Properties

Label 1110.2.l.b.697.15
Level $1110$
Weight $2$
Character 1110.697
Analytic conductor $8.863$
Analytic rank $0$
Dimension $40$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

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: \(40\)
Relative dimension: \(20\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 697.15
Character \(\chi\) \(=\) 1110.697
Dual form 1110.2.l.b.43.15

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000i q^{2} +(0.707107 + 0.707107i) q^{3} -1.00000 q^{4} +(1.88721 + 1.19936i) q^{5} +(-0.707107 + 0.707107i) q^{6} +(-1.50593 - 1.50593i) q^{7} -1.00000i q^{8} +1.00000i q^{9} +O(q^{10})\) \(q+1.00000i q^{2} +(0.707107 + 0.707107i) q^{3} -1.00000 q^{4} +(1.88721 + 1.19936i) q^{5} +(-0.707107 + 0.707107i) q^{6} +(-1.50593 - 1.50593i) q^{7} -1.00000i q^{8} +1.00000i q^{9} +(-1.19936 + 1.88721i) q^{10} +0.249077i q^{11} +(-0.707107 - 0.707107i) q^{12} +2.83382i q^{13} +(1.50593 - 1.50593i) q^{14} +(0.486383 + 2.18253i) q^{15} +1.00000 q^{16} -7.29402 q^{17} -1.00000 q^{18} +(1.89479 + 1.89479i) q^{19} +(-1.88721 - 1.19936i) q^{20} -2.12971i q^{21} -0.249077 q^{22} +8.28835i q^{23} +(0.707107 - 0.707107i) q^{24} +(2.12309 + 4.52686i) q^{25} -2.83382 q^{26} +(-0.707107 + 0.707107i) q^{27} +(1.50593 + 1.50593i) q^{28} +(-2.37266 + 2.37266i) q^{29} +(-2.18253 + 0.486383i) q^{30} +(1.83366 + 1.83366i) q^{31} +1.00000i q^{32} +(-0.176124 + 0.176124i) q^{33} -7.29402i q^{34} +(-1.03586 - 4.64816i) q^{35} -1.00000i q^{36} +(3.06084 - 5.25654i) q^{37} +(-1.89479 + 1.89479i) q^{38} +(-2.00381 + 2.00381i) q^{39} +(1.19936 - 1.88721i) q^{40} +10.3232i q^{41} +2.12971 q^{42} +7.61240i q^{43} -0.249077i q^{44} +(-1.19936 + 1.88721i) q^{45} -8.28835 q^{46} +(-2.82753 - 2.82753i) q^{47} +(0.707107 + 0.707107i) q^{48} -2.46433i q^{49} +(-4.52686 + 2.12309i) q^{50} +(-5.15765 - 5.15765i) q^{51} -2.83382i q^{52} +(4.20587 - 4.20587i) q^{53} +(-0.707107 - 0.707107i) q^{54} +(-0.298732 + 0.470059i) q^{55} +(-1.50593 + 1.50593i) q^{56} +2.67964i q^{57} +(-2.37266 - 2.37266i) q^{58} +(6.26117 + 6.26117i) q^{59} +(-0.486383 - 2.18253i) q^{60} +(-3.22008 - 3.22008i) q^{61} +(-1.83366 + 1.83366i) q^{62} +(1.50593 - 1.50593i) q^{63} -1.00000 q^{64} +(-3.39876 + 5.34800i) q^{65} +(-0.176124 - 0.176124i) q^{66} +(5.68165 - 5.68165i) q^{67} +7.29402 q^{68} +(-5.86075 + 5.86075i) q^{69} +(4.64816 - 1.03586i) q^{70} +3.37315 q^{71} +1.00000 q^{72} +(-7.48228 - 7.48228i) q^{73} +(5.25654 + 3.06084i) q^{74} +(-1.69973 + 4.70223i) q^{75} +(-1.89479 - 1.89479i) q^{76} +(0.375093 - 0.375093i) q^{77} +(-2.00381 - 2.00381i) q^{78} +(5.99818 + 5.99818i) q^{79} +(1.88721 + 1.19936i) q^{80} -1.00000 q^{81} -10.3232 q^{82} +(5.98449 - 5.98449i) q^{83} +2.12971i q^{84} +(-13.7653 - 8.74813i) q^{85} -7.61240 q^{86} -3.35545 q^{87} +0.249077 q^{88} +(5.37576 - 5.37576i) q^{89} +(-1.88721 - 1.19936i) q^{90} +(4.26754 - 4.26754i) q^{91} -8.28835i q^{92} +2.59319i q^{93} +(2.82753 - 2.82753i) q^{94} +(1.30333 + 5.84838i) q^{95} +(-0.707107 + 0.707107i) q^{96} -5.94731 q^{97} +2.46433 q^{98} -0.249077 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 40q - 40q^{4} - 4q^{7} + O(q^{10}) \) \( 40q - 40q^{4} - 4q^{7} + 4q^{14} + 40q^{16} + 24q^{17} - 40q^{18} + 4q^{19} + 8q^{22} + 8q^{25} + 8q^{26} + 4q^{28} + 28q^{31} - 4q^{33} + 20q^{35} + 20q^{37} - 4q^{38} + 4q^{39} + 16q^{42} - 16q^{47} + 16q^{51} + 20q^{53} + 16q^{55} - 4q^{56} - 4q^{59} - 8q^{61} - 28q^{62} + 4q^{63} - 40q^{64} - 4q^{65} - 4q^{66} + 16q^{67} - 24q^{68} - 8q^{69} + 12q^{70} + 40q^{71} + 40q^{72} + 8q^{73} - 8q^{74} + 16q^{75} - 4q^{76} - 24q^{77} + 4q^{78} - 12q^{79} - 40q^{81} - 24q^{82} - 8q^{83} - 8q^{85} + 8q^{87} - 8q^{88} + 12q^{89} - 24q^{91} + 16q^{94} - 28q^{95} + 40q^{97} - 56q^{98} + 8q^{99} + O(q^{100}) \)

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
\(5\) 1.88721 + 1.19936i 0.843984 + 0.536368i
\(6\) −0.707107 + 0.707107i −0.288675 + 0.288675i
\(7\) −1.50593 1.50593i −0.569189 0.569189i 0.362712 0.931901i \(-0.381851\pi\)
−0.931901 + 0.362712i \(0.881851\pi\)
\(8\) 1.00000i 0.353553i
\(9\) 1.00000i 0.333333i
\(10\) −1.19936 + 1.88721i −0.379270 + 0.596787i
\(11\) 0.249077i 0.0750994i 0.999295 + 0.0375497i \(0.0119553\pi\)
−0.999295 + 0.0375497i \(0.988045\pi\)
\(12\) −0.707107 0.707107i −0.204124 0.204124i
\(13\) 2.83382i 0.785959i 0.919547 + 0.392980i \(0.128556\pi\)
−0.919547 + 0.392980i \(0.871444\pi\)
\(14\) 1.50593 1.50593i 0.402478 0.402478i
\(15\) 0.486383 + 2.18253i 0.125583 + 0.563527i
\(16\) 1.00000 0.250000
\(17\) −7.29402 −1.76906 −0.884530 0.466484i \(-0.845520\pi\)
−0.884530 + 0.466484i \(0.845520\pi\)
\(18\) −1.00000 −0.235702
\(19\) 1.89479 + 1.89479i 0.434694 + 0.434694i 0.890222 0.455527i \(-0.150549\pi\)
−0.455527 + 0.890222i \(0.650549\pi\)
\(20\) −1.88721 1.19936i −0.421992 0.268184i
\(21\) 2.12971i 0.464741i
\(22\) −0.249077 −0.0531033
\(23\) 8.28835i 1.72824i 0.503286 + 0.864120i \(0.332124\pi\)
−0.503286 + 0.864120i \(0.667876\pi\)
\(24\) 0.707107 0.707107i 0.144338 0.144338i
\(25\) 2.12309 + 4.52686i 0.424618 + 0.905373i
\(26\) −2.83382 −0.555757
\(27\) −0.707107 + 0.707107i −0.136083 + 0.136083i
\(28\) 1.50593 + 1.50593i 0.284595 + 0.284595i
\(29\) −2.37266 + 2.37266i −0.440592 + 0.440592i −0.892211 0.451619i \(-0.850847\pi\)
0.451619 + 0.892211i \(0.350847\pi\)
\(30\) −2.18253 + 0.486383i −0.398473 + 0.0888009i
\(31\) 1.83366 + 1.83366i 0.329335 + 0.329335i 0.852334 0.522999i \(-0.175187\pi\)
−0.522999 + 0.852334i \(0.675187\pi\)
\(32\) 1.00000i 0.176777i
\(33\) −0.176124 + 0.176124i −0.0306592 + 0.0306592i
\(34\) 7.29402i 1.25091i
\(35\) −1.03586 4.64816i −0.175091 0.785682i
\(36\) 1.00000i 0.166667i
\(37\) 3.06084 5.25654i 0.503200 0.864170i
\(38\) −1.89479 + 1.89479i −0.307375 + 0.307375i
\(39\) −2.00381 + 2.00381i −0.320867 + 0.320867i
\(40\) 1.19936 1.88721i 0.189635 0.298393i
\(41\) 10.3232i 1.61221i 0.591771 + 0.806106i \(0.298429\pi\)
−0.591771 + 0.806106i \(0.701571\pi\)
\(42\) 2.12971 0.328622
\(43\) 7.61240i 1.16088i 0.814303 + 0.580440i \(0.197120\pi\)
−0.814303 + 0.580440i \(0.802880\pi\)
\(44\) 0.249077i 0.0375497i
\(45\) −1.19936 + 1.88721i −0.178789 + 0.281328i
\(46\) −8.28835 −1.22205
\(47\) −2.82753 2.82753i −0.412437 0.412437i 0.470150 0.882587i \(-0.344200\pi\)
−0.882587 + 0.470150i \(0.844200\pi\)
\(48\) 0.707107 + 0.707107i 0.102062 + 0.102062i
\(49\) 2.46433i 0.352047i
\(50\) −4.52686 + 2.12309i −0.640195 + 0.300250i
\(51\) −5.15765 5.15765i −0.722215 0.722215i
\(52\) 2.83382i 0.392980i
\(53\) 4.20587 4.20587i 0.577721 0.577721i −0.356554 0.934275i \(-0.616048\pi\)
0.934275 + 0.356554i \(0.116048\pi\)
\(54\) −0.707107 0.707107i −0.0962250 0.0962250i
\(55\) −0.298732 + 0.470059i −0.0402810 + 0.0633827i
\(56\) −1.50593 + 1.50593i −0.201239 + 0.201239i
\(57\) 2.67964i 0.354926i
\(58\) −2.37266 2.37266i −0.311546 0.311546i
\(59\) 6.26117 + 6.26117i 0.815135 + 0.815135i 0.985398 0.170264i \(-0.0544620\pi\)
−0.170264 + 0.985398i \(0.554462\pi\)
\(60\) −0.486383 2.18253i −0.0627917 0.281763i
\(61\) −3.22008 3.22008i −0.412290 0.412290i 0.470246 0.882535i \(-0.344165\pi\)
−0.882535 + 0.470246i \(0.844165\pi\)
\(62\) −1.83366 + 1.83366i −0.232875 + 0.232875i
\(63\) 1.50593 1.50593i 0.189730 0.189730i
\(64\) −1.00000 −0.125000
\(65\) −3.39876 + 5.34800i −0.421564 + 0.663337i
\(66\) −0.176124 0.176124i −0.0216793 0.0216793i
\(67\) 5.68165 5.68165i 0.694124 0.694124i −0.269013 0.963137i \(-0.586697\pi\)
0.963137 + 0.269013i \(0.0866974\pi\)
\(68\) 7.29402 0.884530
\(69\) −5.86075 + 5.86075i −0.705551 + 0.705551i
\(70\) 4.64816 1.03586i 0.555561 0.123808i
\(71\) 3.37315 0.400320 0.200160 0.979763i \(-0.435854\pi\)
0.200160 + 0.979763i \(0.435854\pi\)
\(72\) 1.00000 0.117851
\(73\) −7.48228 7.48228i −0.875735 0.875735i 0.117355 0.993090i \(-0.462558\pi\)
−0.993090 + 0.117355i \(0.962558\pi\)
\(74\) 5.25654 + 3.06084i 0.611061 + 0.355816i
\(75\) −1.69973 + 4.70223i −0.196267 + 0.542966i
\(76\) −1.89479 1.89479i −0.217347 0.217347i
\(77\) 0.375093 0.375093i 0.0427458 0.0427458i
\(78\) −2.00381 2.00381i −0.226887 0.226887i
\(79\) 5.99818 + 5.99818i 0.674848 + 0.674848i 0.958830 0.283982i \(-0.0916554\pi\)
−0.283982 + 0.958830i \(0.591655\pi\)
\(80\) 1.88721 + 1.19936i 0.210996 + 0.134092i
\(81\) −1.00000 −0.111111
\(82\) −10.3232 −1.14001
\(83\) 5.98449 5.98449i 0.656883 0.656883i −0.297759 0.954641i \(-0.596239\pi\)
0.954641 + 0.297759i \(0.0962390\pi\)
\(84\) 2.12971i 0.232371i
\(85\) −13.7653 8.74813i −1.49306 0.948867i
\(86\) −7.61240 −0.820867
\(87\) −3.35545 −0.359742
\(88\) 0.249077 0.0265517
\(89\) 5.37576 5.37576i 0.569829 0.569829i −0.362251 0.932081i \(-0.617992\pi\)
0.932081 + 0.362251i \(0.117992\pi\)
\(90\) −1.88721 1.19936i −0.198929 0.126423i
\(91\) 4.26754 4.26754i 0.447360 0.447360i
\(92\) 8.28835i 0.864120i
\(93\) 2.59319i 0.268901i
\(94\) 2.82753 2.82753i 0.291637 0.291637i
\(95\) 1.30333 + 5.84838i 0.133719 + 0.600031i
\(96\) −0.707107 + 0.707107i −0.0721688 + 0.0721688i
\(97\) −5.94731 −0.603858 −0.301929 0.953330i \(-0.597631\pi\)
−0.301929 + 0.953330i \(0.597631\pi\)
\(98\) 2.46433 0.248935
\(99\) −0.249077 −0.0250331
\(100\) −2.12309 4.52686i −0.212309 0.452686i
\(101\) 10.2985i 1.02474i −0.858766 0.512368i \(-0.828768\pi\)
0.858766 0.512368i \(-0.171232\pi\)
\(102\) 5.15765 5.15765i 0.510683 0.510683i
\(103\) −8.34427 −0.822186 −0.411093 0.911594i \(-0.634853\pi\)
−0.411093 + 0.911594i \(0.634853\pi\)
\(104\) 2.83382 0.277879
\(105\) 2.55428 4.01920i 0.249273 0.392234i
\(106\) 4.20587 + 4.20587i 0.408511 + 0.408511i
\(107\) −2.10671 2.10671i −0.203663 0.203663i 0.597904 0.801568i \(-0.296000\pi\)
−0.801568 + 0.597904i \(0.796000\pi\)
\(108\) 0.707107 0.707107i 0.0680414 0.0680414i
\(109\) −10.6743 10.6743i −1.02242 1.02242i −0.999743 0.0226738i \(-0.992782\pi\)
−0.0226738 0.999743i \(-0.507218\pi\)
\(110\) −0.470059 0.298732i −0.0448183 0.0284829i
\(111\) 5.88128 1.55259i 0.558226 0.147366i
\(112\) −1.50593 1.50593i −0.142297 0.142297i
\(113\) 4.25290 0.400080 0.200040 0.979788i \(-0.435893\pi\)
0.200040 + 0.979788i \(0.435893\pi\)
\(114\) −2.67964 −0.250971
\(115\) −9.94068 + 15.6418i −0.926973 + 1.45861i
\(116\) 2.37266 2.37266i 0.220296 0.220296i
\(117\) −2.83382 −0.261986
\(118\) −6.26117 + 6.26117i −0.576387 + 0.576387i
\(119\) 10.9843 + 10.9843i 1.00693 + 1.00693i
\(120\) 2.18253 0.486383i 0.199237 0.0444005i
\(121\) 10.9380 0.994360
\(122\) 3.22008 3.22008i 0.291533 0.291533i
\(123\) −7.29960 + 7.29960i −0.658183 + 0.658183i
\(124\) −1.83366 1.83366i −0.164668 0.164668i
\(125\) −1.42262 + 11.0895i −0.127243 + 0.991872i
\(126\) 1.50593 + 1.50593i 0.134159 + 0.134159i
\(127\) 12.5469 + 12.5469i 1.11336 + 1.11336i 0.992693 + 0.120665i \(0.0385026\pi\)
0.120665 + 0.992693i \(0.461497\pi\)
\(128\) 1.00000i 0.0883883i
\(129\) −5.38278 + 5.38278i −0.473928 + 0.473928i
\(130\) −5.34800 3.39876i −0.469050 0.298091i
\(131\) 3.81040 + 3.81040i 0.332916 + 0.332916i 0.853693 0.520777i \(-0.174358\pi\)
−0.520777 + 0.853693i \(0.674358\pi\)
\(132\) 0.176124 0.176124i 0.0153296 0.0153296i
\(133\) 5.70685i 0.494847i
\(134\) 5.68165 + 5.68165i 0.490820 + 0.490820i
\(135\) −2.18253 + 0.486383i −0.187842 + 0.0418612i
\(136\) 7.29402i 0.625457i
\(137\) −2.72768 2.72768i −0.233041 0.233041i 0.580920 0.813961i \(-0.302693\pi\)
−0.813961 + 0.580920i \(0.802693\pi\)
\(138\) −5.86075 5.86075i −0.498900 0.498900i
\(139\) 2.31516 0.196369 0.0981847 0.995168i \(-0.468696\pi\)
0.0981847 + 0.995168i \(0.468696\pi\)
\(140\) 1.03586 + 4.64816i 0.0875457 + 0.392841i
\(141\) 3.99873i 0.336753i
\(142\) 3.37315i 0.283069i
\(143\) −0.705838 −0.0590251
\(144\) 1.00000i 0.0833333i
\(145\) −7.32336 + 1.63203i −0.608172 + 0.135533i
\(146\) 7.48228 7.48228i 0.619238 0.619238i
\(147\) 1.74254 1.74254i 0.143722 0.143722i
\(148\) −3.06084 + 5.25654i −0.251600 + 0.432085i
\(149\) 8.45695i 0.692821i 0.938083 + 0.346410i \(0.112600\pi\)
−0.938083 + 0.346410i \(0.887400\pi\)
\(150\) −4.70223 1.69973i −0.383935 0.138782i
\(151\) 12.3871i 1.00805i −0.863690 0.504024i \(-0.831852\pi\)
0.863690 0.504024i \(-0.168148\pi\)
\(152\) 1.89479 1.89479i 0.153688 0.153688i
\(153\) 7.29402i 0.589686i
\(154\) 0.375093 + 0.375093i 0.0302259 + 0.0302259i
\(155\) 1.26128 + 5.65970i 0.101309 + 0.454598i
\(156\) 2.00381 2.00381i 0.160433 0.160433i
\(157\) −10.3496 10.3496i −0.825986 0.825986i 0.160973 0.986959i \(-0.448537\pi\)
−0.986959 + 0.160973i \(0.948537\pi\)
\(158\) −5.99818 + 5.99818i −0.477190 + 0.477190i
\(159\) 5.94800 0.471707
\(160\) −1.19936 + 1.88721i −0.0948174 + 0.149197i
\(161\) 12.4817 12.4817i 0.983696 0.983696i
\(162\) 1.00000i 0.0785674i
\(163\) −8.69039 −0.680684 −0.340342 0.940302i \(-0.610543\pi\)
−0.340342 + 0.940302i \(0.610543\pi\)
\(164\) 10.3232i 0.806106i
\(165\) −0.543617 + 0.121147i −0.0423205 + 0.00943125i
\(166\) 5.98449 + 5.98449i 0.464486 + 0.464486i
\(167\) −18.5233 −1.43337 −0.716687 0.697395i \(-0.754342\pi\)
−0.716687 + 0.697395i \(0.754342\pi\)
\(168\) −2.12971 −0.164311
\(169\) 4.96948 0.382268
\(170\) 8.74813 13.7653i 0.670951 1.05575i
\(171\) −1.89479 + 1.89479i −0.144898 + 0.144898i
\(172\) 7.61240i 0.580440i
\(173\) 6.60085 + 6.60085i 0.501854 + 0.501854i 0.912014 0.410160i \(-0.134527\pi\)
−0.410160 + 0.912014i \(0.634527\pi\)
\(174\) 3.35545i 0.254376i
\(175\) 3.61993 10.0144i 0.273641 0.757017i
\(176\) 0.249077i 0.0187749i
\(177\) 8.85463i 0.665555i
\(178\) 5.37576 + 5.37576i 0.402930 + 0.402930i
\(179\) 11.1031 11.1031i 0.829883 0.829883i −0.157617 0.987500i \(-0.550381\pi\)
0.987500 + 0.157617i \(0.0503812\pi\)
\(180\) 1.19936 1.88721i 0.0893947 0.140664i
\(181\) 19.1102 1.42045 0.710223 0.703977i \(-0.248594\pi\)
0.710223 + 0.703977i \(0.248594\pi\)
\(182\) 4.26754 + 4.26754i 0.316331 + 0.316331i
\(183\) 4.55389i 0.336633i
\(184\) 8.28835 0.611025
\(185\) 12.0809 6.24913i 0.888206 0.459445i
\(186\) −2.59319 −0.190142
\(187\) 1.81677i 0.132855i
\(188\) 2.82753 + 2.82753i 0.206219 + 0.206219i
\(189\) 2.12971 0.154914
\(190\) −5.84838 + 1.30333i −0.424286 + 0.0945534i
\(191\) −4.13848 + 4.13848i −0.299450 + 0.299450i −0.840798 0.541349i \(-0.817914\pi\)
0.541349 + 0.840798i \(0.317914\pi\)
\(192\) −0.707107 0.707107i −0.0510310 0.0510310i
\(193\) 1.65600i 0.119201i 0.998222 + 0.0596007i \(0.0189827\pi\)
−0.998222 + 0.0596007i \(0.981017\pi\)
\(194\) 5.94731i 0.426992i
\(195\) −6.18489 + 1.37832i −0.442909 + 0.0987035i
\(196\) 2.46433i 0.176023i
\(197\) 14.1878 + 14.1878i 1.01084 + 1.01084i 0.999941 + 0.0108958i \(0.00346830\pi\)
0.0108958 + 0.999941i \(0.496532\pi\)
\(198\) 0.249077i 0.0177011i
\(199\) −3.69181 + 3.69181i −0.261705 + 0.261705i −0.825747 0.564041i \(-0.809246\pi\)
0.564041 + 0.825747i \(0.309246\pi\)
\(200\) 4.52686 2.12309i 0.320098 0.150125i
\(201\) 8.03506 0.566750
\(202\) 10.2985 0.724598
\(203\) 7.14614 0.501561
\(204\) 5.15765 + 5.15765i 0.361108 + 0.361108i
\(205\) −12.3812 + 19.4820i −0.864740 + 1.36068i
\(206\) 8.34427i 0.581373i
\(207\) −8.28835 −0.576080
\(208\) 2.83382i 0.196490i
\(209\) −0.471948 + 0.471948i −0.0326453 + 0.0326453i
\(210\) 4.01920 + 2.55428i 0.277351 + 0.176262i
\(211\) −8.15505 −0.561417 −0.280708 0.959793i \(-0.590569\pi\)
−0.280708 + 0.959793i \(0.590569\pi\)
\(212\) −4.20587 + 4.20587i −0.288861 + 0.288861i
\(213\) 2.38518 + 2.38518i 0.163430 + 0.163430i
\(214\) 2.10671 2.10671i 0.144012 0.144012i
\(215\) −9.12998 + 14.3662i −0.622660 + 0.979765i
\(216\) 0.707107 + 0.707107i 0.0481125 + 0.0481125i
\(217\) 5.52274i 0.374908i
\(218\) 10.6743 10.6743i 0.722958 0.722958i
\(219\) 10.5815i 0.715034i
\(220\) 0.298732 0.470059i 0.0201405 0.0316914i
\(221\) 20.6699i 1.39041i
\(222\) 1.55259 + 5.88128i 0.104203 + 0.394726i
\(223\) 18.0980 18.0980i 1.21193 1.21193i 0.241543 0.970390i \(-0.422346\pi\)
0.970390 0.241543i \(-0.0776536\pi\)
\(224\) 1.50593 1.50593i 0.100619 0.100619i
\(225\) −4.52686 + 2.12309i −0.301791 + 0.141539i
\(226\) 4.25290i 0.282899i
\(227\) −15.2040 −1.00913 −0.504563 0.863375i \(-0.668346\pi\)
−0.504563 + 0.863375i \(0.668346\pi\)
\(228\) 2.67964i 0.177463i
\(229\) 22.1160i 1.46147i −0.682662 0.730735i \(-0.739178\pi\)
0.682662 0.730735i \(-0.260822\pi\)
\(230\) −15.6418 9.94068i −1.03139 0.655469i
\(231\) 0.530462 0.0349018
\(232\) 2.37266 + 2.37266i 0.155773 + 0.155773i
\(233\) −4.77285 4.77285i −0.312680 0.312680i 0.533267 0.845947i \(-0.320964\pi\)
−0.845947 + 0.533267i \(0.820964\pi\)
\(234\) 2.83382i 0.185252i
\(235\) −1.94491 8.72733i −0.126872 0.569308i
\(236\) −6.26117 6.26117i −0.407567 0.407567i
\(237\) 8.48271i 0.551011i
\(238\) −10.9843 + 10.9843i −0.712007 + 0.712007i
\(239\) 19.8498 + 19.8498i 1.28398 + 1.28398i 0.938385 + 0.345593i \(0.112322\pi\)
0.345593 + 0.938385i \(0.387678\pi\)
\(240\) 0.486383 + 2.18253i 0.0313959 + 0.140882i
\(241\) 21.3229 21.3229i 1.37353 1.37353i 0.518380 0.855150i \(-0.326535\pi\)
0.855150 0.518380i \(-0.173465\pi\)
\(242\) 10.9380i 0.703119i
\(243\) −0.707107 0.707107i −0.0453609 0.0453609i
\(244\) 3.22008 + 3.22008i 0.206145 + 0.206145i
\(245\) 2.95561 4.65069i 0.188827 0.297122i
\(246\) −7.29960 7.29960i −0.465405 0.465405i
\(247\) −5.36948 + 5.36948i −0.341652 + 0.341652i
\(248\) 1.83366 1.83366i 0.116438 0.116438i
\(249\) 8.46334 0.536342
\(250\) −11.0895 1.42262i −0.701359 0.0899742i
\(251\) 14.6439 + 14.6439i 0.924315 + 0.924315i 0.997331 0.0730156i \(-0.0232623\pi\)
−0.0730156 + 0.997331i \(0.523262\pi\)
\(252\) −1.50593 + 1.50593i −0.0948649 + 0.0948649i
\(253\) −2.06443 −0.129790
\(254\) −12.5469 + 12.5469i −0.787263 + 0.787263i
\(255\) −3.54768 15.9194i −0.222165 0.996912i
\(256\) 1.00000 0.0625000
\(257\) 17.8930 1.11614 0.558069 0.829795i \(-0.311543\pi\)
0.558069 + 0.829795i \(0.311543\pi\)
\(258\) −5.38278 5.38278i −0.335117 0.335117i
\(259\) −12.5254 + 3.30658i −0.778293 + 0.205461i
\(260\) 3.39876 5.34800i 0.210782 0.331669i
\(261\) −2.37266 2.37266i −0.146864 0.146864i
\(262\) −3.81040 + 3.81040i −0.235407 + 0.235407i
\(263\) 21.7610 + 21.7610i 1.34184 + 1.34184i 0.894225 + 0.447617i \(0.147727\pi\)
0.447617 + 0.894225i \(0.352273\pi\)
\(264\) 0.176124 + 0.176124i 0.0108397 + 0.0108397i
\(265\) 12.9817 2.89301i 0.797459 0.177716i
\(266\) 5.70685 0.349910
\(267\) 7.60247 0.465264
\(268\) −5.68165 + 5.68165i −0.347062 + 0.347062i
\(269\) 17.8478i 1.08820i 0.839020 + 0.544101i \(0.183129\pi\)
−0.839020 + 0.544101i \(0.816871\pi\)
\(270\) −0.486383 2.18253i −0.0296003 0.132824i
\(271\) 2.29360 0.139327 0.0696633 0.997571i \(-0.477808\pi\)
0.0696633 + 0.997571i \(0.477808\pi\)
\(272\) −7.29402 −0.442265
\(273\) 6.03521 0.365268
\(274\) 2.72768 2.72768i 0.164785 0.164785i
\(275\) −1.12754 + 0.528812i −0.0679930 + 0.0318886i
\(276\) 5.86075 5.86075i 0.352776 0.352776i
\(277\) 1.48608i 0.0892897i 0.999003 + 0.0446448i \(0.0142156\pi\)
−0.999003 + 0.0446448i \(0.985784\pi\)
\(278\) 2.31516i 0.138854i
\(279\) −1.83366 + 1.83366i −0.109778 + 0.109778i
\(280\) −4.64816 + 1.03586i −0.277781 + 0.0619042i
\(281\) −18.5876 + 18.5876i −1.10884 + 1.10884i −0.115541 + 0.993303i \(0.536860\pi\)
−0.993303 + 0.115541i \(0.963140\pi\)
\(282\) 3.99873 0.238121
\(283\) −16.6153 −0.987676 −0.493838 0.869554i \(-0.664406\pi\)
−0.493838 + 0.869554i \(0.664406\pi\)
\(284\) −3.37315 −0.200160
\(285\) −3.21384 + 5.05702i −0.190371 + 0.299552i
\(286\) 0.705838i 0.0417371i
\(287\) 15.5460 15.5460i 0.917654 0.917654i
\(288\) −1.00000 −0.0589256
\(289\) 36.2027 2.12957
\(290\) −1.63203 7.32336i −0.0958362 0.430043i
\(291\) −4.20538 4.20538i −0.246524 0.246524i
\(292\) 7.48228 + 7.48228i 0.437867 + 0.437867i
\(293\) 9.37884 9.37884i 0.547918 0.547918i −0.377920 0.925838i \(-0.623361\pi\)
0.925838 + 0.377920i \(0.123361\pi\)
\(294\) 1.74254 + 1.74254i 0.101627 + 0.101627i
\(295\) 4.30674 + 19.3255i 0.250748 + 1.12517i
\(296\) −5.25654 3.06084i −0.305530 0.177908i
\(297\) −0.176124 0.176124i −0.0102197 0.0102197i
\(298\) −8.45695 −0.489898
\(299\) −23.4877 −1.35833
\(300\) 1.69973 4.70223i 0.0981337 0.271483i
\(301\) 11.4638 11.4638i 0.660761 0.660761i
\(302\) 12.3871 0.712797
\(303\) 7.28212 7.28212i 0.418347 0.418347i
\(304\) 1.89479 + 1.89479i 0.108674 + 0.108674i
\(305\) −2.21493 9.93899i −0.126827 0.569105i
\(306\) 7.29402 0.416971
\(307\) 3.36862 3.36862i 0.192258 0.192258i −0.604413 0.796671i \(-0.706592\pi\)
0.796671 + 0.604413i \(0.206592\pi\)
\(308\) −0.375093 + 0.375093i −0.0213729 + 0.0213729i
\(309\) −5.90029 5.90029i −0.335656 0.335656i
\(310\) −5.65970 + 1.26128i −0.321450 + 0.0716360i
\(311\) 22.4334 + 22.4334i 1.27208 + 1.27208i 0.944994 + 0.327087i \(0.106067\pi\)
0.327087 + 0.944994i \(0.393933\pi\)
\(312\) 2.00381 + 2.00381i 0.113443 + 0.113443i
\(313\) 19.2752i 1.08950i 0.838599 + 0.544750i \(0.183375\pi\)
−0.838599 + 0.544750i \(0.816625\pi\)
\(314\) 10.3496 10.3496i 0.584060 0.584060i
\(315\) 4.64816 1.03586i 0.261894 0.0583638i
\(316\) −5.99818 5.99818i −0.337424 0.337424i
\(317\) −3.94817 + 3.94817i −0.221751 + 0.221751i −0.809236 0.587484i \(-0.800118\pi\)
0.587484 + 0.809236i \(0.300118\pi\)
\(318\) 5.94800i 0.333548i
\(319\) −0.590974 0.590974i −0.0330882 0.0330882i
\(320\) −1.88721 1.19936i −0.105498 0.0670461i
\(321\) 2.97934i 0.166291i
\(322\) 12.4817 + 12.4817i 0.695578 + 0.695578i
\(323\) −13.8206 13.8206i −0.769000 0.769000i
\(324\) 1.00000 0.0555556
\(325\) −12.8283 + 6.01645i −0.711586 + 0.333732i
\(326\) 8.69039i 0.481316i
\(327\) 15.0958i 0.834800i
\(328\) 10.3232 0.570003
\(329\) 8.51613i 0.469510i
\(330\) −0.121147 0.543617i −0.00666890 0.0299251i
\(331\) −2.89997 + 2.89997i −0.159397 + 0.159397i −0.782299 0.622902i \(-0.785953\pi\)
0.622902 + 0.782299i \(0.285953\pi\)
\(332\) −5.98449 + 5.98449i −0.328441 + 0.328441i
\(333\) 5.25654 + 3.06084i 0.288057 + 0.167733i
\(334\) 18.5233i 1.01355i
\(335\) 17.5368 3.90812i 0.958135 0.213523i
\(336\) 2.12971i 0.116185i
\(337\) −1.55976 + 1.55976i −0.0849654 + 0.0849654i −0.748312 0.663347i \(-0.769135\pi\)
0.663347 + 0.748312i \(0.269135\pi\)
\(338\) 4.96948i 0.270304i
\(339\) 3.00726 + 3.00726i 0.163332 + 0.163332i
\(340\) 13.7653 + 8.74813i 0.746529 + 0.474434i
\(341\) −0.456722 + 0.456722i −0.0247329 + 0.0247329i
\(342\) −1.89479 1.89479i −0.102458 0.102458i
\(343\) −14.2526 + 14.2526i −0.769571 + 0.769571i
\(344\) 7.61240 0.410433
\(345\) −18.0896 + 4.03131i −0.973909 + 0.217038i
\(346\) −6.60085 + 6.60085i −0.354864 + 0.354864i
\(347\) 9.43617i 0.506560i −0.967393 0.253280i \(-0.918491\pi\)
0.967393 0.253280i \(-0.0815094\pi\)
\(348\) 3.35545 0.179871
\(349\) 7.25908i 0.388569i 0.980945 + 0.194285i \(0.0622386\pi\)
−0.980945 + 0.194285i \(0.937761\pi\)
\(350\) 10.0144 + 3.61993i 0.535292 + 0.193493i
\(351\) −2.00381 2.00381i −0.106956 0.106956i
\(352\) −0.249077 −0.0132758
\(353\) −6.63465 −0.353127 −0.176563 0.984289i \(-0.556498\pi\)
−0.176563 + 0.984289i \(0.556498\pi\)
\(354\) −8.85463 −0.470618
\(355\) 6.36583 + 4.04561i 0.337863 + 0.214719i
\(356\) −5.37576 + 5.37576i −0.284915 + 0.284915i
\(357\) 15.5342i 0.822155i
\(358\) 11.1031 + 11.1031i 0.586816 + 0.586816i
\(359\) 3.64712i 0.192488i −0.995358 0.0962438i \(-0.969317\pi\)
0.995358 0.0962438i \(-0.0306828\pi\)
\(360\) 1.88721 + 1.19936i 0.0994645 + 0.0632116i
\(361\) 11.8196i 0.622082i
\(362\) 19.1102i 1.00441i
\(363\) 7.73431 + 7.73431i 0.405946 + 0.405946i
\(364\) −4.26754 + 4.26754i −0.223680 + 0.223680i
\(365\) −5.14668 23.0945i −0.269390 1.20882i
\(366\) 4.55389 0.238036
\(367\) −2.67398 2.67398i −0.139580 0.139580i 0.633864 0.773444i \(-0.281468\pi\)
−0.773444 + 0.633864i \(0.781468\pi\)
\(368\) 8.28835i 0.432060i
\(369\) −10.3232 −0.537404
\(370\) 6.24913 + 12.0809i 0.324877 + 0.628057i
\(371\) −12.6675 −0.657666
\(372\) 2.59319i 0.134450i
\(373\) 8.22916 + 8.22916i 0.426090 + 0.426090i 0.887294 0.461204i \(-0.152582\pi\)
−0.461204 + 0.887294i \(0.652582\pi\)
\(374\) 1.81677 0.0939429
\(375\) −8.84738 + 6.83549i −0.456877 + 0.352983i
\(376\) −2.82753 + 2.82753i −0.145819 + 0.145819i
\(377\) −6.72369 6.72369i −0.346287 0.346287i
\(378\) 2.12971i 0.109541i
\(379\) 23.2988i 1.19678i 0.801206 + 0.598389i \(0.204192\pi\)
−0.801206 + 0.598389i \(0.795808\pi\)
\(380\) −1.30333 5.84838i −0.0668593 0.300016i
\(381\) 17.7440i 0.909053i
\(382\) −4.13848 4.13848i −0.211743 0.211743i
\(383\) 1.82589i 0.0932984i −0.998911 0.0466492i \(-0.985146\pi\)
0.998911 0.0466492i \(-0.0148543\pi\)
\(384\) 0.707107 0.707107i 0.0360844 0.0360844i
\(385\) 1.15775 0.258007i 0.0590043 0.0131493i
\(386\) −1.65600 −0.0842881
\(387\) −7.61240 −0.386960
\(388\) 5.94731 0.301929
\(389\) 1.87840 + 1.87840i 0.0952388 + 0.0952388i 0.753121 0.657882i \(-0.228547\pi\)
−0.657882 + 0.753121i \(0.728547\pi\)
\(390\) −1.37832 6.18489i −0.0697939 0.313184i
\(391\) 60.4554i 3.05736i
\(392\) −2.46433 −0.124467
\(393\) 5.38872i 0.271825i
\(394\) −14.1878 + 14.1878i −0.714769 + 0.714769i
\(395\) 4.12584 + 18.5138i 0.207594 + 0.931528i
\(396\) 0.249077 0.0125166
\(397\) 12.0046 12.0046i 0.602492 0.602492i −0.338481 0.940973i \(-0.609913\pi\)
0.940973 + 0.338481i \(0.109913\pi\)
\(398\) −3.69181 3.69181i −0.185054 0.185054i
\(399\) 4.03535 4.03535i 0.202020 0.202020i
\(400\) 2.12309 + 4.52686i 0.106154 + 0.226343i
\(401\) −23.2046 23.2046i −1.15878 1.15878i −0.984738 0.174043i \(-0.944317\pi\)
−0.174043 0.984738i \(-0.555683\pi\)
\(402\) 8.03506i 0.400753i
\(403\) −5.19626 + 5.19626i −0.258844 + 0.258844i
\(404\) 10.2985i 0.512368i
\(405\) −1.88721 1.19936i −0.0937760 0.0595965i
\(406\) 7.14614i 0.354657i
\(407\) 1.30928 + 0.762385i 0.0648987 + 0.0377900i
\(408\) −5.15765 + 5.15765i −0.255342 + 0.255342i
\(409\) 12.7469 12.7469i 0.630292 0.630292i −0.317850 0.948141i \(-0.602961\pi\)
0.948141 + 0.317850i \(0.102961\pi\)
\(410\) −19.4820 12.3812i −0.962147 0.611463i
\(411\) 3.85752i 0.190278i
\(412\) 8.34427 0.411093
\(413\) 18.8578i 0.927932i
\(414\) 8.28835i 0.407350i
\(415\) 18.4715 4.11642i 0.906729 0.202067i
\(416\) −2.83382 −0.138939
\(417\) 1.63707 + 1.63707i 0.0801675 + 0.0801675i
\(418\) −0.471948 0.471948i −0.0230837 0.0230837i
\(419\) 22.1539i 1.08229i −0.840929 0.541145i \(-0.817991\pi\)
0.840929 0.541145i \(-0.182009\pi\)
\(420\) −2.55428 + 4.01920i −0.124636 + 0.196117i
\(421\) −18.3106 18.3106i −0.892404 0.892404i 0.102345 0.994749i \(-0.467365\pi\)
−0.994749 + 0.102345i \(0.967365\pi\)
\(422\) 8.15505i 0.396981i
\(423\) 2.82753 2.82753i 0.137479 0.137479i
\(424\) −4.20587 4.20587i −0.204255 0.204255i
\(425\) −15.4858 33.0190i −0.751174 1.60166i
\(426\) −2.38518 + 2.38518i −0.115562 + 0.115562i
\(427\) 9.69847i 0.469342i
\(428\) 2.10671 + 2.10671i 0.101832 + 0.101832i
\(429\) −0.499103 0.499103i −0.0240969 0.0240969i
\(430\) −14.3662 9.12998i −0.692798 0.440287i
\(431\) −8.32782 8.32782i −0.401137 0.401137i 0.477497 0.878634i \(-0.341544\pi\)
−0.878634 + 0.477497i \(0.841544\pi\)
\(432\) −0.707107 + 0.707107i −0.0340207 + 0.0340207i
\(433\) −6.11268 + 6.11268i −0.293757 + 0.293757i −0.838562 0.544806i \(-0.816603\pi\)
0.544806 + 0.838562i \(0.316603\pi\)
\(434\) 5.52274 0.265100
\(435\) −6.33242 4.02438i −0.303616 0.192954i
\(436\) 10.6743 + 10.6743i 0.511208 + 0.511208i
\(437\) −15.7047 + 15.7047i −0.751256 + 0.751256i
\(438\) 10.5815 0.505606
\(439\) 16.2052 16.2052i 0.773431 0.773431i −0.205273 0.978705i \(-0.565808\pi\)
0.978705 + 0.205273i \(0.0658084\pi\)
\(440\) 0.470059 + 0.298732i 0.0224092 + 0.0142415i
\(441\) 2.46433 0.117349
\(442\) 20.6699 0.983167
\(443\) −6.30399 6.30399i −0.299512 0.299512i 0.541311 0.840823i \(-0.317928\pi\)
−0.840823 + 0.541311i \(0.817928\pi\)
\(444\) −5.88128 + 1.55259i −0.279113 + 0.0736828i
\(445\) 16.5926 3.69771i 0.786565 0.175288i
\(446\) 18.0980 + 18.0980i 0.856966 + 0.856966i
\(447\) −5.97997 + 5.97997i −0.282843 + 0.282843i
\(448\) 1.50593 + 1.50593i 0.0711487 + 0.0711487i
\(449\) −19.8634 19.8634i −0.937412 0.937412i 0.0607412 0.998154i \(-0.480654\pi\)
−0.998154 + 0.0607412i \(0.980654\pi\)
\(450\) −2.12309 4.52686i −0.100083 0.213398i
\(451\) −2.57127 −0.121076
\(452\) −4.25290 −0.200040
\(453\) 8.75900 8.75900i 0.411534 0.411534i
\(454\) 15.2040i 0.713560i
\(455\) 13.1720 2.93542i 0.617514 0.137615i
\(456\) 2.67964 0.125485
\(457\) −40.2606 −1.88331 −0.941657 0.336575i \(-0.890731\pi\)
−0.941657 + 0.336575i \(0.890731\pi\)
\(458\) 22.1160 1.03341
\(459\) 5.15765 5.15765i 0.240738 0.240738i
\(460\) 9.94068 15.6418i 0.463487 0.729303i
\(461\) −15.0948 + 15.0948i −0.703036 + 0.703036i −0.965061 0.262025i \(-0.915610\pi\)
0.262025 + 0.965061i \(0.415610\pi\)
\(462\) 0.530462i 0.0246793i
\(463\) 25.5478i 1.18730i 0.804722 + 0.593652i \(0.202315\pi\)
−0.804722 + 0.593652i \(0.797685\pi\)
\(464\) −2.37266 + 2.37266i −0.110148 + 0.110148i
\(465\) −3.11015 + 4.89388i −0.144230 + 0.226948i
\(466\) 4.77285 4.77285i 0.221098 0.221098i
\(467\) −30.7343 −1.42221 −0.711106 0.703085i \(-0.751805\pi\)
−0.711106 + 0.703085i \(0.751805\pi\)
\(468\) 2.83382 0.130993
\(469\) −17.1124 −0.790176
\(470\) 8.72733 1.94491i 0.402562 0.0897121i
\(471\) 14.6365i 0.674415i
\(472\) 6.26117 6.26117i 0.288194 0.288194i
\(473\) −1.89607 −0.0871815
\(474\) −8.48271 −0.389624
\(475\) −4.55464 + 12.6003i −0.208981 + 0.578139i
\(476\) −10.9843 10.9843i −0.503465 0.503465i
\(477\) 4.20587 + 4.20587i 0.192574 + 0.192574i
\(478\) −19.8498 + 19.8498i −0.907909 + 0.907909i
\(479\) −0.00977229 0.00977229i −0.000446507 0.000446507i 0.706883 0.707330i \(-0.250100\pi\)
−0.707330 + 0.706883i \(0.750100\pi\)
\(480\) −2.18253 + 0.486383i −0.0996184 + 0.0222002i
\(481\) 14.8961 + 8.67387i 0.679203 + 0.395495i
\(482\) 21.3229 + 21.3229i 0.971233 + 0.971233i
\(483\) 17.6518 0.803184
\(484\) −10.9380 −0.497180
\(485\) −11.2238 7.13294i −0.509646 0.323890i
\(486\) 0.707107 0.707107i 0.0320750 0.0320750i
\(487\) −0.0126739 −0.000574311 −0.000287155 1.00000i \(-0.500091\pi\)
−0.000287155 1.00000i \(0.500091\pi\)
\(488\) −3.22008 + 3.22008i −0.145766 + 0.145766i
\(489\) −6.14503 6.14503i −0.277888 0.277888i
\(490\) 4.65069 + 2.95561i 0.210097 + 0.133521i
\(491\) 24.8512 1.12152 0.560760 0.827979i \(-0.310509\pi\)
0.560760 + 0.827979i \(0.310509\pi\)
\(492\) 7.29960 7.29960i 0.329091 0.329091i
\(493\) 17.3062 17.3062i 0.779433 0.779433i
\(494\) −5.36948 5.36948i −0.241584 0.241584i
\(495\) −0.470059 0.298732i −0.0211276 0.0134270i
\(496\) 1.83366 + 1.83366i 0.0823338 + 0.0823338i
\(497\) −5.07975 5.07975i −0.227858 0.227858i
\(498\) 8.46334i 0.379251i
\(499\) 30.1549 30.1549i 1.34992 1.34992i 0.464175 0.885744i \(-0.346351\pi\)
0.885744 0.464175i \(-0.153649\pi\)
\(500\) 1.42262 11.0895i 0.0636214 0.495936i
\(501\) −13.0979 13.0979i −0.585172 0.585172i
\(502\) −14.6439 + 14.6439i −0.653590 + 0.653590i
\(503\) 33.2862i 1.48416i 0.670312 + 0.742080i \(0.266160\pi\)
−0.670312 + 0.742080i \(0.733840\pi\)
\(504\) −1.50593 1.50593i −0.0670796 0.0670796i
\(505\) 12.3515 19.4353i 0.549636 0.864861i
\(506\) 2.06443i 0.0917753i
\(507\) 3.51395 + 3.51395i 0.156060 + 0.156060i
\(508\) −12.5469 12.5469i −0.556679 0.556679i
\(509\) 35.6979 1.58228 0.791140 0.611635i \(-0.209488\pi\)
0.791140 + 0.611635i \(0.209488\pi\)
\(510\) 15.9194 3.54768i 0.704923 0.157094i
\(511\) 22.5356i 0.996918i
\(512\) 1.00000i 0.0441942i
\(513\) −2.67964 −0.118309
\(514\) 17.8930i 0.789228i
\(515\) −15.7474 10.0078i −0.693911 0.440994i
\(516\) 5.38278 5.38278i 0.236964 0.236964i
\(517\) 0.704271 0.704271i 0.0309738 0.0309738i
\(518\) −3.30658 12.5254i −0.145283 0.550336i
\(519\) 9.33502i 0.409762i
\(520\) 5.34800 + 3.39876i 0.234525 + 0.149045i
\(521\) 0.701242i 0.0307220i 0.999882 + 0.0153610i \(0.00488975\pi\)
−0.999882 + 0.0153610i \(0.995110\pi\)
\(522\) 2.37266 2.37266i 0.103849 0.103849i
\(523\) 35.1652i 1.53767i 0.639449 + 0.768833i \(0.279162\pi\)
−0.639449 + 0.768833i \(0.720838\pi\)
\(524\) −3.81040 3.81040i −0.166458 0.166458i
\(525\) 9.64092 4.52157i 0.420764 0.197337i
\(526\) −21.7610 + 21.7610i −0.948826 + 0.948826i
\(527\) −13.3747 13.3747i −0.582613 0.582613i
\(528\) −0.176124 + 0.176124i −0.00766480 + 0.00766480i
\(529\) −45.6967 −1.98681
\(530\) 2.89301 + 12.9817i 0.125664 + 0.563889i
\(531\) −6.26117 + 6.26117i −0.271712 + 0.271712i
\(532\) 5.70685i 0.247423i
\(533\) −29.2540 −1.26713
\(534\) 7.60247i 0.328991i
\(535\) −1.44910 6.50250i −0.0626500 0.281127i
\(536\) −5.68165 5.68165i −0.245410 0.245410i
\(537\) 15.7021 0.677597
\(538\) −17.8478 −0.769475
\(539\) 0.613806 0.0264385
\(540\) 2.18253 0.486383i 0.0939211 0.0209306i
\(541\) −5.47295 + 5.47295i −0.235300 + 0.235300i −0.814901 0.579600i \(-0.803209\pi\)
0.579600 + 0.814901i \(0.303209\pi\)
\(542\) 2.29360i 0.0985188i
\(543\) 13.5129 + 13.5129i 0.579895 + 0.579895i
\(544\) 7.29402i 0.312728i
\(545\) −7.34234 32.9470i −0.314511 1.41130i
\(546\) 6.03521i 0.258283i
\(547\) 14.4568i 0.618127i 0.951041 + 0.309064i \(0.100016\pi\)
−0.951041 + 0.309064i \(0.899984\pi\)
\(548\) 2.72768 + 2.72768i 0.116521 + 0.116521i
\(549\) 3.22008 3.22008i 0.137430 0.137430i
\(550\) −0.528812 1.12754i −0.0225486 0.0480783i
\(551\) −8.99138 −0.383046
\(552\) 5.86075 + 5.86075i 0.249450 + 0.249450i
\(553\) 18.0657i 0.768233i
\(554\) −1.48608 −0.0631373
\(555\) 12.9613 + 4.12369i 0.550176 + 0.175041i
\(556\) −2.31516 −0.0981847
\(557\) 16.2684i 0.689316i 0.938728 + 0.344658i \(0.112005\pi\)
−0.938728 + 0.344658i \(0.887995\pi\)
\(558\) −1.83366 1.83366i −0.0776250 0.0776250i
\(559\) −21.5722 −0.912405
\(560\) −1.03586 4.64816i −0.0437729 0.196421i
\(561\) 1.28465 1.28465i 0.0542380 0.0542380i
\(562\) −18.5876 18.5876i −0.784071 0.784071i
\(563\) 6.03926i 0.254525i −0.991869 0.127262i \(-0.959381\pi\)
0.991869 0.127262i \(-0.0406190\pi\)
\(564\) 3.99873i 0.168377i
\(565\) 8.02610 + 5.10075i 0.337661 + 0.214590i
\(566\) 16.6153i 0.698392i
\(567\) 1.50593 + 1.50593i 0.0632433 + 0.0632433i
\(568\) 3.37315i 0.141534i
\(569\) −13.8974 + 13.8974i −0.582609 + 0.582609i −0.935620 0.353010i \(-0.885158\pi\)
0.353010 + 0.935620i \(0.385158\pi\)
\(570\) −5.05702 3.21384i −0.211815 0.134613i
\(571\) −28.3787 −1.18761 −0.593805 0.804609i \(-0.702375\pi\)
−0.593805 + 0.804609i \(0.702375\pi\)
\(572\) 0.705838 0.0295126
\(573\) −5.85269 −0.244500
\(574\) 15.5460 + 15.5460i 0.648879 + 0.648879i
\(575\) −37.5202 + 17.5969i −1.56470 + 0.733841i
\(576\) 1.00000i 0.0416667i
\(577\) −35.3160 −1.47023 −0.735113 0.677945i \(-0.762871\pi\)
−0.735113 + 0.677945i \(0.762871\pi\)
\(578\) 36.2027i 1.50583i
\(579\) −1.17097 + 1.17097i −0.0486638 + 0.0486638i
\(580\) 7.32336 1.63203i 0.304086 0.0677665i
\(581\) −18.0245 −0.747781
\(582\) 4.20538 4.20538i 0.174319 0.174319i
\(583\) 1.04759 + 1.04759i 0.0433865 + 0.0433865i
\(584\) −7.48228 + 7.48228i −0.309619 + 0.309619i
\(585\) −5.34800 3.39876i −0.221112 0.140521i
\(586\) 9.37884 + 9.37884i 0.387436 + 0.387436i
\(587\) 33.3247i 1.37546i −0.725968 0.687729i \(-0.758608\pi\)
0.725968 0.687729i \(-0.241392\pi\)
\(588\) −1.74254 + 1.74254i −0.0718612 + 0.0718612i
\(589\) 6.94879i 0.286320i
\(590\) −19.3255 + 4.30674i −0.795617 + 0.177306i
\(591\) 20.0645i 0.825344i
\(592\) 3.06084 5.25654i 0.125800 0.216043i
\(593\) 29.5804 29.5804i 1.21472 1.21472i 0.245266 0.969456i \(-0.421125\pi\)
0.969456 0.245266i \(-0.0788753\pi\)
\(594\) 0.176124 0.176124i 0.00722645 0.00722645i
\(595\) 7.55555 + 33.9037i 0.309747 + 1.38992i
\(596\) 8.45695i 0.346410i
\(597\) −5.22101 −0.213682
\(598\) 23.4877i 0.960482i
\(599\) 16.4095i 0.670473i 0.942134 + 0.335236i \(0.108816\pi\)
−0.942134 + 0.335236i \(0.891184\pi\)
\(600\) 4.70223 + 1.69973i 0.191968 + 0.0693910i
\(601\) −24.3063 −0.991473 −0.495736 0.868473i \(-0.665102\pi\)
−0.495736 + 0.868473i \(0.665102\pi\)
\(602\) 11.4638 + 11.4638i 0.467229 + 0.467229i
\(603\) 5.68165 + 5.68165i 0.231375 + 0.231375i
\(604\) 12.3871i 0.504024i
\(605\) 20.6422 + 13.1185i 0.839224 + 0.533343i
\(606\) 7.28212 + 7.28212i 0.295816 + 0.295816i
\(607\) 2.93171i 0.118994i −0.998228 0.0594972i \(-0.981050\pi\)
0.998228 0.0594972i \(-0.0189497\pi\)
\(608\) −1.89479 + 1.89479i −0.0768438 + 0.0768438i
\(609\) 5.05308 + 5.05308i 0.204761 + 0.204761i
\(610\) 9.93899 2.21493i 0.402418 0.0896800i
\(611\) 8.01269 8.01269i 0.324159 0.324159i
\(612\) 7.29402i 0.294843i
\(613\) −15.0778 15.0778i −0.608986 0.608986i 0.333695 0.942681i \(-0.391704\pi\)
−0.942681 + 0.333695i \(0.891704\pi\)
\(614\) 3.36862 + 3.36862i 0.135947 + 0.135947i
\(615\) −22.5307 + 5.02102i −0.908524 + 0.202467i
\(616\) −0.375093 0.375093i −0.0151129 0.0151129i
\(617\) −31.1997 + 31.1997i −1.25605 + 1.25605i −0.303091 + 0.952962i \(0.598019\pi\)
−0.952962 + 0.303091i \(0.901981\pi\)
\(618\) 5.90029 5.90029i 0.237345 0.237345i
\(619\) −11.1366 −0.447619 −0.223809 0.974633i \(-0.571849\pi\)
−0.223809 + 0.974633i \(0.571849\pi\)
\(620\) −1.26128 5.65970i −0.0506543 0.227299i
\(621\) −5.86075 5.86075i −0.235184 0.235184i
\(622\) −22.4334 + 22.4334i −0.899497 + 0.899497i
\(623\) −16.1911 −0.648682
\(624\) −2.00381 + 2.00381i −0.0802166 + 0.0802166i
\(625\) −15.9850 + 19.2219i −0.639399 + 0.768875i
\(626\) −19.2752 −0.770393
\(627\) −0.667435 −0.0266548
\(628\) 10.3496 + 10.3496i 0.412993 + 0.412993i
\(629\) −22.3259 + 38.3413i −0.890190 + 1.52877i
\(630\) 1.03586 + 4.64816i 0.0412695 + 0.185187i
\(631\) 19.2236 + 19.2236i 0.765279 + 0.765279i 0.977271 0.211992i \(-0.0679951\pi\)
−0.211992 + 0.977271i \(0.567995\pi\)
\(632\) 5.99818 5.99818i 0.238595 0.238595i
\(633\) −5.76649 5.76649i −0.229197 0.229197i
\(634\) −3.94817 3.94817i −0.156802 0.156802i
\(635\) 8.63038 + 38.7268i 0.342486 + 1.53683i
\(636\) −5.94800 −0.235854
\(637\) 6.98345 0.276694
\(638\) 0.590974 0.590974i 0.0233969 0.0233969i
\(639\) 3.37315i 0.133440i
\(640\) 1.19936 1.88721i 0.0474087 0.0745983i
\(641\) 8.52699 0.336796 0.168398 0.985719i \(-0.446141\pi\)
0.168398 + 0.985719i \(0.446141\pi\)
\(642\) 2.97934 0.117585
\(643\) −11.8650 −0.467910 −0.233955 0.972247i \(-0.575167\pi\)
−0.233955 + 0.972247i \(0.575167\pi\)
\(644\) −12.4817 + 12.4817i −0.491848 + 0.491848i
\(645\) −16.6143 + 3.70254i −0.654187 + 0.145787i
\(646\) 13.8206 13.8206i 0.543765 0.543765i
\(647\) 1.01194i 0.0397836i −0.999802 0.0198918i \(-0.993668\pi\)
0.999802 0.0198918i \(-0.00633217\pi\)
\(648\) 1.00000i 0.0392837i
\(649\) −1.55951 + 1.55951i −0.0612161 + 0.0612161i
\(650\) −6.01645 12.8283i −0.235984 0.503167i
\(651\) 3.90517 3.90517i 0.153056 0.153056i
\(652\) 8.69039 0.340342
\(653\) 14.7798 0.578377 0.289189 0.957272i \(-0.406614\pi\)
0.289189 + 0.957272i \(0.406614\pi\)
\(654\) 15.0958 0.590293
\(655\) 2.62098 + 11.7610i 0.102410 + 0.459541i
\(656\) 10.3232i 0.403053i
\(657\) 7.48228 7.48228i 0.291912 0.291912i
\(658\) −8.51613 −0.331993
\(659\) −1.79646 −0.0699802 −0.0349901 0.999388i \(-0.511140\pi\)
−0.0349901 + 0.999388i \(0.511140\pi\)
\(660\) 0.543617 0.121147i 0.0211603 0.00471562i
\(661\) 11.0318 + 11.0318i 0.429086 + 0.429086i 0.888317 0.459231i \(-0.151875\pi\)
−0.459231 + 0.888317i \(0.651875\pi\)
\(662\) −2.89997 2.89997i −0.112711 0.112711i
\(663\) 14.6158 14.6158i 0.567632 0.567632i
\(664\) −5.98449 5.98449i −0.232243 0.232243i
\(665\) 6.84455 10.7700i 0.265420 0.417643i
\(666\) −3.06084 + 5.25654i −0.118605 + 0.203687i
\(667\) −19.6654 19.6654i −0.761449 0.761449i
\(668\) 18.5233 0.716687
\(669\) 25.5945 0.989539
\(670\) 3.90812 + 17.5368i 0.150984 + 0.677504i
\(671\) 0.802048 0.802048i 0.0309627 0.0309627i
\(672\) 2.12971 0.0821554
\(673\) 12.5759 12.5759i 0.484766 0.484766i −0.421884 0.906650i \(-0.638631\pi\)
0.906650 + 0.421884i \(0.138631\pi\)
\(674\) −1.55976 1.55976i −0.0600796 0.0600796i
\(675\) −4.70223 1.69973i −0.180989 0.0654225i
\(676\) −4.96948 −0.191134
\(677\) −18.9213 + 18.9213i −0.727203 + 0.727203i −0.970062 0.242859i \(-0.921915\pi\)
0.242859 + 0.970062i \(0.421915\pi\)
\(678\) −3.00726 + 3.00726i −0.115493 + 0.115493i
\(679\) 8.95625 + 8.95625i 0.343710 + 0.343710i
\(680\) −8.74813 + 13.7653i −0.335475 + 0.527876i
\(681\) −10.7509 10.7509i −0.411974 0.411974i
\(682\) −0.456722 0.456722i −0.0174888 0.0174888i
\(683\) 36.6018i 1.40053i −0.713883 0.700265i \(-0.753065\pi\)
0.713883 0.700265i \(-0.246935\pi\)
\(684\) 1.89479 1.89479i 0.0724490 0.0724490i
\(685\) −1.87623 8.41915i −0.0716871 0.321679i
\(686\) −14.2526 14.2526i −0.544169 0.544169i
\(687\) 15.6384 15.6384i 0.596642 0.596642i
\(688\) 7.61240i 0.290220i
\(689\) 11.9187 + 11.9187i 0.454066 + 0.454066i
\(690\) −4.03131 18.0896i −0.153469 0.688658i
\(691\) 23.7209i 0.902385i 0.892427 + 0.451193i \(0.149001\pi\)
−0.892427 + 0.451193i \(0.850999\pi\)
\(692\) −6.60085 6.60085i −0.250927 0.250927i
\(693\) 0.375093 + 0.375093i 0.0142486 + 0.0142486i
\(694\) 9.43617 0.358192
\(695\) 4.36918 + 2.77670i 0.165733 + 0.105326i
\(696\) 3.35545i 0.127188i
\(697\) 75.2975i 2.85210i
\(698\) −7.25908 −0.274760
\(699\) 6.74984i 0.255302i
\(700\) −3.61993 + 10.0144i −0.136820 + 0.378508i
\(701\) −12.5087 + 12.5087i −0.472447 + 0.472447i −0.902706 0.430259i \(-0.858422\pi\)
0.430259 + 0.902706i \(0.358422\pi\)
\(702\) 2.00381 2.00381i 0.0756290 0.0756290i
\(703\) 15.7597 4.16038i 0.594388 0.156912i
\(704\) 0.249077i 0.00938743i
\(705\) 4.79590 7.54642i 0.180624 0.284214i
\(706\) 6.63465i 0.249698i
\(707\) −15.5088 + 15.5088i −0.583269 + 0.583269i
\(708\) 8.85463i 0.332777i
\(709\) −16.9567 16.9567i −0.636822 0.636822i 0.312948 0.949770i \(-0.398683\pi\)
−0.949770 + 0.312948i \(0.898683\pi\)
\(710\) −4.04561 + 6.36583i −0.151829 + 0.238906i
\(711\) −5.99818 + 5.99818i −0.224949 + 0.224949i
\(712\) −5.37576 5.37576i −0.201465 0.201465i
\(713\) −15.1980 + 15.1980i −0.569170 + 0.569170i
\(714\) −15.5342 −0.581351
\(715\) −1.33206 0.846551i −0.0498162 0.0316592i
\(716\) −11.1031 + 11.1031i −0.414942 + 0.414942i
\(717\) 28.0719i 1.04836i
\(718\) 3.64712 0.136109
\(719\) 6.40855i 0.238998i 0.992834 + 0.119499i \(0.0381289\pi\)
−0.992834 + 0.119499i \(0.961871\pi\)
\(720\) −1.19936 + 1.88721i −0.0446974 + 0.0703320i
\(721\) 12.5659 + 12.5659i 0.467979 + 0.467979i
\(722\) 11.8196 0.439878
\(723\) 30.1552 1.12148
\(724\) −19.1102 −0.710223
\(725\) −15.7781 5.70334i −0.585983 0.211817i
\(726\) −7.73431 + 7.73431i −0.287047 + 0.287047i
\(727\) 6.09536i 0.226064i −0.993591 0.113032i \(-0.963944\pi\)
0.993591 0.113032i \(-0.0360563\pi\)
\(728\) −4.26754 4.26754i −0.158166 0.158166i
\(729\) 1.00000i 0.0370370i
\(730\) 23.0945 5.14668i 0.854767 0.190487i
\(731\) 55.5250i 2.05367i
\(732\) 4.55389i 0.168317i
\(733\) 5.99617 + 5.99617i 0.221474 + 0.221474i 0.809119 0.587645i \(-0.199945\pi\)
−0.587645 + 0.809119i \(0.699945\pi\)
\(734\) 2.67398 2.67398i 0.0986982 0.0986982i
\(735\) 5.37846 1.19861i 0.198388 0.0442113i
\(736\) −8.28835 −0.305513
\(737\) 1.41517 + 1.41517i 0.0521283 + 0.0521283i
\(738\) 10.3232i 0.380002i
\(739\) 31.2325 1.14891 0.574453 0.818538i \(-0.305215\pi\)
0.574453 + 0.818538i \(0.305215\pi\)
\(740\) −12.0809 + 6.24913i −0.444103 + 0.229723i
\(741\) −7.59360 −0.278958
\(742\) 12.6675i 0.465040i
\(743\) −28.7095 28.7095i −1.05325 1.05325i −0.998500 0.0547482i \(-0.982564\pi\)
−0.0547482 0.998500i \(-0.517436\pi\)
\(744\) 2.59319 0.0950708
\(745\) −10.1429 + 15.9600i −0.371607 + 0.584730i
\(746\) −8.22916 + 8.22916i −0.301291 + 0.301291i
\(747\) 5.98449 + 5.98449i 0.218961 + 0.218961i
\(748\) 1.81677i 0.0664277i
\(749\) 6.34514i 0.231846i
\(750\) −6.83549 8.84738i −0.249597 0.323060i
\(751\) 4.99355i 0.182217i −0.995841 0.0911086i \(-0.970959\pi\)
0.995841 0.0911086i \(-0.0290410\pi\)
\(752\) −2.82753 2.82753i −0.103109 0.103109i
\(753\) 20.7096i 0.754700i
\(754\) 6.72369 6.72369i 0.244862 0.244862i
\(755\) 14.8565 23.3770i 0.540685 0.850776i
\(756\) −2.12971 −0.0774569
\(757\) 20.7849 0.755438 0.377719 0.925920i \(-0.376708\pi\)
0.377719 + 0.925920i \(0.376708\pi\)
\(758\) −23.2988 −0.846250
\(759\) −1.45978 1.45978i −0.0529865 0.0529865i
\(760\) 5.84838 1.30333i 0.212143 0.0472767i
\(761\) 10.4423i 0.378532i 0.981926 + 0.189266i \(0.0606109\pi\)
−0.981926 + 0.189266i \(0.939389\pi\)
\(762\) −17.7440 −0.642798
\(763\) 32.1497i 1.16390i
\(764\) 4.13848 4.13848i 0.149725 0.149725i
\(765\) 8.74813 13.7653i 0.316289 0.497686i
\(766\) 1.82589 0.0659719
\(767\) −17.7430 + 17.7430i −0.640663 + 0.640663i
\(768\) 0.707107 + 0.707107i 0.0255155 + 0.0255155i
\(769\) 36.5206 36.5206i 1.31697 1.31697i 0.400801 0.916165i \(-0.368732\pi\)
0.916165 0.400801i \(-0.131268\pi\)
\(770\) 0.258007 + 1.15775i 0.00929794 + 0.0417223i
\(771\) 12.6523 + 12.6523i 0.455661 + 0.455661i
\(772\) 1.65600i 0.0596007i
\(773\) 36.9436 36.9436i 1.32877 1.32877i 0.422323 0.906445i \(-0.361215\pi\)
0.906445 0.422323i \(-0.138785\pi\)
\(774\) 7.61240i 0.273622i
\(775\) −4.40771 + 12.1938i −0.158329 + 0.438012i
\(776\) 5.94731i 0.213496i
\(777\) −11.1949 6.51872i −0.401616 0.233858i
\(778\) −1.87840 + 1.87840i −0.0673440 + 0.0673440i
\(779\) −19.5603 + 19.5603i −0.700819 + 0.700819i
\(780\) 6.18489