.483494 0.197386i
\(617\) 48.4974 1.95243 0.976216 0.216799i \(-0.0695615\pi\)
0.976216 + 0.216799i \(0.0695615\pi\)
\(618\) −17.3205 + 24.4949i −0.696733 + 0.985329i
\(619\) 9.79796i 0.393813i 0.980422 + 0.196907i \(0.0630896\pi\)
−0.980422 + 0.196907i \(0.936910\pi\)
\(620\) −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
\(630\) −22.8564 20.5569i −0.910621 0.819005i
\(631\) 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
\(645\) −5.07180 18.2832i −0.199702 0.719902i
\(646\) 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
\(651\) 37.8564 24.1432i 1.48371 0.946245i
\(652\) 14.6969i 0.575577i
\(653\) 27.7128 1.08449 0.542243 0.840222i \(-0.317575\pi\)
0.542243 + 0.840222i \(0.317575\pi\)
\(654\) −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 \(-0.0175446\pi\)
\(660\) −2.92820 10.5558i −0.113980 0.410885i
\(661\) 9.79796i 0.381096i −0.981678 0.190548i \(-0.938973\pi\)
0.981678 0.190548i \(-0.0610266\pi\)
\(662\) 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
\(672\) 12.8038 + 20.0764i 0.493919 + 0.774464i
\(673\) 9.79796i 0.377684i 0.982008 + 0.188842i \(0.0604733\pi\)
−0.982008 + 0.188842i \(0.939527\pi\)
\(674\) 33.9411i 1.30736i
\(675\) −1.92820 + 25.9091i −0.0742166 + 0.997242i
\(676\) 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 \(-0.436287\pi\)
0.198825 + 0.980035i \(0.436287\pi\)
\(684\) 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
\(690\) 22.3923 6.21166i 0.852460 0.236474i
\(691\) 9.79796i 0.372732i 0.982480 + 0.186366i \(0.0596710\pi\)
−0.982480 + 0.186366i \(0.940329\pi\)
\(692\) 19.7990i 0.752645i
\(693\) −1.07180 + 22.4243i −0.0407142 + 0.851830i
\(694\) −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
\(705\) −2.92820 10.5558i −0.110283 0.397556i
\(706\) 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
\(714\) −18.9282 + 12.0716i −0.708370 + 0.451768i
\(715\) 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 \(-0.782318\pi\)
−0.775135 + 0.631795i \(0.782318\pi\)
\(720\) 11.3397 31.5660i 0.422607 1.17639i
\(721\) −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
\(735\) −23.7321 13.1069i −0.875370 0.483454i
\(736\) −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 \(-0.646725\pi\)
−0.444799 + 0.895630i \(0.646725\pi\)
\(744\) 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
\(750\) −15.2487 29.8744i −0.556804 1.09086i
\(751\) 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
\(756\) 8.46410 10.8332i 0.307836 0.394001i
\(757\) 29.3939i 1.06834i 0.845378 + 0.534169i \(0.179376\pi\)
−0.845378 + 0.534169i \(0.820624\pi\)
\(758\) 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 \(-0.257322\pi\)
0.690655 + 0.723185i \(0.257322\pi\)
\(762\) −36.0000 25.4558i −1.30414 0.922168i
\(763\) −10.0000 + 24.4949i −0.362024 + 0.886775i
\(764\) 19.7990i 0.716302i
\(765\) 17.8564 + 6.41473i 0.645600 + 0.231925i
\(766\) 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 \(0.114948\pi\)
−0.935501 + 0.353323i \(0.885052\pi\)
\(770\) −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
\(780\) −14.9282 + 4.14110i −0.534515 + 0.148275i
\(781\) −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