Properties

Label 1110.2.l.a.697.14
Level $1110$
Weight $2$
Character 1110.697
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.l (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 697.14
Character \(\chi\) \(=\) 1110.697
Dual form 1110.2.l.a.43.14

$q$-expansion

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

Character values

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

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000i 0.707107i
\(3\) 0.707107 + 0.707107i 0.408248 + 0.408248i
\(4\) −1.00000 −0.500000
\(5\) −1.52512 1.63524i −0.682056 0.731300i
\(6\) 0.707107 0.707107i 0.288675 0.288675i
\(7\) 1.84299 + 1.84299i 0.696583 + 0.696583i 0.963672 0.267089i \(-0.0860617\pi\)
−0.267089 + 0.963672i \(0.586062\pi\)
\(8\) 1.00000i 0.353553i
\(9\) 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
\(13\) 1.82067i 0.504963i 0.967602 + 0.252481i \(0.0812467\pi\)
−0.967602 + 0.252481i \(0.918753\pi\)
\(14\) 1.84299 1.84299i 0.492559 0.492559i
\(15\) 0.0778616 2.23471i 0.0201038 0.577000i
\(16\) 1.00000 0.250000
\(17\) −5.42248 −1.31515 −0.657573 0.753391i \(-0.728417\pi\)
−0.657573 + 0.753391i \(0.728417\pi\)
\(18\) 1.00000 0.235702
\(19\) −0.509592 0.509592i −0.116909 0.116909i 0.646232 0.763141i \(-0.276344\pi\)
−0.763141 + 0.646232i \(0.776344\pi\)
\(20\) 1.52512 + 1.63524i 0.341028 + 0.365650i
\(21\) 2.60638i 0.568758i
\(22\) 3.01042 0.641823
\(23\) 0.0216604i 0.00451651i 0.999997 + 0.00225825i \(0.000718825\pi\)
−0.999997 + 0.00225825i \(0.999281\pi\)
\(24\) −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 −0.992333 0.123591i \(-0.960559\pi\)
0.123591 + 0.992333i \(0.460559\pi\)
\(30\) −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 \(0.686886\pi\)
\(32\) 1.00000i 0.176777i
\(33\) −2.12868 + 2.12868i −0.370556 + 0.370556i
\(34\) 5.42248i 0.929948i
\(35\) 0.202937 5.82450i 0.0343025 0.984520i
\(36\) 1.00000i 0.166667i
\(37\) 5.64218 + 2.27285i 0.927568 + 0.373655i
\(38\) −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 \(0.834688\pi\)
\(42\) 2.60638 0.402173
\(43\) 7.86706i 1.19972i 0.800107 + 0.599858i \(0.204776\pi\)
−0.800107 + 0.599858i \(0.795224\pi\)
\(44\) 3.01042i 0.453837i
\(45\) 1.63524 1.52512i 0.243767 0.227352i
\(46\) 0.0216604 0.00319365
\(47\) −0.176174 0.176174i −0.0256976 0.0256976i 0.694141 0.719839i \(-0.255784\pi\)
−0.719839 + 0.694141i \(0.755784\pi\)
\(48\) 0.707107 + 0.707107i 0.102062 + 0.102062i
\(49\) 0.206804i 0.0295435i
\(50\) 4.98788 + 0.347996i 0.705392 + 0.0492141i
\(51\) −3.83427 3.83427i −0.536906 0.536906i
\(52\) 1.82067i 0.252481i
\(53\) 2.05089 2.05089i 0.281711 0.281711i −0.552080 0.833791i \(-0.686166\pi\)
0.833791 + 0.552080i \(0.186166\pi\)
\(54\) 0.707107 + 0.707107i 0.0962250 + 0.0962250i
\(55\) 4.92274 4.59126i 0.663782 0.619085i
\(56\) −1.84299 + 1.84299i −0.246279 + 0.246279i
\(57\) 0.720673i 0.0954554i
\(58\) 4.67832 + 4.67832i 0.614293 + 0.614293i
\(59\) −2.84934 2.84934i −0.370952 0.370952i 0.496872 0.867824i \(-0.334482\pi\)
−0.867824 + 0.496872i \(0.834482\pi\)
\(60\) −0.0778616 + 2.23471i −0.0100519 + 0.288500i
\(61\) 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 \(-0.639481\pi\)
0.905519 + 0.424305i \(0.139481\pi\)
\(68\) 5.42248 0.657573
\(69\) −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 \(0.320456\pi\)
\(72\) −1.00000 −0.117851
\(73\) 8.50501 + 8.50501i 0.995437 + 0.995437i 0.999990 0.00455309i \(-0.00144930\pi\)
−0.00455309 + 0.999990i \(0.501449\pi\)
\(74\) 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 0.574830 0.818273i \(-0.305068\pi\)
−0.818273 + 0.574830i \(0.805068\pi\)
\(80\) −1.52512 1.63524i −0.170514 0.182825i
\(81\) −1.00000 −0.111111
\(82\) 6.35587 0.701888
\(83\) 0.925954 0.925954i 0.101637 0.101637i −0.654460 0.756097i \(-0.727104\pi\)
0.756097 + 0.654460i \(0.227104\pi\)
\(84\) 2.60638i 0.284379i
\(85\) 8.26996 + 8.86704i 0.897003 + 0.961766i
\(86\) 7.86706 0.848327
\(87\) −6.61614 −0.709325
\(88\) −3.01042 −0.320911
\(89\) 1.03976 1.03976i 0.110214 0.110214i −0.649849 0.760063i \(-0.725168\pi\)
0.760063 + 0.649849i \(0.225168\pi\)
\(90\) −1.52512 1.63524i −0.160762 0.172369i
\(91\) −3.35547 + 3.35547i −0.351749 + 0.351749i
\(92\) 0.0216604i 0.00225825i
\(93\) 2.19350i 0.227455i
\(94\) −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
\(97\) −7.65590 −0.777339 −0.388670 0.921377i \(-0.627065\pi\)
−0.388670 + 0.921377i \(0.627065\pi\)
\(98\) −0.206804 −0.0208904
\(99\) −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
\(103\) −15.2064 −1.49833 −0.749165 0.662383i \(-0.769545\pi\)
−0.749165 + 0.662383i \(0.769545\pi\)
\(104\) −1.82067 −0.178531
\(105\) 4.26204 3.97505i 0.415933 0.387925i
\(106\) −2.05089 2.05089i −0.199200 0.199200i
\(107\) −7.85181 7.85181i −0.759063 0.759063i 0.217089 0.976152i \(-0.430344\pi\)
−0.976152 + 0.217089i \(0.930344\pi\)
\(108\) 0.707107 0.707107i 0.0680414 0.0680414i
\(109\) −5.15891 5.15891i −0.494134 0.494134i 0.415472 0.909606i \(-0.363616\pi\)
−0.909606 + 0.415472i \(0.863616\pi\)
\(110\) −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
\(113\) −3.80319 −0.357774 −0.178887 0.983870i \(-0.557250\pi\)
−0.178887 + 0.983870i \(0.557250\pi\)
\(114\) −0.720673 −0.0674972
\(115\) 0.0354199 0.0330348i 0.00330292 0.00308051i
\(116\) 4.67832 4.67832i 0.434371 0.434371i
\(117\) −1.82067 −0.168321
\(118\) −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
\(125\) 8.68709 7.03807i 0.776997 0.629504i
\(126\) 1.84299 + 1.84299i 0.164186 + 0.164186i
\(127\) 9.77118 + 9.77118i 0.867052 + 0.867052i 0.992145 0.125093i \(-0.0399229\pi\)
−0.125093 + 0.992145i \(0.539923\pi\)
\(128\) 1.00000i 0.0883883i
\(129\) −5.56285 + 5.56285i −0.489782 + 0.489782i
\(130\) −2.77675 2.97723i −0.243537 0.261120i
\(131\) 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
\(133\) 1.87834i 0.162873i
\(134\) −3.93891 3.93891i −0.340270 0.340270i
\(135\) 2.23471 + 0.0778616i 0.192333 + 0.00670126i
\(136\) 5.42248i 0.464974i
\(137\) −5.72235 5.72235i −0.488894 0.488894i 0.419063 0.907957i \(-0.362359\pi\)
−0.907957 + 0.419063i \(0.862359\pi\)
\(138\) 0.0153162 + 0.0153162i 0.00130380 + 0.00130380i
\(139\) 4.18150 0.354670 0.177335 0.984151i \(-0.443252\pi\)
0.177335 + 0.984151i \(0.443252\pi\)
\(140\) −0.202937 + 5.82450i −0.0171513 + 0.492260i
\(141\) 0.249148i 0.0209820i
\(142\) 9.00950i 0.756060i
\(143\) −5.48097 −0.458342
\(144\) 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
\(148\) −5.64218 2.27285i −0.463784 0.186827i
\(149\) 2.65031i 0.217122i 0.994090 + 0.108561i \(0.0346243\pi\)
−0.994090 + 0.108561i \(0.965376\pi\)
\(150\) 3.28089 + 3.77303i 0.267884 + 0.308067i
\(151\) 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
\(153\) 5.42248i 0.438382i
\(154\) 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 −0.999493 0.0318468i \(-0.989861\pi\)
−0.0318468 0.999493i \(-0.510139\pi\)
\(158\) −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
\(162\) 1.00000i 0.0785674i
\(163\) −8.59786 −0.673437 −0.336718 0.941605i \(-0.609317\pi\)
−0.336718 + 0.941605i \(0.609317\pi\)
\(164\) 6.35587i 0.496310i
\(165\) 6.72741 + 0.234396i 0.523728 + 0.0182477i
\(166\) −0.925954 0.925954i −0.0718680 0.0718680i
\(167\) 4.59086 0.355252 0.177626 0.984098i \(-0.443158\pi\)
0.177626 + 0.984098i \(0.443158\pi\)
\(168\) −2.60638 −0.201086
\(169\) 9.68516 0.745012
\(170\) 8.86704 8.26996i 0.680071 0.634277i
\(171\) 0.509592 0.509592i 0.0389695 0.0389695i
\(172\) 7.86706i 0.599858i
\(173\) −6.49792 6.49792i −0.494028 0.494028i 0.415545 0.909573i \(-0.363591\pi\)
−0.909573 + 0.415545i \(0.863591\pi\)
\(174\) 6.61614i 0.501568i
\(175\) −9.83394 + 8.55123i −0.743376 + 0.646412i
\(176\) 3.01042i 0.226919i
\(177\) 4.02957i 0.302881i
\(178\) −1.03976 1.03976i −0.0779333 0.0779333i
\(179\) 11.1786 11.1786i 0.835528 0.835528i −0.152738 0.988267i \(-0.548809\pi\)
0.988267 + 0.152738i \(0.0488092\pi\)
\(180\) −1.63524 + 1.52512i −0.121883 + 0.113676i
\(181\) −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
\(183\) 6.38826i 0.472234i
\(184\) −0.0216604 −0.00159683
\(185\) −4.88836 12.6927i −0.359400 0.933184i
\(186\) 2.19350 0.160835
\(187\) 16.3239i 1.19372i
\(188\) 0.176174 + 0.176174i 0.0128488 + 0.0128488i
\(189\) −2.60638 −0.189586
\(190\) 1.61050 + 0.0561127i 0.116838 + 0.00407084i
\(191\) 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
\(193\) 21.0634i 1.51618i −0.652152 0.758088i \(-0.726134\pi\)
0.652152 0.758088i \(-0.273866\pi\)
\(194\) 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 0.482296 0.876008i \(-0.339803\pi\)
−0.876008 + 0.482296i \(0.839803\pi\)
\(198\) 3.01042i 0.213941i
\(199\) −5.69096 + 5.69096i −0.403421 + 0.403421i −0.879437 0.476015i \(-0.842081\pi\)
0.476015 + 0.879437i \(0.342081\pi\)
\(200\) −4.98788 0.347996i −0.352696 0.0246071i
\(201\) 5.57046 0.392910
\(202\) 16.6519 1.17163
\(203\) −17.2442 −1.21030
\(204\) 3.83427 + 3.83427i 0.268453 + 0.268453i
\(205\) 10.3933 9.69348i 0.725903 0.677022i
\(206\) 15.2064i 1.05948i
\(207\) −0.0216604 −0.00150550
\(208\) 1.82067i 0.126241i
\(209\) 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
\(217\) 5.71708i 0.388101i
\(218\) −5.15891 + 5.15891i −0.349405 + 0.349405i
\(219\) 12.0279i 0.812771i
\(220\) −4.92274 + 4.59126i −0.331891 + 0.309542i
\(221\) 9.87255i 0.664100i
\(222\) 5.59677 2.38247i 0.375631 0.159901i
\(223\) −15.3328 + 15.3328i −1.02676 + 1.02676i −0.0271298 + 0.999632i \(0.508637\pi\)
−0.999632 + 0.0271298i \(0.991363\pi\)
\(224\) 1.84299 1.84299i 0.123140 0.123140i
\(225\) −4.98788 0.347996i −0.332525 0.0231998i
\(226\) 3.80319i 0.252985i
\(227\) −3.20189 −0.212517 −0.106258 0.994339i \(-0.533887\pi\)
−0.106258 + 0.994339i \(0.533887\pi\)
\(228\) 0.720673i 0.0477277i
\(229\) 21.2446i 1.40389i 0.712233 + 0.701943i \(0.247684\pi\)
−0.712233 + 0.701943i \(0.752316\pi\)
\(230\) −0.0330348 0.0354199i −0.00217825 0.00233552i
\(231\) −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 \(-0.0620188\pi\)
−0.193607 + 0.981079i \(0.562019\pi\)
\(234\) 1.82067i 0.119021i
\(235\) −0.0193990 + 0.556773i −0.00126545 + 0.0363199i
\(236\) 2.84934 + 2.84934i 0.185476 + 0.185476i
\(237\) 3.06004i 0.198771i
\(238\) −9.99356 + 9.99356i −0.647786 + 0.647786i
\(239\) 10.1337 + 10.1337i 0.655496 + 0.655496i 0.954311 0.298815i \(-0.0965913\pi\)
−0.298815 + 0.954311i \(0.596591\pi\)
\(240\) 0.0778616 2.23471i 0.00502594 0.144250i
\(241\) 10.2389 10.2389i 0.659546 0.659546i −0.295727 0.955273i \(-0.595562\pi\)
0.955273 + 0.295727i \(0.0955618\pi\)
\(242\) 1.93740i 0.124541i
\(243\) −0.707107 0.707107i −0.0453609 0.0453609i
\(244\) −4.51718 4.51718i −0.289183 0.289183i
\(245\) −0.338174 + 0.315402i −0.0216052 + 0.0201503i
\(246\) 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
\(253\) −0.0652069 −0.00409952
\(254\) 9.77118 9.77118i 0.613099 0.613099i
\(255\) −0.422203 + 12.1177i −0.0264394 + 0.758839i
\(256\) 1.00000 0.0625000
\(257\) −3.13559 −0.195593 −0.0977963 0.995206i \(-0.531179\pi\)
−0.0977963 + 0.995206i \(0.531179\pi\)
\(258\) 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 −0.942567 0.334018i \(-0.891595\pi\)
−0.334018 0.942567i \(-0.608405\pi\)
\(264\) −2.12868 2.12868i −0.131012 0.131012i
\(265\) −6.48154 0.225829i −0.398158 0.0138726i
\(266\) −1.87834 −0.115169
\(267\) 1.47044 0.0899896
\(268\) −3.93891 + 3.93891i −0.240607 + 0.240607i
\(269\) 15.5877i 0.950397i −0.879879 0.475199i \(-0.842376\pi\)
0.879879 0.475199i \(-0.157624\pi\)
\(270\) 0.0778616 2.23471i 0.00473851 0.136000i
\(271\) 30.3127 1.84136 0.920682 0.390314i \(-0.127633\pi\)
0.920682 + 0.390314i \(0.127633\pi\)
\(272\) −5.42248 −0.328786
\(273\) −4.74535 −0.287202
\(274\) −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
\(277\) 14.8230i 0.890629i 0.895374 + 0.445315i \(0.146908\pi\)
−0.895374 + 0.445315i \(0.853092\pi\)
\(278\) 4.18150i 0.250789i
\(279\) −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 \(-0.166459\pi\)
\(282\) −0.249148 −0.0148365
\(283\) −23.6708 −1.40708 −0.703541 0.710655i \(-0.748399\pi\)
−0.703541 + 0.710655i \(0.748399\pi\)
\(284\) −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
\(288\) 1.00000 0.0589256
\(289\) 12.4033 0.729607
\(290\) 0.515143 14.7852i 0.0302503 0.868215i
\(291\) −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 −0.540124 0.841586i \(-0.681623\pi\)
0.841586 + 0.540124i \(0.181623\pi\)
\(294\) −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
\(298\) 2.65031 0.153529
\(299\) −0.0394365 −0.00228067
\(300\) 3.77303 3.28089i 0.217836 0.189422i
\(301\) −14.4989 + 14.4989i −0.835701 + 0.835701i
\(302\) −3.91246 −0.225137
\(303\) −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 \(-0.978997\pi\)
0.0659354 + 0.997824i \(0.478997\pi\)
\(308\) 5.54815 5.54815i 0.316135 0.316135i
\(309\) −10.7525 10.7525i −0.611691 0.611691i
\(310\) −4.90183 0.170789i −0.278405 0.00970017i
\(311\) −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
\(313\) 18.3942i 1.03970i −0.854256 0.519852i \(-0.825987\pi\)
0.854256 0.519852i \(-0.174013\pi\)
\(314\) −12.9226 + 12.9226i −0.729267 + 0.729267i
\(315\) 5.82450 + 0.202937i 0.328173 + 0.0114342i
\(316\) 2.16377 + 2.16377i 0.121722 + 0.121722i
\(317\) 3.40194 3.40194i 0.191072 0.191072i −0.605087 0.796159i \(-0.706862\pi\)
0.796159 + 0.605087i \(0.206862\pi\)
\(318\) 2.90039i 0.162646i
\(319\) −14.0837 14.0837i −0.788535 0.788535i
\(320\) 1.52512 + 1.63524i 0.0852570 + 0.0914125i
\(321\) 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
\(325\) −9.08127 0.633587i −0.503738 0.0351451i
\(326\) 8.59786i 0.476192i
\(327\) 7.29580i 0.403459i
\(328\) −6.35587 −0.350944
\(329\) 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
\(333\) −2.27285 + 5.64218i −0.124552 + 0.309189i
\(334\) 4.59086i 0.251201i
\(335\) −12.4484 0.433725i −0.680128 0.0236969i
\(336\) 2.60638i 0.142189i
\(337\) 3.23500 3.23500i 0.176222 0.176222i −0.613485 0.789707i \(-0.710233\pi\)
0.789707 + 0.613485i \(0.210233\pi\)
\(338\) 9.68516i 0.526803i
\(339\) −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
\(347\) 17.9326i 0.962675i 0.876535 + 0.481337i \(0.159849\pi\)
−0.876535 + 0.481337i \(0.840151\pi\)
\(348\) 6.61614 0.354662
\(349\) 34.1023i 1.82545i 0.408571 + 0.912727i \(0.366027\pi\)
−0.408571 + 0.912727i \(0.633973\pi\)
\(350\) 8.55123 + 9.83394i 0.457083 + 0.525646i
\(351\) −1.28741 1.28741i −0.0687168 0.0687168i
\(352\) 3.01042 0.160456
\(353\) −7.23850 −0.385266 −0.192633 0.981271i \(-0.561703\pi\)
−0.192633 + 0.981271i \(0.561703\pi\)
\(354\) −4.02957 −0.214169
\(355\) −13.7406 14.7327i −0.729275 0.781929i
\(356\) −1.03976 + 1.03976i −0.0551071 + 0.0551071i
\(357\) 14.1330i 0.747999i
\(358\) −11.1786 11.1786i −0.590808 0.590808i
\(359\) 29.3398i 1.54849i 0.632884 + 0.774247i \(0.281871\pi\)
−0.632884 + 0.774247i \(0.718129\pi\)
\(360\) 1.52512 + 1.63524i 0.0803811 + 0.0861845i
\(361\) 18.4806i 0.972665i
\(362\) 12.7902i 0.672239i
\(363\) 1.36995 + 1.36995i 0.0719037 + 0.0719037i
\(364\) 3.35547 3.35547i 0.175874 0.175874i
\(365\) 0.936512 26.8789i 0.0490193 1.40691i
\(366\) 6.38826 0.333920
\(367\) 7.30169 + 7.30169i 0.381145 + 0.381145i 0.871515 0.490370i \(-0.163138\pi\)
−0.490370 + 0.871515i \(0.663138\pi\)
\(368\) 0.0216604i 0.00112913i
\(369\) −6.35587 −0.330873
\(370\) −12.6927 + 4.88836i −0.659861 + 0.254134i
\(371\) 7.55951 0.392470
\(372\) 2.19350i 0.113728i
\(373\) 0.813457 + 0.813457i 0.0421192 + 0.0421192i 0.727853 0.685733i \(-0.240518\pi\)
−0.685733 + 0.727853i \(0.740518\pi\)
\(374\) −16.3239 −0.844090
\(375\) 11.1194 + 1.16604i 0.574202 + 0.0602138i
\(376\) 0.176174 0.176174i 0.00908548 0.00908548i
\(377\) −8.51767 8.51767i −0.438682 0.438682i
\(378\) 2.60638i 0.134058i
\(379\) 14.5201i 0.745847i −0.927862 0.372924i \(-0.878355\pi\)
0.927862 0.372924i \(-0.121645\pi\)
\(380\) 0.0561127 1.61050i 0.00287852 0.0826167i
\(381\) 13.8185i 0.707945i
\(382\) −15.7097 15.7097i −0.803781 0.803781i
\(383\) 14.8639i 0.759507i 0.925088 + 0.379754i \(0.123991\pi\)
−0.925088 + 0.379754i \(0.876009\pi\)
\(384\) −0.707107 + 0.707107i −0.0360844 + 0.0360844i
\(385\) 17.5342 + 0.610923i 0.893624 + 0.0311355i
\(386\) −21.0634 −1.07210
\(387\) −7.86706 −0.399905
\(388\) 7.65590 0.388670
\(389\) 25.0493 + 25.0493i 1.27005 + 1.27005i 0.946062 + 0.323986i \(0.105023\pi\)
0.323986 + 0.946062i \(0.394977\pi\)
\(390\) 0.141760 4.06867i 0.00717831 0.206025i
\(391\) 0.117453i 0.00593987i
\(392\) 0.206804 0.0104452
\(393\) 3.12905i 0.157840i
\(394\) −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 \(-0.689484\pi\)
0.827991 + 0.560741i \(0.189484\pi\)
\(398\) 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 \(0.807616\pi\)
\(402\) 5.57046i 0.277829i
\(403\) −2.82393 + 2.82393i −0.140670 + 0.140670i
\(404\) 16.6519i 0.828465i
\(405\) 1.52512 + 1.63524i 0.0757840 + 0.0812556i
\(406\) 17.2442i 0.855813i
\(407\) −6.84223 + 16.9853i −0.339157 + 0.841930i
\(408\) 3.83427 3.83427i 0.189825 0.189825i
\(409\) 15.3174 15.3174i 0.757396 0.757396i −0.218451 0.975848i \(-0.570101\pi\)
0.975848 + 0.218451i \(0.0701005\pi\)
\(410\) −9.69348 10.3933i −0.478727 0.513291i
\(411\) 8.09263i 0.399180i
\(412\) 15.2064 0.749165
\(413\) 10.5026i 0.516798i
\(414\) 0.0216604i 0.00106455i
\(415\) −2.92635 0.101960i −0.143649 0.00500500i
\(416\) 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 \(0.124654\pi\)
−0.924294 + 0.381680i \(0.875346\pi\)
\(420\) −4.26204 + 3.97505i −0.207966 + 0.193962i
\(421\) 15.7260 + 15.7260i 0.766440 + 0.766440i 0.977478 0.211038i \(-0.0676844\pi\)
−0.211038 + 0.977478i \(0.567684\pi\)
\(422\) 2.18341i 0.106287i
\(423\) 0.176174 0.176174i 0.00856587 0.00856587i
\(424\) 2.05089 + 2.05089i 0.0995998 + 0.0995998i
\(425\) 1.88700 27.0467i 0.0915332 1.31196i
\(426\) 6.37068 6.37068i 0.308660 0.308660i
\(427\) 16.6502i 0.805760i
\(428\) 7.85181 + 7.85181i 0.379532 + 0.379532i
\(429\) −3.87563 3.87563i −0.187117 0.187117i
\(430\) −11.9982 12.8645i −0.578606 0.620381i
\(431\) 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 −0.322065 0.946717i \(-0.604377\pi\)
0.946717 + 0.322065i \(0.104377\pi\)
\(434\) 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
\(438\) 12.0279 0.574716
\(439\) −10.5684 + 10.5684i −0.504400 + 0.504400i −0.912802 0.408402i \(-0.866086\pi\)
0.408402 + 0.912802i \(0.366086\pi\)
\(440\) 4.59126 + 4.92274i 0.218879 + 0.234682i
\(441\) 0.206804 0.00984783
\(442\) −9.87255 −0.469589
\(443\) 17.5773 + 17.5773i 0.835121 + 0.835121i 0.988212 0.153091i \(-0.0489227\pi\)
−0.153091 + 0.988212i \(0.548923\pi\)
\(444\) −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 0.901500 0.432779i \(-0.142467\pi\)
−0.432779 + 0.901500i \(0.642467\pi\)
\(450\) −0.347996 + 4.98788i −0.0164047 + 0.235131i
\(451\) −19.1338 −0.900975
\(452\) 3.80319 0.178887
\(453\) 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
\(457\) 8.27570 0.387121 0.193560 0.981088i \(-0.437996\pi\)
0.193560 + 0.981088i \(0.437996\pi\)
\(458\) 21.2446 0.992697
\(459\) 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 \(0.290969\pi\)
\(462\) 7.84627i 0.365042i
\(463\) 37.2821i 1.73265i −0.499484 0.866323i \(-0.666477\pi\)
0.499484 0.866323i \(-0.333523\pi\)
\(464\) −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
\(467\) 11.9336 0.552219 0.276109 0.961126i \(-0.410955\pi\)
0.276109 + 0.961126i \(0.410955\pi\)
\(468\) 1.82067 0.0841605
\(469\) 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
\(473\) −23.6831 −1.08895
\(474\) −3.06004 −0.140552
\(475\) 2.71912 2.36445i 0.124762 0.108488i
\(476\) 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 0.686170 0.727441i \(-0.259291\pi\)
−0.727441 + 0.686170i \(0.759291\pi\)
\(480\) −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
\(483\) −0.0564552 −0.00256880
\(484\) −1.93740 −0.0880637
\(485\) 11.6762 + 12.5192i 0.530189 + 0.568468i
\(486\) −0.707107 + 0.707107i −0.0320750 + 0.0320750i
\(487\) 1.67383 0.0758483 0.0379241 0.999281i \(-0.487925\pi\)
0.0379241 + 0.999281i \(0.487925\pi\)
\(488\) −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
\(495\) 4.59126 + 4.92274i 0.206362 + 0.221261i
\(496\) 1.55104 + 1.55104i 0.0696436 + 0.0696436i
\(497\) 16.6044 + 16.6044i 0.744808 + 0.744808i
\(498\) 1.30950i 0.0586800i
\(499\) 11.8837 11.8837i 0.531986 0.531986i −0.389177 0.921163i \(-0.627240\pi\)
0.921163 + 0.389177i \(0.127240\pi\)
\(500\) −8.68709 + 7.03807i −0.388499 + 0.314752i
\(501\) 3.24623 + 3.24623i 0.145031 + 0.145031i
\(502\) 3.84833 3.84833i 0.171759 0.171759i
\(503\) 25.4862i 1.13637i 0.822900 + 0.568187i \(0.192355\pi\)
−0.822900 + 0.568187i \(0.807645\pi\)
\(504\) −1.84299 1.84299i −0.0820931 0.0820931i
\(505\) 27.2299 25.3963i 1.21171 1.13012i
\(506\) 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 \(-0.345316\pi\)
0.467053 + 0.884230i \(0.345316\pi\)
\(510\) 12.1177 + 0.422203i 0.536580 + 0.0186955i
\(511\) 31.3492i 1.38681i
\(512\) 1.00000i 0.0441942i
\(513\) 0.720673 0.0318185
\(514\) 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
\(518\) 14.5873 6.20962i 0.640929 0.272835i
\(519\) 9.18945i 0.403372i
\(520\) 2.77675 + 2.97723i 0.121768 + 0.130560i
\(521\) 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
\(523\) 18.6818i 0.816898i −0.912781 0.408449i \(-0.866070\pi\)
0.912781 0.408449i \(-0.133930\pi\)
\(524\) −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
\(532\) 1.87834i 0.0814365i
\(533\) −11.5719 −0.501236
\(534\) 1.47044i 0.0636322i
\(535\) −0.864586 + 24.8146i −0.0373793 + 1.07283i
\(536\) 3.93891 + 3.93891i 0.170135 + 0.170135i
\(537\) 15.8089 0.682206
\(538\) −15.5877 −0.672032
\(539\) 0.622567 0.0268159
\(540\) −2.23471 0.0778616i −0.0961667 0.00335063i
\(541\) −12.5483 + 12.5483i −0.539494 + 0.539494i −0.923380 0.383887i \(-0.874585\pi\)
0.383887 + 0.923380i \(0.374585\pi\)
\(542\) 30.3127i 1.30204i
\(543\) −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
\(547\) 13.3305i 0.569972i 0.958532 + 0.284986i \(0.0919889\pi\)
−0.958532 + 0.284986i \(0.908011\pi\)
\(548\) 5.72235 + 5.72235i 0.244447 + 0.244447i
\(549\) −4.51718 + 4.51718i −0.192789 + 0.192789i
\(550\) −1.04761 + 15.0156i −0.0446704 + 0.640266i
\(551\) 4.76807 0.203127
\(552\) −0.0153162 0.0153162i −0.000651902 0.000651902i
\(553\) 7.97561i 0.339158i
\(554\) 14.8230 0.629770
\(555\) 5.51848 12.4317i 0.234246 0.527695i
\(556\) −4.18150 −0.177335
\(557\) 31.5142i 1.33530i 0.744475 + 0.667650i \(0.232700\pi\)
−0.744475 + 0.667650i \(0.767300\pi\)
\(558\) 1.55104 + 1.55104i 0.0656606 + 0.0656606i
\(559\) −14.3233 −0.605812
\(560\) 0.202937 5.82450i 0.00857563 0.246130i
\(561\) 11.5428 11.5428i 0.487336 0.487336i
\(562\) −22.8948 22.8948i −0.965757 0.965757i
\(563\) 23.8203i 1.00391i 0.864895 + 0.501953i \(0.167385\pi\)
−0.864895 + 0.501953i \(0.832615\pi\)
\(564\) 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
\(568\) 9.00950i 0.378030i
\(569\) −2.20968 + 2.20968i −0.0926346 + 0.0926346i −0.751905 0.659271i \(-0.770865\pi\)
0.659271 + 0.751905i \(0.270865\pi\)
\(570\) 1.09911 + 1.17847i 0.0460368 + 0.0493607i
\(571\) −18.6714 −0.781372 −0.390686 0.920524i \(-0.627762\pi\)
−0.390686 + 0.920524i \(0.627762\pi\)
\(572\) 5.48097 0.229171
\(573\) 22.2169 0.928126
\(574\) 11.7138 + 11.7138i 0.488923 + 0.488923i
\(575\) −0.108039 0.00753775i −0.00450556 0.000314346i
\(576\) 1.00000i 0.0416667i
\(577\) 42.7062 1.77788 0.888941 0.458023i \(-0.151442\pi\)
0.888941 + 0.458023i \(0.151442\pi\)
\(578\) 12.4033i 0.515910i
\(579\) 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
\(587\) 14.4564i 0.596681i −0.954459 0.298341i \(-0.903567\pi\)
0.954459 0.298341i \(-0.0964331\pi\)
\(588\) −0.146233 + 0.146233i −0.00603054 + 0.00603054i
\(589\) 1.58079i 0.0651354i
\(590\) 9.00493 + 0.313749i 0.370727 + 0.0129168i
\(591\) 7.81496i 0.321465i
\(592\) 5.64218 + 2.27285i 0.231892 + 0.0934137i
\(593\) 14.3909 14.3909i 0.590963 0.590963i −0.346928 0.937892i \(-0.612775\pi\)
0.937892 + 0.346928i \(0.112775\pi\)
\(594\) −2.12868 + 2.12868i −0.0873410 + 0.0873410i
\(595\) −1.10042 + 31.5832i −0.0451128 + 1.29479i
\(596\) 2.65031i 0.108561i
\(597\) −8.04823 −0.329392
\(598\) 0.0394365i 0.00161268i
\(599\) 32.8474i 1.34211i 0.741407 + 0.671055i \(0.234159\pi\)
−0.741407 + 0.671055i \(0.765841\pi\)
\(600\) −3.28089 3.77303i −0.133942 0.154033i
\(601\) 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
\(605\) −2.95477 3.16811i −0.120129 0.128802i
\(606\) 11.7747 + 11.7747i 0.478315 + 0.478315i
\(607\) 1.05109i 0.0426623i −0.999772 0.0213312i \(-0.993210\pi\)
0.999772 0.0213312i \(-0.00679044\pi\)
\(608\) −0.509592 + 0.509592i −0.0206667 + 0.0206667i
\(609\) −12.1935 12.1935i −0.494104 0.494104i
\(610\) −14.2759 0.497400i −0.578015 0.0201391i
\(611\) 0.320755 0.320755i 0.0129763 0.0129763i
\(612\) 5.42248i 0.219191i
\(613\) −20.8463 20.8463i −0.841976 0.841976i 0.147140 0.989116i \(-0.452993\pi\)
−0.989116 + 0.147140i \(0.952993\pi\)
\(614\) 16.3280 + 16.3280i 0.658945 + 0.658945i
\(615\) 14.2035 + 0.494878i 0.572742 + 0.0199554i
\(616\) −5.54815 5.54815i −0.223541 0.223541i
\(617\) −11.8344 + 11.8344i −0.476435 + 0.476435i −0.903990 0.427555i \(-0.859375\pi\)
0.427555 + 0.903990i \(0.359375\pi\)
\(618\) −10.7525 + 10.7525i −0.432531 + 0.432531i
\(619\) 2.66335 0.107049 0.0535246 0.998567i \(-0.482954\pi\)
0.0535246 + 0.998567i \(0.482954\pi\)
\(620\) −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
\(623\) 3.83252 0.153547
\(624\) −1.28741 + 1.28741i −0.0515376 + 0.0515376i
\(625\) −24.7578 3.47153i −0.990312 0.138861i
\(626\) −18.3942 −0.735182
\(627\) 2.16952 0.0866424
\(628\) 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
\(635\) 1.07593 30.8805i 0.0426971 1.22545i
\(636\) −2.90039 −0.115008
\(637\) 0.376523 0.0149184
\(638\) −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 \(0.225706\pi\)
\(642\) −11.1041 −0.438245
\(643\) 33.4086 1.31751 0.658754 0.752358i \(-0.271084\pi\)
0.658754 + 0.752358i \(0.271084\pi\)
\(644\) 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
\(647\) 48.3301i 1.90005i −0.312170 0.950026i \(-0.601056\pi\)
0.312170 0.950026i \(-0.398944\pi\)
\(648\) 1.00000i 0.0392837i
\(649\) 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
\(652\) 8.59786 0.336718
\(653\) −20.8734 −0.816839 −0.408420 0.912794i \(-0.633920\pi\)
−0.408420 + 0.912794i \(0.633920\pi\)
\(654\) −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
\(658\) −0.649372 −0.0253152
\(659\) −26.2240 −1.02154 −0.510771 0.859717i \(-0.670640\pi\)
−0.510771 + 0.859717i \(0.670640\pi\)
\(660\) −6.72741 0.234396i −0.261864 0.00912384i
\(661\) 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
\(668\) −4.59086 −0.177626
\(669\) −21.6839 −0.838347
\(670\) −0.433725 + 12.4484i −0.0167563 + 0.480923i
\(671\) −13.5986 + 13.5986i −0.524968 + 0.524968i
\(672\) 2.60638 0.100543
\(673\) 19.5631 19.5631i 0.754102 0.754102i −0.221140 0.975242i \(-0.570978\pi\)
0.975242 + 0.221140i \(0.0709779\pi\)
\(674\) −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 \(-0.787753\pi\)
0.618469 + 0.785809i \(0.287753\pi\)
\(678\) −2.68926 + 2.68926i −0.103281 + 0.103281i
\(679\) −14.1097 14.1097i −0.541481 0.541481i
\(680\) −8.86704 + 8.26996i −0.340036 + 0.317138i
\(681\) −2.26408 2.26408i −0.0867596 0.0867596i
\(682\) 4.66926 + 4.66926i 0.178795 + 0.178795i
\(683\) 28.7474i 1.09999i 0.835168 + 0.549995i \(0.185370\pi\)
−0.835168 + 0.549995i \(0.814630\pi\)
\(684\) −0.509592 + 0.509592i −0.0194848 + 0.0194848i
\(685\) −0.630105 + 18.0847i −0.0240751 + 0.690981i
\(686\) −13.2820 13.2820i −0.507111 0.507111i
\(687\) −15.0222 + 15.0222i −0.573134 + 0.573134i
\(688\) 7.86706i 0.299929i
\(689\) 3.73399 + 3.73399i 0.142254 + 0.142254i
\(690\) 0.00168651 0.0484048i 6.42045e−5 0.00184274i
\(691\) 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
\(695\) −6.37730 6.83773i −0.241905 0.259370i
\(696\) 6.61614i 0.250784i
\(697\) 34.4646i 1.30544i
\(698\) 34.1023 1.29079
\(699\) 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
\(703\) −1.71698 4.03344i −0.0647572 0.152124i
\(704\) 3.01042i 0.113459i
\(705\) −0.407415 + 0.379981i −0.0153441 + 0.0143109i
\(706\) 7.23850i 0.272424i
\(707\) −30.6893 + 30.6893i −1.15419 + 1.15419i
\(708\) 4.02957i 0.151441i
\(709\) 10.8762 + 10.8762i 0.408466 + 0.408466i 0.881203 0.472738i \(-0.156734\pi\)
−0.472738 + 0.881203i \(0.656734\pi\)
\(710\) −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
\(717\) 14.3313i 0.535210i
\(718\) 29.3398 1.09495
\(719\) 28.4189i 1.05985i −0.848045 0.529924i \(-0.822221\pi\)
0.848045 0.529924i \(-0.177779\pi\)
\(720\) 1.63524 1.52512i 0.0609417 0.0568380i
\(721\) −28.0252 28.0252i −1.04371 1.04371i
\(722\) −18.4806 −0.687778
\(723\) 14.4800 0.538517
\(724\) 12.7902 0.475345
\(725\) −21.7068 24.9629i −0.806171 0.927099i
\(726\) 1.36995 1.36995i 0.0508436 0.0508436i
\(727\) 2.22360i 0.0824686i 0.999150 + 0.0412343i \(0.0131290\pi\)
−0.999150 + 0.0412343i \(0.986871\pi\)
\(728\) −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
\(732\) 6.38826i 0.236117i
\(733\) −11.8204 11.8204i −0.436598 0.436598i 0.454268 0.890865i \(-0.349901\pi\)
−0.890865 + 0.454268i \(0.849901\pi\)
\(734\) 7.30169 7.30169i 0.269510 0.269510i
\(735\) −0.462148 0.0161021i −0.0170466 0.000593936i
\(736\) 0.0216604 0.000798414
\(737\) 11.8578 + 11.8578i 0.436786 + 0.436786i
\(738\) 6.35587i 0.233963i
\(739\) 41.0418 1.50975 0.754874 0.655870i \(-0.227698\pi\)
0.754874 + 0.655870i \(0.227698\pi\)
\(740\) 4.88836 + 12.6927i 0.179700 + 0.466592i
\(741\) 1.31211 0.0482014
\(742\) 7.55951i 0.277518i
\(743\) 21.4316 + 21.4316i 0.786249 + 0.786249i 0.980877 0.194628i \(-0.0623499\pi\)
−0.194628 + 0.980877i \(0.562350\pi\)
\(744\) −2.19350 −0.0804175
\(745\) 4.33389 4.04206i 0.158781 0.148090i
\(746\) 0.813457 0.813457i 0.0297828 0.0297828i
\(747\) 0.925954 + 0.925954i 0.0338789 + 0.0338789i
\(748\) 16.3239i 0.596862i
\(749\) 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
\(753\) 5.44236i 0.198331i
\(754\) −8.51767 + 8.51767i −0.310195 + 0.310195i
\(755\) −6.39779 + 5.96698i −0.232840 + 0.217161i
\(756\) 2.60638 0.0947930
\(757\) 47.4098 1.72314 0.861569 0.507640i \(-0.169482\pi\)
0.861569 + 0.507640i \(0.169482\pi\)
\(758\) −14.5201 −0.527394
\(759\) −0.0461082 0.0461082i −0.00167362 0.00167362i
\(760\) −1.61050 0.0561127i −0.0584188 0.00203542i
\(761\) 31.8594i 1.15490i −0.816425 0.577452i \(-0.804047\pi\)
0.816425 0.577452i \(-0.195953\pi\)
\(762\) 13.8185 0.500593
\(763\) 19.0156i 0.688411i
\(764\) −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 −0.916762 0.399433i \(-0.869207\pi\)
0.399433 + 0.916762i \(0.369207\pi\)
\(770\) 0.610923 17.5342i 0.0220161 0.631887i
\(771\) −2.21719 2.21719i −0.0798503 0.0798503i
\(772\) 21.0634i 0.758088i
\(773\) −14.7324 + 14.7324i −0.529887 + 0.529887i −0.920539 0.390652i \(-0.872250\pi\)
0.390652 + 0.920539i \(0.372250\pi\)
\(774\) 7.86706i 0.282776i
\(775\) −8.27613 + 7.19662i −0.297287 + 0.258510i
\(776\) 7.65590i 0.274831i
\(777\) −5.92391 + 14.7056i −0.212519 + 0.527562i
\(778\) 25.0493 25.0493i 0.898060 0.898060i
\(779\) 3.23890 3.23890i 0.116046 0.116046i