Properties

Label 1110.2.l.b.697.3
Level $1110$
Weight $2$
Character 1110.697
Analytic conductor $8.863$
Analytic rank $0$
Dimension $40$
CM no
Inner twists $2$

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Newspace parameters

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

Newform invariants

Self dual: no
Analytic conductor: \(8.86339462436\)
Analytic rank: \(0\)
Dimension: \(40\)
Relative dimension: \(20\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 697.3
Character \(\chi\) \(=\) 1110.697
Dual form 1110.2.l.b.43.3

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000i q^{2} +(-0.707107 - 0.707107i) q^{3} -1.00000 q^{4} +(0.248996 + 2.22216i) q^{5} +(0.707107 - 0.707107i) q^{6} +(-2.88943 - 2.88943i) q^{7} -1.00000i q^{8} +1.00000i q^{9} +O(q^{10})\) \(q+1.00000i q^{2} +(-0.707107 - 0.707107i) q^{3} -1.00000 q^{4} +(0.248996 + 2.22216i) q^{5} +(0.707107 - 0.707107i) q^{6} +(-2.88943 - 2.88943i) q^{7} -1.00000i q^{8} +1.00000i q^{9} +(-2.22216 + 0.248996i) q^{10} -4.93091i q^{11} +(0.707107 + 0.707107i) q^{12} +1.83135i q^{13} +(2.88943 - 2.88943i) q^{14} +(1.39524 - 1.74737i) q^{15} +1.00000 q^{16} +2.74310 q^{17} -1.00000 q^{18} +(5.44485 + 5.44485i) q^{19} +(-0.248996 - 2.22216i) q^{20} +4.08627i q^{21} +4.93091 q^{22} +8.34738i q^{23} +(-0.707107 + 0.707107i) q^{24} +(-4.87600 + 1.10662i) q^{25} -1.83135 q^{26} +(0.707107 - 0.707107i) q^{27} +(2.88943 + 2.88943i) q^{28} +(-0.469514 + 0.469514i) q^{29} +(1.74737 + 1.39524i) q^{30} +(2.48079 + 2.48079i) q^{31} +1.00000i q^{32} +(-3.48668 + 3.48668i) q^{33} +2.74310i q^{34} +(5.70132 - 7.14024i) q^{35} -1.00000i q^{36} +(-2.83501 + 5.38170i) q^{37} +(-5.44485 + 5.44485i) q^{38} +(1.29496 - 1.29496i) q^{39} +(2.22216 - 0.248996i) q^{40} -4.25710i q^{41} -4.08627 q^{42} +5.61051i q^{43} +4.93091i q^{44} +(-2.22216 + 0.248996i) q^{45} -8.34738 q^{46} +(-0.544094 - 0.544094i) q^{47} +(-0.707107 - 0.707107i) q^{48} +9.69763i q^{49} +(-1.10662 - 4.87600i) q^{50} +(-1.93966 - 1.93966i) q^{51} -1.83135i q^{52} +(-7.02831 + 7.02831i) q^{53} +(0.707107 + 0.707107i) q^{54} +(10.9573 - 1.22778i) q^{55} +(-2.88943 + 2.88943i) q^{56} -7.70018i q^{57} +(-0.469514 - 0.469514i) q^{58} +(-7.44209 - 7.44209i) q^{59} +(-1.39524 + 1.74737i) q^{60} +(1.23325 + 1.23325i) q^{61} +(-2.48079 + 2.48079i) q^{62} +(2.88943 - 2.88943i) q^{63} -1.00000 q^{64} +(-4.06955 + 0.455999i) q^{65} +(-3.48668 - 3.48668i) q^{66} +(5.74859 - 5.74859i) q^{67} -2.74310 q^{68} +(5.90249 - 5.90249i) q^{69} +(7.14024 + 5.70132i) q^{70} +13.0269 q^{71} +1.00000 q^{72} +(5.94865 + 5.94865i) q^{73} +(-5.38170 - 2.83501i) q^{74} +(4.23035 + 2.66535i) q^{75} +(-5.44485 - 5.44485i) q^{76} +(-14.2475 + 14.2475i) q^{77} +(1.29496 + 1.29496i) q^{78} +(4.75210 + 4.75210i) q^{79} +(0.248996 + 2.22216i) q^{80} -1.00000 q^{81} +4.25710 q^{82} +(-0.579710 + 0.579710i) q^{83} -4.08627i q^{84} +(0.683022 + 6.09560i) q^{85} -5.61051 q^{86} +0.663993 q^{87} -4.93091 q^{88} +(-2.52805 + 2.52805i) q^{89} +(-0.248996 - 2.22216i) q^{90} +(5.29155 - 5.29155i) q^{91} -8.34738i q^{92} -3.50837i q^{93} +(0.544094 - 0.544094i) q^{94} +(-10.7436 + 13.4551i) q^{95} +(0.707107 - 0.707107i) q^{96} -17.4278 q^{97} -9.69763 q^{98} +4.93091 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 40q - 40q^{4} - 4q^{7} + O(q^{10}) \) \( 40q - 40q^{4} - 4q^{7} + 4q^{14} + 40q^{16} + 24q^{17} - 40q^{18} + 4q^{19} + 8q^{22} + 8q^{25} + 8q^{26} + 4q^{28} + 28q^{31} - 4q^{33} + 20q^{35} + 20q^{37} - 4q^{38} + 4q^{39} + 16q^{42} - 16q^{47} + 16q^{51} + 20q^{53} + 16q^{55} - 4q^{56} - 4q^{59} - 8q^{61} - 28q^{62} + 4q^{63} - 40q^{64} - 4q^{65} - 4q^{66} + 16q^{67} - 24q^{68} - 8q^{69} + 12q^{70} + 40q^{71} + 40q^{72} + 8q^{73} - 8q^{74} + 16q^{75} - 4q^{76} - 24q^{77} + 4q^{78} - 12q^{79} - 40q^{81} - 24q^{82} - 8q^{83} - 8q^{85} + 8q^{87} - 8q^{88} + 12q^{89} - 24q^{91} + 16q^{94} - 28q^{95} + 40q^{97} - 56q^{98} + 8q^{99} + O(q^{100}) \)

Character values

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

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

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000i 0.707107i
\(3\) −0.707107 0.707107i −0.408248 0.408248i
\(4\) −1.00000 −0.500000
\(5\) 0.248996 + 2.22216i 0.111355 + 0.993781i
\(6\) 0.707107 0.707107i 0.288675 0.288675i
\(7\) −2.88943 2.88943i −1.09210 1.09210i −0.995304 0.0967984i \(-0.969140\pi\)
−0.0967984 0.995304i \(-0.530860\pi\)
\(8\) 1.00000i 0.353553i
\(9\) 1.00000i 0.333333i
\(10\) −2.22216 + 0.248996i −0.702709 + 0.0787396i
\(11\) 4.93091i 1.48672i −0.668889 0.743362i \(-0.733230\pi\)
0.668889 0.743362i \(-0.266770\pi\)
\(12\) 0.707107 + 0.707107i 0.204124 + 0.204124i
\(13\) 1.83135i 0.507924i 0.967214 + 0.253962i \(0.0817339\pi\)
−0.967214 + 0.253962i \(0.918266\pi\)
\(14\) 2.88943 2.88943i 0.772233 0.772233i
\(15\) 1.39524 1.74737i 0.360249 0.451170i
\(16\) 1.00000 0.250000
\(17\) 2.74310 0.665299 0.332649 0.943051i \(-0.392057\pi\)
0.332649 + 0.943051i \(0.392057\pi\)
\(18\) −1.00000 −0.235702
\(19\) 5.44485 + 5.44485i 1.24913 + 1.24913i 0.956103 + 0.293030i \(0.0946637\pi\)
0.293030 + 0.956103i \(0.405336\pi\)
\(20\) −0.248996 2.22216i −0.0556773 0.496890i
\(21\) 4.08627i 0.891698i
\(22\) 4.93091 1.05127
\(23\) 8.34738i 1.74055i 0.492567 + 0.870275i \(0.336059\pi\)
−0.492567 + 0.870275i \(0.663941\pi\)
\(24\) −0.707107 + 0.707107i −0.144338 + 0.144338i
\(25\) −4.87600 + 1.10662i −0.975200 + 0.221324i
\(26\) −1.83135 −0.359157
\(27\) 0.707107 0.707107i 0.136083 0.136083i
\(28\) 2.88943 + 2.88943i 0.546051 + 0.546051i
\(29\) −0.469514 + 0.469514i −0.0871866 + 0.0871866i −0.749355 0.662168i \(-0.769636\pi\)
0.662168 + 0.749355i \(0.269636\pi\)
\(30\) 1.74737 + 1.39524i 0.319025 + 0.254734i
\(31\) 2.48079 + 2.48079i 0.445564 + 0.445564i 0.893877 0.448313i \(-0.147975\pi\)
−0.448313 + 0.893877i \(0.647975\pi\)
\(32\) 1.00000i 0.176777i
\(33\) −3.48668 + 3.48668i −0.606952 + 0.606952i
\(34\) 2.74310i 0.470437i
\(35\) 5.70132 7.14024i 0.963700 1.20692i
\(36\) 1.00000i 0.166667i
\(37\) −2.83501 + 5.38170i −0.466073 + 0.884747i
\(38\) −5.44485 + 5.44485i −0.883271 + 0.883271i
\(39\) 1.29496 1.29496i 0.207359 0.207359i
\(40\) 2.22216 0.248996i 0.351355 0.0393698i
\(41\) 4.25710i 0.664848i −0.943130 0.332424i \(-0.892134\pi\)
0.943130 0.332424i \(-0.107866\pi\)
\(42\) −4.08627 −0.630526
\(43\) 5.61051i 0.855595i 0.903875 + 0.427798i \(0.140710\pi\)
−0.903875 + 0.427798i \(0.859290\pi\)
\(44\) 4.93091i 0.743362i
\(45\) −2.22216 + 0.248996i −0.331260 + 0.0371182i
\(46\) −8.34738 −1.23075
\(47\) −0.544094 0.544094i −0.0793643 0.0793643i 0.666310 0.745675i \(-0.267873\pi\)
−0.745675 + 0.666310i \(0.767873\pi\)
\(48\) −0.707107 0.707107i −0.102062 0.102062i
\(49\) 9.69763i 1.38538i
\(50\) −1.10662 4.87600i −0.156500 0.689571i
\(51\) −1.93966 1.93966i −0.271607 0.271607i
\(52\) 1.83135i 0.253962i
\(53\) −7.02831 + 7.02831i −0.965413 + 0.965413i −0.999422 0.0340086i \(-0.989173\pi\)
0.0340086 + 0.999422i \(0.489173\pi\)
\(54\) 0.707107 + 0.707107i 0.0962250 + 0.0962250i
\(55\) 10.9573 1.22778i 1.47748 0.165554i
\(56\) −2.88943 + 2.88943i −0.386117 + 0.386117i
\(57\) 7.70018i 1.01991i
\(58\) −0.469514 0.469514i −0.0616502 0.0616502i
\(59\) −7.44209 7.44209i −0.968878 0.968878i 0.0306521 0.999530i \(-0.490242\pi\)
−0.999530 + 0.0306521i \(0.990242\pi\)
\(60\) −1.39524 + 1.74737i −0.180124 + 0.225585i
\(61\) 1.23325 + 1.23325i 0.157902 + 0.157902i 0.781636 0.623734i \(-0.214385\pi\)
−0.623734 + 0.781636i \(0.714385\pi\)
\(62\) −2.48079 + 2.48079i −0.315061 + 0.315061i
\(63\) 2.88943 2.88943i 0.364034 0.364034i
\(64\) −1.00000 −0.125000
\(65\) −4.06955 + 0.455999i −0.504766 + 0.0565597i
\(66\) −3.48668 3.48668i −0.429180 0.429180i
\(67\) 5.74859 5.74859i 0.702302 0.702302i −0.262602 0.964904i \(-0.584581\pi\)
0.964904 + 0.262602i \(0.0845807\pi\)
\(68\) −2.74310 −0.332649
\(69\) 5.90249 5.90249i 0.710576 0.710576i
\(70\) 7.14024 + 5.70132i 0.853422 + 0.681439i
\(71\) 13.0269 1.54601 0.773007 0.634398i \(-0.218752\pi\)
0.773007 + 0.634398i \(0.218752\pi\)
\(72\) 1.00000 0.117851
\(73\) 5.94865 + 5.94865i 0.696237 + 0.696237i 0.963597 0.267360i \(-0.0861513\pi\)
−0.267360 + 0.963597i \(0.586151\pi\)
\(74\) −5.38170 2.83501i −0.625610 0.329563i
\(75\) 4.23035 + 2.66535i 0.488479 + 0.307769i
\(76\) −5.44485 5.44485i −0.624567 0.624567i
\(77\) −14.2475 + 14.2475i −1.62365 + 1.62365i
\(78\) 1.29496 + 1.29496i 0.146625 + 0.146625i
\(79\) 4.75210 + 4.75210i 0.534652 + 0.534652i 0.921953 0.387301i \(-0.126593\pi\)
−0.387301 + 0.921953i \(0.626593\pi\)
\(80\) 0.248996 + 2.22216i 0.0278387 + 0.248445i
\(81\) −1.00000 −0.111111
\(82\) 4.25710 0.470118
\(83\) −0.579710 + 0.579710i −0.0636314 + 0.0636314i −0.738206 0.674575i \(-0.764327\pi\)
0.674575 + 0.738206i \(0.264327\pi\)
\(84\) 4.08627i 0.445849i
\(85\) 0.683022 + 6.09560i 0.0740841 + 0.661161i
\(86\) −5.61051 −0.604997
\(87\) 0.663993 0.0711875
\(88\) −4.93091 −0.525636
\(89\) −2.52805 + 2.52805i −0.267972 + 0.267972i −0.828283 0.560310i \(-0.810682\pi\)
0.560310 + 0.828283i \(0.310682\pi\)
\(90\) −0.248996 2.22216i −0.0262465 0.234236i
\(91\) 5.29155 5.29155i 0.554706 0.554706i
\(92\) 8.34738i 0.870275i
\(93\) 3.50837i 0.363801i
\(94\) 0.544094 0.544094i 0.0561191 0.0561191i
\(95\) −10.7436 + 13.4551i −1.10227 + 1.38046i
\(96\) 0.707107 0.707107i 0.0721688 0.0721688i
\(97\) −17.4278 −1.76952 −0.884761 0.466045i \(-0.845679\pi\)
−0.884761 + 0.466045i \(0.845679\pi\)
\(98\) −9.69763 −0.979608
\(99\) 4.93091 0.495575
\(100\) 4.87600 1.10662i 0.487600 0.110662i
\(101\) 13.9975i 1.39281i 0.717650 + 0.696404i \(0.245218\pi\)
−0.717650 + 0.696404i \(0.754782\pi\)
\(102\) 1.93966 1.93966i 0.192055 0.192055i
\(103\) 12.0104 1.18342 0.591709 0.806151i \(-0.298453\pi\)
0.591709 + 0.806151i \(0.298453\pi\)
\(104\) 1.83135 0.179578
\(105\) −9.08036 + 1.01747i −0.886152 + 0.0992947i
\(106\) −7.02831 7.02831i −0.682650 0.682650i
\(107\) 10.6057 + 10.6057i 1.02529 + 1.02529i 0.999672 + 0.0256174i \(0.00815516\pi\)
0.0256174 + 0.999672i \(0.491845\pi\)
\(108\) −0.707107 + 0.707107i −0.0680414 + 0.0680414i
\(109\) 11.8333 + 11.8333i 1.13343 + 1.13343i 0.989603 + 0.143824i \(0.0459398\pi\)
0.143824 + 0.989603i \(0.454060\pi\)
\(110\) 1.22778 + 10.9573i 0.117064 + 1.04473i
\(111\) 5.81009 1.80078i 0.551470 0.170923i
\(112\) −2.88943 2.88943i −0.273026 0.273026i
\(113\) 6.01525 0.565867 0.282934 0.959139i \(-0.408692\pi\)
0.282934 + 0.959139i \(0.408692\pi\)
\(114\) 7.70018 0.721188
\(115\) −18.5492 + 2.07847i −1.72972 + 0.193818i
\(116\) 0.469514 0.469514i 0.0435933 0.0435933i
\(117\) −1.83135 −0.169308
\(118\) 7.44209 7.44209i 0.685100 0.685100i
\(119\) −7.92599 7.92599i −0.726574 0.726574i
\(120\) −1.74737 1.39524i −0.159513 0.127367i
\(121\) −13.3138 −1.21035
\(122\) −1.23325 + 1.23325i −0.111654 + 0.111654i
\(123\) −3.01023 + 3.01023i −0.271423 + 0.271423i
\(124\) −2.48079 2.48079i −0.222782 0.222782i
\(125\) −3.67320 10.5597i −0.328541 0.944490i
\(126\) 2.88943 + 2.88943i 0.257411 + 0.257411i
\(127\) −3.19427 3.19427i −0.283446 0.283446i 0.551036 0.834482i \(-0.314233\pi\)
−0.834482 + 0.551036i \(0.814233\pi\)
\(128\) 1.00000i 0.0883883i
\(129\) 3.96723 3.96723i 0.349295 0.349295i
\(130\) −0.455999 4.06955i −0.0399938 0.356923i
\(131\) −1.15532 1.15532i −0.100941 0.100941i 0.654833 0.755774i \(-0.272739\pi\)
−0.755774 + 0.654833i \(0.772739\pi\)
\(132\) 3.48668 3.48668i 0.303476 0.303476i
\(133\) 31.4650i 2.72836i
\(134\) 5.74859 + 5.74859i 0.496602 + 0.496602i
\(135\) 1.74737 + 1.39524i 0.150390 + 0.120083i
\(136\) 2.74310i 0.235219i
\(137\) 7.63981 + 7.63981i 0.652713 + 0.652713i 0.953646 0.300932i \(-0.0972978\pi\)
−0.300932 + 0.953646i \(0.597298\pi\)
\(138\) 5.90249 + 5.90249i 0.502453 + 0.502453i
\(139\) 6.69829 0.568142 0.284071 0.958803i \(-0.408315\pi\)
0.284071 + 0.958803i \(0.408315\pi\)
\(140\) −5.70132 + 7.14024i −0.481850 + 0.603460i
\(141\) 0.769466i 0.0648007i
\(142\) 13.0269i 1.09320i
\(143\) 9.03020 0.755143
\(144\) 1.00000i 0.0833333i
\(145\) −1.16024 0.926429i −0.0963530 0.0769357i
\(146\) −5.94865 + 5.94865i −0.492314 + 0.492314i
\(147\) 6.85726 6.85726i 0.565577 0.565577i
\(148\) 2.83501 5.38170i 0.233036 0.442373i
\(149\) 2.09937i 0.171987i 0.996296 + 0.0859934i \(0.0274064\pi\)
−0.996296 + 0.0859934i \(0.972594\pi\)
\(150\) −2.66535 + 4.23035i −0.217625 + 0.345407i
\(151\) 16.4484i 1.33855i −0.743013 0.669276i \(-0.766604\pi\)
0.743013 0.669276i \(-0.233396\pi\)
\(152\) 5.44485 5.44485i 0.441635 0.441635i
\(153\) 2.74310i 0.221766i
\(154\) −14.2475 14.2475i −1.14810 1.14810i
\(155\) −4.89501 + 6.13043i −0.393177 + 0.492408i
\(156\) −1.29496 + 1.29496i −0.103680 + 0.103680i
\(157\) 13.6581 + 13.6581i 1.09003 + 1.09003i 0.995524 + 0.0945109i \(0.0301287\pi\)
0.0945109 + 0.995524i \(0.469871\pi\)
\(158\) −4.75210 + 4.75210i −0.378056 + 0.378056i
\(159\) 9.93953 0.788256
\(160\) −2.22216 + 0.248996i −0.175677 + 0.0196849i
\(161\) 24.1192 24.1192i 1.90086 1.90086i
\(162\) 1.00000i 0.0785674i
\(163\) −16.1683 −1.26640 −0.633200 0.773988i \(-0.718259\pi\)
−0.633200 + 0.773988i \(0.718259\pi\)
\(164\) 4.25710i 0.332424i
\(165\) −8.61613 6.87979i −0.670765 0.535591i
\(166\) −0.579710 0.579710i −0.0449942 0.0449942i
\(167\) 0.266278 0.0206052 0.0103026 0.999947i \(-0.496721\pi\)
0.0103026 + 0.999947i \(0.496721\pi\)
\(168\) 4.08627 0.315263
\(169\) 9.64617 0.742013
\(170\) −6.09560 + 0.683022i −0.467511 + 0.0523854i
\(171\) −5.44485 + 5.44485i −0.416378 + 0.416378i
\(172\) 5.61051i 0.427798i
\(173\) −18.1556 18.1556i −1.38034 1.38034i −0.843997 0.536348i \(-0.819803\pi\)
−0.536348 0.843997i \(-0.680197\pi\)
\(174\) 0.663993i 0.0503372i
\(175\) 17.2864 + 10.8914i 1.30673 + 0.823310i
\(176\) 4.93091i 0.371681i
\(177\) 10.5247i 0.791086i
\(178\) −2.52805 2.52805i −0.189485 0.189485i
\(179\) −8.43042 + 8.43042i −0.630119 + 0.630119i −0.948098 0.317979i \(-0.896996\pi\)
0.317979 + 0.948098i \(0.396996\pi\)
\(180\) 2.22216 0.248996i 0.165630 0.0185591i
\(181\) 14.9316 1.10985 0.554927 0.831899i \(-0.312746\pi\)
0.554927 + 0.831899i \(0.312746\pi\)
\(182\) 5.29155 + 5.29155i 0.392236 + 0.392236i
\(183\) 1.74408i 0.128926i
\(184\) 8.34738 0.615377
\(185\) −12.6649 4.95982i −0.931143 0.364653i
\(186\) 3.50837 0.257246
\(187\) 13.5260i 0.989116i
\(188\) 0.544094 + 0.544094i 0.0396822 + 0.0396822i
\(189\) −4.08627 −0.297233
\(190\) −13.4551 10.7436i −0.976134 0.779421i
\(191\) −3.66128 + 3.66128i −0.264921 + 0.264921i −0.827050 0.562129i \(-0.809983\pi\)
0.562129 + 0.827050i \(0.309983\pi\)
\(192\) 0.707107 + 0.707107i 0.0510310 + 0.0510310i
\(193\) 7.43122i 0.534911i −0.963570 0.267455i \(-0.913817\pi\)
0.963570 0.267455i \(-0.0861828\pi\)
\(194\) 17.4278i 1.25124i
\(195\) 3.20005 + 2.55517i 0.229160 + 0.182979i
\(196\) 9.69763i 0.692688i
\(197\) −13.1030 13.1030i −0.933552 0.933552i 0.0643735 0.997926i \(-0.479495\pi\)
−0.997926 + 0.0643735i \(0.979495\pi\)
\(198\) 4.93091i 0.350424i
\(199\) 10.2425 10.2425i 0.726071 0.726071i −0.243764 0.969835i \(-0.578382\pi\)
0.969835 + 0.243764i \(0.0783823\pi\)
\(200\) 1.10662 + 4.87600i 0.0782499 + 0.344785i
\(201\) −8.12973 −0.573427
\(202\) −13.9975 −0.984863
\(203\) 2.71326 0.190433
\(204\) 1.93966 + 1.93966i 0.135804 + 0.135804i
\(205\) 9.45997 1.06000i 0.660713 0.0740338i
\(206\) 12.0104i 0.836803i
\(207\) −8.34738 −0.580183
\(208\) 1.83135i 0.126981i
\(209\) 26.8480 26.8480i 1.85712 1.85712i
\(210\) −1.01747 9.08036i −0.0702119 0.626604i
\(211\) 8.47994 0.583783 0.291892 0.956451i \(-0.405715\pi\)
0.291892 + 0.956451i \(0.405715\pi\)
\(212\) 7.02831 7.02831i 0.482706 0.482706i
\(213\) −9.21144 9.21144i −0.631157 0.631157i
\(214\) −10.6057 + 10.6057i −0.724989 + 0.724989i
\(215\) −12.4675 + 1.39700i −0.850274 + 0.0952745i
\(216\) −0.707107 0.707107i −0.0481125 0.0481125i
\(217\) 14.3362i 0.973202i
\(218\) −11.8333 + 11.8333i −0.801454 + 0.801454i
\(219\) 8.41266i 0.568475i
\(220\) −10.9573 + 1.22778i −0.738739 + 0.0827768i
\(221\) 5.02356i 0.337922i
\(222\) 1.80078 + 5.81009i 0.120861 + 0.389948i
\(223\) −16.2856 + 16.2856i −1.09056 + 1.09056i −0.0950945 + 0.995468i \(0.530315\pi\)
−0.995468 + 0.0950945i \(0.969685\pi\)
\(224\) 2.88943 2.88943i 0.193058 0.193058i
\(225\) −1.10662 4.87600i −0.0737747 0.325067i
\(226\) 6.01525i 0.400129i
\(227\) −6.39016 −0.424130 −0.212065 0.977256i \(-0.568019\pi\)
−0.212065 + 0.977256i \(0.568019\pi\)
\(228\) 7.70018i 0.509957i
\(229\) 15.3620i 1.01515i 0.861608 + 0.507574i \(0.169458\pi\)
−0.861608 + 0.507574i \(0.830542\pi\)
\(230\) −2.07847 18.5492i −0.137050 1.22310i
\(231\) 20.1490 1.32571
\(232\) 0.469514 + 0.469514i 0.0308251 + 0.0308251i
\(233\) −14.9071 14.9071i −0.976598 0.976598i 0.0231339 0.999732i \(-0.492636\pi\)
−0.999732 + 0.0231339i \(0.992636\pi\)
\(234\) 1.83135i 0.119719i
\(235\) 1.07359 1.34454i 0.0700332 0.0877083i
\(236\) 7.44209 + 7.44209i 0.484439 + 0.484439i
\(237\) 6.72048i 0.436542i
\(238\) 7.92599 7.92599i 0.513766 0.513766i
\(239\) 8.66507 + 8.66507i 0.560497 + 0.560497i 0.929449 0.368952i \(-0.120283\pi\)
−0.368952 + 0.929449i \(0.620283\pi\)
\(240\) 1.39524 1.74737i 0.0900622 0.112792i
\(241\) 11.1430 11.1430i 0.717782 0.717782i −0.250369 0.968151i \(-0.580552\pi\)
0.968151 + 0.250369i \(0.0805519\pi\)
\(242\) 13.3138i 0.855845i
\(243\) 0.707107 + 0.707107i 0.0453609 + 0.0453609i
\(244\) −1.23325 1.23325i −0.0789510 0.0789510i
\(245\) −21.5497 + 2.41468i −1.37676 + 0.154268i
\(246\) −3.01023 3.01023i −0.191925 0.191925i
\(247\) −9.97141 + 9.97141i −0.634466 + 0.634466i
\(248\) 2.48079 2.48079i 0.157531 0.157531i
\(249\) 0.819833 0.0519548
\(250\) 10.5597 3.67320i 0.667855 0.232313i
\(251\) −9.10789 9.10789i −0.574885 0.574885i 0.358604 0.933490i \(-0.383253\pi\)
−0.933490 + 0.358604i \(0.883253\pi\)
\(252\) −2.88943 + 2.88943i −0.182017 + 0.182017i
\(253\) 41.1601 2.58772
\(254\) 3.19427 3.19427i 0.200427 0.200427i
\(255\) 3.82727 4.79321i 0.239673 0.300163i
\(256\) 1.00000 0.0625000
\(257\) −20.8722 −1.30197 −0.650986 0.759090i \(-0.725644\pi\)
−0.650986 + 0.759090i \(0.725644\pi\)
\(258\) 3.96723 + 3.96723i 0.246989 + 0.246989i
\(259\) 23.7416 7.35850i 1.47523 0.457235i
\(260\) 4.06955 0.455999i 0.252383 0.0282799i
\(261\) −0.469514 0.469514i −0.0290622 0.0290622i
\(262\) 1.15532 1.15532i 0.0713757 0.0713757i
\(263\) −0.897695 0.897695i −0.0553543 0.0553543i 0.678888 0.734242i \(-0.262462\pi\)
−0.734242 + 0.678888i \(0.762462\pi\)
\(264\) 3.48668 + 3.48668i 0.214590 + 0.214590i
\(265\) −17.3681 13.8680i −1.06691 0.851906i
\(266\) 31.4650 1.92924
\(267\) 3.57520 0.218799
\(268\) −5.74859 + 5.74859i −0.351151 + 0.351151i
\(269\) 10.6873i 0.651619i 0.945435 + 0.325810i \(0.105637\pi\)
−0.945435 + 0.325810i \(0.894363\pi\)
\(270\) −1.39524 + 1.74737i −0.0849115 + 0.106342i
\(271\) −21.1698 −1.28597 −0.642986 0.765878i \(-0.722305\pi\)
−0.642986 + 0.765878i \(0.722305\pi\)
\(272\) 2.74310 0.166325
\(273\) −7.48339 −0.452915
\(274\) −7.63981 + 7.63981i −0.461538 + 0.461538i
\(275\) 5.45664 + 24.0431i 0.329048 + 1.44985i
\(276\) −5.90249 + 5.90249i −0.355288 + 0.355288i
\(277\) 27.0099i 1.62287i 0.584443 + 0.811435i \(0.301313\pi\)
−0.584443 + 0.811435i \(0.698687\pi\)
\(278\) 6.69829i 0.401737i
\(279\) −2.48079 + 2.48079i −0.148521 + 0.148521i
\(280\) −7.14024 5.70132i −0.426711 0.340719i
\(281\) 6.59580 6.59580i 0.393473 0.393473i −0.482451 0.875923i \(-0.660253\pi\)
0.875923 + 0.482451i \(0.160253\pi\)
\(282\) −0.769466 −0.0458210
\(283\) 7.61412 0.452613 0.226306 0.974056i \(-0.427335\pi\)
0.226306 + 0.974056i \(0.427335\pi\)
\(284\) −13.0269 −0.773007
\(285\) 17.1110 1.91732i 1.01357 0.113572i
\(286\) 9.03020i 0.533967i
\(287\) −12.3006 + 12.3006i −0.726082 + 0.726082i
\(288\) −1.00000 −0.0589256
\(289\) −9.47542 −0.557378
\(290\) 0.926429 1.16024i 0.0544018 0.0681318i
\(291\) 12.3233 + 12.3233i 0.722404 + 0.722404i
\(292\) −5.94865 5.94865i −0.348118 0.348118i
\(293\) 3.86863 3.86863i 0.226008 0.226008i −0.585015 0.811023i \(-0.698911\pi\)
0.811023 + 0.585015i \(0.198911\pi\)
\(294\) 6.85726 + 6.85726i 0.399923 + 0.399923i
\(295\) 14.6845 18.3906i 0.854963 1.07074i
\(296\) 5.38170 + 2.83501i 0.312805 + 0.164782i
\(297\) −3.48668 3.48668i −0.202317 0.202317i
\(298\) −2.09937 −0.121613
\(299\) −15.2870 −0.884068
\(300\) −4.23035 2.66535i −0.244240 0.153884i
\(301\) 16.2112 16.2112i 0.934398 0.934398i
\(302\) 16.4484 0.946500
\(303\) 9.89776 9.89776i 0.568611 0.568611i
\(304\) 5.44485 + 5.44485i 0.312283 + 0.312283i
\(305\) −2.43341 + 3.04756i −0.139337 + 0.174503i
\(306\) −2.74310 −0.156812
\(307\) 11.5991 11.5991i 0.661998 0.661998i −0.293853 0.955851i \(-0.594937\pi\)
0.955851 + 0.293853i \(0.0949375\pi\)
\(308\) 14.2475 14.2475i 0.811827 0.811827i
\(309\) −8.49263 8.49263i −0.483129 0.483129i
\(310\) −6.13043 4.89501i −0.348185 0.278018i
\(311\) −10.3616 10.3616i −0.587555 0.587555i 0.349414 0.936969i \(-0.386381\pi\)
−0.936969 + 0.349414i \(0.886381\pi\)
\(312\) −1.29496 1.29496i −0.0733126 0.0733126i
\(313\) 22.6679i 1.28126i 0.767848 + 0.640632i \(0.221327\pi\)
−0.767848 + 0.640632i \(0.778673\pi\)
\(314\) −13.6581 + 13.6581i −0.770771 + 0.770771i
\(315\) 7.14024 + 5.70132i 0.402307 + 0.321233i
\(316\) −4.75210 4.75210i −0.267326 0.267326i
\(317\) 18.8950 18.8950i 1.06125 1.06125i 0.0632489 0.997998i \(-0.479854\pi\)
0.997998 0.0632489i \(-0.0201462\pi\)
\(318\) 9.93953i 0.557381i
\(319\) 2.31513 + 2.31513i 0.129622 + 0.129622i
\(320\) −0.248996 2.22216i −0.0139193 0.124223i
\(321\) 14.9987i 0.837145i
\(322\) 24.1192 + 24.1192i 1.34411 + 1.34411i
\(323\) 14.9357 + 14.9357i 0.831047 + 0.831047i
\(324\) 1.00000 0.0555556
\(325\) −2.02661 8.92965i −0.112416 0.495328i
\(326\) 16.1683i 0.895480i
\(327\) 16.7348i 0.925439i
\(328\) −4.25710 −0.235059
\(329\) 3.14425i 0.173348i
\(330\) 6.87979 8.61613i 0.378720 0.474302i
\(331\) −7.58835 + 7.58835i −0.417093 + 0.417093i −0.884201 0.467107i \(-0.845296\pi\)
0.467107 + 0.884201i \(0.345296\pi\)
\(332\) 0.579710 0.579710i 0.0318157 0.0318157i
\(333\) −5.38170 2.83501i −0.294916 0.155358i
\(334\) 0.266278i 0.0145701i
\(335\) 14.2057 + 11.3429i 0.776139 + 0.619730i
\(336\) 4.08627i 0.222924i
\(337\) −15.6272 + 15.6272i −0.851266 + 0.851266i −0.990289 0.139023i \(-0.955604\pi\)
0.139023 + 0.990289i \(0.455604\pi\)
\(338\) 9.64617i 0.524682i
\(339\) −4.25343 4.25343i −0.231014 0.231014i
\(340\) −0.683022 6.09560i −0.0370420 0.330581i
\(341\) 12.2326 12.2326i 0.662430 0.662430i
\(342\) −5.44485 5.44485i −0.294424 0.294424i
\(343\) 7.79461 7.79461i 0.420869 0.420869i
\(344\) 5.61051 0.302499
\(345\) 14.5860 + 11.6466i 0.785283 + 0.627031i
\(346\) 18.1556 18.1556i 0.976051 0.976051i
\(347\) 7.97256i 0.427990i −0.976835 0.213995i \(-0.931352\pi\)
0.976835 0.213995i \(-0.0686476\pi\)
\(348\) −0.663993 −0.0355938
\(349\) 1.39367i 0.0746015i −0.999304 0.0373008i \(-0.988124\pi\)
0.999304 0.0373008i \(-0.0118760\pi\)
\(350\) −10.8914 + 17.2864i −0.582168 + 0.923996i
\(351\) 1.29496 + 1.29496i 0.0691198 + 0.0691198i
\(352\) 4.93091 0.262818
\(353\) 8.13118 0.432779 0.216390 0.976307i \(-0.430572\pi\)
0.216390 + 0.976307i \(0.430572\pi\)
\(354\) −10.5247 −0.559382
\(355\) 3.24366 + 28.9480i 0.172156 + 1.53640i
\(356\) 2.52805 2.52805i 0.133986 0.133986i
\(357\) 11.2090i 0.593246i
\(358\) −8.43042 8.43042i −0.445561 0.445561i
\(359\) 7.41829i 0.391523i −0.980652 0.195761i \(-0.937282\pi\)
0.980652 0.195761i \(-0.0627178\pi\)
\(360\) 0.248996 + 2.22216i 0.0131233 + 0.117118i
\(361\) 40.2927i 2.12067i
\(362\) 14.9316i 0.784785i
\(363\) 9.41430 + 9.41430i 0.494122 + 0.494122i
\(364\) −5.29155 + 5.29155i −0.277353 + 0.277353i
\(365\) −11.7377 + 14.7000i −0.614377 + 0.769436i
\(366\) 1.74408 0.0911648
\(367\) −24.4204 24.4204i −1.27474 1.27474i −0.943574 0.331162i \(-0.892559\pi\)
−0.331162 0.943574i \(-0.607441\pi\)
\(368\) 8.34738i 0.435137i
\(369\) 4.25710 0.221616
\(370\) 4.95982 12.6649i 0.257849 0.658418i
\(371\) 40.6157 2.10866
\(372\) 3.50837i 0.181901i
\(373\) 25.6268 + 25.6268i 1.32690 + 1.32690i 0.908057 + 0.418847i \(0.137566\pi\)
0.418847 + 0.908057i \(0.362434\pi\)
\(374\) 13.5260 0.699410
\(375\) −4.86950 + 10.0642i −0.251460 + 0.519713i
\(376\) −0.544094 + 0.544094i −0.0280595 + 0.0280595i
\(377\) −0.859844 0.859844i −0.0442842 0.0442842i
\(378\) 4.08627i 0.210175i
\(379\) 1.27584i 0.0655357i 0.999463 + 0.0327678i \(0.0104322\pi\)
−0.999463 + 0.0327678i \(0.989568\pi\)
\(380\) 10.7436 13.4551i 0.551134 0.690231i
\(381\) 4.51738i 0.231433i
\(382\) −3.66128 3.66128i −0.187327 0.187327i
\(383\) 20.0723i 1.02565i −0.858494 0.512823i \(-0.828600\pi\)
0.858494 0.512823i \(-0.171400\pi\)
\(384\) −0.707107 + 0.707107i −0.0360844 + 0.0360844i
\(385\) −35.2079 28.1127i −1.79436 1.43276i
\(386\) 7.43122 0.378239
\(387\) −5.61051 −0.285198
\(388\) 17.4278 0.884761
\(389\) −8.42098 8.42098i −0.426961 0.426961i 0.460631 0.887592i \(-0.347623\pi\)
−0.887592 + 0.460631i \(0.847623\pi\)
\(390\) −2.55517 + 3.20005i −0.129386 + 0.162041i
\(391\) 22.8977i 1.15799i
\(392\) 9.69763 0.489804
\(393\) 1.63387i 0.0824176i
\(394\) 13.1030 13.1030i 0.660121 0.660121i
\(395\) −9.37667 + 11.7432i −0.471791 + 0.590863i
\(396\) −4.93091 −0.247787
\(397\) 4.91456 4.91456i 0.246655 0.246655i −0.572942 0.819596i \(-0.694198\pi\)
0.819596 + 0.572942i \(0.194198\pi\)
\(398\) 10.2425 + 10.2425i 0.513409 + 0.513409i
\(399\) −22.2491 + 22.2491i −1.11385 + 1.11385i
\(400\) −4.87600 + 1.10662i −0.243800 + 0.0553310i
\(401\) −9.79743 9.79743i −0.489260 0.489260i 0.418812 0.908073i \(-0.362446\pi\)
−0.908073 + 0.418812i \(0.862446\pi\)
\(402\) 8.12973i 0.405474i
\(403\) −4.54320 + 4.54320i −0.226313 + 0.226313i
\(404\) 13.9975i 0.696404i
\(405\) −0.248996 2.22216i −0.0123727 0.110420i
\(406\) 2.71326i 0.134657i
\(407\) 26.5367 + 13.9792i 1.31537 + 0.692921i
\(408\) −1.93966 + 1.93966i −0.0960276 + 0.0960276i
\(409\) −1.43202 + 1.43202i −0.0708087 + 0.0708087i −0.741624 0.670816i \(-0.765944\pi\)
0.670816 + 0.741624i \(0.265944\pi\)
\(410\) 1.06000 + 9.45997i 0.0523498 + 0.467194i
\(411\) 10.8043i 0.532938i
\(412\) −12.0104 −0.591709
\(413\) 43.0068i 2.11623i
\(414\) 8.34738i 0.410251i
\(415\) −1.43255 1.14386i −0.0703213 0.0561500i
\(416\) −1.83135 −0.0897892
\(417\) −4.73641 4.73641i −0.231943 0.231943i
\(418\) 26.8480 + 26.8480i 1.31318 + 1.31318i
\(419\) 23.3375i 1.14011i −0.821605 0.570057i \(-0.806921\pi\)
0.821605 0.570057i \(-0.193079\pi\)
\(420\) 9.08036 1.01747i 0.443076 0.0496473i
\(421\) −12.1830 12.1830i −0.593762 0.593762i 0.344884 0.938645i \(-0.387918\pi\)
−0.938645 + 0.344884i \(0.887918\pi\)
\(422\) 8.47994i 0.412797i
\(423\) 0.544094 0.544094i 0.0264548 0.0264548i
\(424\) 7.02831 + 7.02831i 0.341325 + 0.341325i
\(425\) −13.3753 + 3.03557i −0.648800 + 0.147247i
\(426\) 9.21144 9.21144i 0.446296 0.446296i
\(427\) 7.12681i 0.344890i
\(428\) −10.6057 10.6057i −0.512645 0.512645i
\(429\) −6.38532 6.38532i −0.308286 0.308286i
\(430\) −1.39700 12.4675i −0.0673692 0.601235i
\(431\) −22.3232 22.3232i −1.07527 1.07527i −0.996927 0.0783421i \(-0.975037\pi\)
−0.0783421 0.996927i \(-0.524963\pi\)
\(432\) 0.707107 0.707107i 0.0340207 0.0340207i
\(433\) −1.25239 + 1.25239i −0.0601862 + 0.0601862i −0.736559 0.676373i \(-0.763551\pi\)
0.676373 + 0.736559i \(0.263551\pi\)
\(434\) 14.3362 0.688158
\(435\) 0.165332 + 1.47550i 0.00792706 + 0.0707448i
\(436\) −11.8333 11.8333i −0.566714 0.566714i
\(437\) −45.4502 + 45.4502i −2.17418 + 2.17418i
\(438\) 8.41266 0.401972
\(439\) −0.852686 + 0.852686i −0.0406965 + 0.0406965i −0.727162 0.686466i \(-0.759161\pi\)
0.686466 + 0.727162i \(0.259161\pi\)
\(440\) −1.22778 10.9573i −0.0585320 0.522367i
\(441\) −9.69763 −0.461792
\(442\) −5.02356 −0.238947
\(443\) −13.9950 13.9950i −0.664922 0.664922i 0.291614 0.956536i \(-0.405808\pi\)
−0.956536 + 0.291614i \(0.905808\pi\)
\(444\) −5.81009 + 1.80078i −0.275735 + 0.0854615i
\(445\) −6.24720 4.98825i −0.296146 0.236466i
\(446\) −16.2856 16.2856i −0.771144 0.771144i
\(447\) 1.48448 1.48448i 0.0702133 0.0702133i
\(448\) 2.88943 + 2.88943i 0.136513 + 0.136513i
\(449\) 2.16577 + 2.16577i 0.102209 + 0.102209i 0.756362 0.654153i \(-0.226975\pi\)
−0.654153 + 0.756362i \(0.726975\pi\)
\(450\) 4.87600 1.10662i 0.229857 0.0521666i
\(451\) −20.9914 −0.988445
\(452\) −6.01525 −0.282934
\(453\) −11.6308 + 11.6308i −0.546462 + 0.546462i
\(454\) 6.39016i 0.299905i
\(455\) 13.0763 + 10.4411i 0.613025 + 0.489487i
\(456\) −7.70018 −0.360594
\(457\) 15.2516 0.713439 0.356720 0.934212i \(-0.383895\pi\)
0.356720 + 0.934212i \(0.383895\pi\)
\(458\) −15.3620 −0.717818
\(459\) 1.93966 1.93966i 0.0905357 0.0905357i
\(460\) 18.5492 2.07847i 0.864862 0.0969091i
\(461\) 14.4647 14.4647i 0.673686 0.673686i −0.284878 0.958564i \(-0.591953\pi\)
0.958564 + 0.284878i \(0.0919530\pi\)
\(462\) 20.1490i 0.937418i
\(463\) 17.5203i 0.814237i −0.913375 0.407118i \(-0.866534\pi\)
0.913375 0.407118i \(-0.133466\pi\)
\(464\) −0.469514 + 0.469514i −0.0217966 + 0.0217966i
\(465\) 7.79617 0.873572i 0.361539 0.0405109i
\(466\) 14.9071 14.9071i 0.690559 0.690559i
\(467\) 17.1724 0.794646 0.397323 0.917679i \(-0.369939\pi\)
0.397323 + 0.917679i \(0.369939\pi\)
\(468\) 1.83135 0.0846541
\(469\) −33.2203 −1.53397
\(470\) 1.34454 + 1.07359i 0.0620191 + 0.0495209i
\(471\) 19.3155i 0.890010i
\(472\) −7.44209 + 7.44209i −0.342550 + 0.342550i
\(473\) 27.6649 1.27203
\(474\) 6.72048 0.308682
\(475\) −32.5745 20.5237i −1.49462 0.941692i
\(476\) 7.92599 + 7.92599i 0.363287 + 0.363287i
\(477\) −7.02831 7.02831i −0.321804 0.321804i
\(478\) −8.66507 + 8.66507i −0.396331 + 0.396331i
\(479\) 16.4237 + 16.4237i 0.750419 + 0.750419i 0.974557 0.224139i \(-0.0719569\pi\)
−0.224139 + 0.974557i \(0.571957\pi\)
\(480\) 1.74737 + 1.39524i 0.0797563 + 0.0636836i
\(481\) −9.85577 5.19189i −0.449384 0.236730i
\(482\) 11.1430 + 11.1430i 0.507548 + 0.507548i
\(483\) −34.1097 −1.55204
\(484\) 13.3138 0.605174
\(485\) −4.33945 38.7273i −0.197044 1.75852i
\(486\) −0.707107 + 0.707107i −0.0320750 + 0.0320750i
\(487\) −17.8636 −0.809478 −0.404739 0.914432i \(-0.632638\pi\)
−0.404739 + 0.914432i \(0.632638\pi\)
\(488\) 1.23325 1.23325i 0.0558268 0.0558268i
\(489\) 11.4327 + 11.4327i 0.517006 + 0.517006i
\(490\) −2.41468 21.5497i −0.109084 0.973516i
\(491\) −38.7653 −1.74945 −0.874726 0.484618i \(-0.838958\pi\)
−0.874726 + 0.484618i \(0.838958\pi\)
\(492\) 3.01023 3.01023i 0.135711 0.135711i
\(493\) −1.28792 + 1.28792i −0.0580051 + 0.0580051i
\(494\) −9.97141 9.97141i −0.448635 0.448635i
\(495\) 1.22778 + 10.9573i 0.0551845 + 0.492493i
\(496\) 2.48079 + 2.48079i 0.111391 + 0.111391i
\(497\) −37.6404 37.6404i −1.68840 1.68840i
\(498\) 0.819833i 0.0367376i
\(499\) −7.54787 + 7.54787i −0.337889 + 0.337889i −0.855572 0.517683i \(-0.826795\pi\)
0.517683 + 0.855572i \(0.326795\pi\)
\(500\) 3.67320 + 10.5597i 0.164270 + 0.472245i
\(501\) −0.188287 0.188287i −0.00841205 0.00841205i
\(502\) 9.10789 9.10789i 0.406505 0.406505i
\(503\) 17.9380i 0.799816i 0.916555 + 0.399908i \(0.130958\pi\)
−0.916555 + 0.399908i \(0.869042\pi\)
\(504\) −2.88943 2.88943i −0.128706 0.128706i
\(505\) −31.1048 + 3.48534i −1.38415 + 0.155096i
\(506\) 41.1601i 1.82979i
\(507\) −6.82087 6.82087i −0.302925 0.302925i
\(508\) 3.19427 + 3.19427i 0.141723 + 0.141723i
\(509\) −14.1696 −0.628055 −0.314028 0.949414i \(-0.601678\pi\)
−0.314028 + 0.949414i \(0.601678\pi\)
\(510\) 4.79321 + 3.82727i 0.212247 + 0.169475i
\(511\) 34.3764i 1.52072i
\(512\) 1.00000i 0.0441942i
\(513\) 7.70018 0.339971
\(514\) 20.8722i 0.920633i
\(515\) 2.99054 + 26.6890i 0.131779 + 1.17606i
\(516\) −3.96723 + 3.96723i −0.174648 + 0.174648i
\(517\) −2.68288 + 2.68288i −0.117993 + 0.117993i
\(518\) 7.35850 + 23.7416i 0.323314 + 1.04315i
\(519\) 25.6759i 1.12705i
\(520\) 0.455999 + 4.06955i 0.0199969 + 0.178462i
\(521\) 14.0818i 0.616936i 0.951235 + 0.308468i \(0.0998162\pi\)
−0.951235 + 0.308468i \(0.900184\pi\)
\(522\) 0.469514 0.469514i 0.0205501 0.0205501i
\(523\) 9.57199i 0.418554i −0.977856 0.209277i \(-0.932889\pi\)
0.977856 0.209277i \(-0.0671110\pi\)
\(524\) 1.15532 + 1.15532i 0.0504703 + 0.0504703i
\(525\) −4.52195 19.9247i −0.197354 0.869584i
\(526\) 0.897695 0.897695i 0.0391414 0.0391414i
\(527\) 6.80506 + 6.80506i 0.296433 + 0.296433i
\(528\) −3.48668 + 3.48668i −0.151738 + 0.151738i
\(529\) −46.6788 −2.02951
\(530\) 13.8680 17.3681i 0.602388 0.754421i
\(531\) 7.44209 7.44209i 0.322959 0.322959i
\(532\) 31.4650i 1.36418i
\(533\) 7.79623 0.337692
\(534\) 3.57520i 0.154714i
\(535\) −20.9267 + 26.2083i −0.904742 + 1.13308i
\(536\) −5.74859 5.74859i −0.248301 0.248301i
\(537\) 11.9224 0.514490
\(538\) −10.6873 −0.460764
\(539\) 47.8181 2.05967
\(540\) −1.74737 1.39524i −0.0751949 0.0600415i
\(541\) −7.51447 + 7.51447i −0.323072 + 0.323072i −0.849944 0.526872i \(-0.823365\pi\)
0.526872 + 0.849944i \(0.323365\pi\)
\(542\) 21.1698i 0.909320i
\(543\) −10.5582 10.5582i −0.453096 0.453096i
\(544\) 2.74310i 0.117609i
\(545\) −23.3491 + 29.2420i −1.00017 + 1.25259i
\(546\) 7.48339i 0.320259i
\(547\) 12.8110i 0.547759i 0.961764 + 0.273880i \(0.0883070\pi\)
−0.961764 + 0.273880i \(0.911693\pi\)
\(548\) −7.63981 7.63981i −0.326357 0.326357i
\(549\) −1.23325 + 1.23325i −0.0526340 + 0.0526340i
\(550\) −24.0431 + 5.45664i −1.02520 + 0.232672i
\(551\) −5.11286 −0.217815
\(552\) −5.90249 5.90249i −0.251227 0.251227i
\(553\) 27.4617i 1.16779i
\(554\) −27.0099 −1.14754
\(555\) 5.44833 + 12.4626i 0.231269 + 0.529007i
\(556\) −6.69829 −0.284071
\(557\) 5.34895i 0.226642i −0.993558 0.113321i \(-0.963851\pi\)
0.993558 0.113321i \(-0.0361489\pi\)
\(558\) −2.48079 2.48079i −0.105020 0.105020i
\(559\) −10.2748 −0.434578
\(560\) 5.70132 7.14024i 0.240925 0.301730i
\(561\) −9.56429 + 9.56429i −0.403805 + 0.403805i
\(562\) 6.59580 + 6.59580i 0.278227 + 0.278227i
\(563\) 39.3536i 1.65856i 0.558836 + 0.829279i \(0.311248\pi\)
−0.558836 + 0.829279i \(0.688752\pi\)
\(564\) 0.769466i 0.0324003i
\(565\) 1.49778 + 13.3669i 0.0630119 + 0.562348i
\(566\) 7.61412i 0.320046i
\(567\) 2.88943 + 2.88943i 0.121345 + 0.121345i
\(568\) 13.0269i 0.546598i
\(569\) 17.8957 17.8957i 0.750226 0.750226i −0.224296 0.974521i \(-0.572008\pi\)
0.974521 + 0.224296i \(0.0720081\pi\)
\(570\) 1.91732 + 17.1110i 0.0803076 + 0.716702i
\(571\) 14.1071 0.590362 0.295181 0.955441i \(-0.404620\pi\)
0.295181 + 0.955441i \(0.404620\pi\)
\(572\) −9.03020 −0.377572
\(573\) 5.17783 0.216307
\(574\) −12.3006 12.3006i −0.513417 0.513417i
\(575\) −9.23738 40.7018i −0.385226 1.69738i
\(576\) 1.00000i 0.0416667i
\(577\) 8.43655 0.351218 0.175609 0.984460i \(-0.443811\pi\)
0.175609 + 0.984460i \(0.443811\pi\)
\(578\) 9.47542i 0.394125i
\(579\) −5.25466 + 5.25466i −0.218376 + 0.218376i
\(580\) 1.16024 + 0.926429i 0.0481765 + 0.0384679i
\(581\) 3.35006 0.138984
\(582\) −12.3233 + 12.3233i −0.510817 + 0.510817i
\(583\) 34.6559 + 34.6559i 1.43530 + 1.43530i
\(584\) 5.94865 5.94865i 0.246157 0.246157i
\(585\) −0.455999 4.06955i −0.0188532 0.168255i
\(586\) 3.86863 + 3.86863i 0.159812 + 0.159812i
\(587\) 23.4466i 0.967743i −0.875139 0.483872i \(-0.839230\pi\)
0.875139 0.483872i \(-0.160770\pi\)
\(588\) −6.85726 + 6.85726i −0.282789 + 0.282789i
\(589\) 27.0151i 1.11314i
\(590\) 18.3906 + 14.6845i 0.757128 + 0.604550i
\(591\) 18.5305i 0.762242i
\(592\) −2.83501 + 5.38170i −0.116518 + 0.221187i
\(593\) −20.7079 + 20.7079i −0.850371 + 0.850371i −0.990179 0.139807i \(-0.955352\pi\)
0.139807 + 0.990179i \(0.455352\pi\)
\(594\) 3.48668 3.48668i 0.143060 0.143060i
\(595\) 15.6393 19.5864i 0.641148 0.802963i
\(596\) 2.09937i 0.0859934i
\(597\) −14.4851 −0.592834
\(598\) 15.2870i 0.625130i
\(599\) 35.8882i 1.46635i 0.680038 + 0.733177i \(0.261963\pi\)
−0.680038 + 0.733177i \(0.738037\pi\)
\(600\) 2.66535 4.23035i 0.108813 0.172703i
\(601\) −2.20315 −0.0898682 −0.0449341 0.998990i \(-0.514308\pi\)
−0.0449341 + 0.998990i \(0.514308\pi\)
\(602\) 16.2112 + 16.2112i 0.660719 + 0.660719i
\(603\) 5.74859 + 5.74859i 0.234101 + 0.234101i
\(604\) 16.4484i 0.669276i
\(605\) −3.31510 29.5855i −0.134778 1.20282i
\(606\) 9.89776 + 9.89776i 0.402069 + 0.402069i
\(607\) 37.3445i 1.51577i 0.652391 + 0.757883i \(0.273766\pi\)
−0.652391 + 0.757883i \(0.726234\pi\)
\(608\) −5.44485 + 5.44485i −0.220818 + 0.220818i
\(609\) −1.91856 1.91856i −0.0777441 0.0777441i
\(610\) −3.04756 2.43341i −0.123392 0.0985260i
\(611\) 0.996426 0.996426i 0.0403111 0.0403111i
\(612\) 2.74310i 0.110883i
\(613\) 6.97292 + 6.97292i 0.281634 + 0.281634i 0.833760 0.552127i \(-0.186183\pi\)
−0.552127 + 0.833760i \(0.686183\pi\)
\(614\) 11.5991 + 11.5991i 0.468103 + 0.468103i
\(615\) −7.43874 5.93967i −0.299959 0.239511i
\(616\) 14.2475 + 14.2475i 0.574049 + 0.574049i
\(617\) 8.33189 8.33189i 0.335429 0.335429i −0.519215 0.854644i \(-0.673775\pi\)
0.854644 + 0.519215i \(0.173775\pi\)
\(618\) 8.49263 8.49263i 0.341623 0.341623i
\(619\) 24.7413 0.994437 0.497218 0.867625i \(-0.334355\pi\)
0.497218 + 0.867625i \(0.334355\pi\)
\(620\) 4.89501 6.13043i 0.196589 0.246204i
\(621\) 5.90249 + 5.90249i 0.236859 + 0.236859i
\(622\) 10.3616 10.3616i 0.415464 0.415464i
\(623\) 14.6092 0.585307
\(624\) 1.29496 1.29496i 0.0518398 0.0518398i
\(625\) 22.5508 10.7918i 0.902031 0.431671i
\(626\) −22.6679 −0.905990
\(627\) −37.9688 −1.51633
\(628\) −13.6581 13.6581i −0.545017 0.545017i
\(629\) −7.77670 + 14.7625i −0.310077 + 0.588621i
\(630\) −5.70132 + 7.14024i −0.227146 + 0.284474i
\(631\) 0.137530 + 0.137530i 0.00547496 + 0.00547496i 0.709839 0.704364i \(-0.248768\pi\)
−0.704364 + 0.709839i \(0.748768\pi\)
\(632\) 4.75210 4.75210i 0.189028 0.189028i
\(633\) −5.99623 5.99623i −0.238329 0.238329i
\(634\) 18.8950 + 18.8950i 0.750415 + 0.750415i
\(635\) 6.30283 7.89355i 0.250120 0.313246i
\(636\) −9.93953 −0.394128
\(637\) −17.7597 −0.703666
\(638\) −2.31513 + 2.31513i −0.0916569 + 0.0916569i
\(639\) 13.0269i 0.515338i
\(640\) 2.22216 0.248996i 0.0878386 0.00984245i
\(641\) 34.7424 1.37224 0.686121 0.727487i \(-0.259312\pi\)
0.686121 + 0.727487i \(0.259312\pi\)
\(642\) 14.9987 0.591951
\(643\) −10.3530 −0.408282 −0.204141 0.978942i \(-0.565440\pi\)
−0.204141 + 0.978942i \(0.565440\pi\)
\(644\) −24.1192 + 24.1192i −0.950429 + 0.950429i
\(645\) 9.80366 + 7.82800i 0.386019 + 0.308227i
\(646\) −14.9357 + 14.9357i −0.587639 + 0.587639i
\(647\) 21.7902i 0.856663i −0.903622 0.428331i \(-0.859102\pi\)
0.903622 0.428331i \(-0.140898\pi\)
\(648\) 1.00000i 0.0392837i
\(649\) −36.6963 + 36.6963i −1.44045 + 1.44045i
\(650\) 8.92965 2.02661i 0.350250 0.0794901i
\(651\) −10.1372 + 10.1372i −0.397308 + 0.397308i
\(652\) 16.1683 0.633200
\(653\) 42.4982 1.66308 0.831541 0.555464i \(-0.187459\pi\)
0.831541 + 0.555464i \(0.187459\pi\)
\(654\) 16.7348 0.654384
\(655\) 2.27963 2.85497i 0.0890726 0.111553i
\(656\) 4.25710i 0.166212i
\(657\) −5.94865 + 5.94865i −0.232079 + 0.232079i
\(658\) −3.14425 −0.122576
\(659\) 17.1397 0.667669 0.333835 0.942632i \(-0.391657\pi\)
0.333835 + 0.942632i \(0.391657\pi\)
\(660\) 8.61613 + 6.87979i 0.335382 + 0.267795i
\(661\) 20.1373 + 20.1373i 0.783252 + 0.783252i 0.980378 0.197126i \(-0.0631609\pi\)
−0.197126 + 0.980378i \(0.563161\pi\)
\(662\) −7.58835 7.58835i −0.294930 0.294930i
\(663\) 3.55220 3.55220i 0.137956 0.137956i
\(664\) 0.579710 + 0.579710i 0.0224971 + 0.0224971i
\(665\) 69.9204 7.83468i 2.71140 0.303816i
\(666\) 2.83501 5.38170i 0.109854 0.208537i
\(667\) −3.91921 3.91921i −0.151753 0.151753i
\(668\) −0.266278 −0.0103026
\(669\) 23.0313 0.890441
\(670\) −11.3429 + 14.2057i −0.438215 + 0.548813i
\(671\) 6.08106 6.08106i 0.234757 0.234757i
\(672\) −4.08627 −0.157631
\(673\) 26.9868 26.9868i 1.04027 1.04027i 0.0411115 0.999155i \(-0.486910\pi\)
0.999155 0.0411115i \(-0.0130899\pi\)
\(674\) −15.6272 15.6272i −0.601936 0.601936i
\(675\) −2.66535 + 4.23035i −0.102590 + 0.162826i
\(676\) −9.64617 −0.371006
\(677\) −5.05044 + 5.05044i −0.194104 + 0.194104i −0.797467 0.603363i \(-0.793827\pi\)
0.603363 + 0.797467i \(0.293827\pi\)
\(678\) 4.25343 4.25343i 0.163352 0.163352i
\(679\) 50.3564 + 50.3564i 1.93250 + 1.93250i
\(680\) 6.09560 0.683022i 0.233756 0.0261927i
\(681\) 4.51853 + 4.51853i 0.173150 + 0.173150i
\(682\) 12.2326 + 12.2326i 0.468409 + 0.468409i
\(683\) 33.7252i 1.29046i −0.763990 0.645229i \(-0.776762\pi\)
0.763990 0.645229i \(-0.223238\pi\)
\(684\) 5.44485 5.44485i 0.208189 0.208189i
\(685\) −15.0746 + 18.8792i −0.575971 + 0.721337i
\(686\) 7.79461 + 7.79461i 0.297600 + 0.297600i
\(687\) 10.8626 10.8626i 0.414433 0.414433i
\(688\) 5.61051i 0.213899i
\(689\) −12.8713 12.8713i −0.490357 0.490357i
\(690\) −11.6466 + 14.5860i −0.443378 + 0.555279i
\(691\) 38.3015i 1.45706i 0.685015 + 0.728529i \(0.259796\pi\)
−0.685015 + 0.728529i \(0.740204\pi\)
\(692\) 18.1556 + 18.1556i 0.690172 + 0.690172i
\(693\) −14.2475 14.2475i −0.541218 0.541218i
\(694\) 7.97256 0.302634
\(695\) 1.66785 + 14.8847i 0.0632652 + 0.564608i
\(696\) 0.663993i 0.0251686i
\(697\) 11.6776i 0.442322i
\(698\) 1.39367 0.0527513
\(699\) 21.0819i 0.797389i
\(700\) −17.2864 10.8914i −0.653364 0.411655i
\(701\) −3.16581 + 3.16581i −0.119571 + 0.119571i −0.764360 0.644789i \(-0.776945\pi\)
0.644789 + 0.764360i \(0.276945\pi\)
\(702\) −1.29496 + 1.29496i −0.0488751 + 0.0488751i
\(703\) −44.7387 + 13.8664i −1.68735 + 0.522980i
\(704\) 4.93091i 0.185840i
\(705\) −1.70988 + 0.191594i −0.0643977 + 0.00721586i
\(706\) 8.13118i 0.306021i
\(707\) 40.4449 40.4449i 1.52109 1.52109i
\(708\) 10.5247i 0.395543i
\(709\) −3.37894 3.37894i −0.126899 0.126899i 0.640805 0.767704i \(-0.278601\pi\)
−0.767704 + 0.640805i \(0.778601\pi\)
\(710\) −28.9480 + 3.24366i −1.08640 + 0.121732i
\(711\) −4.75210 + 4.75210i −0.178217 + 0.178217i
\(712\) 2.52805 + 2.52805i 0.0947426 + 0.0947426i
\(713\) −20.7081 + 20.7081i −0.775526 + 0.775526i
\(714\) −11.2090 −0.419488
\(715\) 2.24849 + 20.0666i 0.0840887 + 0.750447i
\(716\) 8.43042 8.43042i 0.315059 0.315059i
\(717\) 12.2543i 0.457644i
\(718\) 7.41829 0.276848
\(719\) 33.2657i 1.24060i 0.784364 + 0.620301i \(0.212989\pi\)
−0.784364 + 0.620301i \(0.787011\pi\)
\(720\) −2.22216 + 0.248996i −0.0828151 + 0.00927955i
\(721\) −34.7032 34.7032i −1.29241 1.29241i
\(722\) −40.2927 −1.49954
\(723\) −15.7585 −0.586066
\(724\) −14.9316 −0.554927
\(725\) 1.76978 2.80893i 0.0657279 0.104321i
\(726\) −9.41430 + 9.41430i −0.349397 + 0.349397i
\(727\) 0.0260774i 0.000967156i −1.00000 0.000483578i \(-0.999846\pi\)
1.00000 0.000483578i \(-0.000153928\pi\)
\(728\) −5.29155 5.29155i −0.196118 0.196118i
\(729\) 1.00000i 0.0370370i
\(730\) −14.7000 11.7377i −0.544073 0.434430i
\(731\) 15.3902i 0.569226i
\(732\) 1.74408i 0.0644632i
\(733\) −4.32418 4.32418i −0.159717 0.159717i 0.622724 0.782441i \(-0.286026\pi\)
−0.782441 + 0.622724i \(0.786026\pi\)
\(734\) 24.4204 24.4204i 0.901374 0.901374i
\(735\) 16.9454 + 13.5305i 0.625039 + 0.499080i
\(736\) −8.34738 −0.307689
\(737\) −28.3457 28.3457i −1.04413 1.04413i
\(738\) 4.25710i 0.156706i
\(739\) −4.68946 −0.172505 −0.0862523 0.996273i \(-0.527489\pi\)
−0.0862523 + 0.996273i \(0.527489\pi\)
\(740\) 12.6649 + 4.95982i 0.465572 + 0.182327i
\(741\) 14.1017 0.518039
\(742\) 40.6157i 1.49105i
\(743\) −22.9763 22.9763i −0.842918 0.842918i 0.146320 0.989237i \(-0.453257\pi\)
−0.989237 + 0.146320i \(0.953257\pi\)
\(744\) −3.50837 −0.128623
\(745\) −4.66513 + 0.522735i −0.170917 + 0.0191515i
\(746\) −25.6268 + 25.6268i −0.938263 + 0.938263i
\(747\) −0.579710 0.579710i −0.0212105 0.0212105i
\(748\) 13.5260i 0.494558i
\(749\) 61.2887i 2.23944i
\(750\) −10.0642 4.86950i −0.367492 0.177809i
\(751\) 22.7491i 0.830126i −0.909793 0.415063i \(-0.863759\pi\)
0.909793 0.415063i \(-0.136241\pi\)
\(752\) −0.544094 0.544094i −0.0198411 0.0198411i
\(753\) 12.8805i 0.469392i
\(754\) 0.859844 0.859844i 0.0313137 0.0313137i
\(755\) 36.5510 4.09560i 1.33023 0.149054i
\(756\) 4.08627 0.148616
\(757\) 18.9847 0.690010 0.345005 0.938601i \(-0.387877\pi\)
0.345005 + 0.938601i \(0.387877\pi\)
\(758\) −1.27584 −0.0463407
\(759\) −29.1046 29.1046i −1.05643 1.05643i
\(760\) 13.4551 + 10.7436i 0.488067 + 0.389711i
\(761\) 5.29007i 0.191765i −0.995393 0.0958825i \(-0.969433\pi\)
0.995393 0.0958825i \(-0.0305673\pi\)
\(762\) −4.51738 −0.163648
\(763\) 68.3832i 2.47564i
\(764\) 3.66128 3.66128i 0.132461 0.132461i
\(765\) −6.09560 + 0.683022i −0.220387 + 0.0246947i
\(766\) 20.0723 0.725242
\(767\) 13.6291 13.6291i 0.492117 0.492117i
\(768\) −0.707107 0.707107i −0.0255155 0.0255155i
\(769\) 2.00119 2.00119i 0.0721646 0.0721646i −0.670103 0.742268i \(-0.733750\pi\)
0.742268 + 0.670103i \(0.233750\pi\)
\(770\) 28.1127 35.2079i 1.01311 1.26880i
\(771\) 14.7589 + 14.7589i 0.531528 + 0.531528i
\(772\) 7.43122i 0.267455i
\(773\) −12.7879 + 12.7879i −0.459948 + 0.459948i −0.898638 0.438690i \(-0.855443\pi\)
0.438690 + 0.898638i \(0.355443\pi\)
\(774\) 5.61051i 0.201666i
\(775\) −14.8417 9.35106i −0.533128 0.335900i
\(776\) 17.4278i 0.625621i
\(777\) −21.9911 11.5846i −0.788927 0.415596i
\(778\) 8.42098 8.42098i 0.301907 0.301907i
\(779\) 23.1793 23.1793i 0.830483 0.830483i
\(780\) −3.20005 2.55517i