Properties

Label 1110.2.o.a.253.5
Level $1110$
Weight $2$
Character 1110.253
Analytic conductor $8.863$
Analytic rank $0$
Dimension $36$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1110.o (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(8.86339462436\)
Analytic rank: \(0\)
Dimension: \(36\)
Relative dimension: \(18\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 253.5
Character \(\chi\) \(=\) 1110.253
Dual form 1110.2.o.a.487.5

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{2} +(-0.707107 + 0.707107i) q^{3} +1.00000 q^{4} +(1.63524 + 1.52512i) q^{5} +(0.707107 - 0.707107i) q^{6} +(1.84299 - 1.84299i) q^{7} -1.00000 q^{8} -1.00000i q^{9} +O(q^{10})\) \(q-1.00000 q^{2} +(-0.707107 + 0.707107i) q^{3} +1.00000 q^{4} +(1.63524 + 1.52512i) q^{5} +(0.707107 - 0.707107i) q^{6} +(1.84299 - 1.84299i) q^{7} -1.00000 q^{8} -1.00000i q^{9} +(-1.63524 - 1.52512i) q^{10} +3.01042i q^{11} +(-0.707107 + 0.707107i) q^{12} -1.82067 q^{13} +(-1.84299 + 1.84299i) q^{14} +(-2.23471 + 0.0778616i) q^{15} +1.00000 q^{16} +5.42248i q^{17} +1.00000i q^{18} +(0.509592 + 0.509592i) q^{19} +(1.63524 + 1.52512i) q^{20} +2.60638i q^{21} -3.01042i q^{22} -0.0216604 q^{23} +(0.707107 - 0.707107i) q^{24} +(0.347996 + 4.98788i) q^{25} +1.82067 q^{26} +(0.707107 + 0.707107i) q^{27} +(1.84299 - 1.84299i) q^{28} +(4.67832 - 4.67832i) q^{29} +(2.23471 - 0.0778616i) q^{30} +(1.55104 + 1.55104i) q^{31} -1.00000 q^{32} +(-2.12868 - 2.12868i) q^{33} -5.42248i q^{34} +(5.82450 - 0.202937i) q^{35} -1.00000i q^{36} +(2.27285 - 5.64218i) q^{37} +(-0.509592 - 0.509592i) q^{38} +(1.28741 - 1.28741i) q^{39} +(-1.63524 - 1.52512i) q^{40} +6.35587i q^{41} -2.60638i q^{42} -7.86706 q^{43} +3.01042i q^{44} +(1.52512 - 1.63524i) q^{45} +0.0216604 q^{46} +(-0.176174 + 0.176174i) q^{47} +(-0.707107 + 0.707107i) q^{48} +0.206804i q^{49} +(-0.347996 - 4.98788i) q^{50} +(-3.83427 - 3.83427i) q^{51} -1.82067 q^{52} +(2.05089 + 2.05089i) q^{53} +(-0.707107 - 0.707107i) q^{54} +(-4.59126 + 4.92274i) q^{55} +(-1.84299 + 1.84299i) q^{56} -0.720673 q^{57} +(-4.67832 + 4.67832i) q^{58} +(2.84934 + 2.84934i) q^{59} +(-2.23471 + 0.0778616i) q^{60} +(4.51718 + 4.51718i) q^{61} +(-1.55104 - 1.55104i) q^{62} +(-1.84299 - 1.84299i) q^{63} +1.00000 q^{64} +(-2.97723 - 2.77675i) q^{65} +(2.12868 + 2.12868i) q^{66} +(-3.93891 - 3.93891i) q^{67} +5.42248i q^{68} +(0.0153162 - 0.0153162i) q^{69} +(-5.82450 + 0.202937i) q^{70} +9.00950 q^{71} +1.00000i q^{72} +(-8.50501 + 8.50501i) q^{73} +(-2.27285 + 5.64218i) q^{74} +(-3.77303 - 3.28089i) q^{75} +(0.509592 + 0.509592i) q^{76} +(5.54815 + 5.54815i) q^{77} +(-1.28741 + 1.28741i) q^{78} +(2.16377 + 2.16377i) q^{79} +(1.63524 + 1.52512i) q^{80} -1.00000 q^{81} -6.35587i q^{82} +(0.925954 + 0.925954i) q^{83} +2.60638i q^{84} +(-8.26996 + 8.86704i) q^{85} +7.86706 q^{86} +6.61614i q^{87} -3.01042i q^{88} +(-1.03976 + 1.03976i) q^{89} +(-1.52512 + 1.63524i) q^{90} +(-3.35547 + 3.35547i) q^{91} -0.0216604 q^{92} -2.19350 q^{93} +(0.176174 - 0.176174i) q^{94} +(0.0561127 + 1.61050i) q^{95} +(0.707107 - 0.707107i) q^{96} +7.65590i q^{97} -0.206804i q^{98} +3.01042 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 36q - 36q^{2} + 36q^{4} + 4q^{5} + 4q^{7} - 36q^{8} + O(q^{10}) \) \( 36q - 36q^{2} + 36q^{4} + 4q^{5} + 4q^{7} - 36q^{8} - 4q^{10} - 8q^{13} - 4q^{14} + 36q^{16} - 4q^{19} + 4q^{20} + 4q^{25} + 8q^{26} + 4q^{28} - 36q^{29} - 4q^{31} - 36q^{32} + 4q^{33} + 28q^{35} + 28q^{37} + 4q^{38} - 4q^{39} - 4q^{40} - 32q^{43} + 16q^{47} - 4q^{50} - 8q^{52} - 8q^{53} - 8q^{55} - 4q^{56} - 8q^{57} + 36q^{58} + 4q^{59} - 4q^{61} + 4q^{62} - 4q^{63} + 36q^{64} - 52q^{65} - 4q^{66} - 16q^{67} + 8q^{69} - 28q^{70} - 8q^{71} + 4q^{73} - 28q^{74} + 16q^{75} - 4q^{76} - 8q^{77} + 4q^{78} + 12q^{79} + 4q^{80} - 36q^{81} + 8q^{83} - 8q^{85} + 32q^{86} + 24q^{89} + 56q^{91} - 8q^{93} - 16q^{94} + 20q^{95} + 8q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times\).

\(n\) \(371\) \(631\) \(667\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{4}\right)\) \(e\left(\frac{3}{4}\right)\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −0.707107
\(3\) −0.707107 + 0.707107i −0.408248 + 0.408248i
\(4\) 1.00000 0.500000
\(5\) 1.63524 + 1.52512i 0.731300 + 0.682056i
\(6\) 0.707107 0.707107i 0.288675 0.288675i
\(7\) 1.84299 1.84299i 0.696583 0.696583i −0.267089 0.963672i \(-0.586062\pi\)
0.963672 + 0.267089i \(0.0860617\pi\)
\(8\) −1.00000 −0.353553
\(9\) 1.00000i 0.333333i
\(10\) −1.63524 1.52512i −0.517107 0.482286i
\(11\) 3.01042i 0.907674i 0.891085 + 0.453837i \(0.149945\pi\)
−0.891085 + 0.453837i \(0.850055\pi\)
\(12\) −0.707107 + 0.707107i −0.204124 + 0.204124i
\(13\) −1.82067 −0.504963 −0.252481 0.967602i \(-0.581247\pi\)
−0.252481 + 0.967602i \(0.581247\pi\)
\(14\) −1.84299 + 1.84299i −0.492559 + 0.492559i
\(15\) −2.23471 + 0.0778616i −0.577000 + 0.0201038i
\(16\) 1.00000 0.250000
\(17\) 5.42248i 1.31515i 0.753391 + 0.657573i \(0.228417\pi\)
−0.753391 + 0.657573i \(0.771583\pi\)
\(18\) 1.00000i 0.235702i
\(19\) 0.509592 + 0.509592i 0.116909 + 0.116909i 0.763141 0.646232i \(-0.223656\pi\)
−0.646232 + 0.763141i \(0.723656\pi\)
\(20\) 1.63524 + 1.52512i 0.365650 + 0.341028i
\(21\) 2.60638i 0.568758i
\(22\) 3.01042i 0.641823i
\(23\) −0.0216604 −0.00451651 −0.00225825 0.999997i \(-0.500719\pi\)
−0.00225825 + 0.999997i \(0.500719\pi\)
\(24\) 0.707107 0.707107i 0.144338 0.144338i
\(25\) 0.347996 + 4.98788i 0.0695993 + 0.997575i
\(26\) 1.82067 0.357063
\(27\) 0.707107 + 0.707107i 0.136083 + 0.136083i
\(28\) 1.84299 1.84299i 0.348292 0.348292i
\(29\) 4.67832 4.67832i 0.868742 0.868742i −0.123591 0.992333i \(-0.539441\pi\)
0.992333 + 0.123591i \(0.0394412\pi\)
\(30\) 2.23471 0.0778616i 0.408001 0.0142155i
\(31\) 1.55104 + 1.55104i 0.278574 + 0.278574i 0.832540 0.553965i \(-0.186886\pi\)
−0.553965 + 0.832540i \(0.686886\pi\)
\(32\) −1.00000 −0.176777
\(33\) −2.12868 2.12868i −0.370556 0.370556i
\(34\) 5.42248i 0.929948i
\(35\) 5.82450 0.202937i 0.984520 0.0343025i
\(36\) 1.00000i 0.166667i
\(37\) 2.27285 5.64218i 0.373655 0.927568i
\(38\) −0.509592 0.509592i −0.0826668 0.0826668i
\(39\) 1.28741 1.28741i 0.206150 0.206150i
\(40\) −1.63524 1.52512i −0.258554 0.241143i
\(41\) 6.35587i 0.992619i 0.868146 + 0.496310i \(0.165312\pi\)
−0.868146 + 0.496310i \(0.834688\pi\)
\(42\) 2.60638i 0.402173i
\(43\) −7.86706 −1.19972 −0.599858 0.800107i \(-0.704776\pi\)
−0.599858 + 0.800107i \(0.704776\pi\)
\(44\) 3.01042i 0.453837i
\(45\) 1.52512 1.63524i 0.227352 0.243767i
\(46\) 0.0216604 0.00319365
\(47\) −0.176174 + 0.176174i −0.0256976 + 0.0256976i −0.719839 0.694141i \(-0.755784\pi\)
0.694141 + 0.719839i \(0.255784\pi\)
\(48\) −0.707107 + 0.707107i −0.102062 + 0.102062i
\(49\) 0.206804i 0.0295435i
\(50\) −0.347996 4.98788i −0.0492141 0.705392i
\(51\) −3.83427 3.83427i −0.536906 0.536906i
\(52\) −1.82067 −0.252481
\(53\) 2.05089 + 2.05089i 0.281711 + 0.281711i 0.833791 0.552080i \(-0.186166\pi\)
−0.552080 + 0.833791i \(0.686166\pi\)
\(54\) −0.707107 0.707107i −0.0962250 0.0962250i
\(55\) −4.59126 + 4.92274i −0.619085 + 0.663782i
\(56\) −1.84299 + 1.84299i −0.246279 + 0.246279i
\(57\) −0.720673 −0.0954554
\(58\) −4.67832 + 4.67832i −0.614293 + 0.614293i
\(59\) 2.84934 + 2.84934i 0.370952 + 0.370952i 0.867824 0.496872i \(-0.165518\pi\)
−0.496872 + 0.867824i \(0.665518\pi\)
\(60\) −2.23471 + 0.0778616i −0.288500 + 0.0100519i
\(61\) 4.51718 + 4.51718i 0.578366 + 0.578366i 0.934453 0.356087i \(-0.115889\pi\)
−0.356087 + 0.934453i \(0.615889\pi\)
\(62\) −1.55104 1.55104i −0.196982 0.196982i
\(63\) −1.84299 1.84299i −0.232194 0.232194i
\(64\) 1.00000 0.125000
\(65\) −2.97723 2.77675i −0.369279 0.344413i
\(66\) 2.12868 + 2.12868i 0.262023 + 0.262023i
\(67\) −3.93891 3.93891i −0.481215 0.481215i 0.424305 0.905519i \(-0.360519\pi\)
−0.905519 + 0.424305i \(0.860519\pi\)
\(68\) 5.42248i 0.657573i
\(69\) 0.0153162 0.0153162i 0.00184386 0.00184386i
\(70\) −5.82450 + 0.202937i −0.696161 + 0.0242556i
\(71\) 9.00950 1.06923 0.534615 0.845095i \(-0.320456\pi\)
0.534615 + 0.845095i \(0.320456\pi\)
\(72\) 1.00000i 0.117851i
\(73\) −8.50501 + 8.50501i −0.995437 + 0.995437i −0.999990 0.00455309i \(-0.998551\pi\)
0.00455309 + 0.999990i \(0.498551\pi\)
\(74\) −2.27285 + 5.64218i −0.264214 + 0.655890i
\(75\) −3.77303 3.28089i −0.435672 0.378845i
\(76\) 0.509592 + 0.509592i 0.0584543 + 0.0584543i
\(77\) 5.54815 + 5.54815i 0.632271 + 0.632271i
\(78\) −1.28741 + 1.28741i −0.145770 + 0.145770i
\(79\) 2.16377 + 2.16377i 0.243444 + 0.243444i 0.818273 0.574830i \(-0.194932\pi\)
−0.574830 + 0.818273i \(0.694932\pi\)
\(80\) 1.63524 + 1.52512i 0.182825 + 0.170514i
\(81\) −1.00000 −0.111111
\(82\) 6.35587i 0.701888i
\(83\) 0.925954 + 0.925954i 0.101637 + 0.101637i 0.756097 0.654460i \(-0.227104\pi\)
−0.654460 + 0.756097i \(0.727104\pi\)
\(84\) 2.60638i 0.284379i
\(85\) −8.26996 + 8.86704i −0.897003 + 0.961766i
\(86\) 7.86706 0.848327
\(87\) 6.61614i 0.709325i
\(88\) 3.01042i 0.320911i
\(89\) −1.03976 + 1.03976i −0.110214 + 0.110214i −0.760063 0.649849i \(-0.774832\pi\)
0.649849 + 0.760063i \(0.274832\pi\)
\(90\) −1.52512 + 1.63524i −0.160762 + 0.172369i
\(91\) −3.35547 + 3.35547i −0.351749 + 0.351749i
\(92\) −0.0216604 −0.00225825
\(93\) −2.19350 −0.227455
\(94\) 0.176174 0.176174i 0.0181710 0.0181710i
\(95\) 0.0561127 + 1.61050i 0.00575704 + 0.165233i
\(96\) 0.707107 0.707107i 0.0721688 0.0721688i
\(97\) 7.65590i 0.777339i 0.921377 + 0.388670i \(0.127065\pi\)
−0.921377 + 0.388670i \(0.872935\pi\)
\(98\) 0.206804i 0.0208904i
\(99\) 3.01042 0.302558
\(100\) 0.347996 + 4.98788i 0.0347996 + 0.498788i
\(101\) 16.6519i 1.65693i 0.560040 + 0.828465i \(0.310786\pi\)
−0.560040 + 0.828465i \(0.689214\pi\)
\(102\) 3.83427 + 3.83427i 0.379650 + 0.379650i
\(103\) 15.2064i 1.49833i −0.662383 0.749165i \(-0.730455\pi\)
0.662383 0.749165i \(-0.269545\pi\)
\(104\) 1.82067 0.178531
\(105\) −3.97505 + 4.26204i −0.387925 + 0.415933i
\(106\) −2.05089 2.05089i −0.199200 0.199200i
\(107\) −7.85181 + 7.85181i −0.759063 + 0.759063i −0.976152 0.217089i \(-0.930344\pi\)
0.217089 + 0.976152i \(0.430344\pi\)
\(108\) 0.707107 + 0.707107i 0.0680414 + 0.0680414i
\(109\) 5.15891 + 5.15891i 0.494134 + 0.494134i 0.909606 0.415472i \(-0.136384\pi\)
−0.415472 + 0.909606i \(0.636384\pi\)
\(110\) 4.59126 4.92274i 0.437759 0.469365i
\(111\) 2.38247 + 5.59677i 0.226134 + 0.531222i
\(112\) 1.84299 1.84299i 0.174146 0.174146i
\(113\) 3.80319i 0.357774i −0.983870 0.178887i \(-0.942750\pi\)
0.983870 0.178887i \(-0.0572497\pi\)
\(114\) 0.720673 0.0674972
\(115\) −0.0354199 0.0330348i −0.00330292 0.00308051i
\(116\) 4.67832 4.67832i 0.434371 0.434371i
\(117\) 1.82067i 0.168321i
\(118\) −2.84934 2.84934i −0.262303 0.262303i
\(119\) 9.99356 + 9.99356i 0.916108 + 0.916108i
\(120\) 2.23471 0.0778616i 0.204000 0.00710776i
\(121\) 1.93740 0.176127
\(122\) −4.51718 4.51718i −0.408966 0.408966i
\(123\) −4.49428 4.49428i −0.405235 0.405235i
\(124\) 1.55104 + 1.55104i 0.139287 + 0.139287i
\(125\) −7.03807 + 8.68709i −0.629504 + 0.776997i
\(126\) 1.84299 + 1.84299i 0.164186 + 0.164186i
\(127\) 9.77118 9.77118i 0.867052 0.867052i −0.125093 0.992145i \(-0.539923\pi\)
0.992145 + 0.125093i \(0.0399229\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 5.56285 5.56285i 0.489782 0.489782i
\(130\) 2.97723 + 2.77675i 0.261120 + 0.243537i
\(131\) 2.21257 + 2.21257i 0.193313 + 0.193313i 0.797126 0.603813i \(-0.206353\pi\)
−0.603813 + 0.797126i \(0.706353\pi\)
\(132\) −2.12868 2.12868i −0.185278 0.185278i
\(133\) 1.87834 0.162873
\(134\) 3.93891 + 3.93891i 0.340270 + 0.340270i
\(135\) 0.0778616 + 2.23471i 0.00670126 + 0.192333i
\(136\) 5.42248i 0.464974i
\(137\) −5.72235 + 5.72235i −0.488894 + 0.488894i −0.907957 0.419063i \(-0.862359\pi\)
0.419063 + 0.907957i \(0.362359\pi\)
\(138\) −0.0153162 + 0.0153162i −0.00130380 + 0.00130380i
\(139\) −4.18150 −0.354670 −0.177335 0.984151i \(-0.556748\pi\)
−0.177335 + 0.984151i \(0.556748\pi\)
\(140\) 5.82450 0.202937i 0.492260 0.0171513i
\(141\) 0.249148i 0.0209820i
\(142\) −9.00950 −0.756060
\(143\) 5.48097i 0.458342i
\(144\) 1.00000i 0.0833333i
\(145\) 14.7852 0.515143i 1.22784 0.0427803i
\(146\) 8.50501 8.50501i 0.703880 0.703880i
\(147\) −0.146233 0.146233i −0.0120611 0.0120611i
\(148\) 2.27285 5.64218i 0.186827 0.463784i
\(149\) 2.65031i 0.217122i −0.994090 0.108561i \(-0.965376\pi\)
0.994090 0.108561i \(-0.0346243\pi\)
\(150\) 3.77303 + 3.28089i 0.308067 + 0.267884i
\(151\) 3.91246i 0.318391i −0.987247 0.159196i \(-0.949110\pi\)
0.987247 0.159196i \(-0.0508901\pi\)
\(152\) −0.509592 0.509592i −0.0413334 0.0413334i
\(153\) 5.42248 0.438382
\(154\) −5.54815 5.54815i −0.447083 0.447083i
\(155\) 0.170789 + 4.90183i 0.0137181 + 0.393725i
\(156\) 1.28741 1.28741i 0.103075 0.103075i
\(157\) −12.9226 + 12.9226i −1.03134 + 1.03134i −0.0318468 + 0.999493i \(0.510139\pi\)
−0.999493 + 0.0318468i \(0.989861\pi\)
\(158\) −2.16377 2.16377i −0.172141 0.172141i
\(159\) −2.90039 −0.230016
\(160\) −1.63524 1.52512i −0.129277 0.120572i
\(161\) −0.0399199 + 0.0399199i −0.00314613 + 0.00314613i
\(162\) 1.00000 0.0785674
\(163\) 8.59786i 0.673437i −0.941605 0.336718i \(-0.890683\pi\)
0.941605 0.336718i \(-0.109317\pi\)
\(164\) 6.35587i 0.496310i
\(165\) −0.234396 6.72741i −0.0182477 0.523728i
\(166\) −0.925954 0.925954i −0.0718680 0.0718680i
\(167\) 4.59086i 0.355252i −0.984098 0.177626i \(-0.943158\pi\)
0.984098 0.177626i \(-0.0568417\pi\)
\(168\) 2.60638i 0.201086i
\(169\) −9.68516 −0.745012
\(170\) 8.26996 8.86704i 0.634277 0.680071i
\(171\) 0.509592 0.509592i 0.0389695 0.0389695i
\(172\) −7.86706 −0.599858
\(173\) 6.49792 6.49792i 0.494028 0.494028i −0.415545 0.909573i \(-0.636409\pi\)
0.909573 + 0.415545i \(0.136409\pi\)
\(174\) 6.61614i 0.501568i
\(175\) 9.83394 + 8.55123i 0.743376 + 0.646412i
\(176\) 3.01042i 0.226919i
\(177\) −4.02957 −0.302881
\(178\) 1.03976 1.03976i 0.0779333 0.0779333i
\(179\) −11.1786 + 11.1786i −0.835528 + 0.835528i −0.988267 0.152738i \(-0.951191\pi\)
0.152738 + 0.988267i \(0.451191\pi\)
\(180\) 1.52512 1.63524i 0.113676 0.121883i
\(181\) −12.7902 −0.950689 −0.475345 0.879800i \(-0.657677\pi\)
−0.475345 + 0.879800i \(0.657677\pi\)
\(182\) 3.35547 3.35547i 0.248724 0.248724i
\(183\) −6.38826 −0.472234
\(184\) 0.0216604 0.00159683
\(185\) 12.3217 5.75991i 0.905907 0.423477i
\(186\) 2.19350 0.160835
\(187\) −16.3239 −1.19372
\(188\) −0.176174 + 0.176174i −0.0128488 + 0.0128488i
\(189\) 2.60638 0.189586
\(190\) −0.0561127 1.61050i −0.00407084 0.116838i
\(191\) 15.7097 15.7097i 1.13672 1.13672i 0.147683 0.989035i \(-0.452819\pi\)
0.989035 0.147683i \(-0.0471814\pi\)
\(192\) −0.707107 + 0.707107i −0.0510310 + 0.0510310i
\(193\) 21.0634 1.51618 0.758088 0.652152i \(-0.226134\pi\)
0.758088 + 0.652152i \(0.226134\pi\)
\(194\) 7.65590i 0.549662i
\(195\) 4.06867 0.141760i 0.291364 0.0101517i
\(196\) 0.206804i 0.0147717i
\(197\) −5.52601 + 5.52601i −0.393712 + 0.393712i −0.876008 0.482296i \(-0.839803\pi\)
0.482296 + 0.876008i \(0.339803\pi\)
\(198\) −3.01042 −0.213941
\(199\) 5.69096 5.69096i 0.403421 0.403421i −0.476015 0.879437i \(-0.657919\pi\)
0.879437 + 0.476015i \(0.157919\pi\)
\(200\) −0.347996 4.98788i −0.0246071 0.352696i
\(201\) 5.57046 0.392910
\(202\) 16.6519i 1.17163i
\(203\) 17.2442i 1.21030i
\(204\) −3.83427 3.83427i −0.268453 0.268453i
\(205\) −9.69348 + 10.3933i −0.677022 + 0.725903i
\(206\) 15.2064i 1.05948i
\(207\) 0.0216604i 0.00150550i
\(208\) −1.82067 −0.126241
\(209\) −1.53408 + 1.53408i −0.106115 + 0.106115i
\(210\) 3.97505 4.26204i 0.274304 0.294109i
\(211\) 2.18341 0.150312 0.0751561 0.997172i \(-0.476054\pi\)
0.0751561 + 0.997172i \(0.476054\pi\)
\(212\) 2.05089 + 2.05089i 0.140855 + 0.140855i
\(213\) −6.37068 + 6.37068i −0.436512 + 0.436512i
\(214\) 7.85181 7.85181i 0.536739 0.536739i
\(215\) −12.8645 11.9982i −0.877352 0.818273i
\(216\) −0.707107 0.707107i −0.0481125 0.0481125i
\(217\) 5.71708 0.388101
\(218\) −5.15891 5.15891i −0.349405 0.349405i
\(219\) 12.0279i 0.812771i
\(220\) −4.59126 + 4.92274i −0.309542 + 0.331891i
\(221\) 9.87255i 0.664100i
\(222\) −2.38247 5.59677i −0.159901 0.375631i
\(223\) −15.3328 15.3328i −1.02676 1.02676i −0.999632 0.0271298i \(-0.991363\pi\)
−0.0271298 0.999632i \(-0.508637\pi\)
\(224\) −1.84299 + 1.84299i −0.123140 + 0.123140i
\(225\) 4.98788 0.347996i 0.332525 0.0231998i
\(226\) 3.80319i 0.252985i
\(227\) 3.20189i 0.212517i 0.994339 + 0.106258i \(0.0338870\pi\)
−0.994339 + 0.106258i \(0.966113\pi\)
\(228\) −0.720673 −0.0477277
\(229\) 21.2446i 1.40389i −0.712233 0.701943i \(-0.752316\pi\)
0.712233 0.701943i \(-0.247684\pi\)
\(230\) 0.0354199 + 0.0330348i 0.00233552 + 0.00217825i
\(231\) −7.84627 −0.516247
\(232\) −4.67832 + 4.67832i −0.307147 + 0.307147i
\(233\) −12.0202 + 12.0202i −0.787472 + 0.787472i −0.981079 0.193607i \(-0.937981\pi\)
0.193607 + 0.981079i \(0.437981\pi\)
\(234\) 1.82067i 0.119021i
\(235\) −0.556773 + 0.0193990i −0.0363199 + 0.00126545i
\(236\) 2.84934 + 2.84934i 0.185476 + 0.185476i
\(237\) −3.06004 −0.198771
\(238\) −9.99356 9.99356i −0.647786 0.647786i
\(239\) −10.1337 10.1337i −0.655496 0.655496i 0.298815 0.954311i \(-0.403409\pi\)
−0.954311 + 0.298815i \(0.903409\pi\)
\(240\) −2.23471 + 0.0778616i −0.144250 + 0.00502594i
\(241\) 10.2389 10.2389i 0.659546 0.659546i −0.295727 0.955273i \(-0.595562\pi\)
0.955273 + 0.295727i \(0.0955618\pi\)
\(242\) −1.93740 −0.124541
\(243\) 0.707107 0.707107i 0.0453609 0.0453609i
\(244\) 4.51718 + 4.51718i 0.289183 + 0.289183i
\(245\) −0.315402 + 0.338174i −0.0201503 + 0.0216052i
\(246\) 4.49428 + 4.49428i 0.286545 + 0.286545i
\(247\) −0.927800 0.927800i −0.0590345 0.0590345i
\(248\) −1.55104 1.55104i −0.0984909 0.0984909i
\(249\) −1.30950 −0.0829860
\(250\) 7.03807 8.68709i 0.445127 0.549420i
\(251\) 3.84833 + 3.84833i 0.242905 + 0.242905i 0.818051 0.575146i \(-0.195055\pi\)
−0.575146 + 0.818051i \(0.695055\pi\)
\(252\) −1.84299 1.84299i −0.116097 0.116097i
\(253\) 0.0652069i 0.00409952i
\(254\) −9.77118 + 9.77118i −0.613099 + 0.613099i
\(255\) −0.422203 12.1177i −0.0264394 0.758839i
\(256\) 1.00000 0.0625000
\(257\) 3.13559i 0.195593i 0.995206 + 0.0977963i \(0.0311794\pi\)
−0.995206 + 0.0977963i \(0.968821\pi\)
\(258\) −5.56285 + 5.56285i −0.346328 + 0.346328i
\(259\) −6.20962 14.5873i −0.385847 0.906410i
\(260\) −2.97723 2.77675i −0.184640 0.172207i
\(261\) −4.67832 4.67832i −0.289581 0.289581i
\(262\) −2.21257 2.21257i −0.136693 0.136693i
\(263\) 20.7027 20.7027i 1.27658 1.27658i 0.334018 0.942567i \(-0.391595\pi\)
0.942567 0.334018i \(-0.108405\pi\)
\(264\) 2.12868 + 2.12868i 0.131012 + 0.131012i
\(265\) 0.225829 + 6.48154i 0.0138726 + 0.398158i
\(266\) −1.87834 −0.115169
\(267\) 1.47044i 0.0899896i
\(268\) −3.93891 3.93891i −0.240607 0.240607i
\(269\) 15.5877i 0.950397i 0.879879 + 0.475199i \(0.157624\pi\)
−0.879879 + 0.475199i \(0.842376\pi\)
\(270\) −0.0778616 2.23471i −0.00473851 0.136000i
\(271\) 30.3127 1.84136 0.920682 0.390314i \(-0.127633\pi\)
0.920682 + 0.390314i \(0.127633\pi\)
\(272\) 5.42248i 0.328786i
\(273\) 4.74535i 0.287202i
\(274\) 5.72235 5.72235i 0.345700 0.345700i
\(275\) −15.0156 + 1.04761i −0.905473 + 0.0631735i
\(276\) 0.0153162 0.0153162i 0.000921929 0.000921929i
\(277\) 14.8230 0.890629 0.445315 0.895374i \(-0.353092\pi\)
0.445315 + 0.895374i \(0.353092\pi\)
\(278\) 4.18150 0.250789
\(279\) 1.55104 1.55104i 0.0928581 0.0928581i
\(280\) −5.82450 + 0.202937i −0.348080 + 0.0121278i
\(281\) 22.8948 22.8948i 1.36579 1.36579i 0.499436 0.866351i \(-0.333541\pi\)
0.866351 0.499436i \(-0.166459\pi\)
\(282\) 0.249148i 0.0148365i
\(283\) 23.6708i 1.40708i −0.710655 0.703541i \(-0.751601\pi\)
0.710655 0.703541i \(-0.248399\pi\)
\(284\) 9.00950 0.534615
\(285\) −1.17847 1.09911i −0.0698065 0.0651059i
\(286\) 5.48097i 0.324097i
\(287\) 11.7138 + 11.7138i 0.691442 + 0.691442i
\(288\) 1.00000i 0.0589256i
\(289\) −12.4033 −0.729607
\(290\) −14.7852 + 0.515143i −0.868215 + 0.0302503i
\(291\) −5.41354 5.41354i −0.317347 0.317347i
\(292\) −8.50501 + 8.50501i −0.497718 + 0.497718i
\(293\) 5.16020 + 5.16020i 0.301462 + 0.301462i 0.841586 0.540124i \(-0.181623\pi\)
−0.540124 + 0.841586i \(0.681623\pi\)
\(294\) 0.146233 + 0.146233i 0.00852847 + 0.00852847i
\(295\) 0.313749 + 9.00493i 0.0182672 + 0.524287i
\(296\) −2.27285 + 5.64218i −0.132107 + 0.327945i
\(297\) −2.12868 + 2.12868i −0.123519 + 0.123519i
\(298\) 2.65031i 0.153529i
\(299\) 0.0394365 0.00228067
\(300\) −3.77303 3.28089i −0.217836 0.189422i
\(301\) −14.4989 + 14.4989i −0.835701 + 0.835701i
\(302\) 3.91246i 0.225137i
\(303\) −11.7747 11.7747i −0.676439 0.676439i
\(304\) 0.509592 + 0.509592i 0.0292271 + 0.0292271i
\(305\) 0.497400 + 14.2759i 0.0284810 + 0.817437i
\(306\) −5.42248 −0.309983
\(307\) 16.3280 + 16.3280i 0.931889 + 0.931889i 0.997824 0.0659354i \(-0.0210031\pi\)
−0.0659354 + 0.997824i \(0.521003\pi\)
\(308\) 5.54815 + 5.54815i 0.316135 + 0.316135i
\(309\) 10.7525 + 10.7525i 0.611691 + 0.611691i
\(310\) −0.170789 4.90183i −0.00970017 0.278405i
\(311\) −20.2566 20.2566i −1.14865 1.14865i −0.986819 0.161827i \(-0.948261\pi\)
−0.161827 0.986819i \(-0.551739\pi\)
\(312\) −1.28741 + 1.28741i −0.0728851 + 0.0728851i
\(313\) 18.3942 1.03970 0.519852 0.854256i \(-0.325987\pi\)
0.519852 + 0.854256i \(0.325987\pi\)
\(314\) 12.9226 12.9226i 0.729267 0.729267i
\(315\) −0.202937 5.82450i −0.0114342 0.328173i
\(316\) 2.16377 + 2.16377i 0.121722 + 0.121722i
\(317\) −3.40194 3.40194i −0.191072 0.191072i 0.605087 0.796159i \(-0.293138\pi\)
−0.796159 + 0.605087i \(0.793138\pi\)
\(318\) 2.90039 0.162646
\(319\) 14.0837 + 14.0837i 0.788535 + 0.788535i
\(320\) 1.63524 + 1.52512i 0.0914125 + 0.0852570i
\(321\) 11.1041i 0.619773i
\(322\) 0.0399199 0.0399199i 0.00222465 0.00222465i
\(323\) −2.76326 + 2.76326i −0.153752 + 0.153752i
\(324\) −1.00000 −0.0555556
\(325\) −0.633587 9.08127i −0.0351451 0.503738i
\(326\) 8.59786i 0.476192i
\(327\) −7.29580 −0.403459
\(328\) 6.35587i 0.350944i
\(329\) 0.649372i 0.0358010i
\(330\) 0.234396 + 6.72741i 0.0129031 + 0.370332i
\(331\) 2.61136 2.61136i 0.143533 0.143533i −0.631689 0.775222i \(-0.717638\pi\)
0.775222 + 0.631689i \(0.217638\pi\)
\(332\) 0.925954 + 0.925954i 0.0508183 + 0.0508183i
\(333\) −5.64218 2.27285i −0.309189 0.124552i
\(334\) 4.59086i 0.251201i
\(335\) −0.433725 12.4484i −0.0236969 0.680128i
\(336\) 2.60638i 0.142189i
\(337\) −3.23500 3.23500i −0.176222 0.176222i 0.613485 0.789707i \(-0.289767\pi\)
−0.789707 + 0.613485i \(0.789767\pi\)
\(338\) 9.68516 0.526803
\(339\) 2.68926 + 2.68926i 0.146061 + 0.146061i
\(340\) −8.26996 + 8.86704i −0.448501 + 0.480883i
\(341\) −4.66926 + 4.66926i −0.252855 + 0.252855i
\(342\) −0.509592 + 0.509592i −0.0275556 + 0.0275556i
\(343\) 13.2820 + 13.2820i 0.717163 + 0.717163i
\(344\) 7.86706 0.424163
\(345\) 0.0484048 0.00168651i 0.00260603 9.07989e-5i
\(346\) −6.49792 + 6.49792i −0.349330 + 0.349330i
\(347\) 17.9326 0.962675 0.481337 0.876535i \(-0.340151\pi\)
0.481337 + 0.876535i \(0.340151\pi\)
\(348\) 6.61614i 0.354662i
\(349\) 34.1023i 1.82545i −0.408571 0.912727i \(-0.633973\pi\)
0.408571 0.912727i \(-0.366027\pi\)
\(350\) −9.83394 8.55123i −0.525646 0.457083i
\(351\) −1.28741 1.28741i −0.0687168 0.0687168i
\(352\) 3.01042i 0.160456i
\(353\) 7.23850i 0.385266i −0.981271 0.192633i \(-0.938297\pi\)
0.981271 0.192633i \(-0.0617027\pi\)
\(354\) 4.02957 0.214169
\(355\) 14.7327 + 13.7406i 0.781929 + 0.729275i
\(356\) −1.03976 + 1.03976i −0.0551071 + 0.0551071i
\(357\) −14.1330 −0.747999
\(358\) 11.1786 11.1786i 0.590808 0.590808i
\(359\) 29.3398i 1.54849i −0.632884 0.774247i \(-0.718129\pi\)
0.632884 0.774247i \(-0.281871\pi\)
\(360\) −1.52512 + 1.63524i −0.0803811 + 0.0861845i
\(361\) 18.4806i 0.972665i
\(362\) 12.7902 0.672239
\(363\) −1.36995 + 1.36995i −0.0719037 + 0.0719037i
\(364\) −3.35547 + 3.35547i −0.175874 + 0.175874i
\(365\) −26.8789 + 0.936512i −1.40691 + 0.0490193i
\(366\) 6.38826 0.333920
\(367\) 7.30169 7.30169i 0.381145 0.381145i −0.490370 0.871515i \(-0.663138\pi\)
0.871515 + 0.490370i \(0.163138\pi\)
\(368\) −0.0216604 −0.00112913
\(369\) 6.35587 0.330873
\(370\) −12.3217 + 5.75991i −0.640573 + 0.299443i
\(371\) 7.55951 0.392470
\(372\) −2.19350 −0.113728
\(373\) −0.813457 + 0.813457i −0.0421192 + 0.0421192i −0.727853 0.685733i \(-0.759482\pi\)
0.685733 + 0.727853i \(0.259482\pi\)
\(374\) 16.3239 0.844090
\(375\) −1.16604 11.1194i −0.0602138 0.574202i
\(376\) 0.176174 0.176174i 0.00908548 0.00908548i
\(377\) −8.51767 + 8.51767i −0.438682 + 0.438682i
\(378\) −2.60638 −0.134058
\(379\) 14.5201i 0.745847i 0.927862 + 0.372924i \(0.121645\pi\)
−0.927862 + 0.372924i \(0.878355\pi\)
\(380\) 0.0561127 + 1.61050i 0.00287852 + 0.0826167i
\(381\) 13.8185i 0.707945i
\(382\) −15.7097 + 15.7097i −0.803781 + 0.803781i
\(383\) −14.8639 −0.759507 −0.379754 0.925088i \(-0.623991\pi\)
−0.379754 + 0.925088i \(0.623991\pi\)
\(384\) 0.707107 0.707107i 0.0360844 0.0360844i
\(385\) 0.610923 + 17.5342i 0.0311355 + 0.893624i
\(386\) −21.0634 −1.07210
\(387\) 7.86706i 0.399905i
\(388\) 7.65590i 0.388670i
\(389\) −25.0493 25.0493i −1.27005 1.27005i −0.946062 0.323986i \(-0.894977\pi\)
−0.323986 0.946062i \(-0.605023\pi\)
\(390\) −4.06867 + 0.141760i −0.206025 + 0.00717831i
\(391\) 0.117453i 0.00593987i
\(392\) 0.206804i 0.0104452i
\(393\) −3.12905 −0.157840
\(394\) 5.52601 5.52601i 0.278396 0.278396i
\(395\) 0.238260 + 6.83831i 0.0119881 + 0.344073i
\(396\) 3.01042 0.151279
\(397\) −5.32491 5.32491i −0.267250 0.267250i 0.560741 0.827991i \(-0.310516\pi\)
−0.827991 + 0.560741i \(0.810516\pi\)
\(398\) −5.69096 + 5.69096i −0.285262 + 0.285262i
\(399\) −1.32819 + 1.32819i −0.0664926 + 0.0664926i
\(400\) 0.347996 + 4.98788i 0.0173998 + 0.249394i
\(401\) −5.09805 5.09805i −0.254584 0.254584i 0.568263 0.822847i \(-0.307616\pi\)
−0.822847 + 0.568263i \(0.807616\pi\)
\(402\) −5.57046 −0.277829
\(403\) −2.82393 2.82393i −0.140670 0.140670i
\(404\) 16.6519i 0.828465i
\(405\) −1.63524 1.52512i −0.0812556 0.0757840i
\(406\) 17.2442i 0.855813i
\(407\) 16.9853 + 6.84223i 0.841930 + 0.339157i
\(408\) 3.83427 + 3.83427i 0.189825 + 0.189825i
\(409\) −15.3174 + 15.3174i −0.757396 + 0.757396i −0.975848 0.218451i \(-0.929899\pi\)
0.218451 + 0.975848i \(0.429899\pi\)
\(410\) 9.69348 10.3933i 0.478727 0.513291i
\(411\) 8.09263i 0.399180i
\(412\) 15.2064i 0.749165i
\(413\) 10.5026 0.516798
\(414\) 0.0216604i 0.00106455i
\(415\) 0.101960 + 2.92635i 0.00500500 + 0.143649i
\(416\) 1.82067 0.0892657
\(417\) 2.95676 2.95676i 0.144793 0.144793i
\(418\) 1.53408 1.53408i 0.0750345 0.0750345i
\(419\) 15.6256i 0.763360i −0.924294 0.381680i \(-0.875346\pi\)
0.924294 0.381680i \(-0.124654\pi\)
\(420\) −3.97505 + 4.26204i −0.193962 + 0.207966i
\(421\) 15.7260 + 15.7260i 0.766440 + 0.766440i 0.977478 0.211038i \(-0.0676844\pi\)
−0.211038 + 0.977478i \(0.567684\pi\)
\(422\) −2.18341 −0.106287
\(423\) 0.176174 + 0.176174i 0.00856587 + 0.00856587i
\(424\) −2.05089 2.05089i −0.0995998 0.0995998i
\(425\) −27.0467 + 1.88700i −1.31196 + 0.0915332i
\(426\) 6.37068 6.37068i 0.308660 0.308660i
\(427\) 16.6502 0.805760
\(428\) −7.85181 + 7.85181i −0.379532 + 0.379532i
\(429\) 3.87563 + 3.87563i 0.187117 + 0.187117i
\(430\) 12.8645 + 11.9982i 0.620381 + 0.578606i
\(431\) 7.16507 + 7.16507i 0.345129 + 0.345129i 0.858292 0.513162i \(-0.171526\pi\)
−0.513162 + 0.858292i \(0.671526\pi\)
\(432\) 0.707107 + 0.707107i 0.0340207 + 0.0340207i
\(433\) 12.9982 + 12.9982i 0.624652 + 0.624652i 0.946717 0.322065i \(-0.104377\pi\)
−0.322065 + 0.946717i \(0.604377\pi\)
\(434\) −5.71708 −0.274429
\(435\) −10.0904 + 10.8190i −0.483799 + 0.518729i
\(436\) 5.15891 + 5.15891i 0.247067 + 0.247067i
\(437\) −0.0110380 0.0110380i −0.000528019 0.000528019i
\(438\) 12.0279i 0.574716i
\(439\) 10.5684 10.5684i 0.504400 0.504400i −0.408402 0.912802i \(-0.633914\pi\)
0.912802 + 0.408402i \(0.133914\pi\)
\(440\) 4.59126 4.92274i 0.218879 0.234682i
\(441\) 0.206804 0.00984783
\(442\) 9.87255i 0.469589i
\(443\) −17.5773 + 17.5773i −0.835121 + 0.835121i −0.988212 0.153091i \(-0.951077\pi\)
0.153091 + 0.988212i \(0.451077\pi\)
\(444\) 2.38247 + 5.59677i 0.113067 + 0.265611i
\(445\) −3.28601 + 0.114491i −0.155772 + 0.00542739i
\(446\) 15.3328 + 15.3328i 0.726030 + 0.726030i
\(447\) 1.87406 + 1.87406i 0.0886398 + 0.0886398i
\(448\) 1.84299 1.84299i 0.0870729 0.0870729i
\(449\) −9.93203 9.93203i −0.468722 0.468722i 0.432779 0.901500i \(-0.357533\pi\)
−0.901500 + 0.432779i \(0.857533\pi\)
\(450\) −4.98788 + 0.347996i −0.235131 + 0.0164047i
\(451\) −19.1338 −0.900975
\(452\) 3.80319i 0.178887i
\(453\) 2.76653 + 2.76653i 0.129983 + 0.129983i
\(454\) 3.20189i 0.150272i
\(455\) −10.6045 + 0.369480i −0.497146 + 0.0173215i
\(456\) 0.720673 0.0337486
\(457\) 8.27570i 0.387121i −0.981088 0.193560i \(-0.937996\pi\)
0.981088 0.193560i \(-0.0620036\pi\)
\(458\) 21.2446i 0.992697i
\(459\) −3.83427 + 3.83427i −0.178969 + 0.178969i
\(460\) −0.0354199 0.0330348i −0.00165146 0.00154026i
\(461\) −3.89734 + 3.89734i −0.181517 + 0.181517i −0.792017 0.610499i \(-0.790969\pi\)
0.610499 + 0.792017i \(0.290969\pi\)
\(462\) 7.84627 0.365042
\(463\) 37.2821 1.73265 0.866323 0.499484i \(-0.166477\pi\)
0.866323 + 0.499484i \(0.166477\pi\)
\(464\) 4.67832 4.67832i 0.217185 0.217185i
\(465\) −3.58689 3.34535i −0.166338 0.155137i
\(466\) 12.0202 12.0202i 0.556827 0.556827i
\(467\) 11.9336i 0.552219i −0.961126 0.276109i \(-0.910955\pi\)
0.961126 0.276109i \(-0.0890452\pi\)
\(468\) 1.82067i 0.0841605i
\(469\) −14.5187 −0.670412
\(470\) 0.556773 0.0193990i 0.0256820 0.000894810i
\(471\) 18.2754i 0.842085i
\(472\) −2.84934 2.84934i −0.131151 0.131151i
\(473\) 23.6831i 1.08895i
\(474\) 3.06004 0.140552
\(475\) −2.36445 + 2.71912i −0.108488 + 0.124762i
\(476\) 9.99356 + 9.99356i 0.458054 + 0.458054i
\(477\) 2.05089 2.05089i 0.0939036 0.0939036i
\(478\) 10.1337 + 10.1337i 0.463506 + 0.463506i
\(479\) 0.903277 + 0.903277i 0.0412718 + 0.0412718i 0.727441 0.686170i \(-0.240709\pi\)
−0.686170 + 0.727441i \(0.740709\pi\)
\(480\) 2.23471 0.0778616i 0.102000 0.00355388i
\(481\) −4.13811 + 10.2725i −0.188682 + 0.468387i
\(482\) −10.2389 + 10.2389i −0.466369 + 0.466369i
\(483\) 0.0564552i 0.00256880i
\(484\) 1.93740 0.0880637
\(485\) −11.6762 + 12.5192i −0.530189 + 0.568468i
\(486\) −0.707107 + 0.707107i −0.0320750 + 0.0320750i
\(487\) 1.67383i 0.0758483i −0.999281 0.0379241i \(-0.987925\pi\)
0.999281 0.0379241i \(-0.0120745\pi\)
\(488\) −4.51718 4.51718i −0.204483 0.204483i
\(489\) 6.07961 + 6.07961i 0.274929 + 0.274929i
\(490\) 0.315402 0.338174i 0.0142484 0.0152772i
\(491\) 9.36601 0.422682 0.211341 0.977412i \(-0.432217\pi\)
0.211341 + 0.977412i \(0.432217\pi\)
\(492\) −4.49428 4.49428i −0.202618 0.202618i
\(493\) 25.3681 + 25.3681i 1.14252 + 1.14252i
\(494\) 0.927800 + 0.927800i 0.0417437 + 0.0417437i
\(495\) 4.92274 + 4.59126i 0.221261 + 0.206362i
\(496\) 1.55104 + 1.55104i 0.0696436 + 0.0696436i
\(497\) 16.6044 16.6044i 0.744808 0.744808i
\(498\) 1.30950 0.0586800
\(499\) −11.8837 + 11.8837i −0.531986 + 0.531986i −0.921163 0.389177i \(-0.872760\pi\)
0.389177 + 0.921163i \(0.372760\pi\)
\(500\) −7.03807 + 8.68709i −0.314752 + 0.388499i
\(501\) 3.24623 + 3.24623i 0.145031 + 0.145031i
\(502\) −3.84833 3.84833i −0.171759 0.171759i
\(503\) −25.4862 −1.13637 −0.568187 0.822900i \(-0.692355\pi\)
−0.568187 + 0.822900i \(0.692355\pi\)
\(504\) 1.84299 + 1.84299i 0.0820931 + 0.0820931i
\(505\) −25.3963 + 27.2299i −1.13012 + 1.21171i
\(506\) 0.0652069i 0.00289880i
\(507\) 6.84844 6.84844i 0.304150 0.304150i
\(508\) 9.77118 9.77118i 0.433526 0.433526i
\(509\) −21.0744 −0.934105 −0.467053 0.884230i \(-0.654684\pi\)
−0.467053 + 0.884230i \(0.654684\pi\)
\(510\) 0.422203 + 12.1177i 0.0186955 + 0.536580i
\(511\) 31.3492i 1.38681i
\(512\) −1.00000 −0.0441942
\(513\) 0.720673i 0.0318185i
\(514\) 3.13559i 0.138305i
\(515\) 23.1916 24.8660i 1.02195 1.09573i
\(516\) 5.56285 5.56285i 0.244891 0.244891i
\(517\) −0.530357 0.530357i −0.0233251 0.0233251i
\(518\) 6.20962 + 14.5873i 0.272835 + 0.640929i
\(519\) 9.18945i 0.403372i
\(520\) 2.97723 + 2.77675i 0.130560 + 0.121768i
\(521\) 26.1425i 1.14532i 0.819792 + 0.572661i \(0.194089\pi\)
−0.819792 + 0.572661i \(0.805911\pi\)
\(522\) 4.67832 + 4.67832i 0.204764 + 0.204764i
\(523\) 18.6818 0.816898 0.408449 0.912781i \(-0.366070\pi\)
0.408449 + 0.912781i \(0.366070\pi\)
\(524\) 2.21257 + 2.21257i 0.0966567 + 0.0966567i
\(525\) −13.0003 + 0.907010i −0.567379 + 0.0395851i
\(526\) −20.7027 + 20.7027i −0.902682 + 0.902682i
\(527\) −8.41047 + 8.41047i −0.366366 + 0.366366i
\(528\) −2.12868 2.12868i −0.0926391 0.0926391i
\(529\) −22.9995 −0.999980
\(530\) −0.225829 6.48154i −0.00980939 0.281540i
\(531\) 2.84934 2.84934i 0.123651 0.123651i
\(532\) 1.87834 0.0814365
\(533\) 11.5719i 0.501236i
\(534\) 1.47044i 0.0636322i
\(535\) −24.8146 + 0.864586i −1.07283 + 0.0373793i
\(536\) 3.93891 + 3.93891i 0.170135 + 0.170135i
\(537\) 15.8089i 0.682206i
\(538\) 15.5877i 0.672032i
\(539\) −0.622567 −0.0268159
\(540\) 0.0778616 + 2.23471i 0.00335063 + 0.0961667i
\(541\) −12.5483 + 12.5483i −0.539494 + 0.539494i −0.923380 0.383887i \(-0.874585\pi\)
0.383887 + 0.923380i \(0.374585\pi\)
\(542\) −30.3127 −1.30204
\(543\) 9.04405 9.04405i 0.388117 0.388117i
\(544\) 5.42248i 0.232487i
\(545\) 0.568062 + 16.3040i 0.0243331 + 0.698387i
\(546\) 4.74535i 0.203082i
\(547\) 13.3305 0.569972 0.284986 0.958532i \(-0.408011\pi\)
0.284986 + 0.958532i \(0.408011\pi\)
\(548\) −5.72235 + 5.72235i −0.244447 + 0.244447i
\(549\) 4.51718 4.51718i 0.192789 0.192789i
\(550\) 15.0156 1.04761i 0.640266 0.0446704i
\(551\) 4.76807 0.203127
\(552\) −0.0153162 + 0.0153162i −0.000651902 + 0.000651902i
\(553\) 7.97561 0.339158
\(554\) −14.8230 −0.629770
\(555\) −4.63986 + 12.7856i −0.196951 + 0.542719i
\(556\) −4.18150 −0.177335
\(557\) 31.5142 1.33530 0.667650 0.744475i \(-0.267300\pi\)
0.667650 + 0.744475i \(0.267300\pi\)
\(558\) −1.55104 + 1.55104i −0.0656606 + 0.0656606i
\(559\) 14.3233 0.605812
\(560\) 5.82450 0.202937i 0.246130 0.00857563i
\(561\) 11.5428 11.5428i 0.487336 0.487336i
\(562\) −22.8948 + 22.8948i −0.965757 + 0.965757i
\(563\) −23.8203 −1.00391 −0.501953 0.864895i \(-0.667385\pi\)
−0.501953 + 0.864895i \(0.667385\pi\)
\(564\) 0.249148i 0.0104910i
\(565\) 5.80034 6.21912i 0.244022 0.261640i
\(566\) 23.6708i 0.994957i
\(567\) −1.84299 + 1.84299i −0.0773981 + 0.0773981i
\(568\) −9.00950 −0.378030
\(569\) 2.20968 2.20968i 0.0926346 0.0926346i −0.659271 0.751905i \(-0.729135\pi\)
0.751905 + 0.659271i \(0.229135\pi\)
\(570\) 1.17847 + 1.09911i 0.0493607 + 0.0460368i
\(571\) −18.6714 −0.781372 −0.390686 0.920524i \(-0.627762\pi\)
−0.390686 + 0.920524i \(0.627762\pi\)
\(572\) 5.48097i 0.229171i
\(573\) 22.2169i 0.928126i
\(574\) −11.7138 11.7138i −0.488923 0.488923i
\(575\) −0.00753775 0.108039i −0.000314346 0.00450556i
\(576\) 1.00000i 0.0416667i
\(577\) 42.7062i 1.77788i −0.458023 0.888941i \(-0.651442\pi\)
0.458023 0.888941i \(-0.348558\pi\)
\(578\) 12.4033 0.515910
\(579\) −14.8941 + 14.8941i −0.618976 + 0.618976i
\(580\) 14.7852 0.515143i 0.613921 0.0213902i
\(581\) 3.41304 0.141597
\(582\) 5.41354 + 5.41354i 0.224398 + 0.224398i
\(583\) −6.17402 + 6.17402i −0.255702 + 0.255702i
\(584\) 8.50501 8.50501i 0.351940 0.351940i
\(585\) −2.77675 + 2.97723i −0.114804 + 0.123093i
\(586\) −5.16020 5.16020i −0.213166 0.213166i
\(587\) −14.4564 −0.596681 −0.298341 0.954459i \(-0.596433\pi\)
−0.298341 + 0.954459i \(0.596433\pi\)
\(588\) −0.146233 0.146233i −0.00603054 0.00603054i
\(589\) 1.58079i 0.0651354i
\(590\) −0.313749 9.00493i −0.0129168 0.370727i
\(591\) 7.81496i 0.321465i
\(592\) 2.27285 5.64218i 0.0934137 0.231892i
\(593\) 14.3909 + 14.3909i 0.590963 + 0.590963i 0.937892 0.346928i \(-0.112775\pi\)
−0.346928 + 0.937892i \(0.612775\pi\)
\(594\) 2.12868 2.12868i 0.0873410 0.0873410i
\(595\) 1.10042 + 31.5832i 0.0451128 + 1.29479i
\(596\) 2.65031i 0.108561i
\(597\) 8.04823i 0.329392i
\(598\) −0.0394365 −0.00161268
\(599\) 32.8474i 1.34211i −0.741407 0.671055i \(-0.765841\pi\)
0.741407 0.671055i \(-0.234159\pi\)
\(600\) 3.77303 + 3.28089i 0.154033 + 0.133942i
\(601\) 42.6376 1.73922 0.869611 0.493737i \(-0.164369\pi\)
0.869611 + 0.493737i \(0.164369\pi\)
\(602\) 14.4989 14.4989i 0.590930 0.590930i
\(603\) −3.93891 + 3.93891i −0.160405 + 0.160405i
\(604\) 3.91246i 0.159196i
\(605\) 3.16811 + 2.95477i 0.128802 + 0.120129i
\(606\) 11.7747 + 11.7747i 0.478315 + 0.478315i
\(607\) −1.05109 −0.0426623 −0.0213312 0.999772i \(-0.506790\pi\)
−0.0213312 + 0.999772i \(0.506790\pi\)
\(608\) −0.509592 0.509592i −0.0206667 0.0206667i
\(609\) 12.1935 + 12.1935i 0.494104 + 0.494104i
\(610\) −0.497400 14.2759i −0.0201391 0.578015i
\(611\) 0.320755 0.320755i 0.0129763 0.0129763i
\(612\) 5.42248 0.219191
\(613\) 20.8463 20.8463i 0.841976 0.841976i −0.147140 0.989116i \(-0.547007\pi\)
0.989116 + 0.147140i \(0.0470067\pi\)
\(614\) −16.3280 16.3280i −0.658945 0.658945i
\(615\) −0.494878 14.2035i −0.0199554 0.572742i
\(616\) −5.54815 5.54815i −0.223541 0.223541i
\(617\) 11.8344 + 11.8344i 0.476435 + 0.476435i 0.903990 0.427555i \(-0.140625\pi\)
−0.427555 + 0.903990i \(0.640625\pi\)
\(618\) −10.7525 10.7525i −0.432531 0.432531i
\(619\) −2.66335 −0.107049 −0.0535246 0.998567i \(-0.517046\pi\)
−0.0535246 + 0.998567i \(0.517046\pi\)
\(620\) 0.170789 + 4.90183i 0.00685906 + 0.196862i
\(621\) −0.0153162 0.0153162i −0.000614619 0.000614619i
\(622\) 20.2566 + 20.2566i 0.812216 + 0.812216i
\(623\) 3.83252i 0.153547i
\(624\) 1.28741 1.28741i 0.0515376 0.0515376i
\(625\) −24.7578 + 3.47153i −0.990312 + 0.138861i
\(626\) −18.3942 −0.735182
\(627\) 2.16952i 0.0866424i
\(628\) −12.9226 + 12.9226i −0.515670 + 0.515670i
\(629\) 30.5946 + 12.3245i 1.21989 + 0.491410i
\(630\) 0.202937 + 5.82450i 0.00808519 + 0.232054i
\(631\) −20.5443 20.5443i −0.817854 0.817854i 0.167943 0.985797i \(-0.446288\pi\)
−0.985797 + 0.167943i \(0.946288\pi\)
\(632\) −2.16377 2.16377i −0.0860703 0.0860703i
\(633\) −1.54391 + 1.54391i −0.0613647 + 0.0613647i
\(634\) 3.40194 + 3.40194i 0.135108 + 0.135108i
\(635\) 30.8805 1.07593i 1.22545 0.0426971i
\(636\) −2.90039 −0.115008
\(637\) 0.376523i 0.0149184i
\(638\) −14.0837 14.0837i −0.557578 0.557578i
\(639\) 9.00950i 0.356410i
\(640\) −1.63524 1.52512i −0.0646384 0.0602858i
\(641\) 38.4309 1.51793 0.758964 0.651132i \(-0.225706\pi\)
0.758964 + 0.651132i \(0.225706\pi\)
\(642\) 11.1041i 0.438245i
\(643\) 33.4086i 1.31751i 0.752358 + 0.658754i \(0.228916\pi\)
−0.752358 + 0.658754i \(0.771084\pi\)
\(644\) −0.0399199 + 0.0399199i −0.00157306 + 0.00157306i
\(645\) 17.5806 0.612542i 0.692236 0.0241188i
\(646\) 2.76326 2.76326i 0.108719 0.108719i
\(647\) −48.3301 −1.90005 −0.950026 0.312170i \(-0.898944\pi\)
−0.950026 + 0.312170i \(0.898944\pi\)
\(648\) 1.00000 0.0392837
\(649\) −8.57769 + 8.57769i −0.336704 + 0.336704i
\(650\) 0.633587 + 9.08127i 0.0248513 + 0.356197i
\(651\) −4.04258 + 4.04258i −0.158441 + 0.158441i
\(652\) 8.59786i 0.336718i
\(653\) 20.8734i 0.816839i −0.912794 0.408420i \(-0.866080\pi\)
0.912794 0.408420i \(-0.133920\pi\)
\(654\) 7.29580 0.285288
\(655\) 0.243633 + 6.99253i 0.00951952 + 0.273221i
\(656\) 6.35587i 0.248155i
\(657\) 8.50501 + 8.50501i 0.331812 + 0.331812i
\(658\) 0.649372i 0.0253152i
\(659\) 26.2240 1.02154 0.510771 0.859717i \(-0.329360\pi\)
0.510771 + 0.859717i \(0.329360\pi\)
\(660\) −0.234396 6.72741i −0.00912384 0.261864i
\(661\) 15.8166 + 15.8166i 0.615196 + 0.615196i 0.944295 0.329100i \(-0.106745\pi\)
−0.329100 + 0.944295i \(0.606745\pi\)
\(662\) −2.61136 + 2.61136i −0.101493 + 0.101493i
\(663\) 6.98095 + 6.98095i 0.271118 + 0.271118i
\(664\) −0.925954 0.925954i −0.0359340 0.0359340i
\(665\) 3.07154 + 2.86471i 0.119109 + 0.111089i
\(666\) 5.64218 + 2.27285i 0.218630 + 0.0880712i
\(667\) −0.101334 + 0.101334i −0.00392368 + 0.00392368i
\(668\) 4.59086i 0.177626i
\(669\) 21.6839 0.838347
\(670\) 0.433725 + 12.4484i 0.0167563 + 0.480923i
\(671\) −13.5986 + 13.5986i −0.524968 + 0.524968i
\(672\) 2.60638i 0.100543i
\(673\) 19.5631 + 19.5631i 0.754102 + 0.754102i 0.975242 0.221140i \(-0.0709779\pi\)
−0.221140 + 0.975242i \(0.570978\pi\)
\(674\) 3.23500 + 3.23500i 0.124608 + 0.124608i
\(675\) −3.28089 + 3.77303i −0.126282 + 0.145224i
\(676\) −9.68516 −0.372506
\(677\) 4.35406 + 4.35406i 0.167340 + 0.167340i 0.785809 0.618469i \(-0.212247\pi\)
−0.618469 + 0.785809i \(0.712247\pi\)
\(678\) −2.68926 2.68926i −0.103281 0.103281i
\(679\) 14.1097 + 14.1097i 0.541481 + 0.541481i
\(680\) 8.26996 8.86704i 0.317138 0.340036i
\(681\) −2.26408 2.26408i −0.0867596 0.0867596i
\(682\) 4.66926 4.66926i 0.178795 0.178795i
\(683\) −28.7474 −1.09999 −0.549995 0.835168i \(-0.685370\pi\)
−0.549995 + 0.835168i \(0.685370\pi\)
\(684\) 0.509592 0.509592i 0.0194848 0.0194848i
\(685\) −18.0847 + 0.630105i −0.690981 + 0.0240751i
\(686\) −13.2820 13.2820i −0.507111 0.507111i
\(687\) 15.0222 + 15.0222i 0.573134 + 0.573134i
\(688\) −7.86706 −0.299929
\(689\) −3.73399 3.73399i −0.142254 0.142254i
\(690\) −0.0484048 + 0.00168651i −0.00184274 + 6.42045e-5i
\(691\) 43.9902i 1.67347i −0.547610 0.836733i \(-0.684462\pi\)
0.547610 0.836733i \(-0.315538\pi\)
\(692\) 6.49792 6.49792i 0.247014 0.247014i
\(693\) 5.54815 5.54815i 0.210757 0.210757i
\(694\) −17.9326 −0.680714
\(695\) −6.83773 6.37730i −0.259370 0.241905i
\(696\) 6.61614i 0.250784i
\(697\) −34.4646 −1.30544
\(698\) 34.1023i 1.29079i
\(699\) 16.9992i 0.642968i
\(700\) 9.83394 + 8.55123i 0.371688 + 0.323206i
\(701\) −9.73870 + 9.73870i −0.367826 + 0.367826i −0.866684 0.498858i \(-0.833753\pi\)
0.498858 + 0.866684i \(0.333753\pi\)
\(702\) 1.28741 + 1.28741i 0.0485901 + 0.0485901i
\(703\) 4.03344 1.71698i 0.152124 0.0647572i
\(704\) 3.01042i 0.113459i
\(705\) 0.379981 0.407415i 0.0143109 0.0153441i
\(706\) 7.23850i 0.272424i
\(707\) 30.6893 + 30.6893i 1.15419 + 1.15419i
\(708\) −4.02957 −0.151441
\(709\) −10.8762 10.8762i −0.408466 0.408466i 0.472738 0.881203i \(-0.343266\pi\)
−0.881203 + 0.472738i \(0.843266\pi\)
\(710\) −14.7327 13.7406i −0.552907 0.515676i
\(711\) 2.16377 2.16377i 0.0811479 0.0811479i
\(712\) 1.03976 1.03976i 0.0389666 0.0389666i
\(713\) −0.0335961 0.0335961i −0.00125818 0.00125818i
\(714\) 14.1330 0.528915
\(715\) 8.35916 8.96269i 0.312615 0.335185i
\(716\) −11.1786 + 11.1786i −0.417764 + 0.417764i
\(717\) 14.3313 0.535210
\(718\) 29.3398i 1.09495i
\(719\) 28.4189i 1.05985i 0.848045 + 0.529924i \(0.177779\pi\)
−0.848045 + 0.529924i \(0.822221\pi\)
\(720\) 1.52512 1.63524i 0.0568380 0.0609417i
\(721\) −28.0252 28.0252i −1.04371 1.04371i
\(722\) 18.4806i 0.687778i
\(723\) 14.4800i 0.538517i
\(724\) −12.7902 −0.475345
\(725\) 24.9629 + 21.7068i 0.927099 + 0.806171i
\(726\) 1.36995 1.36995i 0.0508436 0.0508436i
\(727\) 2.22360 0.0824686 0.0412343 0.999150i \(-0.486871\pi\)
0.0412343 + 0.999150i \(0.486871\pi\)
\(728\) 3.35547 3.35547i 0.124362 0.124362i
\(729\) 1.00000i 0.0370370i
\(730\) 26.8789 0.936512i 0.994833 0.0346619i
\(731\) 42.6590i 1.57780i
\(732\) −6.38826 −0.236117
\(733\) 11.8204 11.8204i 0.436598 0.436598i −0.454268 0.890865i \(-0.650099\pi\)
0.890865 + 0.454268i \(0.150099\pi\)
\(734\) −7.30169 + 7.30169i −0.269510 + 0.269510i
\(735\) −0.0161021 0.462148i −0.000593936 0.0170466i
\(736\) 0.0216604 0.000798414
\(737\) 11.8578 11.8578i 0.436786 0.436786i
\(738\) −6.35587 −0.233963
\(739\) −41.0418 −1.50975 −0.754874 0.655870i \(-0.772302\pi\)
−0.754874 + 0.655870i \(0.772302\pi\)
\(740\) 12.3217 5.75991i 0.452953 0.211739i
\(741\) 1.31211 0.0482014
\(742\) −7.55951 −0.277518
\(743\) −21.4316 + 21.4316i −0.786249 + 0.786249i −0.980877 0.194628i \(-0.937650\pi\)
0.194628 + 0.980877i \(0.437650\pi\)
\(744\) 2.19350 0.0804175
\(745\) 4.04206 4.33389i 0.148090 0.158781i
\(746\) 0.813457 0.813457i 0.0297828 0.0297828i
\(747\) 0.925954 0.925954i 0.0338789 0.0338789i
\(748\) −16.3239 −0.596862
\(749\) 28.9416i 1.05750i
\(750\) 1.16604 + 11.1194i 0.0425776 + 0.406022i
\(751\) 38.7551i 1.41419i 0.707117 + 0.707097i \(0.249995\pi\)
−0.707117 + 0.707097i \(0.750005\pi\)
\(752\) −0.176174 + 0.176174i −0.00642440 + 0.00642440i
\(753\) −5.44236 −0.198331
\(754\) 8.51767 8.51767i 0.310195 0.310195i
\(755\) 5.96698 6.39779i 0.217161 0.232840i
\(756\) 2.60638 0.0947930
\(757\) 47.4098i 1.72314i −0.507640 0.861569i \(-0.669482\pi\)
0.507640 0.861569i \(-0.330518\pi\)
\(758\) 14.5201i 0.527394i
\(759\) 0.0461082 + 0.0461082i 0.00167362 + 0.00167362i
\(760\) −0.0561127 1.61050i −0.00203542 0.0584188i
\(761\) 31.8594i 1.15490i −0.816425 0.577452i \(-0.804047\pi\)
0.816425 0.577452i \(-0.195953\pi\)
\(762\) 13.8185i 0.500593i
\(763\) 19.0156 0.688411
\(764\) 15.7097 15.7097i 0.568359 0.568359i
\(765\) 8.86704 + 8.26996i 0.320589 + 0.299001i
\(766\) 14.8639 0.537053
\(767\) −5.18770 5.18770i −0.187317 0.187317i
\(768\) −0.707107 + 0.707107i −0.0255155 + 0.0255155i
\(769\) 14.3460 14.3460i 0.517329 0.517329i −0.399433 0.916762i \(-0.630793\pi\)
0.916762 + 0.399433i \(0.130793\pi\)
\(770\) −0.610923 17.5342i −0.0220161 0.631887i
\(771\) −2.21719 2.21719i −0.0798503 0.0798503i
\(772\) 21.0634 0.758088
\(773\) −14.7324 14.7324i −0.529887 0.529887i 0.390652 0.920539i \(-0.372250\pi\)
−0.920539 + 0.390652i \(0.872250\pi\)
\(774\) 7.86706i 0.282776i
\(775\) −7.19662 + 8.27613i −0.258510 + 0.297287i
\(776\) 7.65590i 0.274831i
\(777\) 14.7056 + 5.92391i 0.527562 + 0.212519i
\(778\) 25.0493 + 25.0493i 0.898060 + 0.898060i
\(779\) −3.23890 + 3.23890i −0.116046 + 0.116046i