Properties

Label 1110.2.u.e.401.10
Level $1110$
Weight $2$
Character 1110.401
Analytic conductor $8.863$
Analytic rank $0$
Dimension $40$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1110.u (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 401.10
Character \(\chi\) \(=\) 1110.401
Dual form 1110.2.u.e.191.10

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.707107 + 0.707107i) q^{2} +(1.55689 - 0.759006i) q^{3} -1.00000i q^{4} +(-0.707107 - 0.707107i) q^{5} +(-0.564190 + 1.63759i) q^{6} +1.92521 q^{7} +(0.707107 + 0.707107i) q^{8} +(1.84782 - 2.36338i) q^{9} +O(q^{10})\) \(q+(-0.707107 + 0.707107i) q^{2} +(1.55689 - 0.759006i) q^{3} -1.00000i q^{4} +(-0.707107 - 0.707107i) q^{5} +(-0.564190 + 1.63759i) q^{6} +1.92521 q^{7} +(0.707107 + 0.707107i) q^{8} +(1.84782 - 2.36338i) q^{9} +1.00000 q^{10} +5.18734 q^{11} +(-0.759006 - 1.55689i) q^{12} +(-3.96677 + 3.96677i) q^{13} +(-1.36133 + 1.36133i) q^{14} +(-1.63759 - 0.564190i) q^{15} -1.00000 q^{16} +(3.83800 + 3.83800i) q^{17} +(0.364556 + 2.97777i) q^{18} +(0.0989804 - 0.0989804i) q^{19} +(-0.707107 + 0.707107i) q^{20} +(2.99733 - 1.46124i) q^{21} +(-3.66800 + 3.66800i) q^{22} +(1.07572 + 1.07572i) q^{23} +(1.63759 + 0.564190i) q^{24} +1.00000i q^{25} -5.60986i q^{26} +(1.08303 - 5.08203i) q^{27} -1.92521i q^{28} +(1.77763 - 1.77763i) q^{29} +(1.55689 - 0.759006i) q^{30} +(-4.45832 - 4.45832i) q^{31} +(0.707107 - 0.707107i) q^{32} +(8.07612 - 3.93722i) q^{33} -5.42775 q^{34} +(-1.36133 - 1.36133i) q^{35} +(-2.36338 - 1.84782i) q^{36} +(-5.86944 + 1.59678i) q^{37} +0.139979i q^{38} +(-3.16503 + 9.18664i) q^{39} -1.00000i q^{40} +12.4094 q^{41} +(-1.08618 + 3.15269i) q^{42} +(7.21797 - 7.21797i) q^{43} -5.18734i q^{44} +(-2.97777 + 0.364556i) q^{45} -1.52130 q^{46} -3.47762i q^{47} +(-1.55689 + 0.759006i) q^{48} -3.29358 q^{49} +(-0.707107 - 0.707107i) q^{50} +(8.88841 + 3.06228i) q^{51} +(3.96677 + 3.96677i) q^{52} +3.95819i q^{53} +(2.82772 + 4.35936i) q^{54} +(-3.66800 - 3.66800i) q^{55} +(1.36133 + 1.36133i) q^{56} +(0.0789750 - 0.229228i) q^{57} +2.51395i q^{58} +(-7.83820 - 7.83820i) q^{59} +(-0.564190 + 1.63759i) q^{60} +(9.10908 + 9.10908i) q^{61} +6.30502 q^{62} +(3.55743 - 4.54999i) q^{63} +1.00000i q^{64} +5.60986 q^{65} +(-2.92664 + 8.49472i) q^{66} +9.29823i q^{67} +(3.83800 - 3.83800i) q^{68} +(2.49127 + 0.858304i) q^{69} +1.92521 q^{70} -1.23955i q^{71} +(2.97777 - 0.364556i) q^{72} -6.92368i q^{73} +(3.02123 - 5.27941i) q^{74} +(0.759006 + 1.55689i) q^{75} +(-0.0989804 - 0.0989804i) q^{76} +9.98669 q^{77} +(-4.25792 - 8.73394i) q^{78} +(-0.761048 + 0.761048i) q^{79} +(0.707107 + 0.707107i) q^{80} +(-2.17113 - 8.73420i) q^{81} +(-8.77480 + 8.77480i) q^{82} -9.18336i q^{83} +(-1.46124 - 2.99733i) q^{84} -5.42775i q^{85} +10.2078i q^{86} +(1.41835 - 4.11681i) q^{87} +(3.66800 + 3.66800i) q^{88} +(5.54999 - 5.54999i) q^{89} +(1.84782 - 2.36338i) q^{90} +(-7.63685 + 7.63685i) q^{91} +(1.07572 - 1.07572i) q^{92} +(-10.3250 - 3.55723i) q^{93} +(2.45905 + 2.45905i) q^{94} -0.139979 q^{95} +(0.564190 - 1.63759i) q^{96} +(3.84448 - 3.84448i) q^{97} +(2.32892 - 2.32892i) q^{98} +(9.58527 - 12.2597i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 40q - 24q^{7} - 8q^{9} + O(q^{10}) \) \( 40q - 24q^{7} - 8q^{9} + 40q^{10} - 8q^{12} - 16q^{13} - 40q^{16} + 8q^{18} + 16q^{19} - 24q^{31} + 24q^{33} - 8q^{34} + 16q^{39} - 20q^{42} - 32q^{43} - 8q^{45} + 72q^{46} + 96q^{49} + 20q^{51} + 16q^{52} + 24q^{54} - 16q^{57} + 40q^{61} - 24q^{63} - 44q^{66} - 24q^{70} + 8q^{72} + 8q^{75} - 16q^{76} + 48q^{79} + 24q^{81} - 56q^{82} - 8q^{84} + 12q^{87} - 8q^{90} - 64q^{91} + 12q^{93} + 24q^{94} + 8q^{97} + O(q^{100}) \)

Character values

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

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

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.707107 + 0.707107i −0.500000 + 0.500000i
\(3\) 1.55689 0.759006i 0.898871 0.438212i
\(4\) 1.00000i 0.500000i
\(5\) −0.707107 0.707107i −0.316228 0.316228i
\(6\) −0.564190 + 1.63759i −0.230330 + 0.668542i
\(7\) 1.92521 0.727659 0.363830 0.931466i \(-0.381469\pi\)
0.363830 + 0.931466i \(0.381469\pi\)
\(8\) 0.707107 + 0.707107i 0.250000 + 0.250000i
\(9\) 1.84782 2.36338i 0.615940 0.787793i
\(10\) 1.00000 0.316228
\(11\) 5.18734 1.56404 0.782021 0.623252i \(-0.214189\pi\)
0.782021 + 0.623252i \(0.214189\pi\)
\(12\) −0.759006 1.55689i −0.219106 0.449436i
\(13\) −3.96677 + 3.96677i −1.10018 + 1.10018i −0.105797 + 0.994388i \(0.533739\pi\)
−0.994388 + 0.105797i \(0.966261\pi\)
\(14\) −1.36133 + 1.36133i −0.363830 + 0.363830i
\(15\) −1.63759 0.564190i −0.422823 0.145673i
\(16\) −1.00000 −0.250000
\(17\) 3.83800 + 3.83800i 0.930851 + 0.930851i 0.997759 0.0669078i \(-0.0213133\pi\)
−0.0669078 + 0.997759i \(0.521313\pi\)
\(18\) 0.364556 + 2.97777i 0.0859267 + 0.701867i
\(19\) 0.0989804 0.0989804i 0.0227077 0.0227077i −0.695662 0.718369i \(-0.744889\pi\)
0.718369 + 0.695662i \(0.244889\pi\)
\(20\) −0.707107 + 0.707107i −0.158114 + 0.158114i
\(21\) 2.99733 1.46124i 0.654072 0.318869i
\(22\) −3.66800 + 3.66800i −0.782021 + 0.782021i
\(23\) 1.07572 + 1.07572i 0.224304 + 0.224304i 0.810308 0.586004i \(-0.199300\pi\)
−0.586004 + 0.810308i \(0.699300\pi\)
\(24\) 1.63759 + 0.564190i 0.334271 + 0.115165i
\(25\) 1.00000i 0.200000i
\(26\) 5.60986i 1.10018i
\(27\) 1.08303 5.08203i 0.208430 0.978037i
\(28\) 1.92521i 0.363830i
\(29\) 1.77763 1.77763i 0.330098 0.330098i −0.522526 0.852624i \(-0.675010\pi\)
0.852624 + 0.522526i \(0.175010\pi\)
\(30\) 1.55689 0.759006i 0.284248 0.138575i
\(31\) −4.45832 4.45832i −0.800738 0.800738i 0.182472 0.983211i \(-0.441590\pi\)
−0.983211 + 0.182472i \(0.941590\pi\)
\(32\) 0.707107 0.707107i 0.125000 0.125000i
\(33\) 8.07612 3.93722i 1.40587 0.685382i
\(34\) −5.42775 −0.930851
\(35\) −1.36133 1.36133i −0.230106 0.230106i
\(36\) −2.36338 1.84782i −0.393897 0.307970i
\(37\) −5.86944 + 1.59678i −0.964930 + 0.262508i
\(38\) 0.139979i 0.0227077i
\(39\) −3.16503 + 9.18664i −0.506810 + 1.47104i
\(40\) 1.00000i 0.158114i
\(41\) 12.4094 1.93803 0.969014 0.247005i \(-0.0794464\pi\)
0.969014 + 0.247005i \(0.0794464\pi\)
\(42\) −1.08618 + 3.15269i −0.167601 + 0.486471i
\(43\) 7.21797 7.21797i 1.10073 1.10073i 0.106408 0.994323i \(-0.466065\pi\)
0.994323 0.106408i \(-0.0339349\pi\)
\(44\) 5.18734i 0.782021i
\(45\) −2.97777 + 0.364556i −0.443899 + 0.0543448i
\(46\) −1.52130 −0.224304
\(47\) 3.47762i 0.507263i −0.967301 0.253632i \(-0.918375\pi\)
0.967301 0.253632i \(-0.0816251\pi\)
\(48\) −1.55689 + 0.759006i −0.224718 + 0.109553i
\(49\) −3.29358 −0.470512
\(50\) −0.707107 0.707107i −0.100000 0.100000i
\(51\) 8.88841 + 3.06228i 1.24463 + 0.428805i
\(52\) 3.96677 + 3.96677i 0.550092 + 0.550092i
\(53\) 3.95819i 0.543699i 0.962340 + 0.271849i \(0.0876352\pi\)
−0.962340 + 0.271849i \(0.912365\pi\)
\(54\) 2.82772 + 4.35936i 0.384804 + 0.593234i
\(55\) −3.66800 3.66800i −0.494593 0.494593i
\(56\) 1.36133 + 1.36133i 0.181915 + 0.181915i
\(57\) 0.0789750 0.229228i 0.0104605 0.0303620i
\(58\) 2.51395i 0.330098i
\(59\) −7.83820 7.83820i −1.02045 1.02045i −0.999787 0.0206604i \(-0.993423\pi\)
−0.0206604 0.999787i \(-0.506577\pi\)
\(60\) −0.564190 + 1.63759i −0.0728366 + 0.211412i
\(61\) 9.10908 + 9.10908i 1.16630 + 1.16630i 0.983070 + 0.183228i \(0.0586547\pi\)
0.183228 + 0.983070i \(0.441345\pi\)
\(62\) 6.30502 0.800738
\(63\) 3.55743 4.54999i 0.448194 0.573245i
\(64\) 1.00000i 0.125000i
\(65\) 5.60986 0.695818
\(66\) −2.92664 + 8.49472i −0.360245 + 1.04563i
\(67\) 9.29823i 1.13596i 0.823043 + 0.567980i \(0.192275\pi\)
−0.823043 + 0.567980i \(0.807725\pi\)
\(68\) 3.83800 3.83800i 0.465426 0.465426i
\(69\) 2.49127 + 0.858304i 0.299913 + 0.103328i
\(70\) 1.92521 0.230106
\(71\) 1.23955i 0.147107i −0.997291 0.0735537i \(-0.976566\pi\)
0.997291 0.0735537i \(-0.0234340\pi\)
\(72\) 2.97777 0.364556i 0.350933 0.0429633i
\(73\) 6.92368i 0.810355i −0.914238 0.405178i \(-0.867210\pi\)
0.914238 0.405178i \(-0.132790\pi\)
\(74\) 3.02123 5.27941i 0.351211 0.613719i
\(75\) 0.759006 + 1.55689i 0.0876425 + 0.179774i
\(76\) −0.0989804 0.0989804i −0.0113538 0.0113538i
\(77\) 9.98669 1.13809
\(78\) −4.25792 8.73394i −0.482114 0.988925i
\(79\) −0.761048 + 0.761048i −0.0856246 + 0.0856246i −0.748622 0.662997i \(-0.769284\pi\)
0.662997 + 0.748622i \(0.269284\pi\)
\(80\) 0.707107 + 0.707107i 0.0790569 + 0.0790569i
\(81\) −2.17113 8.73420i −0.241236 0.970466i
\(82\) −8.77480 + 8.77480i −0.969014 + 0.969014i
\(83\) 9.18336i 1.00800i −0.863702 0.504002i \(-0.831860\pi\)
0.863702 0.504002i \(-0.168140\pi\)
\(84\) −1.46124 2.99733i −0.159435 0.327036i
\(85\) 5.42775i 0.588722i
\(86\) 10.2078i 1.10073i
\(87\) 1.41835 4.11681i 0.152063 0.441369i
\(88\) 3.66800 + 3.66800i 0.391010 + 0.391010i
\(89\) 5.54999 5.54999i 0.588297 0.588297i −0.348873 0.937170i \(-0.613435\pi\)
0.937170 + 0.348873i \(0.113435\pi\)
\(90\) 1.84782 2.36338i 0.194777 0.249122i
\(91\) −7.63685 + 7.63685i −0.800559 + 0.800559i
\(92\) 1.07572 1.07572i 0.112152 0.112152i
\(93\) −10.3250 3.55723i −1.07065 0.368867i
\(94\) 2.45905 + 2.45905i 0.253632 + 0.253632i
\(95\) −0.139979 −0.0143616
\(96\) 0.564190 1.63759i 0.0575824 0.167135i
\(97\) 3.84448 3.84448i 0.390347 0.390347i −0.484464 0.874811i \(-0.660985\pi\)
0.874811 + 0.484464i \(0.160985\pi\)
\(98\) 2.32892 2.32892i 0.235256 0.235256i
\(99\) 9.58527 12.2597i 0.963356 1.23214i
\(100\) 1.00000 0.100000
\(101\) −3.35861 −0.334194 −0.167097 0.985940i \(-0.553439\pi\)
−0.167097 + 0.985940i \(0.553439\pi\)
\(102\) −8.45041 + 4.11969i −0.836716 + 0.407911i
\(103\) −10.7788 10.7788i −1.06207 1.06207i −0.997942 0.0641240i \(-0.979575\pi\)
−0.0641240 0.997942i \(-0.520425\pi\)
\(104\) −5.60986 −0.550092
\(105\) −3.15269 1.08618i −0.307671 0.106000i
\(106\) −2.79886 2.79886i −0.271849 0.271849i
\(107\) 11.3682i 1.09901i 0.835492 + 0.549503i \(0.185183\pi\)
−0.835492 + 0.549503i \(0.814817\pi\)
\(108\) −5.08203 1.08303i −0.489019 0.104215i
\(109\) −11.3249 + 11.3249i −1.08473 + 1.08473i −0.0886661 + 0.996061i \(0.528260\pi\)
−0.996061 + 0.0886661i \(0.971740\pi\)
\(110\) 5.18734 0.494593
\(111\) −7.92611 + 6.94095i −0.752313 + 0.658805i
\(112\) −1.92521 −0.181915
\(113\) −14.1216 + 14.1216i −1.32844 + 1.32844i −0.421716 + 0.906728i \(0.638572\pi\)
−0.906728 + 0.421716i \(0.861428\pi\)
\(114\) 0.106245 + 0.217933i 0.00995078 + 0.0204113i
\(115\) 1.52130i 0.141862i
\(116\) −1.77763 1.77763i −0.165049 0.165049i
\(117\) 2.04511 + 16.7049i 0.189070 + 1.54437i
\(118\) 11.0849 1.02045
\(119\) 7.38893 + 7.38893i 0.677343 + 0.677343i
\(120\) −0.759006 1.55689i −0.0692875 0.142124i
\(121\) 15.9085 1.44623
\(122\) −12.8822 −1.16630
\(123\) 19.3201 9.41884i 1.74204 0.849268i
\(124\) −4.45832 + 4.45832i −0.400369 + 0.400369i
\(125\) 0.707107 0.707107i 0.0632456 0.0632456i
\(126\) 0.701845 + 5.73281i 0.0625253 + 0.510720i
\(127\) 6.10120 0.541394 0.270697 0.962665i \(-0.412746\pi\)
0.270697 + 0.962665i \(0.412746\pi\)
\(128\) −0.707107 0.707107i −0.0625000 0.0625000i
\(129\) 5.75911 16.7161i 0.507061 1.47177i
\(130\) −3.96677 + 3.96677i −0.347909 + 0.347909i
\(131\) −5.14147 + 5.14147i −0.449212 + 0.449212i −0.895093 0.445880i \(-0.852891\pi\)
0.445880 + 0.895093i \(0.352891\pi\)
\(132\) −3.93722 8.07612i −0.342691 0.702936i
\(133\) 0.190558 0.190558i 0.0165234 0.0165234i
\(134\) −6.57484 6.57484i −0.567980 0.567980i
\(135\) −4.35936 + 2.82772i −0.375194 + 0.243371i
\(136\) 5.42775i 0.465426i
\(137\) 2.67319i 0.228386i 0.993459 + 0.114193i \(0.0364282\pi\)
−0.993459 + 0.114193i \(0.963572\pi\)
\(138\) −2.36850 + 1.15468i −0.201620 + 0.0982928i
\(139\) 10.8710i 0.922067i −0.887383 0.461034i \(-0.847479\pi\)
0.887383 0.461034i \(-0.152521\pi\)
\(140\) −1.36133 + 1.36133i −0.115053 + 0.115053i
\(141\) −2.63954 5.41428i −0.222289 0.455964i
\(142\) 0.876494 + 0.876494i 0.0735537 + 0.0735537i
\(143\) −20.5770 + 20.5770i −1.72073 + 1.72073i
\(144\) −1.84782 + 2.36338i −0.153985 + 0.196948i
\(145\) −2.51395 −0.208772
\(146\) 4.89578 + 4.89578i 0.405178 + 0.405178i
\(147\) −5.12775 + 2.49985i −0.422930 + 0.206184i
\(148\) 1.59678 + 5.86944i 0.131254 + 0.482465i
\(149\) 9.44249i 0.773559i −0.922172 0.386779i \(-0.873587\pi\)
0.922172 0.386779i \(-0.126413\pi\)
\(150\) −1.63759 0.564190i −0.133708 0.0460659i
\(151\) 12.4031i 1.00935i −0.863310 0.504673i \(-0.831613\pi\)
0.863310 0.504673i \(-0.168387\pi\)
\(152\) 0.139979 0.0113538
\(153\) 16.1626 1.97872i 1.30667 0.159970i
\(154\) −7.06166 + 7.06166i −0.569045 + 0.569045i
\(155\) 6.30502i 0.506431i
\(156\) 9.18664 + 3.16503i 0.735519 + 0.253405i
\(157\) 7.28854 0.581689 0.290844 0.956770i \(-0.406064\pi\)
0.290844 + 0.956770i \(0.406064\pi\)
\(158\) 1.07628i 0.0856246i
\(159\) 3.00429 + 6.16247i 0.238256 + 0.488715i
\(160\) −1.00000 −0.0790569
\(161\) 2.07099 + 2.07099i 0.163217 + 0.163217i
\(162\) 7.71123 + 4.64079i 0.605851 + 0.364615i
\(163\) 14.2334 + 14.2334i 1.11484 + 1.11484i 0.992486 + 0.122356i \(0.0390450\pi\)
0.122356 + 0.992486i \(0.460955\pi\)
\(164\) 12.4094i 0.969014i
\(165\) −8.49472 2.92664i −0.661313 0.227839i
\(166\) 6.49361 + 6.49361i 0.504002 + 0.504002i
\(167\) 12.7580 + 12.7580i 0.987247 + 0.987247i 0.999920 0.0126725i \(-0.00403390\pi\)
−0.0126725 + 0.999920i \(0.504034\pi\)
\(168\) 3.15269 + 1.08618i 0.243235 + 0.0838007i
\(169\) 18.4706i 1.42081i
\(170\) 3.83800 + 3.83800i 0.294361 + 0.294361i
\(171\) −0.0510303 0.416826i −0.00390239 0.0318755i
\(172\) −7.21797 7.21797i −0.550365 0.550365i
\(173\) 4.28631 0.325882 0.162941 0.986636i \(-0.447902\pi\)
0.162941 + 0.986636i \(0.447902\pi\)
\(174\) 1.90810 + 3.91395i 0.144653 + 0.296716i
\(175\) 1.92521i 0.145532i
\(176\) −5.18734 −0.391010
\(177\) −18.1525 6.25398i −1.36442 0.470078i
\(178\) 7.84887i 0.588297i
\(179\) −6.48181 + 6.48181i −0.484473 + 0.484473i −0.906557 0.422084i \(-0.861299\pi\)
0.422084 + 0.906557i \(0.361299\pi\)
\(180\) 0.364556 + 2.97777i 0.0271724 + 0.221950i
\(181\) −13.5004 −1.00347 −0.501737 0.865020i \(-0.667305\pi\)
−0.501737 + 0.865020i \(0.667305\pi\)
\(182\) 10.8001i 0.800559i
\(183\) 21.0957 + 7.26800i 1.55944 + 0.537266i
\(184\) 1.52130i 0.112152i
\(185\) 5.27941 + 3.02123i 0.388150 + 0.222125i
\(186\) 9.81623 4.78555i 0.719761 0.350894i
\(187\) 19.9090 + 19.9090i 1.45589 + 1.45589i
\(188\) −3.47762 −0.253632
\(189\) 2.08506 9.78395i 0.151666 0.711678i
\(190\) 0.0989804 0.0989804i 0.00718079 0.00718079i
\(191\) 9.94316 + 9.94316i 0.719462 + 0.719462i 0.968495 0.249033i \(-0.0801129\pi\)
−0.249033 + 0.968495i \(0.580113\pi\)
\(192\) 0.759006 + 1.55689i 0.0547765 + 0.112359i
\(193\) −14.9338 + 14.9338i −1.07496 + 1.07496i −0.0780070 + 0.996953i \(0.524856\pi\)
−0.996953 + 0.0780070i \(0.975144\pi\)
\(194\) 5.43691i 0.390347i
\(195\) 8.73394 4.25792i 0.625451 0.304916i
\(196\) 3.29358i 0.235256i
\(197\) 10.0071i 0.712980i 0.934299 + 0.356490i \(0.116027\pi\)
−0.934299 + 0.356490i \(0.883973\pi\)
\(198\) 1.89108 + 15.4467i 0.134393 + 1.09775i
\(199\) −12.2484 12.2484i −0.868264 0.868264i 0.124016 0.992280i \(-0.460423\pi\)
−0.992280 + 0.124016i \(0.960423\pi\)
\(200\) −0.707107 + 0.707107i −0.0500000 + 0.0500000i
\(201\) 7.05741 + 14.4763i 0.497791 + 1.02108i
\(202\) 2.37490 2.37490i 0.167097 0.167097i
\(203\) 3.42231 3.42231i 0.240199 0.240199i
\(204\) 3.06228 8.88841i 0.214403 0.622313i
\(205\) −8.77480 8.77480i −0.612858 0.612858i
\(206\) 15.2435 1.06207
\(207\) 4.53009 0.554600i 0.314863 0.0385474i
\(208\) 3.96677 3.96677i 0.275046 0.275046i
\(209\) 0.513445 0.513445i 0.0355157 0.0355157i
\(210\) 2.99733 1.46124i 0.206836 0.100835i
\(211\) −22.1119 −1.52225 −0.761124 0.648606i \(-0.775352\pi\)
−0.761124 + 0.648606i \(0.775352\pi\)
\(212\) 3.95819 0.271849
\(213\) −0.940826 1.92984i −0.0644643 0.132231i
\(214\) −8.03854 8.03854i −0.549503 0.549503i
\(215\) −10.2078 −0.696163
\(216\) 4.35936 2.82772i 0.296617 0.192402i
\(217\) −8.58319 8.58319i −0.582665 0.582665i
\(218\) 16.0158i 1.08473i
\(219\) −5.25511 10.7794i −0.355108 0.728405i
\(220\) −3.66800 + 3.66800i −0.247297 + 0.247297i
\(221\) −30.4489 −2.04822
\(222\) 0.696619 10.5126i 0.0467540 0.705559i
\(223\) 15.3186 1.02581 0.512904 0.858446i \(-0.328570\pi\)
0.512904 + 0.858446i \(0.328570\pi\)
\(224\) 1.36133 1.36133i 0.0909574 0.0909574i
\(225\) 2.36338 + 1.84782i 0.157559 + 0.123188i
\(226\) 19.9709i 1.32844i
\(227\) −13.6849 13.6849i −0.908298 0.908298i 0.0878367 0.996135i \(-0.472005\pi\)
−0.996135 + 0.0878367i \(0.972005\pi\)
\(228\) −0.229228 0.0789750i −0.0151810 0.00523024i
\(229\) −11.4150 −0.754322 −0.377161 0.926148i \(-0.623100\pi\)
−0.377161 + 0.926148i \(0.623100\pi\)
\(230\) 1.07572 + 1.07572i 0.0709311 + 0.0709311i
\(231\) 15.5482 7.57996i 1.02300 0.498725i
\(232\) 2.51395 0.165049
\(233\) −15.1403 −0.991875 −0.495937 0.868358i \(-0.665175\pi\)
−0.495937 + 0.868358i \(0.665175\pi\)
\(234\) −13.2582 10.3660i −0.866718 0.677648i
\(235\) −2.45905 + 2.45905i −0.160411 + 0.160411i
\(236\) −7.83820 + 7.83820i −0.510223 + 0.510223i
\(237\) −0.607229 + 1.76251i −0.0394437 + 0.114487i
\(238\) −10.4495 −0.677343
\(239\) −5.80735 5.80735i −0.375647 0.375647i 0.493882 0.869529i \(-0.335577\pi\)
−0.869529 + 0.493882i \(0.835577\pi\)
\(240\) 1.63759 + 0.564190i 0.105706 + 0.0364183i
\(241\) −18.6269 + 18.6269i −1.19987 + 1.19987i −0.225659 + 0.974206i \(0.572453\pi\)
−0.974206 + 0.225659i \(0.927547\pi\)
\(242\) −11.2490 + 11.2490i −0.723113 + 0.723113i
\(243\) −10.0095 11.9503i −0.642111 0.766612i
\(244\) 9.10908 9.10908i 0.583149 0.583149i
\(245\) 2.32892 + 2.32892i 0.148789 + 0.148789i
\(246\) −7.00128 + 20.3215i −0.446385 + 1.29565i
\(247\) 0.785265i 0.0499652i
\(248\) 6.30502i 0.400369i
\(249\) −6.97022 14.2975i −0.441720 0.906067i
\(250\) 1.00000i 0.0632456i
\(251\) 8.68049 8.68049i 0.547908 0.547908i −0.377927 0.925835i \(-0.623363\pi\)
0.925835 + 0.377927i \(0.123363\pi\)
\(252\) −4.54999 3.55743i −0.286622 0.224097i
\(253\) 5.58015 + 5.58015i 0.350821 + 0.350821i
\(254\) −4.31420 + 4.31420i −0.270697 + 0.270697i
\(255\) −4.11969 8.45041i −0.257985 0.529185i
\(256\) 1.00000 0.0625000
\(257\) 6.47192 + 6.47192i 0.403707 + 0.403707i 0.879537 0.475830i \(-0.157852\pi\)
−0.475830 + 0.879537i \(0.657852\pi\)
\(258\) 7.74775 + 15.8924i 0.482354 + 0.989415i
\(259\) −11.2999 + 3.07412i −0.702140 + 0.191017i
\(260\) 5.60986i 0.347909i
\(261\) −0.916476 7.48596i −0.0567284 0.463369i
\(262\) 7.27114i 0.449212i
\(263\) −21.9588 −1.35404 −0.677019 0.735966i \(-0.736728\pi\)
−0.677019 + 0.735966i \(0.736728\pi\)
\(264\) 8.49472 + 2.92664i 0.522814 + 0.180122i
\(265\) 2.79886 2.79886i 0.171933 0.171933i
\(266\) 0.269489i 0.0165234i
\(267\) 4.42825 12.8532i 0.271005 0.786603i
\(268\) 9.29823 0.567980
\(269\) 0.470491i 0.0286863i −0.999897 0.0143432i \(-0.995434\pi\)
0.999897 0.0143432i \(-0.00456573\pi\)
\(270\) 1.08303 5.08203i 0.0659114 0.309283i
\(271\) 1.85985 0.112978 0.0564891 0.998403i \(-0.482009\pi\)
0.0564891 + 0.998403i \(0.482009\pi\)
\(272\) −3.83800 3.83800i −0.232713 0.232713i
\(273\) −6.09333 + 17.6862i −0.368785 + 1.07042i
\(274\) −1.89023 1.89023i −0.114193 0.114193i
\(275\) 5.18734i 0.312808i
\(276\) 0.858304 2.49127i 0.0516638 0.149957i
\(277\) −20.9504 20.9504i −1.25879 1.25879i −0.951672 0.307118i \(-0.900635\pi\)
−0.307118 0.951672i \(-0.599365\pi\)
\(278\) 7.68697 + 7.68697i 0.461034 + 0.461034i
\(279\) −18.7749 + 2.29853i −1.12402 + 0.137610i
\(280\) 1.92521i 0.115053i
\(281\) −16.4406 16.4406i −0.980762 0.980762i 0.0190566 0.999818i \(-0.493934\pi\)
−0.999818 + 0.0190566i \(0.993934\pi\)
\(282\) 5.69490 + 1.96204i 0.339127 + 0.116838i
\(283\) 3.56217 + 3.56217i 0.211749 + 0.211749i 0.805010 0.593261i \(-0.202160\pi\)
−0.593261 + 0.805010i \(0.702160\pi\)
\(284\) −1.23955 −0.0735537
\(285\) −0.217933 + 0.106245i −0.0129092 + 0.00629342i
\(286\) 29.1003i 1.72073i
\(287\) 23.8907 1.41022
\(288\) −0.364556 2.97777i −0.0214817 0.175467i
\(289\) 12.4605i 0.732968i
\(290\) 1.77763 1.77763i 0.104386 0.104386i
\(291\) 3.06745 8.90341i 0.179817 0.521927i
\(292\) −6.92368 −0.405178
\(293\) 22.5243i 1.31588i 0.753069 + 0.657942i \(0.228573\pi\)
−0.753069 + 0.657942i \(0.771427\pi\)
\(294\) 1.85821 5.39353i 0.108373 0.314557i
\(295\) 11.0849i 0.645387i
\(296\) −5.27941 3.02123i −0.306860 0.175605i
\(297\) 5.61807 26.3622i 0.325993 1.52969i
\(298\) 6.67685 + 6.67685i 0.386779 + 0.386779i
\(299\) −8.53430 −0.493552
\(300\) 1.55689 0.759006i 0.0898871 0.0438212i
\(301\) 13.8961 13.8961i 0.800957 0.800957i
\(302\) 8.77029 + 8.77029i 0.504673 + 0.504673i
\(303\) −5.22899 + 2.54921i −0.300398 + 0.146448i
\(304\) −0.0989804 + 0.0989804i −0.00567691 + 0.00567691i
\(305\) 12.8822i 0.737632i
\(306\) −10.0295 + 12.8278i −0.573348 + 0.733318i
\(307\) 11.0158i 0.628707i 0.949306 + 0.314353i \(0.101788\pi\)
−0.949306 + 0.314353i \(0.898212\pi\)
\(308\) 9.98669i 0.569045i
\(309\) −24.9626 8.60024i −1.42007 0.489250i
\(310\) −4.45832 4.45832i −0.253216 0.253216i
\(311\) 18.1688 18.1688i 1.03026 1.03026i 0.0307306 0.999528i \(-0.490217\pi\)
0.999528 0.0307306i \(-0.00978340\pi\)
\(312\) −8.73394 + 4.25792i −0.494462 + 0.241057i
\(313\) 3.51658 3.51658i 0.198769 0.198769i −0.600703 0.799472i \(-0.705113\pi\)
0.799472 + 0.600703i \(0.205113\pi\)
\(314\) −5.15378 + 5.15378i −0.290844 + 0.290844i
\(315\) −5.73281 + 0.701845i −0.323007 + 0.0395445i
\(316\) 0.761048 + 0.761048i 0.0428123 + 0.0428123i
\(317\) 11.6758 0.655777 0.327889 0.944716i \(-0.393663\pi\)
0.327889 + 0.944716i \(0.393663\pi\)
\(318\) −6.48187 2.23317i −0.363485 0.125230i
\(319\) 9.22118 9.22118i 0.516287 0.516287i
\(320\) 0.707107 0.707107i 0.0395285 0.0395285i
\(321\) 8.62854 + 17.6991i 0.481598 + 0.987865i
\(322\) −2.92882 −0.163217
\(323\) 0.759773 0.0422749
\(324\) −8.73420 + 2.17113i −0.485233 + 0.120618i
\(325\) −3.96677 3.96677i −0.220037 0.220037i
\(326\) −20.1290 −1.11484
\(327\) −9.03596 + 26.2273i −0.499690 + 1.45037i
\(328\) 8.77480 + 8.77480i 0.484507 + 0.484507i
\(329\) 6.69513i 0.369115i
\(330\) 8.07612 3.93722i 0.444576 0.216737i
\(331\) −0.607386 + 0.607386i −0.0333850 + 0.0333850i −0.723602 0.690217i \(-0.757515\pi\)
0.690217 + 0.723602i \(0.257515\pi\)
\(332\) −9.18336 −0.504002
\(333\) −7.07188 + 16.8223i −0.387536 + 0.921854i
\(334\) −18.0426 −0.987247
\(335\) 6.57484 6.57484i 0.359222 0.359222i
\(336\) −2.99733 + 1.46124i −0.163518 + 0.0797173i
\(337\) 1.97402i 0.107532i −0.998554 0.0537659i \(-0.982878\pi\)
0.998554 0.0537659i \(-0.0171225\pi\)
\(338\) 13.0607 + 13.0607i 0.710406 + 0.710406i
\(339\) −11.2674 + 32.7041i −0.611960 + 1.77624i
\(340\) −5.42775 −0.294361
\(341\) −23.1268 23.1268i −1.25239 1.25239i
\(342\) 0.330824 + 0.258657i 0.0178889 + 0.0139866i
\(343\) −19.8173 −1.07003
\(344\) 10.2078 0.550365
\(345\) −1.15468 2.36850i −0.0621658 0.127516i
\(346\) −3.03088 + 3.03088i −0.162941 + 0.162941i
\(347\) 2.87749 2.87749i 0.154472 0.154472i −0.625640 0.780112i \(-0.715162\pi\)
0.780112 + 0.625640i \(0.215162\pi\)
\(348\) −4.11681 1.41835i −0.220684 0.0760313i
\(349\) 5.35928 0.286876 0.143438 0.989659i \(-0.454184\pi\)
0.143438 + 0.989659i \(0.454184\pi\)
\(350\) −1.36133 1.36133i −0.0727659 0.0727659i
\(351\) 15.8631 + 24.4554i 0.846710 + 1.30533i
\(352\) 3.66800 3.66800i 0.195505 0.195505i
\(353\) −8.81237 + 8.81237i −0.469035 + 0.469035i −0.901602 0.432567i \(-0.857608\pi\)
0.432567 + 0.901602i \(0.357608\pi\)
\(354\) 17.2580 8.41350i 0.917251 0.447172i
\(355\) −0.876494 + 0.876494i −0.0465195 + 0.0465195i
\(356\) −5.54999 5.54999i −0.294149 0.294149i
\(357\) 17.1120 + 5.89552i 0.905664 + 0.312024i
\(358\) 9.16666i 0.484473i
\(359\) 10.4710i 0.552637i −0.961066 0.276319i \(-0.910886\pi\)
0.961066 0.276319i \(-0.0891145\pi\)
\(360\) −2.36338 1.84782i −0.124561 0.0973886i
\(361\) 18.9804i 0.998969i
\(362\) 9.54619 9.54619i 0.501737 0.501737i
\(363\) 24.7678 12.0746i 1.29997 0.633754i
\(364\) 7.63685 + 7.63685i 0.400280 + 0.400280i
\(365\) −4.89578 + 4.89578i −0.256257 + 0.256257i
\(366\) −20.0562 + 9.77766i −1.04835 + 0.511086i
\(367\) −15.6683 −0.817877 −0.408938 0.912562i \(-0.634101\pi\)
−0.408938 + 0.912562i \(0.634101\pi\)
\(368\) −1.07572 1.07572i −0.0560760 0.0560760i
\(369\) 22.9304 29.3282i 1.19371 1.52677i
\(370\) −5.86944 + 1.59678i −0.305138 + 0.0830124i
\(371\) 7.62032i 0.395627i
\(372\) −3.55723 + 10.3250i −0.184434 + 0.535327i
\(373\) 4.20515i 0.217735i 0.994056 + 0.108867i \(0.0347224\pi\)
−0.994056 + 0.108867i \(0.965278\pi\)
\(374\) −28.1556 −1.45589
\(375\) 0.564190 1.63759i 0.0291346 0.0845646i
\(376\) 2.45905 2.45905i 0.126816 0.126816i
\(377\) 14.1029i 0.726337i
\(378\) 5.44394 + 8.39266i 0.280006 + 0.431672i
\(379\) 10.8211 0.555842 0.277921 0.960604i \(-0.410355\pi\)
0.277921 + 0.960604i \(0.410355\pi\)
\(380\) 0.139979i 0.00718079i
\(381\) 9.49890 4.63084i 0.486643 0.237245i
\(382\) −14.0617 −0.719462
\(383\) 3.27972 + 3.27972i 0.167586 + 0.167586i 0.785917 0.618332i \(-0.212191\pi\)
−0.618332 + 0.785917i \(0.712191\pi\)
\(384\) −1.63759 0.564190i −0.0835677 0.0287912i
\(385\) −7.06166 7.06166i −0.359895 0.359895i
\(386\) 21.1196i 1.07496i
\(387\) −3.72130 30.3963i −0.189164 1.54513i
\(388\) −3.84448 3.84448i −0.195174 0.195174i
\(389\) −17.5886 17.5886i −0.891778 0.891778i 0.102912 0.994690i \(-0.467184\pi\)
−0.994690 + 0.102912i \(0.967184\pi\)
\(390\) −3.16503 + 9.18664i −0.160267 + 0.465183i
\(391\) 8.25726i 0.417587i
\(392\) −2.32892 2.32892i −0.117628 0.117628i
\(393\) −4.10230 + 11.9071i −0.206934 + 0.600634i
\(394\) −7.07612 7.07612i −0.356490 0.356490i
\(395\) 1.07628 0.0541537
\(396\) −12.2597 9.58527i −0.616071 0.481678i
\(397\) 29.2824i 1.46964i 0.678262 + 0.734820i \(0.262734\pi\)
−0.678262 + 0.734820i \(0.737266\pi\)
\(398\) 17.3218 0.868264
\(399\) 0.152043 0.441312i 0.00761167 0.0220932i
\(400\) 1.00000i 0.0500000i
\(401\) 19.3076 19.3076i 0.964177 0.964177i −0.0352035 0.999380i \(-0.511208\pi\)
0.999380 + 0.0352035i \(0.0112079\pi\)
\(402\) −15.2267 5.24597i −0.759436 0.261645i
\(403\) 35.3703 1.76192
\(404\) 3.35861i 0.167097i
\(405\) −4.64079 + 7.71123i −0.230603 + 0.383174i
\(406\) 4.83987i 0.240199i
\(407\) −30.4468 + 8.28302i −1.50919 + 0.410574i
\(408\) 4.11969 + 8.45041i 0.203955 + 0.418358i
\(409\) 6.57668 + 6.57668i 0.325196 + 0.325196i 0.850756 0.525560i \(-0.176144\pi\)
−0.525560 + 0.850756i \(0.676144\pi\)
\(410\) 12.4094 0.612858
\(411\) 2.02897 + 4.16186i 0.100082 + 0.205290i
\(412\) −10.7788 + 10.7788i −0.531033 + 0.531033i
\(413\) −15.0901 15.0901i −0.742538 0.742538i
\(414\) −2.81109 + 3.59542i −0.138158 + 0.176705i
\(415\) −6.49361 + 6.49361i −0.318759 + 0.318759i
\(416\) 5.60986i 0.275046i
\(417\) −8.25116 16.9250i −0.404061 0.828820i
\(418\) 0.726121i 0.0355157i
\(419\) 26.3846i 1.28897i 0.764617 + 0.644485i \(0.222928\pi\)
−0.764617 + 0.644485i \(0.777072\pi\)
\(420\) −1.08618 + 3.15269i −0.0530002 + 0.153836i
\(421\) −21.6083 21.6083i −1.05312 1.05312i −0.998507 0.0546159i \(-0.982607\pi\)
−0.0546159 0.998507i \(-0.517393\pi\)
\(422\) 15.6355 15.6355i 0.761124 0.761124i
\(423\) −8.21894 6.42601i −0.399618 0.312444i
\(424\) −2.79886 + 2.79886i −0.135925 + 0.135925i
\(425\) −3.83800 + 3.83800i −0.186170 + 0.186170i
\(426\) 2.02987 + 0.699341i 0.0983475 + 0.0338832i
\(427\) 17.5369 + 17.5369i 0.848668 + 0.848668i
\(428\) 11.3682 0.549503
\(429\) −16.4181 + 47.6542i −0.792672 + 2.30077i
\(430\) 7.21797 7.21797i 0.348082 0.348082i
\(431\) −16.8691 + 16.8691i −0.812557 + 0.812557i −0.985017 0.172460i \(-0.944828\pi\)
0.172460 + 0.985017i \(0.444828\pi\)
\(432\) −1.08303 + 5.08203i −0.0521075 + 0.244509i
\(433\) −20.9643 −1.00748 −0.503740 0.863855i \(-0.668043\pi\)
−0.503740 + 0.863855i \(0.668043\pi\)
\(434\) 12.1385 0.582665
\(435\) −3.91395 + 1.90810i −0.187659 + 0.0914866i
\(436\) 11.3249 + 11.3249i 0.542364 + 0.542364i
\(437\) 0.212951 0.0101868
\(438\) 11.3381 + 3.90627i 0.541756 + 0.186649i
\(439\) −1.59624 1.59624i −0.0761842 0.0761842i 0.667988 0.744172i \(-0.267156\pi\)
−0.744172 + 0.667988i \(0.767156\pi\)
\(440\) 5.18734i 0.247297i
\(441\) −6.08595 + 7.78399i −0.289807 + 0.370666i
\(442\) 21.5306 21.5306i 1.02411 1.02411i
\(443\) −26.6898 −1.26807 −0.634035 0.773304i \(-0.718603\pi\)
−0.634035 + 0.773304i \(0.718603\pi\)
\(444\) 6.94095 + 7.92611i 0.329403 + 0.376157i
\(445\) −7.84887 −0.372072
\(446\) −10.8319 + 10.8319i −0.512904 + 0.512904i
\(447\) −7.16691 14.7009i −0.338983 0.695330i
\(448\) 1.92521i 0.0909574i
\(449\) −9.86107 9.86107i −0.465372 0.465372i 0.435039 0.900412i \(-0.356735\pi\)
−0.900412 + 0.435039i \(0.856735\pi\)
\(450\) −2.97777 + 0.364556i −0.140373 + 0.0171853i
\(451\) 64.3720 3.03116
\(452\) 14.1216 + 14.1216i 0.664222 + 0.664222i
\(453\) −9.41400 19.3102i −0.442308 0.907273i
\(454\) 19.3534 0.908298
\(455\) 10.8001 0.506318
\(456\) 0.217933 0.106245i 0.0102056 0.00497539i
\(457\) 6.55173 6.55173i 0.306477 0.306477i −0.537064 0.843541i \(-0.680467\pi\)
0.843541 + 0.537064i \(0.180467\pi\)
\(458\) 8.07160 8.07160i 0.377161 0.377161i
\(459\) 23.6615 15.3481i 1.10442 0.716390i
\(460\) −1.52130 −0.0709311
\(461\) 14.2328 + 14.2328i 0.662887 + 0.662887i 0.956060 0.293172i \(-0.0947110\pi\)
−0.293172 + 0.956060i \(0.594711\pi\)
\(462\) −5.63439 + 16.3541i −0.262136 + 0.760860i
\(463\) −3.29627 + 3.29627i −0.153191 + 0.153191i −0.779541 0.626351i \(-0.784548\pi\)
0.626351 + 0.779541i \(0.284548\pi\)
\(464\) −1.77763 + 1.77763i −0.0825245 + 0.0825245i
\(465\) 4.78555 + 9.81623i 0.221925 + 0.455217i
\(466\) 10.7058 10.7058i 0.495937 0.495937i
\(467\) 8.25546 + 8.25546i 0.382017 + 0.382017i 0.871828 0.489811i \(-0.162934\pi\)
−0.489811 + 0.871828i \(0.662934\pi\)
\(468\) 16.7049 2.04511i 0.772183 0.0945352i
\(469\) 17.9010i 0.826591i
\(470\) 3.47762i 0.160411i
\(471\) 11.3475 5.53205i 0.522863 0.254903i
\(472\) 11.0849i 0.510223i
\(473\) 37.4421 37.4421i 1.72159 1.72159i
\(474\) −0.816906 1.67566i −0.0375218 0.0769655i
\(475\) 0.0989804 + 0.0989804i 0.00454153 + 0.00454153i
\(476\) 7.38893 7.38893i 0.338671 0.338671i
\(477\) 9.35470 + 7.31401i 0.428322 + 0.334886i
\(478\) 8.21284 0.375647
\(479\) 15.7716 + 15.7716i 0.720622 + 0.720622i 0.968732 0.248110i \(-0.0798095\pi\)
−0.248110 + 0.968732i \(0.579810\pi\)
\(480\) −1.55689 + 0.759006i −0.0710620 + 0.0346437i
\(481\) 16.9487 29.6168i 0.772793 1.35041i
\(482\) 26.3424i 1.19987i
\(483\) 4.79620 + 1.65241i 0.218235 + 0.0751873i
\(484\) 15.9085i 0.723113i
\(485\) −5.43691 −0.246877
\(486\) 15.5279 + 1.37234i 0.704361 + 0.0622506i
\(487\) 12.9849 12.9849i 0.588400 0.588400i −0.348798 0.937198i \(-0.613410\pi\)
0.937198 + 0.348798i \(0.113410\pi\)
\(488\) 12.8822i 0.583149i
\(489\) 32.9630 + 11.3566i 1.49064 + 0.513562i
\(490\) −3.29358 −0.148789
\(491\) 30.8895i 1.39402i 0.717059 + 0.697012i \(0.245488\pi\)
−0.717059 + 0.697012i \(0.754512\pi\)
\(492\) −9.41884 19.3201i −0.424634 0.871019i
\(493\) 13.6451 0.614544
\(494\) −0.555266 0.555266i −0.0249826 0.0249826i
\(495\) −15.4467 + 1.89108i −0.694277 + 0.0849975i
\(496\) 4.45832 + 4.45832i 0.200185 + 0.200185i
\(497\) 2.38639i 0.107044i
\(498\) 15.0385 + 5.18116i 0.673893 + 0.232173i
\(499\) 20.2463 + 20.2463i 0.906350 + 0.906350i 0.995976 0.0896254i \(-0.0285670\pi\)
−0.0896254 + 0.995976i \(0.528567\pi\)
\(500\) −0.707107 0.707107i −0.0316228 0.0316228i
\(501\) 29.5463 + 10.1795i 1.32003 + 0.454784i
\(502\) 12.2761i 0.547908i
\(503\) 19.1000 + 19.1000i 0.851627 + 0.851627i 0.990333 0.138707i \(-0.0442946\pi\)
−0.138707 + 0.990333i \(0.544295\pi\)
\(504\) 5.73281 0.701845i 0.255360 0.0312627i
\(505\) 2.37490 + 2.37490i 0.105681 + 0.105681i
\(506\) −7.89152 −0.350821
\(507\) −14.0193 28.7566i −0.622617 1.27713i
\(508\) 6.10120i 0.270697i
\(509\) 30.8742 1.36848 0.684238 0.729259i \(-0.260135\pi\)
0.684238 + 0.729259i \(0.260135\pi\)
\(510\) 8.88841 + 3.06228i 0.393585 + 0.135600i
\(511\) 13.3295i 0.589662i
\(512\) −0.707107 + 0.707107i −0.0312500 + 0.0312500i
\(513\) −0.395822 0.610220i −0.0174760 0.0269419i
\(514\) −9.15268 −0.403707
\(515\) 15.2435i 0.671709i
\(516\) −16.7161 5.75911i −0.735884 0.253531i
\(517\) 18.0396i 0.793381i
\(518\) 5.81649 10.1639i 0.255562 0.446578i
\(519\) 6.67332 3.25333i 0.292926 0.142806i
\(520\) 3.96677 + 3.96677i 0.173954 + 0.173954i
\(521\) −19.1245 −0.837858 −0.418929 0.908019i \(-0.637594\pi\)
−0.418929 + 0.908019i \(0.637594\pi\)
\(522\) 5.94142 + 4.64533i 0.260049 + 0.203321i
\(523\) −5.56709 + 5.56709i −0.243432 + 0.243432i −0.818268 0.574836i \(-0.805066\pi\)
0.574836 + 0.818268i \(0.305066\pi\)
\(524\) 5.14147 + 5.14147i 0.224606 + 0.224606i
\(525\) 1.46124 + 2.99733i 0.0637738 + 0.130814i
\(526\) 15.5272 15.5272i 0.677019 0.677019i
\(527\) 34.2221i 1.49074i
\(528\) −8.07612 + 3.93722i −0.351468 + 0.171346i
\(529\) 20.6856i 0.899375i
\(530\) 3.95819i 0.171933i
\(531\) −33.0082 + 4.04106i −1.43244 + 0.175367i
\(532\) −0.190558 0.190558i −0.00826172 0.00826172i
\(533\) −49.2254 + 49.2254i −2.13219 + 2.13219i
\(534\) 5.95734 + 12.2198i 0.257799 + 0.528804i
\(535\) 8.03854 8.03854i 0.347536 0.347536i
\(536\) −6.57484 + 6.57484i −0.283990 + 0.283990i
\(537\) −5.17174 + 15.0112i −0.223177 + 0.647781i
\(538\) 0.332687 + 0.332687i 0.0143432 + 0.0143432i
\(539\) −17.0849 −0.735901
\(540\) 2.82772 + 4.35936i 0.121686 + 0.187597i
\(541\) −4.99094 + 4.99094i −0.214577 + 0.214577i −0.806209 0.591631i \(-0.798484\pi\)
0.591631 + 0.806209i \(0.298484\pi\)
\(542\) −1.31512 + 1.31512i −0.0564891 + 0.0564891i
\(543\) −21.0186 + 10.2469i −0.901994 + 0.439735i
\(544\) 5.42775 0.232713
\(545\) 16.0158 0.686042
\(546\) −8.19737 16.8146i −0.350815 0.719600i
\(547\) −24.8167 24.8167i −1.06108 1.06108i −0.998009 0.0630758i \(-0.979909\pi\)
−0.0630758 0.998009i \(-0.520091\pi\)
\(548\) 2.67319 0.114193
\(549\) 38.3602 4.69628i 1.63717 0.200432i
\(550\) −3.66800 3.66800i −0.156404 0.156404i
\(551\) 0.351901i 0.0149915i
\(552\) 1.15468 + 2.36850i 0.0491464 + 0.100810i
\(553\) −1.46517 + 1.46517i −0.0623055 + 0.0623055i
\(554\) 29.6284 1.25879
\(555\) 10.5126 + 0.696619i 0.446235 + 0.0295698i
\(556\) −10.8710 −0.461034
\(557\) −4.85816 + 4.85816i −0.205847 + 0.205847i −0.802500 0.596653i \(-0.796497\pi\)
0.596653 + 0.802500i \(0.296497\pi\)
\(558\) 11.6505 14.9012i 0.493207 0.630816i
\(559\) 57.2641i 2.42201i
\(560\) 1.36133 + 1.36133i 0.0575265 + 0.0575265i
\(561\) 46.1072 + 15.8851i 1.94665 + 0.670669i
\(562\) 23.2505 0.980762
\(563\) 18.9481 + 18.9481i 0.798568 + 0.798568i 0.982870 0.184302i \(-0.0590025\pi\)
−0.184302 + 0.982870i \(0.559002\pi\)
\(564\) −5.41428 + 2.63954i −0.227982 + 0.111144i
\(565\) 19.9709 0.840182
\(566\) −5.03767 −0.211749
\(567\) −4.17986 16.8151i −0.175538 0.706169i
\(568\) 0.876494 0.876494i 0.0367769 0.0367769i
\(569\) −8.68225 + 8.68225i −0.363979 + 0.363979i −0.865276 0.501297i \(-0.832857\pi\)
0.501297 + 0.865276i \(0.332857\pi\)
\(570\) 0.0789750 0.229228i 0.00330790 0.00960132i
\(571\) −1.59002 −0.0665404 −0.0332702 0.999446i \(-0.510592\pi\)
−0.0332702 + 0.999446i \(0.510592\pi\)
\(572\) 20.5770 + 20.5770i 0.860367 + 0.860367i
\(573\) 23.0273 + 7.93350i 0.961980 + 0.331427i
\(574\) −16.8933 + 16.8933i −0.705112 + 0.705112i
\(575\) −1.07572 + 1.07572i −0.0448608 + 0.0448608i
\(576\) 2.36338 + 1.84782i 0.0984741 + 0.0769925i
\(577\) −1.81221 + 1.81221i −0.0754435 + 0.0754435i −0.743822 0.668378i \(-0.766989\pi\)
0.668378 + 0.743822i \(0.266989\pi\)
\(578\) −8.81088 8.81088i −0.366484 0.366484i
\(579\) −11.9155 + 34.5852i −0.495190 + 1.43731i
\(580\) 2.51395i 0.104386i
\(581\) 17.6798i 0.733484i
\(582\) 4.12665 + 8.46468i 0.171055 + 0.350872i
\(583\) 20.5325i 0.850367i
\(584\) 4.89578 4.89578i 0.202589 0.202589i
\(585\) 10.3660 13.2582i 0.428582 0.548161i
\(586\) −15.9271 15.9271i −0.657942 0.657942i
\(587\) 26.2589 26.2589i 1.08382 1.08382i 0.0876694 0.996150i \(-0.472058\pi\)
0.996150 0.0876694i \(-0.0279419\pi\)
\(588\) 2.49985 + 5.12775i 0.103092 + 0.211465i
\(589\) −0.882573 −0.0363658
\(590\) −7.83820 7.83820i −0.322694 0.322694i
\(591\) 7.59549 + 15.5800i 0.312437 + 0.640877i
\(592\) 5.86944 1.59678i 0.241232 0.0656271i
\(593\) 44.3173i 1.81989i −0.414727 0.909946i \(-0.636123\pi\)
0.414727 0.909946i \(-0.363877\pi\)
\(594\) 14.6683 + 22.6135i 0.601849 + 0.927842i
\(595\) 10.4495i 0.428389i
\(596\) −9.44249 −0.386779
\(597\) −28.3660 9.77279i −1.16094 0.399974i
\(598\) 6.03466 6.03466i 0.246776 0.246776i
\(599\) 9.25641i 0.378207i 0.981957 + 0.189103i \(0.0605581\pi\)
−0.981957 + 0.189103i \(0.939442\pi\)
\(600\) −0.564190 + 1.63759i −0.0230330 + 0.0668542i
\(601\) −1.16650 −0.0475826 −0.0237913 0.999717i \(-0.507574\pi\)
−0.0237913 + 0.999717i \(0.507574\pi\)
\(602\) 19.6520i 0.800957i
\(603\) 21.9752 + 17.1814i 0.894901 + 0.699682i
\(604\) −12.4031 −0.504673
\(605\) −11.2490 11.2490i −0.457337 0.457337i
\(606\) 1.89489 5.50001i 0.0769748 0.223423i
\(607\) 15.4706 + 15.4706i 0.627934 + 0.627934i 0.947548 0.319614i \(-0.103553\pi\)
−0.319614 + 0.947548i \(0.603553\pi\)
\(608\) 0.139979i 0.00567691i
\(609\) 2.73061 7.92571i 0.110650 0.321166i
\(610\) 9.10908 + 9.10908i 0.368816 + 0.368816i
\(611\) 13.7949 + 13.7949i 0.558083 + 0.558083i
\(612\) −1.97872 16.1626i −0.0799850 0.653333i
\(613\) 2.39296i 0.0966506i 0.998832 + 0.0483253i \(0.0153884\pi\)
−0.998832 + 0.0483253i \(0.984612\pi\)
\(614\) −7.78937 7.78937i −0.314353 0.314353i
\(615\) −20.3215 7.00128i −0.819443 0.282319i
\(616\) 7.06166 + 7.06166i 0.284522 + 0.284522i
\(617\) −8.86781 −0.357005 −0.178502 0.983939i \(-0.557125\pi\)
−0.178502 + 0.983939i \(0.557125\pi\)
\(618\) 23.7325 11.5699i 0.954661 0.465410i
\(619\) 17.1208i 0.688141i 0.938944 + 0.344071i \(0.111806\pi\)
−0.938944 + 0.344071i \(0.888194\pi\)
\(620\) 6.30502 0.253216
\(621\) 6.63191 4.30182i 0.266129 0.172626i
\(622\) 25.6946i 1.03026i
\(623\) 10.6849 10.6849i 0.428080 0.428080i
\(624\) 3.16503 9.18664i 0.126703 0.367760i
\(625\) −1.00000 −0.0400000
\(626\) 4.97320i 0.198769i
\(627\) 0.409670 1.18909i 0.0163606 0.0474875i
\(628\) 7.28854i 0.290844i
\(629\) −28.6553 16.3985i −1.14256 0.653850i
\(630\) 3.55743 4.54999i 0.141731 0.181276i
\(631\) −22.6451 22.6451i −0.901487 0.901487i 0.0940780 0.995565i \(-0.470010\pi\)
−0.995565 + 0.0940780i \(0.970010\pi\)
\(632\) −1.07628 −0.0428123
\(633\) −34.4259 + 16.7831i −1.36831 + 0.667068i
\(634\) −8.25603 + 8.25603i −0.327889 + 0.327889i
\(635\) −4.31420 4.31420i −0.171204 0.171204i
\(636\) 6.16247 3.00429i 0.244358 0.119128i
\(637\) 13.0649 13.0649i 0.517650 0.517650i
\(638\) 13.0407i 0.516287i
\(639\) −2.92953 2.29046i −0.115890 0.0906094i
\(640\) 1.00000i 0.0395285i
\(641\) 12.4293i 0.490929i −0.969406 0.245465i \(-0.921059\pi\)
0.969406 0.245465i \(-0.0789405\pi\)
\(642\) −18.6164 6.41383i −0.734732 0.253134i
\(643\) −10.0677 10.0677i −0.397030 0.397030i 0.480154 0.877184i \(-0.340581\pi\)
−0.877184 + 0.480154i \(0.840581\pi\)
\(644\) 2.07099 2.07099i 0.0816084 0.0816084i
\(645\) −15.8924 + 7.74775i −0.625761 + 0.305067i
\(646\) −0.537241 + 0.537241i −0.0211375 + 0.0211375i
\(647\) 23.6939 23.6939i 0.931504 0.931504i −0.0662961 0.997800i \(-0.521118\pi\)
0.997800 + 0.0662961i \(0.0211182\pi\)
\(648\) 4.64079 7.71123i 0.182308 0.302926i
\(649\) −40.6594 40.6594i −1.59602 1.59602i
\(650\) 5.60986 0.220037
\(651\) −19.8778 6.84840i −0.779072 0.268410i
\(652\) 14.2334 14.2334i 0.557421 0.557421i
\(653\) −16.2030 + 16.2030i −0.634071 + 0.634071i −0.949087 0.315016i \(-0.897990\pi\)
0.315016 + 0.949087i \(0.397990\pi\)
\(654\) −12.1561 24.9349i −0.475341 0.975031i
\(655\) 7.27114 0.284107
\(656\) −12.4094 −0.484507
\(657\) −16.3633 12.7937i −0.638392 0.499130i
\(658\) 4.73417 + 4.73417i 0.184557 + 0.184557i
\(659\) −22.4489 −0.874484 −0.437242 0.899344i \(-0.644045\pi\)
−0.437242 + 0.899344i \(0.644045\pi\)
\(660\) −2.92664 + 8.49472i −0.113919 + 0.330656i
\(661\) 20.3735 + 20.3735i 0.792436 + 0.792436i 0.981890 0.189453i \(-0.0606716\pi\)
−0.189453 + 0.981890i \(0.560672\pi\)
\(662\) 0.858974i 0.0333850i
\(663\) −47.4057 + 23.1109i −1.84108 + 0.897554i
\(664\) 6.49361 6.49361i 0.252001 0.252001i
\(665\) −0.269489 −0.0104503
\(666\) −6.89457 16.8957i −0.267159 0.654695i
\(667\) 3.82448 0.148085
\(668\) 12.7580 12.7580i 0.493624 0.493624i
\(669\) 23.8494 11.6269i 0.922070 0.449522i
\(670\) 9.29823i 0.359222i
\(671\) 47.2519 + 47.2519i 1.82414 + 1.82414i
\(672\) 1.08618 3.15269i 0.0419004 0.121618i
\(673\) 27.9883 1.07887 0.539435 0.842027i \(-0.318638\pi\)
0.539435 + 0.842027i \(0.318638\pi\)
\(674\) 1.39584 + 1.39584i 0.0537659 + 0.0537659i
\(675\) 5.08203 + 1.08303i 0.195607 + 0.0416860i
\(676\) −18.4706 −0.710406
\(677\) 36.3628 1.39754 0.698769 0.715348i \(-0.253732\pi\)
0.698769 + 0.715348i \(0.253732\pi\)
\(678\) −15.1580 31.0925i −0.582141 1.19410i
\(679\) 7.40140 7.40140i 0.284040 0.284040i
\(680\) 3.83800 3.83800i 0.147181 0.147181i
\(681\) −31.6928 10.9190i −1.21447 0.418416i
\(682\) 32.7063 1.25239
\(683\) 31.9090 + 31.9090i 1.22097 + 1.22097i 0.967289 + 0.253677i \(0.0816399\pi\)
0.253677 + 0.967289i \(0.418360\pi\)
\(684\) −0.416826 + 0.0510303i −0.0159377 + 0.00195119i
\(685\) 1.89023 1.89023i 0.0722220 0.0722220i
\(686\) 14.0129 14.0129i 0.535016 0.535016i
\(687\) −17.7719 + 8.66403i −0.678039 + 0.330553i
\(688\) −7.21797 + 7.21797i −0.275183 + 0.275183i
\(689\) −15.7012 15.7012i −0.598169 0.598169i
\(690\) 2.49127 + 0.858304i 0.0948409 + 0.0326751i
\(691\) 35.8528i 1.36391i 0.731396 + 0.681953i \(0.238869\pi\)
−0.731396 + 0.681953i \(0.761131\pi\)
\(692\) 4.28631i 0.162941i
\(693\) 18.4536 23.6023i 0.700994 0.896579i
\(694\) 4.06939i 0.154472i
\(695\) −7.68697 + 7.68697i −0.291583 + 0.291583i
\(696\) 3.91395 1.90810i 0.148358 0.0723265i
\(697\) 47.6274 + 47.6274i 1.80402 + 1.80402i
\(698\) −3.78958 + 3.78958i −0.143438 + 0.143438i
\(699\) −23.5718 + 11.4916i −0.891568 + 0.434652i
\(700\) 1.92521 0.0727659
\(701\) −8.81865 8.81865i −0.333076 0.333076i 0.520678 0.853753i \(-0.325679\pi\)
−0.853753 + 0.520678i \(0.825679\pi\)
\(702\) −28.5095 6.07567i −1.07602 0.229312i
\(703\) −0.422910 + 0.739009i −0.0159503 + 0.0278722i
\(704\) 5.18734i 0.195505i
\(705\) −1.96204 + 5.69490i −0.0738946 + 0.214483i
\(706\) 12.4626i 0.469035i
\(707\) −6.46601 −0.243179
\(708\) −6.25398 + 18.1525i −0.235039 + 0.682212i
\(709\) 26.8621 26.8621i 1.00883 1.00883i 0.00886777 0.999961i \(-0.497177\pi\)
0.999961 0.00886777i \(-0.00282274\pi\)
\(710\) 1.23955i 0.0465195i
\(711\) 0.392366 + 3.20492i 0.0147149 + 0.120194i
\(712\) 7.84887 0.294149
\(713\) 9.59185i 0.359218i
\(714\) −16.2688 + 7.93126i −0.608844 + 0.296820i
\(715\) 29.1003 1.08829
\(716\) 6.48181 + 6.48181i 0.242237 + 0.242237i
\(717\) −13.4492 4.63360i −0.502271 0.173045i
\(718\) 7.40410 + 7.40410i 0.276319 + 0.276319i
\(719\) 32.4752i 1.21112i −0.795799 0.605561i \(-0.792949\pi\)
0.795799 0.605561i \(-0.207051\pi\)
\(720\) 2.97777 0.364556i 0.110975 0.0135862i
\(721\) −20.7514 20.7514i −0.772822 0.772822i
\(722\) −13.4212 13.4212i −0.499484 0.499484i
\(723\) −14.8621 + 43.1380i −0.552729 + 1.60432i
\(724\) 13.5004i 0.501737i
\(725\) 1.77763 + 1.77763i 0.0660196 + 0.0660196i
\(726\) −8.97541 + 26.0515i −0.333109 + 0.966863i
\(727\) 15.5520 + 15.5520i 0.576792 + 0.576792i 0.934018 0.357226i \(-0.116277\pi\)
−0.357226 + 0.934018i \(0.616277\pi\)
\(728\) −10.8001 −0.400280
\(729\) −24.6541 11.0080i −0.913114 0.407705i
\(730\) 6.92368i 0.256257i
\(731\) 55.4051 2.04923
\(732\) 7.26800 21.0957i 0.268633 0.779719i
\(733\) 20.2890i 0.749390i −0.927148 0.374695i \(-0.877747\pi\)
0.927148 0.374695i \(-0.122253\pi\)
\(734\) 11.0791 11.0791i 0.408938 0.408938i
\(735\) 5.39353 + 1.85821i 0.198943 + 0.0685410i
\(736\) 1.52130 0.0560760
\(737\) 48.2331i 1.77669i
\(738\) 4.52393 + 36.9524i 0.166528 + 1.36024i
\(739\) 16.8745i 0.620738i 0.950616 + 0.310369i \(0.100453\pi\)
−0.950616 + 0.310369i \(0.899547\pi\)
\(740\) 3.02123 5.27941i 0.111063 0.194075i
\(741\) 0.596021 + 1.22257i 0.0218954 + 0.0449123i
\(742\) −5.38838 5.38838i −0.197814 0.197814i
\(743\) 19.1398 0.702172 0.351086 0.936343i \(-0.385813\pi\)
0.351086 + 0.936343i \(0.385813\pi\)
\(744\) −4.78555 9.81623i −0.175447 0.359880i
\(745\) −6.67685 + 6.67685i −0.244621 + 0.244621i
\(746\) −2.97349 2.97349i −0.108867 0.108867i
\(747\) −21.7038 16.9692i −0.794099 0.620870i
\(748\) 19.9090 19.9090i 0.727945 0.727945i
\(749\) 21.8861i 0.799702i
\(750\) 0.759006 + 1.55689i 0.0277150 + 0.0568496i
\(751\) 3.29443i 0.120216i 0.998192 + 0.0601078i \(0.0191444\pi\)
−0.998192 + 0.0601078i \(0.980856\pi\)
\(752\) 3.47762i 0.126816i
\(753\) 6.92603 20.1031i 0.252399 0.732599i
\(754\) −9.97227 9.97227i −0.363169 0.363169i
\(755\) −8.77029 + 8.77029i −0.319183 + 0.319183i
\(756\) −9.78395 2.08506i −0.355839 0.0758330i
\(757\) −26.1797 + 26.1797i −0.951518 + 0.951518i −0.998878 0.0473602i \(-0.984919\pi\)
0.0473602 + 0.998878i \(0.484919\pi\)
\(758\) −7.65167 + 7.65167i −0.277921 + 0.277921i
\(759\) 12.9230 + 4.45231i 0.469077 + 0.161609i
\(760\) −0.0989804 0.0989804i −0.00359040 0.00359040i
\(761\) 13.0239 0.472118 0.236059 0.971739i \(-0.424144\pi\)
0.236059 + 0.971739i \(0.424144\pi\)
\(762\) −3.44223 + 9.99124i −0.124699 + 0.361944i
\(763\) −21.8027 + 21.8027i −0.789312 + 0.789312i
\(764\) 9.94316 9.94316i 0.359731 0.359731i
\(765\) −12.8278 10.0295i −0.463791 0.362617i
\(766\) −4.63822 −0.167586
\(767\) 62.1847 2.24536
\(768\) 1.55689 0.759006i 0.0561795 0.0273883i
\(769\) −22.4249 22.4249i −0.808662 0.808662i 0.175769 0.984431i \(-0.443759\pi\)
−0.984431 + 0.175769i \(0.943759\pi\)
\(770\) 9.98669 0.359895
\(771\) 14.9883 + 5.16385i 0.539791 + 0.185971i
\(772\) 14.9338 + 14.9338i 0.537480 + 0.537480i
\(773\) 20.2597i 0.728691i −0.931264 0.364345i \(-0.881293\pi\)
0.931264 0.364345i \(-0.118707\pi\)
\(774\) 24.1248 + 18.8621i 0.867148 + 0.677984i
\(775\) 4.45832 4.45832i 0.160148 0.160148i
\(776\) 5.43691 0.195174
\(777\) −15.2594 + 13.3627i −0.547428 + 0.479386i
\(778\) 24.8741 0.891778
\(779\)