Properties

Label 1110.2.u.e.191.5
Level $1110$
Weight $2$
Character 1110.191
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 191.5
Character \(\chi\) \(=\) 1110.191
Dual form 1110.2.u.e.401.5

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.707107 - 0.707107i) q^{2} +(-1.08352 - 1.35129i) q^{3} +1.00000i q^{4} +(-0.707107 + 0.707107i) q^{5} +(-0.189341 + 1.72167i) q^{6} -3.77650 q^{7} +(0.707107 - 0.707107i) q^{8} +(-0.651967 + 2.92830i) q^{9} +O(q^{10})\) \(q+(-0.707107 - 0.707107i) q^{2} +(-1.08352 - 1.35129i) q^{3} +1.00000i q^{4} +(-0.707107 + 0.707107i) q^{5} +(-0.189341 + 1.72167i) q^{6} -3.77650 q^{7} +(0.707107 - 0.707107i) q^{8} +(-0.651967 + 2.92830i) q^{9} +1.00000 q^{10} +1.81549 q^{11} +(1.35129 - 1.08352i) q^{12} +(-3.90798 - 3.90798i) q^{13} +(2.67039 + 2.67039i) q^{14} +(1.72167 + 0.189341i) q^{15} -1.00000 q^{16} +(-1.04463 + 1.04463i) q^{17} +(2.53163 - 1.60961i) q^{18} +(-1.01091 - 1.01091i) q^{19} +(-0.707107 - 0.707107i) q^{20} +(4.09191 + 5.10314i) q^{21} +(-1.28375 - 1.28375i) q^{22} +(-5.79126 + 5.79126i) q^{23} +(-1.72167 - 0.189341i) q^{24} -1.00000i q^{25} +5.52672i q^{26} +(4.66340 - 2.29188i) q^{27} -3.77650i q^{28} +(3.80924 + 3.80924i) q^{29} +(-1.08352 - 1.35129i) q^{30} +(4.46840 - 4.46840i) q^{31} +(0.707107 + 0.707107i) q^{32} +(-1.96712 - 2.45325i) q^{33} +1.47733 q^{34} +(2.67039 - 2.67039i) q^{35} +(-2.92830 - 0.651967i) q^{36} +(5.83886 + 1.70519i) q^{37} +1.42964i q^{38} +(-1.04644 + 9.51519i) q^{39} +1.00000i q^{40} +9.74155 q^{41} +(0.715047 - 6.50188i) q^{42} +(6.17939 + 6.17939i) q^{43} +1.81549i q^{44} +(-1.60961 - 2.53163i) q^{45} +8.19007 q^{46} -7.59431i q^{47} +(1.08352 + 1.35129i) q^{48} +7.26192 q^{49} +(-0.707107 + 0.707107i) q^{50} +(2.54347 + 0.279720i) q^{51} +(3.90798 - 3.90798i) q^{52} +1.46832i q^{53} +(-4.91812 - 1.67692i) q^{54} +(-1.28375 + 1.28375i) q^{55} +(-2.67039 + 2.67039i) q^{56} +(-0.270690 + 2.46137i) q^{57} -5.38709i q^{58} +(-3.27282 + 3.27282i) q^{59} +(-0.189341 + 1.72167i) q^{60} +(-0.251587 + 0.251587i) q^{61} -6.31927 q^{62} +(2.46215 - 11.0587i) q^{63} -1.00000i q^{64} +5.52672 q^{65} +(-0.343748 + 3.12568i) q^{66} +1.79916i q^{67} +(-1.04463 - 1.04463i) q^{68} +(14.1006 + 1.55072i) q^{69} -3.77650 q^{70} -14.5030i q^{71} +(1.60961 + 2.53163i) q^{72} +7.13983i q^{73} +(-2.92295 - 5.33445i) q^{74} +(-1.35129 + 1.08352i) q^{75} +(1.01091 - 1.01091i) q^{76} -6.85620 q^{77} +(7.46820 - 5.98831i) q^{78} +(-8.05198 - 8.05198i) q^{79} +(0.707107 - 0.707107i) q^{80} +(-8.14988 - 3.81831i) q^{81} +(-6.88832 - 6.88832i) q^{82} -7.15345i q^{83} +(-5.10314 + 4.09191i) q^{84} -1.47733i q^{85} -8.73898i q^{86} +(1.02000 - 9.27479i) q^{87} +(1.28375 - 1.28375i) q^{88} +(7.47158 + 7.47158i) q^{89} +(-0.651967 + 2.92830i) q^{90} +(14.7585 + 14.7585i) q^{91} +(-5.79126 - 5.79126i) q^{92} +(-10.8797 - 1.19650i) q^{93} +(-5.36999 + 5.36999i) q^{94} +1.42964 q^{95} +(0.189341 - 1.72167i) q^{96} +(3.22614 + 3.22614i) q^{97} +(-5.13495 - 5.13495i) q^{98} +(-1.18364 + 5.31630i) 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 \(\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times\).

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

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
\(3\) −1.08352 1.35129i −0.625571 0.780167i
\(4\) 1.00000i 0.500000i
\(5\) −0.707107 + 0.707107i −0.316228 + 0.316228i
\(6\) −0.189341 + 1.72167i −0.0772983 + 0.702869i
\(7\) −3.77650 −1.42738 −0.713691 0.700461i \(-0.752978\pi\)
−0.713691 + 0.700461i \(0.752978\pi\)
\(8\) 0.707107 0.707107i 0.250000 0.250000i
\(9\) −0.651967 + 2.92830i −0.217322 + 0.976100i
\(10\) 1.00000 0.316228
\(11\) 1.81549 0.547391 0.273696 0.961816i \(-0.411754\pi\)
0.273696 + 0.961816i \(0.411754\pi\)
\(12\) 1.35129 1.08352i 0.390084 0.312785i
\(13\) −3.90798 3.90798i −1.08388 1.08388i −0.996144 0.0877350i \(-0.972037\pi\)
−0.0877350 0.996144i \(-0.527963\pi\)
\(14\) 2.67039 + 2.67039i 0.713691 + 0.713691i
\(15\) 1.72167 + 0.189341i 0.444533 + 0.0488878i
\(16\) −1.00000 −0.250000
\(17\) −1.04463 + 1.04463i −0.253360 + 0.253360i −0.822347 0.568987i \(-0.807336\pi\)
0.568987 + 0.822347i \(0.307336\pi\)
\(18\) 2.53163 1.60961i 0.596711 0.379389i
\(19\) −1.01091 1.01091i −0.231918 0.231918i 0.581575 0.813493i \(-0.302437\pi\)
−0.813493 + 0.581575i \(0.802437\pi\)
\(20\) −0.707107 0.707107i −0.158114 0.158114i
\(21\) 4.09191 + 5.10314i 0.892928 + 1.11360i
\(22\) −1.28375 1.28375i −0.273696 0.273696i
\(23\) −5.79126 + 5.79126i −1.20756 + 1.20756i −0.235746 + 0.971815i \(0.575753\pi\)
−0.971815 + 0.235746i \(0.924247\pi\)
\(24\) −1.72167 0.189341i −0.351435 0.0386492i
\(25\) 1.00000i 0.200000i
\(26\) 5.52672i 1.08388i
\(27\) 4.66340 2.29188i 0.897472 0.441072i
\(28\) 3.77650i 0.713691i
\(29\) 3.80924 + 3.80924i 0.707359 + 0.707359i 0.965979 0.258620i \(-0.0832678\pi\)
−0.258620 + 0.965979i \(0.583268\pi\)
\(30\) −1.08352 1.35129i −0.197823 0.246711i
\(31\) 4.46840 4.46840i 0.802548 0.802548i −0.180945 0.983493i \(-0.557916\pi\)
0.983493 + 0.180945i \(0.0579156\pi\)
\(32\) 0.707107 + 0.707107i 0.125000 + 0.125000i
\(33\) −1.96712 2.45325i −0.342432 0.427057i
\(34\) 1.47733 0.253360
\(35\) 2.67039 2.67039i 0.451378 0.451378i
\(36\) −2.92830 0.651967i −0.488050 0.108661i
\(37\) 5.83886 + 1.70519i 0.959903 + 0.280332i
\(38\) 1.42964i 0.231918i
\(39\) −1.04644 + 9.51519i −0.167564 + 1.52365i
\(40\) 1.00000i 0.158114i
\(41\) 9.74155 1.52138 0.760688 0.649118i \(-0.224862\pi\)
0.760688 + 0.649118i \(0.224862\pi\)
\(42\) 0.715047 6.50188i 0.110334 1.00326i
\(43\) 6.17939 + 6.17939i 0.942348 + 0.942348i 0.998426 0.0560783i \(-0.0178596\pi\)
−0.0560783 + 0.998426i \(0.517860\pi\)
\(44\) 1.81549i 0.273696i
\(45\) −1.60961 2.53163i −0.239946 0.377393i
\(46\) 8.19007 1.20756
\(47\) 7.59431i 1.10774i −0.832602 0.553872i \(-0.813150\pi\)
0.832602 0.553872i \(-0.186850\pi\)
\(48\) 1.08352 + 1.35129i 0.156393 + 0.195042i
\(49\) 7.26192 1.03742
\(50\) −0.707107 + 0.707107i −0.100000 + 0.100000i
\(51\) 2.54347 + 0.279720i 0.356157 + 0.0391686i
\(52\) 3.90798 3.90798i 0.541939 0.541939i
\(53\) 1.46832i 0.201689i 0.994902 + 0.100844i \(0.0321544\pi\)
−0.994902 + 0.100844i \(0.967846\pi\)
\(54\) −4.91812 1.67692i −0.669272 0.228200i
\(55\) −1.28375 + 1.28375i −0.173100 + 0.173100i
\(56\) −2.67039 + 2.67039i −0.356845 + 0.356845i
\(57\) −0.270690 + 2.46137i −0.0358537 + 0.326016i
\(58\) 5.38709i 0.707359i
\(59\) −3.27282 + 3.27282i −0.426084 + 0.426084i −0.887292 0.461208i \(-0.847416\pi\)
0.461208 + 0.887292i \(0.347416\pi\)
\(60\) −0.189341 + 1.72167i −0.0244439 + 0.222267i
\(61\) −0.251587 + 0.251587i −0.0322125 + 0.0322125i −0.723030 0.690817i \(-0.757251\pi\)
0.690817 + 0.723030i \(0.257251\pi\)
\(62\) −6.31927 −0.802548
\(63\) 2.46215 11.0587i 0.310202 1.39327i
\(64\) 1.00000i 0.125000i
\(65\) 5.52672 0.685505
\(66\) −0.343748 + 3.12568i −0.0423124 + 0.384744i
\(67\) 1.79916i 0.219802i 0.993943 + 0.109901i \(0.0350534\pi\)
−0.993943 + 0.109901i \(0.964947\pi\)
\(68\) −1.04463 1.04463i −0.126680 0.126680i
\(69\) 14.1006 + 1.55072i 1.69751 + 0.186685i
\(70\) −3.77650 −0.451378
\(71\) 14.5030i 1.72119i −0.509292 0.860594i \(-0.670093\pi\)
0.509292 0.860594i \(-0.329907\pi\)
\(72\) 1.60961 + 2.53163i 0.189694 + 0.298356i
\(73\) 7.13983i 0.835653i 0.908527 + 0.417827i \(0.137208\pi\)
−0.908527 + 0.417827i \(0.862792\pi\)
\(74\) −2.92295 5.33445i −0.339786 0.620118i
\(75\) −1.35129 + 1.08352i −0.156033 + 0.125114i
\(76\) 1.01091 1.01091i 0.115959 0.115959i
\(77\) −6.85620 −0.781336
\(78\) 7.46820 5.98831i 0.845607 0.678043i
\(79\) −8.05198 8.05198i −0.905918 0.905918i 0.0900218 0.995940i \(-0.471306\pi\)
−0.995940 + 0.0900218i \(0.971306\pi\)
\(80\) 0.707107 0.707107i 0.0790569 0.0790569i
\(81\) −8.14988 3.81831i −0.905542 0.424257i
\(82\) −6.88832 6.88832i −0.760688 0.760688i
\(83\) 7.15345i 0.785193i −0.919711 0.392597i \(-0.871577\pi\)
0.919711 0.392597i \(-0.128423\pi\)
\(84\) −5.10314 + 4.09191i −0.556798 + 0.446464i
\(85\) 1.47733i 0.160239i
\(86\) 8.73898i 0.942348i
\(87\) 1.02000 9.27479i 0.109355 0.994361i
\(88\) 1.28375 1.28375i 0.136848 0.136848i
\(89\) 7.47158 + 7.47158i 0.791985 + 0.791985i 0.981817 0.189831i \(-0.0607941\pi\)
−0.189831 + 0.981817i \(0.560794\pi\)
\(90\) −0.651967 + 2.92830i −0.0687234 + 0.308670i
\(91\) 14.7585 + 14.7585i 1.54711 + 1.54711i
\(92\) −5.79126 5.79126i −0.603780 0.603780i
\(93\) −10.8797 1.19650i −1.12817 0.124071i
\(94\) −5.36999 + 5.36999i −0.553872 + 0.553872i
\(95\) 1.42964 0.146678
\(96\) 0.189341 1.72167i 0.0193246 0.175717i
\(97\) 3.22614 + 3.22614i 0.327565 + 0.327565i 0.851660 0.524095i \(-0.175596\pi\)
−0.524095 + 0.851660i \(0.675596\pi\)
\(98\) −5.13495 5.13495i −0.518709 0.518709i
\(99\) −1.18364 + 5.31630i −0.118960 + 0.534309i
\(100\) 1.00000 0.100000
\(101\) −1.91970 −0.191017 −0.0955085 0.995429i \(-0.530448\pi\)
−0.0955085 + 0.995429i \(0.530448\pi\)
\(102\) −1.60072 1.99630i −0.158494 0.197663i
\(103\) 11.1661 11.1661i 1.10022 1.10022i 0.105842 0.994383i \(-0.466246\pi\)
0.994383 0.105842i \(-0.0337537\pi\)
\(104\) −5.52672 −0.541939
\(105\) −6.50188 0.715047i −0.634519 0.0697815i
\(106\) 1.03826 1.03826i 0.100844 0.100844i
\(107\) 16.4971i 1.59484i 0.603428 + 0.797418i \(0.293801\pi\)
−0.603428 + 0.797418i \(0.706199\pi\)
\(108\) 2.29188 + 4.66340i 0.220536 + 0.448736i
\(109\) 5.92062 + 5.92062i 0.567093 + 0.567093i 0.931313 0.364220i \(-0.118664\pi\)
−0.364220 + 0.931313i \(0.618664\pi\)
\(110\) 1.81549 0.173100
\(111\) −4.02232 9.73761i −0.381782 0.924253i
\(112\) 3.77650 0.356845
\(113\) 7.61785 + 7.61785i 0.716627 + 0.716627i 0.967913 0.251286i \(-0.0808534\pi\)
−0.251286 + 0.967913i \(0.580853\pi\)
\(114\) 1.93185 1.54904i 0.180935 0.145081i
\(115\) 8.19007i 0.763728i
\(116\) −3.80924 + 3.80924i −0.353679 + 0.353679i
\(117\) 13.9916 8.89586i 1.29353 0.822423i
\(118\) 4.62846 0.426084
\(119\) 3.94504 3.94504i 0.361641 0.361641i
\(120\) 1.35129 1.08352i 0.123355 0.0989114i
\(121\) −7.70399 −0.700363
\(122\) 0.355798 0.0322125
\(123\) −10.5552 13.1637i −0.951728 1.18693i
\(124\) 4.46840 + 4.46840i 0.401274 + 0.401274i
\(125\) 0.707107 + 0.707107i 0.0632456 + 0.0632456i
\(126\) −9.56069 + 6.07869i −0.851734 + 0.541532i
\(127\) 17.1125 1.51849 0.759245 0.650805i \(-0.225568\pi\)
0.759245 + 0.650805i \(0.225568\pi\)
\(128\) −0.707107 + 0.707107i −0.0625000 + 0.0625000i
\(129\) 1.65465 15.0456i 0.145684 1.32469i
\(130\) −3.90798 3.90798i −0.342753 0.342753i
\(131\) −3.38184 3.38184i −0.295473 0.295473i 0.543765 0.839238i \(-0.316998\pi\)
−0.839238 + 0.543765i \(0.816998\pi\)
\(132\) 2.45325 1.96712i 0.213528 0.171216i
\(133\) 3.81768 + 3.81768i 0.331035 + 0.331035i
\(134\) 1.27220 1.27220i 0.109901 0.109901i
\(135\) −1.67692 + 4.91812i −0.144326 + 0.423285i
\(136\) 1.47733i 0.126680i
\(137\) 4.14104i 0.353793i 0.984229 + 0.176896i \(0.0566057\pi\)
−0.984229 + 0.176896i \(0.943394\pi\)
\(138\) −8.87411 11.0672i −0.755414 0.942099i
\(139\) 1.38210i 0.117229i 0.998281 + 0.0586143i \(0.0186682\pi\)
−0.998281 + 0.0586143i \(0.981332\pi\)
\(140\) 2.67039 + 2.67039i 0.225689 + 0.225689i
\(141\) −10.2621 + 8.22859i −0.864226 + 0.692972i
\(142\) −10.2552 + 10.2552i −0.860594 + 0.860594i
\(143\) −7.09491 7.09491i −0.593306 0.593306i
\(144\) 0.651967 2.92830i 0.0543306 0.244025i
\(145\) −5.38709 −0.447373
\(146\) 5.04862 5.04862i 0.417827 0.417827i
\(147\) −7.86844 9.81296i −0.648978 0.809359i
\(148\) −1.70519 + 5.83886i −0.140166 + 0.479952i
\(149\) 10.6466i 0.872206i 0.899897 + 0.436103i \(0.143642\pi\)
−0.899897 + 0.436103i \(0.856358\pi\)
\(150\) 1.72167 + 0.189341i 0.140574 + 0.0154597i
\(151\) 5.50361i 0.447877i −0.974603 0.223939i \(-0.928108\pi\)
0.974603 0.223939i \(-0.0718915\pi\)
\(152\) −1.42964 −0.115959
\(153\) −2.37792 3.74005i −0.192244 0.302365i
\(154\) 4.84806 + 4.84806i 0.390668 + 0.390668i
\(155\) 6.31927i 0.507576i
\(156\) −9.51519 1.04644i −0.761825 0.0837820i
\(157\) −12.5462 −1.00130 −0.500649 0.865650i \(-0.666905\pi\)
−0.500649 + 0.865650i \(0.666905\pi\)
\(158\) 11.3872i 0.905918i
\(159\) 1.98412 1.59095i 0.157351 0.126171i
\(160\) −1.00000 −0.0790569
\(161\) 21.8707 21.8707i 1.72365 1.72365i
\(162\) 3.06288 + 8.46279i 0.240643 + 0.664899i
\(163\) 15.7971 15.7971i 1.23732 1.23732i 0.276233 0.961091i \(-0.410914\pi\)
0.961091 0.276233i \(-0.0890863\pi\)
\(164\) 9.74155i 0.760688i
\(165\) 3.12568 + 0.343748i 0.243334 + 0.0267607i
\(166\) −5.05825 + 5.05825i −0.392597 + 0.392597i
\(167\) 1.29474 1.29474i 0.100190 0.100190i −0.655235 0.755425i \(-0.727430\pi\)
0.755425 + 0.655235i \(0.227430\pi\)
\(168\) 6.50188 + 0.715047i 0.501631 + 0.0551671i
\(169\) 17.5446i 1.34959i
\(170\) −1.04463 + 1.04463i −0.0801194 + 0.0801194i
\(171\) 3.61932 2.30116i 0.276776 0.175974i
\(172\) −6.17939 + 6.17939i −0.471174 + 0.471174i
\(173\) 2.17732 0.165538 0.0827691 0.996569i \(-0.473624\pi\)
0.0827691 + 0.996569i \(0.473624\pi\)
\(174\) −7.27951 + 5.83702i −0.551858 + 0.442503i
\(175\) 3.77650i 0.285476i
\(176\) −1.81549 −0.136848
\(177\) 7.96869 + 0.876360i 0.598963 + 0.0658712i
\(178\) 10.5664i 0.791985i
\(179\) 1.96418 + 1.96418i 0.146810 + 0.146810i 0.776691 0.629881i \(-0.216897\pi\)
−0.629881 + 0.776691i \(0.716897\pi\)
\(180\) 2.53163 1.60961i 0.188697 0.119973i
\(181\) 21.1962 1.57550 0.787749 0.615997i \(-0.211247\pi\)
0.787749 + 0.615997i \(0.211247\pi\)
\(182\) 20.8716i 1.54711i
\(183\) 0.612567 + 0.0673674i 0.0452823 + 0.00497994i
\(184\) 8.19007i 0.603780i
\(185\) −5.33445 + 2.92295i −0.392197 + 0.214899i
\(186\) 6.84706 + 8.53917i 0.502051 + 0.626122i
\(187\) −1.89651 + 1.89651i −0.138687 + 0.138687i
\(188\) 7.59431 0.553872
\(189\) −17.6113 + 8.65526i −1.28103 + 0.629577i
\(190\) −1.01091 1.01091i −0.0733389 0.0733389i
\(191\) −17.7208 + 17.7208i −1.28223 + 1.28223i −0.342832 + 0.939397i \(0.611386\pi\)
−0.939397 + 0.342832i \(0.888614\pi\)
\(192\) −1.35129 + 1.08352i −0.0975209 + 0.0781963i
\(193\) 13.8252 + 13.8252i 0.995162 + 0.995162i 0.999988 0.00482599i \(-0.00153616\pi\)
−0.00482599 + 0.999988i \(0.501536\pi\)
\(194\) 4.56246i 0.327565i
\(195\) −5.98831 7.46820i −0.428832 0.534809i
\(196\) 7.26192i 0.518709i
\(197\) 14.5766i 1.03854i 0.854610 + 0.519271i \(0.173796\pi\)
−0.854610 + 0.519271i \(0.826204\pi\)
\(198\) 4.59615 2.92223i 0.326635 0.207674i
\(199\) −5.37468 + 5.37468i −0.381001 + 0.381001i −0.871463 0.490462i \(-0.836828\pi\)
0.490462 + 0.871463i \(0.336828\pi\)
\(200\) −0.707107 0.707107i −0.0500000 0.0500000i
\(201\) 2.43118 1.94942i 0.171482 0.137502i
\(202\) 1.35743 + 1.35743i 0.0955085 + 0.0955085i
\(203\) −14.3856 14.3856i −1.00967 1.00967i
\(204\) −0.279720 + 2.54347i −0.0195843 + 0.178079i
\(205\) −6.88832 + 6.88832i −0.481101 + 0.481101i
\(206\) −15.7912 −1.10022
\(207\) −13.1828 20.7342i −0.916270 1.44113i
\(208\) 3.90798 + 3.90798i 0.270970 + 0.270970i
\(209\) −1.83529 1.83529i −0.126950 0.126950i
\(210\) 4.09191 + 5.10314i 0.282369 + 0.352150i
\(211\) −9.97747 −0.686877 −0.343439 0.939175i \(-0.611592\pi\)
−0.343439 + 0.939175i \(0.611592\pi\)
\(212\) −1.46832 −0.100844
\(213\) −19.5977 + 15.7143i −1.34281 + 1.07672i
\(214\) 11.6652 11.6652i 0.797418 0.797418i
\(215\) −8.73898 −0.595993
\(216\) 1.67692 4.91812i 0.114100 0.334636i
\(217\) −16.8749 + 16.8749i −1.14554 + 1.14554i
\(218\) 8.37303i 0.567093i
\(219\) 9.64797 7.73615i 0.651950 0.522760i
\(220\) −1.28375 1.28375i −0.0865502 0.0865502i
\(221\) 8.16478 0.549222
\(222\) −4.04132 + 9.72974i −0.271236 + 0.653017i
\(223\) 15.2765 1.02299 0.511493 0.859287i \(-0.329092\pi\)
0.511493 + 0.859287i \(0.329092\pi\)
\(224\) −2.67039 2.67039i −0.178423 0.178423i
\(225\) 2.92830 + 0.651967i 0.195220 + 0.0434645i
\(226\) 10.7733i 0.716627i
\(227\) 0.894036 0.894036i 0.0593392 0.0593392i −0.676814 0.736154i \(-0.736640\pi\)
0.736154 + 0.676814i \(0.236640\pi\)
\(228\) −2.46137 0.270690i −0.163008 0.0179269i
\(229\) −22.6190 −1.49471 −0.747354 0.664426i \(-0.768676\pi\)
−0.747354 + 0.664426i \(0.768676\pi\)
\(230\) −5.79126 + 5.79126i −0.381864 + 0.381864i
\(231\) 7.42883 + 9.26471i 0.488781 + 0.609573i
\(232\) 5.38709 0.353679
\(233\) −2.55770 −0.167561 −0.0837804 0.996484i \(-0.526699\pi\)
−0.0837804 + 0.996484i \(0.526699\pi\)
\(234\) −16.1839 3.60324i −1.05797 0.235551i
\(235\) 5.36999 + 5.36999i 0.350299 + 0.350299i
\(236\) −3.27282 3.27282i −0.213042 0.213042i
\(237\) −2.15607 + 19.6050i −0.140052 + 1.27348i
\(238\) −5.57912 −0.361641
\(239\) −20.5707 + 20.5707i −1.33061 + 1.33061i −0.425785 + 0.904825i \(0.640002\pi\)
−0.904825 + 0.425785i \(0.859998\pi\)
\(240\) −1.72167 0.189341i −0.111133 0.0122219i
\(241\) 4.22260 + 4.22260i 0.272001 + 0.272001i 0.829905 0.557904i \(-0.188394\pi\)
−0.557904 + 0.829905i \(0.688394\pi\)
\(242\) 5.44754 + 5.44754i 0.350181 + 0.350181i
\(243\) 3.67091 + 15.1501i 0.235489 + 0.971877i
\(244\) −0.251587 0.251587i −0.0161062 0.0161062i
\(245\) −5.13495 + 5.13495i −0.328060 + 0.328060i
\(246\) −1.84448 + 16.7717i −0.117600 + 1.06933i
\(247\) 7.90121i 0.502742i
\(248\) 6.31927i 0.401274i
\(249\) −9.66638 + 7.75091i −0.612582 + 0.491194i
\(250\) 1.00000i 0.0632456i
\(251\) 16.0961 + 16.0961i 1.01597 + 1.01597i 0.999870 + 0.0161034i \(0.00512610\pi\)
0.0161034 + 0.999870i \(0.494874\pi\)
\(252\) 11.0587 + 2.46215i 0.696633 + 0.155101i
\(253\) −10.5140 + 10.5140i −0.661008 + 0.661008i
\(254\) −12.1004 12.1004i −0.759245 0.759245i
\(255\) −1.99630 + 1.60072i −0.125013 + 0.100241i
\(256\) 1.00000 0.0625000
\(257\) 1.47800 1.47800i 0.0921953 0.0921953i −0.659505 0.751700i \(-0.729234\pi\)
0.751700 + 0.659505i \(0.229234\pi\)
\(258\) −11.8089 + 9.46886i −0.735189 + 0.589505i
\(259\) −22.0504 6.43965i −1.37015 0.400140i
\(260\) 5.52672i 0.342753i
\(261\) −13.6381 + 8.67111i −0.844178 + 0.536728i
\(262\) 4.78265i 0.295473i
\(263\) 10.6468 0.656507 0.328253 0.944590i \(-0.393540\pi\)
0.328253 + 0.944590i \(0.393540\pi\)
\(264\) −3.12568 0.343748i −0.192372 0.0211562i
\(265\) −1.03826 1.03826i −0.0637796 0.0637796i
\(266\) 5.39902i 0.331035i
\(267\) 2.00066 18.1919i 0.122438 1.11332i
\(268\) −1.79916 −0.109901
\(269\) 5.61239i 0.342194i 0.985254 + 0.171097i \(0.0547311\pi\)
−0.985254 + 0.171097i \(0.945269\pi\)
\(270\) 4.66340 2.29188i 0.283806 0.139479i
\(271\) 21.9439 1.33300 0.666499 0.745506i \(-0.267792\pi\)
0.666499 + 0.745506i \(0.267792\pi\)
\(272\) 1.04463 1.04463i 0.0633399 0.0633399i
\(273\) 3.95187 35.9341i 0.239178 2.17483i
\(274\) 2.92815 2.92815i 0.176896 0.176896i
\(275\) 1.81549i 0.109478i
\(276\) −1.55072 + 14.1006i −0.0933424 + 0.848757i
\(277\) 9.61698 9.61698i 0.577829 0.577829i −0.356476 0.934305i \(-0.616022\pi\)
0.934305 + 0.356476i \(0.116022\pi\)
\(278\) 0.977295 0.977295i 0.0586143 0.0586143i
\(279\) 10.1716 + 15.9981i 0.608956 + 0.957779i
\(280\) 3.77650i 0.225689i
\(281\) −0.242604 + 0.242604i −0.0144726 + 0.0144726i −0.714306 0.699833i \(-0.753258\pi\)
0.699833 + 0.714306i \(0.253258\pi\)
\(282\) 13.0749 + 1.43792i 0.778599 + 0.0856268i
\(283\) −16.6943 + 16.6943i −0.992374 + 0.992374i −0.999971 0.00759709i \(-0.997582\pi\)
0.00759709 + 0.999971i \(0.497582\pi\)
\(284\) 14.5030 0.860594
\(285\) −1.54904 1.93185i −0.0917573 0.114433i
\(286\) 10.0337i 0.593306i
\(287\) −36.7889 −2.17158
\(288\) −2.53163 + 1.60961i −0.149178 + 0.0948472i
\(289\) 14.8175i 0.871618i
\(290\) 3.80924 + 3.80924i 0.223687 + 0.223687i
\(291\) 0.863862 7.85505i 0.0506405 0.460471i
\(292\) −7.13983 −0.417827
\(293\) 26.8829i 1.57051i −0.619170 0.785257i \(-0.712531\pi\)
0.619170 0.785257i \(-0.287469\pi\)
\(294\) −1.37498 + 12.5026i −0.0801906 + 0.729169i
\(295\) 4.62846i 0.269479i
\(296\) 5.33445 2.92295i 0.310059 0.169893i
\(297\) 8.46636 4.16088i 0.491268 0.241439i
\(298\) 7.52830 7.52830i 0.436103 0.436103i
\(299\) 45.2642 2.61770
\(300\) −1.08352 1.35129i −0.0625571 0.0780167i
\(301\) −23.3364 23.3364i −1.34509 1.34509i
\(302\) −3.89164 + 3.89164i −0.223939 + 0.223939i
\(303\) 2.08003 + 2.59407i 0.119495 + 0.149025i
\(304\) 1.01091 + 1.01091i 0.0579795 + 0.0579795i
\(305\) 0.355798i 0.0203729i
\(306\) −0.963170 + 4.32606i −0.0550608 + 0.247304i
\(307\) 26.7254i 1.52530i 0.646812 + 0.762649i \(0.276102\pi\)
−0.646812 + 0.762649i \(0.723898\pi\)
\(308\) 6.85620i 0.390668i
\(309\) −27.1872 2.98993i −1.54663 0.170091i
\(310\) 4.46840 4.46840i 0.253788 0.253788i
\(311\) −3.11089 3.11089i −0.176403 0.176403i 0.613383 0.789786i \(-0.289808\pi\)
−0.789786 + 0.613383i \(0.789808\pi\)
\(312\) 5.98831 + 7.46820i 0.339021 + 0.422803i
\(313\) 1.42025 + 1.42025i 0.0802770 + 0.0802770i 0.746105 0.665828i \(-0.231922\pi\)
−0.665828 + 0.746105i \(0.731922\pi\)
\(314\) 8.87153 + 8.87153i 0.500649 + 0.500649i
\(315\) 6.07869 + 9.56069i 0.342495 + 0.538684i
\(316\) 8.05198 8.05198i 0.452959 0.452959i
\(317\) −1.15291 −0.0647537 −0.0323768 0.999476i \(-0.510308\pi\)
−0.0323768 + 0.999476i \(0.510308\pi\)
\(318\) −2.52796 0.278013i −0.141761 0.0155902i
\(319\) 6.91565 + 6.91565i 0.387202 + 0.387202i
\(320\) 0.707107 + 0.707107i 0.0395285 + 0.0395285i
\(321\) 22.2924 17.8749i 1.24424 0.997682i
\(322\) −30.9298 −1.72365
\(323\) 2.11204 0.117517
\(324\) 3.81831 8.14988i 0.212128 0.452771i
\(325\) −3.90798 + 3.90798i −0.216776 + 0.216776i
\(326\) −22.3405 −1.23732
\(327\) 1.58536 14.4156i 0.0876707 0.797184i
\(328\) 6.88832 6.88832i 0.380344 0.380344i
\(329\) 28.6799i 1.58117i
\(330\) −1.96712 2.45325i −0.108287 0.135047i
\(331\) −20.7988 20.7988i −1.14321 1.14321i −0.987860 0.155348i \(-0.950350\pi\)
−0.155348 0.987860i \(-0.549650\pi\)
\(332\) 7.15345 0.392597
\(333\) −8.80006 + 15.9862i −0.482240 + 0.876039i
\(334\) −1.83104 −0.100190
\(335\) −1.27220 1.27220i −0.0695075 0.0695075i
\(336\) −4.09191 5.10314i −0.223232 0.278399i
\(337\) 30.6964i 1.67214i −0.548625 0.836069i \(-0.684848\pi\)
0.548625 0.836069i \(-0.315152\pi\)
\(338\) 12.4059 12.4059i 0.674793 0.674793i
\(339\) 2.03983 18.5480i 0.110788 1.00739i
\(340\) 1.47733 0.0801194
\(341\) 8.11234 8.11234i 0.439308 0.439308i
\(342\) −4.18641 0.932077i −0.226375 0.0504010i
\(343\) −0.989146 −0.0534088
\(344\) 8.73898 0.471174
\(345\) −11.0672 + 8.87411i −0.595836 + 0.477766i
\(346\) −1.53960 1.53960i −0.0827691 0.0827691i
\(347\) −9.91190 9.91190i −0.532099 0.532099i 0.389098 0.921196i \(-0.372787\pi\)
−0.921196 + 0.389098i \(0.872787\pi\)
\(348\) 9.27479 + 1.02000i 0.497181 + 0.0546777i
\(349\) −2.62293 −0.140402 −0.0702011 0.997533i \(-0.522364\pi\)
−0.0702011 + 0.997533i \(0.522364\pi\)
\(350\) 2.67039 2.67039i 0.142738 0.142738i
\(351\) −27.1811 9.26788i −1.45082 0.494683i
\(352\) 1.28375 + 1.28375i 0.0684239 + 0.0684239i
\(353\) 22.8322 + 22.8322i 1.21523 + 1.21523i 0.969282 + 0.245950i \(0.0791000\pi\)
0.245950 + 0.969282i \(0.420900\pi\)
\(354\) −5.01503 6.25439i −0.266546 0.332417i
\(355\) 10.2552 + 10.2552i 0.544287 + 0.544287i
\(356\) −7.47158 + 7.47158i −0.395993 + 0.395993i
\(357\) −9.60541 1.05636i −0.508372 0.0559085i
\(358\) 2.77777i 0.146810i
\(359\) 6.29555i 0.332266i −0.986103 0.166133i \(-0.946872\pi\)
0.986103 0.166133i \(-0.0531282\pi\)
\(360\) −2.92830 0.651967i −0.154335 0.0343617i
\(361\) 16.9561i 0.892428i
\(362\) −14.9879 14.9879i −0.787749 0.787749i
\(363\) 8.34743 + 10.4103i 0.438126 + 0.546400i
\(364\) −14.7585 + 14.7585i −0.773554 + 0.773554i
\(365\) −5.04862 5.04862i −0.264257 0.264257i
\(366\) −0.385515 0.480787i −0.0201512 0.0251311i
\(367\) 31.6625 1.65277 0.826386 0.563105i \(-0.190393\pi\)
0.826386 + 0.563105i \(0.190393\pi\)
\(368\) 5.79126 5.79126i 0.301890 0.301890i
\(369\) −6.35118 + 28.5262i −0.330629 + 1.48501i
\(370\) 5.83886 + 1.70519i 0.303548 + 0.0886487i
\(371\) 5.54509i 0.287887i
\(372\) 1.19650 10.8797i 0.0620357 0.564086i
\(373\) 9.39721i 0.486569i 0.969955 + 0.243284i \(0.0782248\pi\)
−0.969955 + 0.243284i \(0.921775\pi\)
\(374\) 2.68208 0.138687
\(375\) 0.189341 1.72167i 0.00977755 0.0889067i
\(376\) −5.36999 5.36999i −0.276936 0.276936i
\(377\) 29.7729i 1.53338i
\(378\) 18.5733 + 6.33289i 0.955306 + 0.325729i
\(379\) −10.9284 −0.561354 −0.280677 0.959802i \(-0.590559\pi\)
−0.280677 + 0.959802i \(0.590559\pi\)
\(380\) 1.42964i 0.0733389i
\(381\) −18.5418 23.1240i −0.949923 1.18468i
\(382\) 25.0609 1.28223
\(383\) 4.41045 4.41045i 0.225363 0.225363i −0.585389 0.810752i \(-0.699058\pi\)
0.810752 + 0.585389i \(0.199058\pi\)
\(384\) 1.72167 + 0.189341i 0.0878586 + 0.00966229i
\(385\) 4.84806 4.84806i 0.247080 0.247080i
\(386\) 19.5518i 0.995162i
\(387\) −22.1239 + 14.0663i −1.12462 + 0.715032i
\(388\) −3.22614 + 3.22614i −0.163783 + 0.163783i
\(389\) 6.54945 6.54945i 0.332071 0.332071i −0.521302 0.853372i \(-0.674553\pi\)
0.853372 + 0.521302i \(0.174553\pi\)
\(390\) −1.04644 + 9.51519i −0.0529884 + 0.481820i
\(391\) 12.0994i 0.611894i
\(392\) 5.13495 5.13495i 0.259354 0.259354i
\(393\) −0.905554 + 8.23415i −0.0456792 + 0.415358i
\(394\) 10.3072 10.3072i 0.519271 0.519271i
\(395\) 11.3872 0.572953
\(396\) −5.31630 1.18364i −0.267154 0.0594802i
\(397\) 17.8138i 0.894049i −0.894522 0.447024i \(-0.852484\pi\)
0.894522 0.447024i \(-0.147516\pi\)
\(398\) 7.60095 0.381001
\(399\) 1.02226 9.29534i 0.0511769 0.465349i
\(400\) 1.00000i 0.0500000i
\(401\) −15.1233 15.1233i −0.755220 0.755220i 0.220229 0.975448i \(-0.429320\pi\)
−0.975448 + 0.220229i \(0.929320\pi\)
\(402\) −3.09756 0.340655i −0.154492 0.0169903i
\(403\) −34.9248 −1.73973
\(404\) 1.91970i 0.0955085i
\(405\) 8.46279 3.06288i 0.420519 0.152196i
\(406\) 20.3443i 1.00967i
\(407\) 10.6004 + 3.09576i 0.525443 + 0.153451i
\(408\) 1.99630 1.60072i 0.0988315 0.0792472i
\(409\) −17.1329 + 17.1329i −0.847169 + 0.847169i −0.989779 0.142610i \(-0.954451\pi\)
0.142610 + 0.989779i \(0.454451\pi\)
\(410\) 9.74155 0.481101
\(411\) 5.59574 4.48690i 0.276017 0.221322i
\(412\) 11.1661 + 11.1661i 0.550112 + 0.550112i
\(413\) 12.3598 12.3598i 0.608185 0.608185i
\(414\) −5.33966 + 23.9830i −0.262430 + 1.17870i
\(415\) 5.05825 + 5.05825i 0.248300 + 0.248300i
\(416\) 5.52672i 0.270970i
\(417\) 1.86762 1.49754i 0.0914579 0.0733347i
\(418\) 2.59550i 0.126950i
\(419\) 2.98599i 0.145875i 0.997337 + 0.0729375i \(0.0232374\pi\)
−0.997337 + 0.0729375i \(0.976763\pi\)
\(420\) 0.715047 6.50188i 0.0348907 0.317259i
\(421\) 22.4754 22.4754i 1.09538 1.09538i 0.100440 0.994943i \(-0.467975\pi\)
0.994943 0.100440i \(-0.0320251\pi\)
\(422\) 7.05514 + 7.05514i 0.343439 + 0.343439i
\(423\) 22.2384 + 4.95124i 1.08127 + 0.240738i
\(424\) 1.03826 + 1.03826i 0.0504222 + 0.0504222i
\(425\) 1.04463 + 1.04463i 0.0506719 + 0.0506719i
\(426\) 24.9694 + 2.74602i 1.20977 + 0.133045i
\(427\) 0.950119 0.950119i 0.0459795 0.0459795i
\(428\) −16.4971 −0.797418
\(429\) −1.89980 + 17.2747i −0.0917231 + 0.834033i
\(430\) 6.17939 + 6.17939i 0.297997 + 0.297997i
\(431\) 3.42819 + 3.42819i 0.165130 + 0.165130i 0.784835 0.619705i \(-0.212748\pi\)
−0.619705 + 0.784835i \(0.712748\pi\)
\(432\) −4.66340 + 2.29188i −0.224368 + 0.110268i
\(433\) −5.54788 −0.266614 −0.133307 0.991075i \(-0.542560\pi\)
−0.133307 + 0.991075i \(0.542560\pi\)
\(434\) 23.8647 1.14554
\(435\) 5.83702 + 7.27951i 0.279864 + 0.349026i
\(436\) −5.92062 + 5.92062i −0.283546 + 0.283546i
\(437\) 11.7088 0.560110
\(438\) −12.2924 1.35187i −0.587355 0.0645946i
\(439\) −19.5185 + 19.5185i −0.931565 + 0.931565i −0.997804 0.0662388i \(-0.978900\pi\)
0.0662388 + 0.997804i \(0.478900\pi\)
\(440\) 1.81549i 0.0865502i
\(441\) −4.73454 + 21.2651i −0.225454 + 1.01262i
\(442\) −5.77337 5.77337i −0.274611 0.274611i
\(443\) −34.0155 −1.61612 −0.808062 0.589098i \(-0.799483\pi\)
−0.808062 + 0.589098i \(0.799483\pi\)
\(444\) 9.73761 4.02232i 0.462126 0.190891i
\(445\) −10.5664 −0.500896
\(446\) −10.8021 10.8021i −0.511493 0.511493i
\(447\) 14.3867 11.5358i 0.680467 0.545626i
\(448\) 3.77650i 0.178423i
\(449\) 13.9432 13.9432i 0.658020 0.658020i −0.296891 0.954911i \(-0.595950\pi\)
0.954911 + 0.296891i \(0.0959498\pi\)
\(450\) −1.60961 2.53163i −0.0758777 0.119342i
\(451\) 17.6857 0.832788
\(452\) −7.61785 + 7.61785i −0.358314 + 0.358314i
\(453\) −7.43697 + 5.96327i −0.349419 + 0.280179i
\(454\) −1.26436 −0.0593392
\(455\) −20.8716 −0.978477
\(456\) 1.54904 + 1.93185i 0.0725405 + 0.0904674i
\(457\) 22.7546 + 22.7546i 1.06442 + 1.06442i 0.997777 + 0.0666382i \(0.0212273\pi\)
0.0666382 + 0.997777i \(0.478773\pi\)
\(458\) 15.9941 + 15.9941i 0.747354 + 0.747354i
\(459\) −2.47736 + 7.26568i −0.115633 + 0.339133i
\(460\) 8.19007 0.381864
\(461\) −19.4728 + 19.4728i −0.906938 + 0.906938i −0.996024 0.0890855i \(-0.971606\pi\)
0.0890855 + 0.996024i \(0.471606\pi\)
\(462\) 1.29816 11.8041i 0.0603960 0.549177i
\(463\) −5.56886 5.56886i −0.258807 0.258807i 0.565762 0.824569i \(-0.308582\pi\)
−0.824569 + 0.565762i \(0.808582\pi\)
\(464\) −3.80924 3.80924i −0.176840 0.176840i
\(465\) 8.53917 6.84706i 0.395994 0.317525i
\(466\) 1.80857 + 1.80857i 0.0837804 + 0.0837804i
\(467\) −2.99722 + 2.99722i −0.138695 + 0.138695i −0.773045 0.634351i \(-0.781268\pi\)
0.634351 + 0.773045i \(0.281268\pi\)
\(468\) 8.89586 + 13.9916i 0.411211 + 0.646763i
\(469\) 6.79451i 0.313741i
\(470\) 7.59431i 0.350299i
\(471\) 13.5941 + 16.9536i 0.626383 + 0.781181i
\(472\) 4.62846i 0.213042i
\(473\) 11.2186 + 11.2186i 0.515833 + 0.515833i
\(474\) 15.3874 12.3383i 0.706768 0.566716i
\(475\) −1.01091 + 1.01091i −0.0463836 + 0.0463836i
\(476\) 3.94504 + 3.94504i 0.180820 + 0.180820i
\(477\) −4.29967 0.957294i −0.196868 0.0438315i
\(478\) 29.0914 1.33061
\(479\) 4.22623 4.22623i 0.193101 0.193101i −0.603933 0.797035i \(-0.706401\pi\)
0.797035 + 0.603933i \(0.206401\pi\)
\(480\) 1.08352 + 1.35129i 0.0494557 + 0.0616777i
\(481\) −16.1543 29.4820i −0.736573 1.34426i
\(482\) 5.97165i 0.272001i
\(483\) −53.2509 5.85629i −2.42300 0.266470i
\(484\) 7.70399i 0.350181i
\(485\) −4.56246 −0.207170
\(486\) 8.11699 13.3084i 0.368194 0.603683i
\(487\) 3.09555 + 3.09555i 0.140273 + 0.140273i 0.773756 0.633483i \(-0.218376\pi\)
−0.633483 + 0.773756i \(0.718376\pi\)
\(488\) 0.355798i 0.0161062i
\(489\) −38.4629 4.22998i −1.73935 0.191286i
\(490\) 7.26192 0.328060
\(491\) 14.1328i 0.637804i 0.947788 + 0.318902i \(0.103314\pi\)
−0.947788 + 0.318902i \(0.896686\pi\)
\(492\) 13.1637 10.5552i 0.593464 0.475864i
\(493\) −7.95849 −0.358433
\(494\) 5.58700 5.58700i 0.251371 0.251371i
\(495\) −2.92223 4.59615i −0.131345 0.206582i
\(496\) −4.46840 + 4.46840i −0.200637 + 0.200637i
\(497\) 54.7704i 2.45679i
\(498\) 12.3159 + 1.35445i 0.551888 + 0.0606941i
\(499\) 9.16440 9.16440i 0.410255 0.410255i −0.471572 0.881827i \(-0.656313\pi\)
0.881827 + 0.471572i \(0.156313\pi\)
\(500\) −0.707107 + 0.707107i −0.0316228 + 0.0316228i
\(501\) −3.15245 0.346692i −0.140841 0.0154890i
\(502\) 22.7633i 1.01597i
\(503\) −6.66777 + 6.66777i −0.297301 + 0.297301i −0.839956 0.542655i \(-0.817419\pi\)
0.542655 + 0.839956i \(0.317419\pi\)
\(504\) −6.07869 9.56069i −0.270766 0.425867i
\(505\) 1.35743 1.35743i 0.0604049 0.0604049i
\(506\) 14.8690 0.661008
\(507\) 23.7079 19.0100i 1.05290 0.844262i
\(508\) 17.1125i 0.759245i
\(509\) 7.17963 0.318232 0.159116 0.987260i \(-0.449136\pi\)
0.159116 + 0.987260i \(0.449136\pi\)
\(510\) 2.54347 + 0.279720i 0.112627 + 0.0123862i
\(511\) 26.9635i 1.19280i
\(512\) −0.707107 0.707107i −0.0312500 0.0312500i
\(513\) −7.03113 2.39739i −0.310432 0.105847i
\(514\) −2.09021 −0.0921953
\(515\) 15.7912i 0.695843i
\(516\) 15.0456 + 1.65465i 0.662347 + 0.0728419i
\(517\) 13.7874i 0.606370i
\(518\) 11.0385 + 20.1455i 0.485004 + 0.885144i
\(519\) −2.35917 2.94218i −0.103556 0.129148i
\(520\) 3.90798 3.90798i 0.171376 0.171376i
\(521\) 2.92647 0.128211 0.0641056 0.997943i \(-0.479581\pi\)
0.0641056 + 0.997943i \(0.479581\pi\)
\(522\) 15.7750 + 3.51220i 0.690453 + 0.153725i
\(523\) 24.4456 + 24.4456i 1.06893 + 1.06893i 0.997441 + 0.0714897i \(0.0227753\pi\)
0.0714897 + 0.997441i \(0.477225\pi\)
\(524\) 3.38184 3.38184i 0.147737 0.147737i
\(525\) 5.10314 4.09191i 0.222719 0.178586i
\(526\) −7.52839 7.52839i −0.328253 0.328253i
\(527\) 9.33564i 0.406667i
\(528\) 1.96712 + 2.45325i 0.0856080 + 0.106764i
\(529\) 44.0773i 1.91640i
\(530\) 1.46832i 0.0637796i
\(531\) −7.45002 11.7176i −0.323303 0.508499i
\(532\) −3.81768 + 3.81768i −0.165518 + 0.165518i
\(533\) −38.0698 38.0698i −1.64899 1.64899i
\(534\) −14.2783 + 11.4489i −0.617881 + 0.495443i
\(535\) −11.6652 11.6652i −0.504331 0.504331i
\(536\) 1.27220 + 1.27220i 0.0549505 + 0.0549505i
\(537\) 0.525948 4.78241i 0.0226963 0.206376i
\(538\) 3.96856 3.96856i 0.171097 0.171097i
\(539\) 13.1840 0.567873
\(540\) −4.91812 1.67692i −0.211642 0.0721632i
\(541\) 4.39040 + 4.39040i 0.188758 + 0.188758i 0.795159 0.606401i \(-0.207387\pi\)
−0.606401 + 0.795159i \(0.707387\pi\)
\(542\) −15.5167 15.5167i −0.666499 0.666499i
\(543\) −22.9665 28.6421i −0.985585 1.22915i
\(544\) −1.47733 −0.0633399
\(545\) −8.37303 −0.358661
\(546\) −28.2036 + 22.6148i −1.20700 + 0.967826i
\(547\) 19.6365 19.6365i 0.839596 0.839596i −0.149210 0.988806i \(-0.547673\pi\)
0.988806 + 0.149210i \(0.0476730\pi\)
\(548\) −4.14104 −0.176896
\(549\) −0.572696 0.900750i −0.0244421 0.0384431i
\(550\) −1.28375 + 1.28375i −0.0547391 + 0.0547391i
\(551\) 7.70158i 0.328098i
\(552\) 11.0672 8.87411i 0.471050 0.377707i
\(553\) 30.4083 + 30.4083i 1.29309 + 1.29309i
\(554\) −13.6005 −0.577829
\(555\) 9.72974 + 4.04132i 0.413004 + 0.171544i
\(556\) −1.38210 −0.0586143
\(557\) 18.2860 + 18.2860i 0.774802 + 0.774802i 0.978942 0.204139i \(-0.0654396\pi\)
−0.204139 + 0.978942i \(0.565440\pi\)
\(558\) 4.11996 18.5047i 0.174412 0.783367i
\(559\) 48.2979i 2.04278i
\(560\) −2.67039 + 2.67039i −0.112844 + 0.112844i
\(561\) 4.61765 + 0.507829i 0.194957 + 0.0214405i
\(562\) 0.343094 0.0144726
\(563\) 18.2223 18.2223i 0.767978 0.767978i −0.209772 0.977750i \(-0.567272\pi\)
0.977750 + 0.209772i \(0.0672722\pi\)
\(564\) −8.22859 10.2621i −0.346486 0.432113i
\(565\) −10.7733 −0.453235
\(566\) 23.6093 0.992374
\(567\) 30.7780 + 14.4198i 1.29255 + 0.605576i
\(568\) −10.2552 10.2552i −0.430297 0.430297i
\(569\) 20.9822 + 20.9822i 0.879619 + 0.879619i 0.993495 0.113876i \(-0.0363266\pi\)
−0.113876 + 0.993495i \(0.536327\pi\)
\(570\) −0.270690 + 2.46137i −0.0113379 + 0.103095i
\(571\) 18.1815 0.760873 0.380437 0.924807i \(-0.375774\pi\)
0.380437 + 0.924807i \(0.375774\pi\)
\(572\) 7.09491 7.09491i 0.296653 0.296653i
\(573\) 43.1467 + 4.74507i 1.80248 + 0.198228i
\(574\) 26.0137 + 26.0137i 1.08579 + 1.08579i
\(575\) 5.79126 + 5.79126i 0.241512 + 0.241512i
\(576\) 2.92830 + 0.651967i 0.122012 + 0.0271653i
\(577\) −1.13510 1.13510i −0.0472550 0.0472550i 0.683084 0.730339i \(-0.260638\pi\)
−0.730339 + 0.683084i \(0.760638\pi\)
\(578\) 10.4776 10.4776i 0.435809 0.435809i
\(579\) 3.70197 33.6618i 0.153849 1.39894i
\(580\) 5.38709i 0.223687i
\(581\) 27.0150i 1.12077i
\(582\) −6.16520 + 4.94351i −0.255556 + 0.204915i
\(583\) 2.66571i 0.110403i
\(584\) 5.04862 + 5.04862i 0.208913 + 0.208913i
\(585\) −3.60324 + 16.1839i −0.148976 + 0.669122i
\(586\) −19.0091 + 19.0091i −0.785257 + 0.785257i
\(587\) −14.5649 14.5649i −0.601156 0.601156i 0.339463 0.940619i \(-0.389755\pi\)
−0.940619 + 0.339463i \(0.889755\pi\)
\(588\) 9.81296 7.86844i 0.404680 0.324489i
\(589\) −9.03427 −0.372251
\(590\) −3.27282 + 3.27282i −0.134740 + 0.134740i
\(591\) 19.6972 15.7941i 0.810236 0.649681i
\(592\) −5.83886 1.70519i −0.239976 0.0700830i
\(593\) 5.14451i 0.211260i 0.994406 + 0.105630i \(0.0336859\pi\)
−0.994406 + 0.105630i \(0.966314\pi\)
\(594\) −8.92881 3.04444i −0.366354 0.124915i
\(595\) 5.57912i 0.228722i
\(596\) −10.6466 −0.436103
\(597\) 13.0863 + 1.43917i 0.535588 + 0.0589015i
\(598\) −32.0066 32.0066i −1.30885 1.30885i
\(599\) 21.5927i 0.882252i −0.897445 0.441126i \(-0.854579\pi\)
0.897445 0.441126i \(-0.145421\pi\)
\(600\) −0.189341 + 1.72167i −0.00772983 + 0.0702869i
\(601\) 26.1906 1.06834 0.534168 0.845379i \(-0.320625\pi\)
0.534168 + 0.845379i \(0.320625\pi\)
\(602\) 33.0027i 1.34509i
\(603\) −5.26847 1.17299i −0.214549 0.0477679i
\(604\) 5.50361 0.223939
\(605\) 5.44754 5.44754i 0.221474 0.221474i
\(606\) 0.363478 3.30509i 0.0147653 0.134260i
\(607\) −5.21725 + 5.21725i −0.211761 + 0.211761i −0.805015 0.593254i \(-0.797843\pi\)
0.593254 + 0.805015i \(0.297843\pi\)
\(608\) 1.42964i 0.0579795i
\(609\) −3.85202 + 35.0262i −0.156092 + 1.41933i
\(610\) −0.251587 + 0.251587i −0.0101865 + 0.0101865i
\(611\) −29.6784 + 29.6784i −1.20066 + 1.20066i
\(612\) 3.74005 2.37792i 0.151183 0.0961218i
\(613\) 23.3868i 0.944582i −0.881443 0.472291i \(-0.843427\pi\)
0.881443 0.472291i \(-0.156573\pi\)
\(614\) 18.8977 18.8977i 0.762649 0.762649i
\(615\) 16.7717 + 1.84448i 0.676302 + 0.0743766i
\(616\) −4.84806 + 4.84806i −0.195334 + 0.195334i
\(617\) −17.0385 −0.685946 −0.342973 0.939345i \(-0.611434\pi\)
−0.342973 + 0.939345i \(0.611434\pi\)
\(618\) 17.1101 + 21.3385i 0.688268 + 0.858360i
\(619\) 37.2757i 1.49824i −0.662435 0.749119i \(-0.730477\pi\)
0.662435 0.749119i \(-0.269523\pi\)
\(620\) −6.31927 −0.253788
\(621\) −13.7341 + 40.2798i −0.551131 + 1.61637i
\(622\) 4.39947i 0.176403i
\(623\) −28.2164 28.2164i −1.13047 1.13047i
\(624\) 1.04644 9.51519i 0.0418910 0.380912i
\(625\) −1.00000 −0.0400000
\(626\) 2.00853i 0.0802770i
\(627\) −0.491435 + 4.46859i −0.0196260 + 0.178458i
\(628\) 12.5462i 0.500649i
\(629\) −7.88074 + 4.31815i −0.314226 + 0.172176i
\(630\) 2.46215 11.0587i 0.0980945 0.440590i
\(631\) 16.9809 16.9809i 0.676000 0.676000i −0.283093 0.959093i \(-0.591360\pi\)
0.959093 + 0.283093i \(0.0913604\pi\)
\(632\) −11.3872 −0.452959
\(633\) 10.8108 + 13.4825i 0.429690 + 0.535879i
\(634\) 0.815228 + 0.815228i 0.0323768 + 0.0323768i
\(635\) −12.1004 + 12.1004i −0.480189 + 0.480189i
\(636\) 1.59095 + 1.98412i 0.0630853 + 0.0786755i
\(637\) −28.3794 28.3794i −1.12443 1.12443i
\(638\) 9.78021i 0.387202i
\(639\) 42.4691 + 9.45547i 1.68005 + 0.374053i
\(640\) 1.00000i 0.0395285i
\(641\) 15.5373i 0.613687i 0.951760 + 0.306844i \(0.0992729\pi\)
−0.951760 + 0.306844i \(0.900727\pi\)
\(642\) −28.4026 3.12359i −1.12096 0.123278i
\(643\) 17.0643 17.0643i 0.672950 0.672950i −0.285445 0.958395i \(-0.592141\pi\)
0.958395 + 0.285445i \(0.0921414\pi\)
\(644\) 21.8707 + 21.8707i 0.861825 + 0.861825i
\(645\) 9.46886 + 11.8089i 0.372836 + 0.464975i
\(646\) −1.49344 1.49344i −0.0587586 0.0587586i
\(647\) 3.54892 + 3.54892i 0.139522 + 0.139522i 0.773418 0.633896i \(-0.218545\pi\)
−0.633896 + 0.773418i \(0.718545\pi\)
\(648\) −8.46279 + 3.06288i −0.332450 + 0.120321i
\(649\) −5.94177 + 5.94177i −0.233235 + 0.233235i
\(650\) 5.52672 0.216776
\(651\) 41.0872 + 4.51858i 1.61033 + 0.177097i
\(652\) 15.7971 + 15.7971i 0.618662 + 0.618662i
\(653\) 23.7536 + 23.7536i 0.929549 + 0.929549i 0.997677 0.0681273i \(-0.0217024\pi\)
−0.0681273 + 0.997677i \(0.521702\pi\)
\(654\) −11.3144 + 9.07234i −0.442427 + 0.354757i
\(655\) 4.78265 0.186874
\(656\) −9.74155 −0.380344
\(657\) −20.9075 4.65493i −0.815681 0.181606i
\(658\) 20.2797 20.2797i 0.790587 0.790587i
\(659\) 35.4935 1.38263 0.691315 0.722553i \(-0.257032\pi\)
0.691315 + 0.722553i \(0.257032\pi\)
\(660\) −0.343748 + 3.12568i −0.0133804 + 0.121667i
\(661\) 0.325551 0.325551i 0.0126625 0.0126625i −0.700747 0.713410i \(-0.747150\pi\)
0.713410 + 0.700747i \(0.247150\pi\)
\(662\) 29.4140i 1.14321i
\(663\) −8.84670 11.0330i −0.343578 0.428486i
\(664\) −5.05825 5.05825i −0.196298 0.196298i
\(665\) −5.39902 −0.209365
\(666\) 17.5265 5.08137i 0.679140 0.196899i
\(667\) −44.1206 −1.70836
\(668\) 1.29474 + 1.29474i 0.0500950 + 0.0500950i
\(669\) −16.5523 20.6429i −0.639951 0.798101i
\(670\) 1.79916i 0.0695075i
\(671\) −0.456755 + 0.456755i −0.0176328 + 0.0176328i
\(672\) −0.715047 + 6.50188i −0.0275836 + 0.250816i
\(673\) −38.7813 −1.49491 −0.747455 0.664312i \(-0.768725\pi\)
−0.747455 + 0.664312i \(0.768725\pi\)
\(674\) −21.7056 + 21.7056i −0.836069 + 0.836069i
\(675\) −2.29188 4.66340i −0.0882143 0.179494i
\(676\) −17.5446 −0.674793
\(677\) −12.6745 −0.487122 −0.243561 0.969886i \(-0.578316\pi\)
−0.243561 + 0.969886i \(0.578316\pi\)
\(678\) −14.5578 + 11.6731i −0.559089 + 0.448301i
\(679\) −12.1835 12.1835i −0.467560 0.467560i
\(680\) −1.04463 1.04463i −0.0400597 0.0400597i
\(681\) −2.17681 0.239395i −0.0834154 0.00917365i
\(682\) −11.4726 −0.439308
\(683\) 14.3090 14.3090i 0.547518 0.547518i −0.378204 0.925722i \(-0.623458\pi\)
0.925722 + 0.378204i \(0.123458\pi\)
\(684\) 2.30116 + 3.61932i 0.0879870 + 0.138388i
\(685\) −2.92815 2.92815i −0.111879 0.111879i
\(686\) 0.699432 + 0.699432i 0.0267044 + 0.0267044i
\(687\) 24.5082 + 30.5649i 0.935045 + 1.16612i
\(688\) −6.17939 6.17939i −0.235587 0.235587i
\(689\) 5.73815 5.73815i 0.218606 0.218606i
\(690\) 14.1006 + 1.55072i 0.536801 + 0.0590349i
\(691\) 40.9622i 1.55827i 0.626854 + 0.779137i \(0.284342\pi\)
−0.626854 + 0.779137i \(0.715658\pi\)
\(692\) 2.17732i 0.0827691i
\(693\) 4.47002 20.0770i 0.169802 0.762662i
\(694\) 14.0175i 0.532099i
\(695\) −0.977295 0.977295i −0.0370709 0.0370709i
\(696\) −5.83702 7.27951i −0.221252 0.275929i
\(697\) −10.1763 + 10.1763i −0.385455 + 0.385455i
\(698\) 1.85469 + 1.85469i 0.0702011 + 0.0702011i
\(699\) 2.77132 + 3.45620i 0.104821 + 0.130725i
\(700\) −3.77650 −0.142738
\(701\) 28.6764 28.6764i 1.08309 1.08309i 0.0868723 0.996219i \(-0.472313\pi\)
0.996219 0.0868723i \(-0.0276872\pi\)
\(702\) 12.6666 + 25.7733i 0.478068 + 0.972751i
\(703\) −4.17875 7.62633i −0.157605 0.287633i
\(704\) 1.81549i 0.0684239i
\(705\) 1.43792 13.0749i 0.0541551 0.492429i
\(706\) 32.2895i 1.21523i
\(707\) 7.24973 0.272654
\(708\) −0.876360 + 7.96869i −0.0329356 + 0.299482i
\(709\) 18.4451 + 18.4451i 0.692722 + 0.692722i 0.962830 0.270108i \(-0.0870594\pi\)
−0.270108 + 0.962830i \(0.587059\pi\)
\(710\) 14.5030i 0.544287i
\(711\) 28.8282 18.3290i 1.08114 0.687390i
\(712\) 10.5664 0.395993
\(713\) 51.7553i 1.93825i
\(714\) 6.04509 + 7.53901i 0.226232 + 0.282140i
\(715\) 10.0337 0.375240
\(716\) −1.96418 + 1.96418i −0.0734050 + 0.0734050i
\(717\) 50.0858 + 5.50821i 1.87049 + 0.205708i
\(718\) −4.45163 + 4.45163i −0.166133 + 0.166133i
\(719\) 48.9218i 1.82448i −0.409660 0.912238i \(-0.634353\pi\)
0.409660 0.912238i \(-0.365647\pi\)
\(720\) 1.60961 + 2.53163i 0.0599866 + 0.0943483i
\(721\) −42.1686 + 42.1686i −1.57044 + 1.57044i
\(722\) −11.9898 + 11.9898i −0.446214 + 0.446214i
\(723\) 1.13068 10.2812i 0.0420505 0.382363i
\(724\) 21.1962i 0.787749i
\(725\) 3.80924 3.80924i 0.141472 0.141472i
\(726\) 1.45869 13.2637i 0.0541369 0.492263i
\(727\) −8.85958 + 8.85958i −0.328584 + 0.328584i −0.852048 0.523464i \(-0.824639\pi\)
0.523464 + 0.852048i \(0.324639\pi\)
\(728\) 20.8716 0.773554
\(729\) 16.4946 21.3759i 0.610912 0.791699i
\(730\) 7.13983i 0.264257i
\(731\) −12.9103 −0.477506
\(732\) −0.0673674 + 0.612567i −0.00248997 + 0.0226411i
\(733\) 8.30705i 0.306828i 0.988162 + 0.153414i \(0.0490268\pi\)
−0.988162 + 0.153414i \(0.950973\pi\)
\(734\) −22.3888 22.3888i −0.826386 0.826386i
\(735\) 12.5026 + 1.37498i 0.461167 + 0.0507170i
\(736\) −8.19007 −0.301890
\(737\) 3.26636i 0.120318i
\(738\) 24.6620 15.6801i 0.907822 0.577193i
\(739\) 17.1146i 0.629569i −0.949163 0.314785i \(-0.898068\pi\)
0.949163 0.314785i \(-0.101932\pi\)
\(740\) −2.92295 5.33445i −0.107450 0.196098i
\(741\) 10.6768 8.56112i 0.392223 0.314501i
\(742\) −3.92097 + 3.92097i −0.143943 + 0.143943i
\(743\) −12.6952 −0.465743 −0.232871 0.972508i \(-0.574812\pi\)
−0.232871 + 0.972508i \(0.574812\pi\)
\(744\) −8.53917 + 6.84706i −0.313061 + 0.251025i
\(745\) −7.52830 7.52830i −0.275816 0.275816i
\(746\) 6.64483 6.64483i 0.243284 0.243284i
\(747\) 20.9474 + 4.66382i 0.766427 + 0.170640i
\(748\) −1.89651 1.89651i −0.0693435 0.0693435i
\(749\) 62.3012i 2.27644i
\(750\) −1.35129 + 1.08352i −0.0493421 + 0.0395646i
\(751\) 28.7797i 1.05018i 0.851045 + 0.525092i \(0.175969\pi\)
−0.851045 + 0.525092i \(0.824031\pi\)
\(752\) 7.59431i 0.276936i
\(753\) 4.31003 39.1908i 0.157066 1.42819i
\(754\) −21.0526 + 21.0526i −0.766691 + 0.766691i
\(755\) 3.89164 + 3.89164i 0.141631 + 0.141631i
\(756\) −8.65526 17.6113i −0.314789 0.640517i
\(757\) −10.1110 10.1110i −0.367489 0.367489i 0.499072 0.866561i \(-0.333674\pi\)
−0.866561 + 0.499072i \(0.833674\pi\)
\(758\) 7.72755 + 7.72755i 0.280677 + 0.280677i
\(759\) 25.5995 + 2.81532i 0.929204 + 0.102190i
\(760\) 1.01091 1.01091i 0.0366694 0.0366694i
\(761\) 47.0638 1.70606 0.853031 0.521860i \(-0.174762\pi\)
0.853031 + 0.521860i \(0.174762\pi\)
\(762\) −3.24011 + 29.4621i −0.117377 + 1.06730i
\(763\) −22.3592 22.3592i −0.809458 0.809458i
\(764\) −17.7208 17.7208i −0.641114 0.641114i
\(765\) 4.32606 + 0.963170i 0.156409 + 0.0348235i
\(766\) −6.23731 −0.225363
\(767\) 25.5802 0.923648
\(768\) −1.08352 1.35129i −0.0390982 0.0487605i
\(769\) −5.52401 + 5.52401i −0.199201 + 0.199201i −0.799657 0.600457i \(-0.794986\pi\)
0.600457 + 0.799657i \(0.294986\pi\)
\(770\) −6.85620 −0.247080
\(771\) −3.59866 0.395764i −0.129602 0.0142531i
\(772\) −13.8252 + 13.8252i −0.497581 + 0.497581i
\(773\) 1.33377i 0.0479722i 0.999712 + 0.0239861i \(0.00763575\pi\)
−0.999712 + 0.0239861i \(0.992364\pi\)
\(774\) 25.5903 + 5.69753i 0.919826 + 0.204793i
\(775\) −4.46840 4.46840i −0.160510 0.160510i
\(776\) 4.56246 0.163783
\(777\) 15.1903 + 36.7740i 0.544948 + 1.31926i
\(778\) −9.26233 −0.332071
\(779\) −9.84780