Properties

Label 731.2.m.c.87.18
Level 731
Weight 2
Character 731.87
Analytic conductor 5.837
Analytic rank 0
Dimension 128
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) = \( 731 = 17 \cdot 43 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 731.m (of order \(8\), degree \(4\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.83706438776\)
Analytic rank: \(0\)
Dimension: \(128\)
Relative dimension: \(32\) over \(\Q(\zeta_{8})\)
Coefficient ring index: multiple of None
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label 87.18
Character \(\chi\) = 731.87
Dual form 731.2.m.c.689.18

$q$-expansion

\(f(q)\) \(=\) \(q+(0.493410 + 0.493410i) q^{2} +(2.20257 - 0.912334i) q^{3} -1.51309i q^{4} +(-1.26013 - 3.04222i) q^{5} +(1.53692 + 0.636615i) q^{6} +(-1.60257 + 3.86896i) q^{7} +(1.73339 - 1.73339i) q^{8} +(1.89764 - 1.89764i) q^{9} +O(q^{10})\) \(q+(0.493410 + 0.493410i) q^{2} +(2.20257 - 0.912334i) q^{3} -1.51309i q^{4} +(-1.26013 - 3.04222i) q^{5} +(1.53692 + 0.636615i) q^{6} +(-1.60257 + 3.86896i) q^{7} +(1.73339 - 1.73339i) q^{8} +(1.89764 - 1.89764i) q^{9} +(0.879301 - 2.12282i) q^{10} +(0.798554 + 0.330772i) q^{11} +(-1.38045 - 3.33269i) q^{12} -4.97189i q^{13} +(-2.69971 + 1.11826i) q^{14} +(-5.55104 - 5.55104i) q^{15} -1.31564 q^{16} +(-0.463963 - 4.09692i) q^{17} +1.87263 q^{18} +(0.523830 + 0.523830i) q^{19} +(-4.60316 + 1.90669i) q^{20} +9.98374i q^{21} +(0.230808 + 0.557221i) q^{22} +(6.47869 + 2.68356i) q^{23} +(2.23649 - 5.39936i) q^{24} +(-4.13164 + 4.13164i) q^{25} +(2.45318 - 2.45318i) q^{26} +(-0.288600 + 0.696741i) q^{27} +(5.85410 + 2.42485i) q^{28} +(-0.419969 - 1.01389i) q^{29} -5.47788i q^{30} +(-1.54250 + 0.638926i) q^{31} +(-4.11594 - 4.11594i) q^{32} +2.06065 q^{33} +(1.79254 - 2.25038i) q^{34} +13.7897 q^{35} +(-2.87131 - 2.87131i) q^{36} +(1.02087 - 0.422858i) q^{37} +0.516926i q^{38} +(-4.53603 - 10.9509i) q^{39} +(-7.45767 - 3.08907i) q^{40} +(-1.36744 + 3.30130i) q^{41} +(-4.92607 + 4.92607i) q^{42} +(-0.707107 + 0.707107i) q^{43} +(0.500489 - 1.20829i) q^{44} +(-8.16431 - 3.38177i) q^{45} +(1.87255 + 4.52075i) q^{46} +4.76167i q^{47} +(-2.89779 + 1.20030i) q^{48} +(-7.45084 - 7.45084i) q^{49} -4.07718 q^{50} +(-4.75967 - 8.60046i) q^{51} -7.52294 q^{52} +(0.708903 + 0.708903i) q^{53} +(-0.486177 + 0.201381i) q^{54} -2.84619i q^{55} +(3.92854 + 9.48433i) q^{56} +(1.63168 + 0.675864i) q^{57} +(0.293049 - 0.707482i) q^{58} +(5.32071 - 5.32071i) q^{59} +(-8.39925 + 8.39925i) q^{60} +(0.461102 - 1.11320i) q^{61} +(-1.07634 - 0.445834i) q^{62} +(4.30078 + 10.3830i) q^{63} -1.43041i q^{64} +(-15.1256 + 6.26523i) q^{65} +(1.01674 + 1.01674i) q^{66} +14.3801 q^{67} +(-6.19902 + 0.702020i) q^{68} +16.7181 q^{69} +(6.80396 + 6.80396i) q^{70} +(9.57871 - 3.96763i) q^{71} -6.57872i q^{72} +(3.54002 + 8.54636i) q^{73} +(0.712349 + 0.295065i) q^{74} +(-5.33079 + 12.8697i) q^{75} +(0.792604 - 0.792604i) q^{76} +(-2.55949 + 2.55949i) q^{77} +(3.16518 - 7.64143i) q^{78} +(5.43583 + 2.25160i) q^{79} +(1.65787 + 4.00246i) q^{80} +9.84893i q^{81} +(-2.30360 + 0.954184i) q^{82} +(7.05417 + 7.05417i) q^{83} +15.1063 q^{84} +(-11.8791 + 6.57412i) q^{85} -0.697787 q^{86} +(-1.85002 - 1.85002i) q^{87} +(1.95757 - 0.810851i) q^{88} -6.34024i q^{89} +(-2.35975 - 5.69695i) q^{90} +(19.2361 + 7.96783i) q^{91} +(4.06048 - 9.80287i) q^{92} +(-2.81456 + 2.81456i) q^{93} +(-2.34946 + 2.34946i) q^{94} +(0.933512 - 2.25370i) q^{95} +(-12.8208 - 5.31053i) q^{96} +(-0.907902 - 2.19187i) q^{97} -7.35264i q^{98} +(2.14305 - 0.887682i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 128q + 4q^{2} + 4q^{3} + 8q^{5} - 12q^{6} + 4q^{7} - 4q^{8} + 8q^{9} + O(q^{10}) \) \( 128q + 4q^{2} + 4q^{3} + 8q^{5} - 12q^{6} + 4q^{7} - 4q^{8} + 8q^{9} - 8q^{10} - 4q^{11} + 12q^{12} + 12q^{14} - 12q^{15} - 144q^{16} - 12q^{17} + 64q^{18} - 28q^{19} - 8q^{20} - 12q^{22} + 16q^{23} - 16q^{24} - 20q^{25} + 16q^{26} - 8q^{27} + 20q^{28} + 12q^{31} - 4q^{32} - 104q^{33} + 20q^{34} + 32q^{35} - 96q^{36} - 12q^{37} + 8q^{39} + 216q^{40} + 24q^{41} - 4q^{42} + 24q^{44} - 28q^{45} - 48q^{46} + 28q^{48} - 80q^{50} - 20q^{51} + 56q^{52} - 36q^{53} - 12q^{54} - 8q^{56} + 72q^{57} - 32q^{58} + 48q^{59} - 40q^{60} - 76q^{61} - 44q^{62} + 36q^{65} - 68q^{66} - 48q^{67} + 32q^{68} + 216q^{69} - 196q^{70} + 4q^{71} + 20q^{73} + 88q^{74} + 80q^{75} + 72q^{76} + 28q^{77} - 120q^{78} + 68q^{79} - 68q^{80} + 28q^{82} - 36q^{83} - 152q^{84} + 28q^{85} - 24q^{86} - 56q^{87} + 20q^{88} - 112q^{90} + 96q^{91} - 28q^{92} + 24q^{93} - 36q^{94} - 108q^{95} + 272q^{96} + 8q^{97} - 20q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/731\mathbb{Z}\right)^\times\).

\(n\) \(173\) \(562\)
\(\chi(n)\) \(e\left(\frac{7}{8}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.493410 + 0.493410i 0.348893 + 0.348893i 0.859697 0.510804i \(-0.170652\pi\)
−0.510804 + 0.859697i \(0.670652\pi\)
\(3\) 2.20257 0.912334i 1.27165 0.526737i 0.358188 0.933650i \(-0.383395\pi\)
0.913467 + 0.406913i \(0.133395\pi\)
\(4\) 1.51309i 0.756547i
\(5\) −1.26013 3.04222i −0.563547 1.36052i −0.906912 0.421320i \(-0.861567\pi\)
0.343365 0.939202i \(-0.388433\pi\)
\(6\) 1.53692 + 0.636615i 0.627447 + 0.259897i
\(7\) −1.60257 + 3.86896i −0.605716 + 1.46233i 0.261900 + 0.965095i \(0.415651\pi\)
−0.867617 + 0.497234i \(0.834349\pi\)
\(8\) 1.73339 1.73339i 0.612848 0.612848i
\(9\) 1.89764 1.89764i 0.632547 0.632547i
\(10\) 0.879301 2.12282i 0.278059 0.671295i
\(11\) 0.798554 + 0.330772i 0.240773 + 0.0997315i 0.499807 0.866137i \(-0.333404\pi\)
−0.259034 + 0.965868i \(0.583404\pi\)
\(12\) −1.38045 3.33269i −0.398501 0.962066i
\(13\) 4.97189i 1.37896i −0.724307 0.689478i \(-0.757840\pi\)
0.724307 0.689478i \(-0.242160\pi\)
\(14\) −2.69971 + 1.11826i −0.721527 + 0.298866i
\(15\) −5.55104 5.55104i −1.43327 1.43327i
\(16\) −1.31564 −0.328910
\(17\) −0.463963 4.09692i −0.112528 0.993649i
\(18\) 1.87263 0.441383
\(19\) 0.523830 + 0.523830i 0.120175 + 0.120175i 0.764637 0.644462i \(-0.222919\pi\)
−0.644462 + 0.764637i \(0.722919\pi\)
\(20\) −4.60316 + 1.90669i −1.02930 + 0.426349i
\(21\) 9.98374i 2.17863i
\(22\) 0.230808 + 0.557221i 0.0492085 + 0.118800i
\(23\) 6.47869 + 2.68356i 1.35090 + 0.559561i 0.936543 0.350553i \(-0.114006\pi\)
0.414358 + 0.910114i \(0.364006\pi\)
\(24\) 2.23649 5.39936i 0.456521 1.10214i
\(25\) −4.13164 + 4.13164i −0.826328 + 0.826328i
\(26\) 2.45318 2.45318i 0.481108 0.481108i
\(27\) −0.288600 + 0.696741i −0.0555410 + 0.134088i
\(28\) 5.85410 + 2.42485i 1.10632 + 0.458253i
\(29\) −0.419969 1.01389i −0.0779863 0.188275i 0.880078 0.474829i \(-0.157490\pi\)
−0.958064 + 0.286554i \(0.907490\pi\)
\(30\) 5.47788i 1.00012i
\(31\) −1.54250 + 0.638926i −0.277042 + 0.114755i −0.516879 0.856059i \(-0.672906\pi\)
0.239837 + 0.970813i \(0.422906\pi\)
\(32\) −4.11594 4.11594i −0.727602 0.727602i
\(33\) 2.06065 0.358712
\(34\) 1.79254 2.25038i 0.307417 0.385938i
\(35\) 13.7897 2.33088
\(36\) −2.87131 2.87131i −0.478551 0.478551i
\(37\) 1.02087 0.422858i 0.167830 0.0695174i −0.297187 0.954819i \(-0.596048\pi\)
0.465017 + 0.885302i \(0.346048\pi\)
\(38\) 0.516926i 0.0838564i
\(39\) −4.53603 10.9509i −0.726346 1.75355i
\(40\) −7.45767 3.08907i −1.17916 0.488424i
\(41\) −1.36744 + 3.30130i −0.213559 + 0.515576i −0.993965 0.109696i \(-0.965012\pi\)
0.780406 + 0.625273i \(0.215012\pi\)
\(42\) −4.92607 + 4.92607i −0.760110 + 0.760110i
\(43\) −0.707107 + 0.707107i −0.107833 + 0.107833i
\(44\) 0.500489 1.20829i 0.0754515 0.182156i
\(45\) −8.16431 3.38177i −1.21706 0.504124i
\(46\) 1.87255 + 4.52075i 0.276093 + 0.666548i
\(47\) 4.76167i 0.694561i 0.937761 + 0.347281i \(0.112895\pi\)
−0.937761 + 0.347281i \(0.887105\pi\)
\(48\) −2.89779 + 1.20030i −0.418260 + 0.173249i
\(49\) −7.45084 7.45084i −1.06441 1.06441i
\(50\) −4.07718 −0.576601
\(51\) −4.75967 8.60046i −0.666487 1.20431i
\(52\) −7.52294 −1.04324
\(53\) 0.708903 + 0.708903i 0.0973754 + 0.0973754i 0.754116 0.656741i \(-0.228065\pi\)
−0.656741 + 0.754116i \(0.728065\pi\)
\(54\) −0.486177 + 0.201381i −0.0661603 + 0.0274045i
\(55\) 2.84619i 0.383780i
\(56\) 3.92854 + 9.48433i 0.524973 + 1.26740i
\(57\) 1.63168 + 0.675864i 0.216121 + 0.0895204i
\(58\) 0.293049 0.707482i 0.0384792 0.0928970i
\(59\) 5.32071 5.32071i 0.692697 0.692697i −0.270127 0.962825i \(-0.587066\pi\)
0.962825 + 0.270127i \(0.0870658\pi\)
\(60\) −8.39925 + 8.39925i −1.08434 + 1.08434i
\(61\) 0.461102 1.11320i 0.0590380 0.142530i −0.891608 0.452808i \(-0.850422\pi\)
0.950646 + 0.310278i \(0.100422\pi\)
\(62\) −1.07634 0.445834i −0.136695 0.0566210i
\(63\) 4.30078 + 10.3830i 0.541847 + 1.30814i
\(64\) 1.43041i 0.178801i
\(65\) −15.1256 + 6.26523i −1.87610 + 0.777106i
\(66\) 1.01674 + 1.01674i 0.125152 + 0.125152i
\(67\) 14.3801 1.75681 0.878406 0.477916i \(-0.158608\pi\)
0.878406 + 0.477916i \(0.158608\pi\)
\(68\) −6.19902 + 0.702020i −0.751742 + 0.0851324i
\(69\) 16.7181 2.01262
\(70\) 6.80396 + 6.80396i 0.813229 + 0.813229i
\(71\) 9.57871 3.96763i 1.13678 0.470871i 0.266702 0.963779i \(-0.414066\pi\)
0.870082 + 0.492908i \(0.164066\pi\)
\(72\) 6.57872i 0.775310i
\(73\) 3.54002 + 8.54636i 0.414328 + 1.00028i 0.983962 + 0.178378i \(0.0570849\pi\)
−0.569634 + 0.821898i \(0.692915\pi\)
\(74\) 0.712349 + 0.295065i 0.0828089 + 0.0343006i
\(75\) −5.33079 + 12.8697i −0.615547 + 1.48606i
\(76\) 0.792604 0.792604i 0.0909179 0.0909179i
\(77\) −2.55949 + 2.55949i −0.291680 + 0.291680i
\(78\) 3.16518 7.64143i 0.358386 0.865221i
\(79\) 5.43583 + 2.25160i 0.611579 + 0.253324i 0.666904 0.745144i \(-0.267619\pi\)
−0.0553244 + 0.998468i \(0.517619\pi\)
\(80\) 1.65787 + 4.00246i 0.185356 + 0.447489i
\(81\) 9.84893i 1.09433i
\(82\) −2.30360 + 0.954184i −0.254390 + 0.105372i
\(83\) 7.05417 + 7.05417i 0.774296 + 0.774296i 0.978854 0.204559i \(-0.0655759\pi\)
−0.204559 + 0.978854i \(0.565576\pi\)
\(84\) 15.1063 1.64824
\(85\) −11.8791 + 6.57412i −1.28847 + 0.713064i
\(86\) −0.697787 −0.0752443
\(87\) −1.85002 1.85002i −0.198343 0.198343i
\(88\) 1.95757 0.810851i 0.208677 0.0864370i
\(89\) 6.34024i 0.672064i −0.941850 0.336032i \(-0.890915\pi\)
0.941850 0.336032i \(-0.109085\pi\)
\(90\) −2.35975 5.69695i −0.248740 0.600511i
\(91\) 19.2361 + 7.96783i 2.01649 + 0.835256i
\(92\) 4.06048 9.80287i 0.423334 1.02202i
\(93\) −2.81456 + 2.81456i −0.291856 + 0.291856i
\(94\) −2.34946 + 2.34946i −0.242328 + 0.242328i
\(95\) 0.933512 2.25370i 0.0957764 0.231225i
\(96\) −12.8208 5.31053i −1.30851 0.542004i
\(97\) −0.907902 2.19187i −0.0921835 0.222551i 0.871062 0.491173i \(-0.163432\pi\)
−0.963246 + 0.268622i \(0.913432\pi\)
\(98\) 7.35264i 0.742729i
\(99\) 2.14305 0.887682i 0.215385 0.0892154i
\(100\) 6.25156 + 6.25156i 0.625156 + 0.625156i
\(101\) 4.88521 0.486097 0.243048 0.970014i \(-0.421853\pi\)
0.243048 + 0.970014i \(0.421853\pi\)
\(102\) 1.89508 6.59202i 0.187641 0.652707i
\(103\) −17.9635 −1.76999 −0.884996 0.465599i \(-0.845839\pi\)
−0.884996 + 0.465599i \(0.845839\pi\)
\(104\) −8.61826 8.61826i −0.845090 0.845090i
\(105\) 30.3727 12.5808i 2.96407 1.22776i
\(106\) 0.699560i 0.0679473i
\(107\) 7.28425 + 17.5857i 0.704195 + 1.70008i 0.714019 + 0.700126i \(0.246873\pi\)
−0.00982415 + 0.999952i \(0.503127\pi\)
\(108\) 1.05423 + 0.436678i 0.101444 + 0.0420194i
\(109\) −4.96245 + 11.9804i −0.475316 + 1.14752i 0.486466 + 0.873700i \(0.338286\pi\)
−0.961782 + 0.273816i \(0.911714\pi\)
\(110\) 1.40434 1.40434i 0.133898 0.133898i
\(111\) 1.86275 1.86275i 0.176804 0.176804i
\(112\) 2.10841 5.09015i 0.199226 0.480974i
\(113\) 0.740888 + 0.306886i 0.0696969 + 0.0288694i 0.417260 0.908787i \(-0.362991\pi\)
−0.347563 + 0.937657i \(0.612991\pi\)
\(114\) 0.471609 + 1.13856i 0.0441702 + 0.106636i
\(115\) 23.0912i 2.15327i
\(116\) −1.53412 + 0.635452i −0.142439 + 0.0590002i
\(117\) −9.43487 9.43487i −0.872254 0.872254i
\(118\) 5.25058 0.483355
\(119\) 16.5943 + 4.77056i 1.52120 + 0.437317i
\(120\) −19.2443 −1.75676
\(121\) −7.24990 7.24990i −0.659081 0.659081i
\(122\) 0.776775 0.321751i 0.0703259 0.0291299i
\(123\) 8.51891i 0.768124i
\(124\) 0.966755 + 2.33395i 0.0868172 + 0.209595i
\(125\) 2.56466 + 1.06232i 0.229390 + 0.0950166i
\(126\) −3.00103 + 7.24512i −0.267353 + 0.645447i
\(127\) −7.11232 + 7.11232i −0.631116 + 0.631116i −0.948348 0.317232i \(-0.897247\pi\)
0.317232 + 0.948348i \(0.397247\pi\)
\(128\) −7.52610 + 7.52610i −0.665219 + 0.665219i
\(129\) −0.912334 + 2.20257i −0.0803266 + 0.193925i
\(130\) −10.5544 4.37179i −0.925686 0.383432i
\(131\) 0.639274 + 1.54334i 0.0558536 + 0.134843i 0.949343 0.314242i \(-0.101750\pi\)
−0.893489 + 0.449084i \(0.851750\pi\)
\(132\) 3.11795i 0.271383i
\(133\) −2.86615 + 1.18720i −0.248527 + 0.102943i
\(134\) 7.09529 + 7.09529i 0.612940 + 0.612940i
\(135\) 2.48331 0.213730
\(136\) −7.90581 6.29734i −0.677917 0.539993i
\(137\) 20.1168 1.71869 0.859346 0.511395i \(-0.170871\pi\)
0.859346 + 0.511395i \(0.170871\pi\)
\(138\) 8.24886 + 8.24886i 0.702190 + 0.702190i
\(139\) 12.6486 5.23921i 1.07284 0.444384i 0.224846 0.974394i \(-0.427812\pi\)
0.847991 + 0.530010i \(0.177812\pi\)
\(140\) 20.8651i 1.76342i
\(141\) 4.34424 + 10.4879i 0.365851 + 0.883242i
\(142\) 6.68390 + 2.76856i 0.560900 + 0.232333i
\(143\) 1.64456 3.97033i 0.137525 0.332015i
\(144\) −2.49661 + 2.49661i −0.208051 + 0.208051i
\(145\) −2.55527 + 2.55527i −0.212204 + 0.212204i
\(146\) −2.47018 + 5.96354i −0.204433 + 0.493546i
\(147\) −23.2087 9.61334i −1.91422 0.792895i
\(148\) −0.639824 1.54467i −0.0525932 0.126971i
\(149\) 12.4345i 1.01868i −0.860566 0.509338i \(-0.829890\pi\)
0.860566 0.509338i \(-0.170110\pi\)
\(150\) −8.98028 + 3.71976i −0.733237 + 0.303717i
\(151\) 5.65632 + 5.65632i 0.460305 + 0.460305i 0.898755 0.438451i \(-0.144473\pi\)
−0.438451 + 0.898755i \(0.644473\pi\)
\(152\) 1.81601 0.147298
\(153\) −8.65491 6.89404i −0.699708 0.557350i
\(154\) −2.52575 −0.203531
\(155\) 3.88751 + 3.88751i 0.312252 + 0.312252i
\(156\) −16.5698 + 6.86344i −1.32665 + 0.549515i
\(157\) 12.1765i 0.971792i −0.874017 0.485896i \(-0.838493\pi\)
0.874017 0.485896i \(-0.161507\pi\)
\(158\) 1.57113 + 3.79305i 0.124993 + 0.301759i
\(159\) 2.20817 + 0.914653i 0.175119 + 0.0725367i
\(160\) −7.33498 + 17.7082i −0.579881 + 1.39996i
\(161\) −20.7652 + 20.7652i −1.63653 + 1.63653i
\(162\) −4.85956 + 4.85956i −0.381803 + 0.381803i
\(163\) 8.58330 20.7219i 0.672296 1.62307i −0.105404 0.994430i \(-0.533614\pi\)
0.777700 0.628636i \(-0.216386\pi\)
\(164\) 4.99518 + 2.06907i 0.390058 + 0.161567i
\(165\) −2.59668 6.26894i −0.202151 0.488036i
\(166\) 6.96119i 0.540293i
\(167\) −17.7664 + 7.35908i −1.37480 + 0.569463i −0.943087 0.332546i \(-0.892092\pi\)
−0.431718 + 0.902009i \(0.642092\pi\)
\(168\) 17.3058 + 17.3058i 1.33517 + 1.33517i
\(169\) −11.7197 −0.901518
\(170\) −9.10499 2.61751i −0.698321 0.200754i
\(171\) 1.98808 0.152032
\(172\) 1.06992 + 1.06992i 0.0815805 + 0.0815805i
\(173\) −20.4762 + 8.48153i −1.55678 + 0.644839i −0.984526 0.175238i \(-0.943930\pi\)
−0.572253 + 0.820077i \(0.693930\pi\)
\(174\) 1.82564i 0.138401i
\(175\) −9.36388 22.6064i −0.707843 1.70888i
\(176\) −1.05061 0.435176i −0.0791926 0.0328027i
\(177\) 6.86497 16.5735i 0.516003 1.24574i
\(178\) 3.12834 3.12834i 0.234479 0.234479i
\(179\) −16.7400 + 16.7400i −1.25120 + 1.25120i −0.296021 + 0.955181i \(0.595660\pi\)
−0.955181 + 0.296021i \(0.904340\pi\)
\(180\) −5.11693 + 12.3534i −0.381394 + 0.920765i
\(181\) −10.3020 4.26723i −0.765742 0.317181i −0.0345958 0.999401i \(-0.511014\pi\)
−0.731146 + 0.682221i \(0.761014\pi\)
\(182\) 5.55985 + 13.4227i 0.412123 + 0.994954i
\(183\) 2.87257i 0.212347i
\(184\) 15.8818 6.57846i 1.17082 0.484970i
\(185\) −2.57285 2.57285i −0.189160 0.189160i
\(186\) −2.77746 −0.203653
\(187\) 0.984646 3.42508i 0.0720044 0.250466i
\(188\) 7.20486 0.525468
\(189\) −2.23316 2.23316i −0.162438 0.162438i
\(190\) 1.57260 0.651393i 0.114088 0.0472570i
\(191\) 20.5429i 1.48643i 0.669052 + 0.743216i \(0.266700\pi\)
−0.669052 + 0.743216i \(0.733300\pi\)
\(192\) −1.30501 3.15058i −0.0941812 0.227374i
\(193\) 18.9208 + 7.83726i 1.36195 + 0.564138i 0.939594 0.342292i \(-0.111203\pi\)
0.422356 + 0.906430i \(0.361203\pi\)
\(194\) 0.633522 1.52946i 0.0454843 0.109809i
\(195\) −27.5992 + 27.5992i −1.97642 + 1.97642i
\(196\) −11.2738 + 11.2738i −0.805273 + 0.805273i
\(197\) 4.37960 10.5733i 0.312033 0.753315i −0.687596 0.726093i \(-0.741334\pi\)
0.999629 0.0272218i \(-0.00866603\pi\)
\(198\) 1.49540 + 0.619413i 0.106273 + 0.0440198i
\(199\) −9.10677 21.9857i −0.645562 1.55852i −0.819071 0.573692i \(-0.805511\pi\)
0.173510 0.984832i \(-0.444489\pi\)
\(200\) 14.3235i 1.01283i
\(201\) 31.6732 13.1195i 2.23406 0.925377i
\(202\) 2.41041 + 2.41041i 0.169596 + 0.169596i
\(203\) 4.59575 0.322558
\(204\) −13.0133 + 7.20183i −0.911113 + 0.504229i
\(205\) 11.7664 0.821803
\(206\) −8.86334 8.86334i −0.617538 0.617538i
\(207\) 17.3867 7.20179i 1.20846 0.500559i
\(208\) 6.54122i 0.453552i
\(209\) 0.245038 + 0.591575i 0.0169497 + 0.0409201i
\(210\) 21.1937 + 8.77871i 1.46250 + 0.605789i
\(211\) −0.597832 + 1.44329i −0.0411565 + 0.0993605i −0.943121 0.332450i \(-0.892125\pi\)
0.901965 + 0.431810i \(0.142125\pi\)
\(212\) 1.07264 1.07264i 0.0736690 0.0736690i
\(213\) 17.4780 17.4780i 1.19757 1.19757i
\(214\) −5.08286 + 12.2711i −0.347457 + 0.838835i
\(215\) 3.04222 + 1.26013i 0.207478 + 0.0859401i
\(216\) 0.707470 + 1.70798i 0.0481373 + 0.116214i
\(217\) 6.99181i 0.474635i
\(218\) −8.35977 + 3.46273i −0.566195 + 0.234526i
\(219\) 15.5943 + 15.5943i 1.05376 + 1.05376i
\(220\) −4.30655 −0.290348
\(221\) −20.3694 + 2.30678i −1.37020 + 0.155171i
\(222\) 1.83820 0.123372
\(223\) −19.2534 19.2534i −1.28930 1.28930i −0.935211 0.354090i \(-0.884791\pi\)
−0.354090 0.935211i \(-0.615209\pi\)
\(224\) 22.5205 9.32829i 1.50471 0.623273i
\(225\) 15.6807i 1.04538i
\(226\) 0.214141 + 0.516982i 0.0142444 + 0.0343891i
\(227\) 2.08090 + 0.861939i 0.138114 + 0.0572089i 0.450670 0.892691i \(-0.351185\pi\)
−0.312556 + 0.949899i \(0.601185\pi\)
\(228\) 1.02265 2.46888i 0.0677264 0.163506i
\(229\) 3.77452 3.77452i 0.249427 0.249427i −0.571308 0.820736i \(-0.693564\pi\)
0.820736 + 0.571308i \(0.193564\pi\)
\(230\) 11.3934 11.3934i 0.751261 0.751261i
\(231\) −3.30234 + 7.97255i −0.217278 + 0.524555i
\(232\) −2.48545 1.02951i −0.163178 0.0675905i
\(233\) −5.63286 13.5989i −0.369021 0.890896i −0.993911 0.110183i \(-0.964856\pi\)
0.624890 0.780713i \(-0.285144\pi\)
\(234\) 9.31051i 0.608647i
\(235\) 14.4861 6.00032i 0.944966 0.391418i
\(236\) −8.05073 8.05073i −0.524058 0.524058i
\(237\) 14.0270 0.911152
\(238\) 5.83397 + 10.5417i 0.378160 + 0.683314i
\(239\) −11.2997 −0.730916 −0.365458 0.930828i \(-0.619088\pi\)
−0.365458 + 0.930828i \(0.619088\pi\)
\(240\) 7.30317 + 7.30317i 0.471418 + 0.471418i
\(241\) 12.9254 5.35387i 0.832598 0.344873i 0.0746672 0.997209i \(-0.476211\pi\)
0.757931 + 0.652335i \(0.226211\pi\)
\(242\) 7.15434i 0.459898i
\(243\) 8.11972 + 19.6027i 0.520880 + 1.25752i
\(244\) −1.68437 0.697690i −0.107831 0.0446650i
\(245\) −13.2781 + 32.0561i −0.848305 + 2.04799i
\(246\) −4.20331 + 4.20331i −0.267993 + 0.267993i
\(247\) 2.60443 2.60443i 0.165716 0.165716i
\(248\) −1.56626 + 3.78128i −0.0994574 + 0.240111i
\(249\) 21.9731 + 9.10154i 1.39249 + 0.576787i
\(250\) 0.741271 + 1.78959i 0.0468821 + 0.113183i
\(251\) 22.2513i 1.40449i 0.711936 + 0.702245i \(0.247819\pi\)
−0.711936 + 0.702245i \(0.752181\pi\)
\(252\) 15.7105 6.50748i 0.989666 0.409933i
\(253\) 4.28594 + 4.28594i 0.269455 + 0.269455i
\(254\) −7.01858 −0.440385
\(255\) −20.1667 + 25.3176i −1.26289 + 1.58545i
\(256\) −10.2877 −0.642983
\(257\) 0.547062 + 0.547062i 0.0341248 + 0.0341248i 0.723963 0.689838i \(-0.242318\pi\)
−0.689838 + 0.723963i \(0.742318\pi\)
\(258\) −1.53692 + 0.636615i −0.0956847 + 0.0396339i
\(259\) 4.62736i 0.287530i
\(260\) 9.47987 + 22.8864i 0.587917 + 1.41936i
\(261\) −2.72096 1.12706i −0.168423 0.0697631i
\(262\) −0.446077 + 1.07692i −0.0275587 + 0.0665326i
\(263\) −11.5750 + 11.5750i −0.713748 + 0.713748i −0.967317 0.253570i \(-0.918395\pi\)
0.253570 + 0.967317i \(0.418395\pi\)
\(264\) 3.57191 3.57191i 0.219836 0.219836i
\(265\) 1.26333 3.04995i 0.0776058 0.187357i
\(266\) −1.99996 0.828412i −0.122626 0.0507932i
\(267\) −5.78442 13.9648i −0.354001 0.854634i
\(268\) 21.7585i 1.32911i
\(269\) −11.2996 + 4.68047i −0.688952 + 0.285373i −0.699563 0.714571i \(-0.746622\pi\)
0.0106117 + 0.999944i \(0.496622\pi\)
\(270\) 1.22529 + 1.22529i 0.0745688 + 0.0745688i
\(271\) −28.9720 −1.75993 −0.879963 0.475043i \(-0.842433\pi\)
−0.879963 + 0.475043i \(0.842433\pi\)
\(272\) 0.610408 + 5.39007i 0.0370114 + 0.326821i
\(273\) 49.6381 3.00423
\(274\) 9.92581 + 9.92581i 0.599640 + 0.599640i
\(275\) −4.66597 + 1.93271i −0.281369 + 0.116547i
\(276\) 25.2960i 1.52264i
\(277\) −12.0297 29.0423i −0.722795 1.74498i −0.665228 0.746640i \(-0.731666\pi\)
−0.0575667 0.998342i \(-0.518334\pi\)
\(278\) 8.82600 + 3.65585i 0.529349 + 0.219263i
\(279\) −1.71467 + 4.13957i −0.102654 + 0.247830i
\(280\) 23.9029 23.9029i 1.42847 1.42847i
\(281\) −7.93647 + 7.93647i −0.473450 + 0.473450i −0.903029 0.429579i \(-0.858662\pi\)
0.429579 + 0.903029i \(0.358662\pi\)
\(282\) −3.03135 + 7.31833i −0.180514 + 0.435800i
\(283\) 2.88169 + 1.19364i 0.171299 + 0.0709542i 0.466685 0.884424i \(-0.345448\pi\)
−0.295386 + 0.955378i \(0.595448\pi\)
\(284\) −6.00340 14.4935i −0.356236 0.860030i
\(285\) 5.81560i 0.344487i
\(286\) 2.77044 1.14755i 0.163820 0.0678563i
\(287\) −10.5812 10.5812i −0.624586 0.624586i
\(288\) −15.6211 −0.920485
\(289\) −16.5695 + 3.80164i −0.974675 + 0.223626i
\(290\) −2.52160 −0.148073
\(291\) −3.99944 3.99944i −0.234451 0.234451i
\(292\) 12.9314 5.35638i 0.756756 0.313458i
\(293\) 18.7640i 1.09620i 0.836412 + 0.548101i \(0.184649\pi\)
−0.836412 + 0.548101i \(0.815351\pi\)
\(294\) −6.70806 16.1947i −0.391222 0.944494i
\(295\) −22.8915 9.48198i −1.33280 0.552062i
\(296\) 1.03659 2.50255i 0.0602506 0.145458i
\(297\) −0.460925 + 0.460925i −0.0267456 + 0.0267456i
\(298\) 6.13532 6.13532i 0.355409 0.355409i
\(299\) 13.3424 32.2114i 0.771610 1.86283i
\(300\) 19.4730 + 8.06599i 1.12427 + 0.465690i
\(301\) −1.60257 3.86896i −0.0923709 0.223003i
\(302\) 5.58176i 0.321194i
\(303\) 10.7600 4.45694i 0.618147 0.256045i
\(304\) −0.689171 0.689171i −0.0395267 0.0395267i
\(305\) −3.96764 −0.227186
\(306\) −0.868831 7.67201i −0.0496678 0.438579i
\(307\) −28.2956 −1.61492 −0.807458 0.589926i \(-0.799157\pi\)
−0.807458 + 0.589926i \(0.799157\pi\)
\(308\) 3.87274 + 3.87274i 0.220670 + 0.220670i
\(309\) −39.5658 + 16.3887i −2.25082 + 0.932319i
\(310\) 3.83627i 0.217885i
\(311\) 8.44991 + 20.3999i 0.479150 + 1.15677i 0.960008 + 0.279972i \(0.0903253\pi\)
−0.480858 + 0.876799i \(0.659675\pi\)
\(312\) −26.8450 11.1196i −1.51980 0.629522i
\(313\) 3.13665 7.57255i 0.177294 0.428026i −0.810103 0.586287i \(-0.800589\pi\)
0.987397 + 0.158262i \(0.0505890\pi\)
\(314\) 6.00801 6.00801i 0.339052 0.339052i
\(315\) 26.1678 26.1678i 1.47439 1.47439i
\(316\) 3.40688 8.22493i 0.191652 0.462688i
\(317\) 10.7210 + 4.44079i 0.602152 + 0.249420i 0.662869 0.748735i \(-0.269339\pi\)
−0.0607166 + 0.998155i \(0.519339\pi\)
\(318\) 0.638233 + 1.54083i 0.0357903 + 0.0864054i
\(319\) 0.948563i 0.0531094i
\(320\) −4.35162 + 1.80250i −0.243263 + 0.100763i
\(321\) 32.0882 + 32.0882i 1.79099 + 1.79099i
\(322\) −20.4915 −1.14195
\(323\) 1.90305 2.38913i 0.105889 0.132935i
\(324\) 14.9023 0.827908
\(325\) 20.5421 + 20.5421i 1.13947 + 1.13947i
\(326\) 14.4595 5.98931i 0.800836 0.331717i
\(327\) 30.9151i 1.70961i
\(328\) 3.35214 + 8.09278i 0.185091 + 0.446849i
\(329\) −18.4227 7.63094i −1.01568 0.420707i
\(330\) 1.81193 4.37438i 0.0997434 0.240802i
\(331\) −3.94127 + 3.94127i −0.216632 + 0.216632i −0.807077 0.590446i \(-0.798952\pi\)
0.590446 + 0.807077i \(0.298952\pi\)
\(332\) 10.6736 10.6736i 0.585791 0.585791i
\(333\) 1.13481 2.73968i 0.0621873 0.150133i
\(334\) −12.3972 5.13507i −0.678342 0.280979i
\(335\) −18.1208 43.7475i −0.990045 2.39018i
\(336\) 13.1350i 0.716573i
\(337\) −5.62406 + 2.32956i −0.306362 + 0.126899i −0.530568 0.847643i \(-0.678021\pi\)
0.224206 + 0.974542i \(0.428021\pi\)
\(338\) −5.78263 5.78263i −0.314534 0.314534i
\(339\) 1.91184 0.103837
\(340\) 9.94726 + 17.9741i 0.539466 + 0.974785i
\(341\) −1.44311 −0.0781489
\(342\) 0.980939 + 0.980939i 0.0530431 + 0.0530431i
\(343\) 13.6848 5.66844i 0.738911 0.306067i
\(344\) 2.45139i 0.132170i
\(345\) −21.0669 50.8601i −1.13421 2.73821i
\(346\) −14.2880 5.91830i −0.768130 0.318170i
\(347\) −9.59765 + 23.1708i −0.515229 + 1.24387i 0.425576 + 0.904923i \(0.360072\pi\)
−0.940805 + 0.338949i \(0.889928\pi\)
\(348\) −2.79926 + 2.79926i −0.150056 + 0.150056i
\(349\) −18.3680 + 18.3680i −0.983218 + 0.983218i −0.999861 0.0166439i \(-0.994702\pi\)
0.0166439 + 0.999861i \(0.494702\pi\)
\(350\) 6.53399 15.7745i 0.349257 0.843180i
\(351\) 3.46412 + 1.43489i 0.184901 + 0.0765886i
\(352\) −1.92536 4.64824i −0.102622 0.247752i
\(353\) 1.30967i 0.0697069i 0.999392 + 0.0348535i \(0.0110965\pi\)
−0.999392 + 0.0348535i \(0.988904\pi\)
\(354\) 11.5648 4.79028i 0.614660 0.254601i
\(355\) −24.1408 24.1408i −1.28126 1.28126i
\(356\) −9.59338 −0.508448
\(357\) 40.9025 4.63209i 2.16479 0.245156i
\(358\) −16.5193 −0.873073
\(359\) −16.4436 16.4436i −0.867859 0.867859i 0.124376 0.992235i \(-0.460307\pi\)
−0.992235 + 0.124376i \(0.960307\pi\)
\(360\) −20.0139 + 8.29003i −1.05483 + 0.436923i
\(361\) 18.4512i 0.971116i
\(362\) −2.97762 7.18861i −0.156500 0.377825i
\(363\) −22.5827 9.35407i −1.18529 0.490962i
\(364\) 12.0561 29.1059i 0.631910 1.52557i
\(365\) 21.5390 21.5390i 1.12740 1.12740i
\(366\) 1.41736 1.41736i 0.0740864 0.0740864i
\(367\) 0.966966 2.33446i 0.0504752 0.121858i −0.896631 0.442779i \(-0.853993\pi\)
0.947106 + 0.320921i \(0.103993\pi\)
\(368\) −8.52362 3.53060i −0.444324 0.184045i
\(369\) 3.66976 + 8.85960i 0.191040 + 0.461212i
\(370\) 2.53894i 0.131993i
\(371\) −3.87879 + 1.60665i −0.201377 + 0.0834130i
\(372\) 4.25869 + 4.25869i 0.220803 + 0.220803i
\(373\) 2.69393 0.139487 0.0697433 0.997565i \(-0.477782\pi\)
0.0697433 + 0.997565i \(0.477782\pi\)
\(374\) 2.17580 1.20413i 0.112508 0.0622642i
\(375\) 6.61803 0.341754
\(376\) 8.25386 + 8.25386i 0.425660 + 0.425660i
\(377\) −5.04098 + 2.08804i −0.259623 + 0.107540i
\(378\) 2.20373i 0.113347i
\(379\) 12.6177 + 30.4617i 0.648126 + 1.56471i 0.815460 + 0.578814i \(0.196484\pi\)
−0.167334 + 0.985900i \(0.553516\pi\)
\(380\) −3.41006 1.41249i −0.174932 0.0724593i
\(381\) −9.17657 + 22.1542i −0.470130 + 1.13499i
\(382\) −10.1361 + 10.1361i −0.518606 + 0.518606i
\(383\) 18.8344 18.8344i 0.962395 0.962395i −0.0369228 0.999318i \(-0.511756\pi\)
0.999318 + 0.0369228i \(0.0117556\pi\)
\(384\) −9.71044 + 23.4431i −0.495534 + 1.19632i
\(385\) 11.0118 + 4.56124i 0.561213 + 0.232462i
\(386\) 5.46874 + 13.2027i 0.278351 + 0.672000i
\(387\) 2.68367i 0.136419i
\(388\) −3.31650 + 1.37374i −0.168370 + 0.0697411i
\(389\) 7.54968 + 7.54968i 0.382784 + 0.382784i 0.872104 0.489320i \(-0.162755\pi\)
−0.489320 + 0.872104i \(0.662755\pi\)
\(390\) −27.2354 −1.37912
\(391\) 7.98846 27.7877i 0.403994 1.40529i
\(392\) −25.8305 −1.30464
\(393\) 2.81609 + 2.81609i 0.142053 + 0.142053i
\(394\) 7.37790 3.05603i 0.371693 0.153960i
\(395\) 19.3743i 0.974827i
\(396\) −1.34315 3.24264i −0.0674957 0.162949i
\(397\) 14.2267 + 5.89287i 0.714016 + 0.295755i 0.709965 0.704237i \(-0.248711\pi\)
0.00405044 + 0.999992i \(0.498711\pi\)
\(398\) 6.35458 15.3413i 0.318526 0.768991i
\(399\) −5.22978 + 5.22978i −0.261816 + 0.261816i
\(400\) 5.43575 5.43575i 0.271787 0.271787i
\(401\) 14.0886 34.0129i 0.703551 1.69852i −0.0119678 0.999928i \(-0.503810\pi\)
0.715519 0.698594i \(-0.246190\pi\)
\(402\) 22.1012 + 9.15460i 1.10231 + 0.456590i
\(403\) 3.17667 + 7.66917i 0.158241 + 0.382028i
\(404\) 7.39178i 0.367755i
\(405\) 29.9626 12.4109i 1.48885 0.616703i
\(406\) 2.26759 + 2.26759i 0.112538 + 0.112538i
\(407\) 0.955089 0.0473420
\(408\) −23.1584 6.65760i −1.14651 0.329600i
\(409\) 7.07974 0.350071 0.175035 0.984562i \(-0.443996\pi\)
0.175035 + 0.984562i \(0.443996\pi\)
\(410\) 5.80567 + 5.80567i 0.286722 + 0.286722i
\(411\) 44.3086 18.3532i 2.18558 0.905298i
\(412\) 27.1804i 1.33908i
\(413\) 12.0588 + 29.1124i 0.593373 + 1.43253i
\(414\) 12.1322 + 5.02532i 0.596264 + 0.246981i
\(415\) 12.5712 30.3495i 0.617095 1.48980i
\(416\) −20.4640 + 20.4640i −1.00333 + 1.00333i
\(417\) 23.0794 23.0794i 1.13021 1.13021i
\(418\) −0.170984 + 0.412793i −0.00836312 + 0.0201904i
\(419\) −6.77868 2.80782i −0.331160 0.137171i 0.210907 0.977506i \(-0.432358\pi\)
−0.542067 + 0.840335i \(0.682358\pi\)
\(420\) −19.0359 45.9568i −0.928857 2.24246i
\(421\) 5.54226i 0.270113i 0.990838 + 0.135057i \(0.0431217\pi\)
−0.990838 + 0.135057i \(0.956878\pi\)
\(422\) −1.00711 + 0.417159i −0.0490254 + 0.0203070i
\(423\) 9.03594 + 9.03594i 0.439343 + 0.439343i
\(424\) 2.45762 0.119353
\(425\) 18.8439 + 15.0101i 0.914065 + 0.728095i
\(426\) 17.2476 0.835649
\(427\) 3.56797 + 3.56797i 0.172666 + 0.172666i
\(428\) 26.6089 11.0218i 1.28619 0.532757i
\(429\) 10.2453i 0.494648i
\(430\) 0.879301 + 2.12282i 0.0424037 + 0.102372i
\(431\) 19.9233 + 8.25251i 0.959673 + 0.397509i 0.806858 0.590746i \(-0.201166\pi\)
0.152815 + 0.988255i \(0.451166\pi\)
\(432\) 0.379693 0.916660i 0.0182680 0.0441028i
\(433\) 9.39245 9.39245i 0.451373 0.451373i −0.444437 0.895810i \(-0.646596\pi\)
0.895810 + 0.444437i \(0.146596\pi\)
\(434\) 3.44983 3.44983i 0.165597 0.165597i
\(435\) −3.29691 + 7.95944i −0.158075 + 0.381626i
\(436\) 18.1275 + 7.50865i 0.868149 + 0.359599i
\(437\) 1.98800 + 4.79946i 0.0950991 + 0.229589i
\(438\) 15.3887i 0.735302i
\(439\) −5.13843 + 2.12841i −0.245244 + 0.101583i −0.501920 0.864914i \(-0.667373\pi\)
0.256676 + 0.966498i \(0.417373\pi\)
\(440\) −4.93357 4.93357i −0.235199 0.235199i
\(441\) −28.2780 −1.34657
\(442\) −11.1887 8.91230i −0.532191 0.423915i
\(443\) 16.5604 0.786810 0.393405 0.919365i \(-0.371297\pi\)
0.393405 + 0.919365i \(0.371297\pi\)
\(444\) −2.81851 2.81851i −0.133761 0.133761i
\(445\) −19.2884 + 7.98952i −0.914358 + 0.378740i
\(446\) 18.9996i 0.899658i
\(447\) −11.3444 27.3879i −0.536574 1.29540i
\(448\) 5.53420 + 2.29234i 0.261466 + 0.108303i
\(449\) −7.10203 + 17.1458i −0.335166 + 0.809162i 0.663000 + 0.748619i \(0.269283\pi\)
−0.998166 + 0.0605421i \(0.980717\pi\)
\(450\) −7.73703 + 7.73703i −0.364727 + 0.364727i
\(451\) −2.18395 + 2.18395i −0.102838 + 0.102838i
\(452\) 0.464347 1.12103i 0.0218410 0.0527289i
\(453\) 17.6189 + 7.29798i 0.827808 + 0.342889i
\(454\) 0.601449 + 1.45203i 0.0282274 + 0.0681470i
\(455\) 68.5608i 3.21418i
\(456\) 3.99989 1.65681i 0.187312 0.0775871i
\(457\) −3.92622 3.92622i −0.183661 0.183661i 0.609288 0.792949i \(-0.291455\pi\)
−0.792949 + 0.609288i \(0.791455\pi\)
\(458\) 3.72477 0.174047
\(459\) 2.98839 + 0.859107i 0.139486 + 0.0400997i
\(460\) −34.9392 −1.62905
\(461\) 5.00301 + 5.00301i 0.233013 + 0.233013i 0.813949 0.580936i \(-0.197313\pi\)
−0.580936 + 0.813949i \(0.697313\pi\)
\(462\) −5.56314 + 2.30433i −0.258821 + 0.107207i
\(463\) 11.5955i 0.538888i −0.963016 0.269444i \(-0.913160\pi\)
0.963016 0.269444i \(-0.0868398\pi\)
\(464\) 0.552527 + 1.33392i 0.0256504 + 0.0619256i
\(465\) 12.1092 + 5.01580i 0.561551 + 0.232602i
\(466\) 3.93054 9.48916i 0.182079 0.439577i
\(467\) 4.73985 4.73985i 0.219334 0.219334i −0.588884 0.808218i \(-0.700432\pi\)
0.808218 + 0.588884i \(0.200432\pi\)
\(468\) −14.2758 + 14.2758i −0.659901 + 0.659901i
\(469\) −23.0452 + 55.6361i −1.06413 + 2.56904i
\(470\) 10.1082 + 4.18694i 0.466256 + 0.193129i
\(471\) −11.1091 26.8196i −0.511878 1.23578i
\(472\) 18.4458i 0.849036i
\(473\) −0.798554 + 0.330772i −0.0367176 + 0.0152089i
\(474\) 6.92107 + 6.92107i 0.317895 + 0.317895i
\(475\) −4.32855 −0.198608
\(476\) 7.21831 25.1088i 0.330851 1.15086i
\(477\) 2.69049 0.123189
\(478\) −5.57538 5.57538i −0.255012 0.255012i
\(479\) 22.9360 9.50042i 1.04797 0.434085i 0.208806 0.977957i \(-0.433042\pi\)
0.839168 + 0.543872i \(0.183042\pi\)
\(480\) 45.6955i 2.08570i
\(481\) −2.10241 5.07566i −0.0958614 0.231430i
\(482\) 9.01917 + 3.73586i 0.410812 + 0.170164i
\(483\) −26.7920 + 64.6815i −1.21908 + 2.94311i
\(484\) −10.9698 + 10.9698i −0.498626 + 0.498626i
\(485\) −5.52408 + 5.52408i −0.250835 + 0.250835i
\(486\) −5.66583 + 13.6785i −0.257007 + 0.620471i
\(487\) −8.88432 3.68001i −0.402587 0.166757i 0.172196 0.985063i \(-0.444914\pi\)
−0.574783 + 0.818306i \(0.694914\pi\)
\(488\) −1.13034 2.72888i −0.0511681 0.123531i
\(489\) 53.4723i 2.41810i
\(490\) −22.3683 + 9.26527i −1.01050 + 0.418562i
\(491\) −11.5347 11.5347i −0.520554 0.520554i 0.397185 0.917739i \(-0.369987\pi\)
−0.917739 + 0.397185i \(0.869987\pi\)
\(492\) 12.8899 0.581122
\(493\) −3.95899 + 2.19099i −0.178304 + 0.0986771i
\(494\) 2.57010 0.115634
\(495\) −5.40105 5.40105i −0.242759 0.242759i
\(496\) 2.02938 0.840596i 0.0911218 0.0377439i
\(497\) 43.4181i 1.94757i
\(498\) 6.35094 + 15.3325i 0.284592 + 0.687067i
\(499\) 11.6573 + 4.82861i 0.521852 + 0.216158i 0.628030 0.778189i \(-0.283861\pi\)
−0.106178 + 0.994347i \(0.533861\pi\)
\(500\) 1.60739 3.88057i 0.0718845 0.173544i
\(501\) −32.4178 + 32.4178i −1.44832 + 1.44832i
\(502\) −10.9790 + 10.9790i −0.490017 + 0.490017i
\(503\) −0.171212 + 0.413344i −0.00763399 + 0.0184301i −0.927651 0.373449i \(-0.878175\pi\)
0.920017 + 0.391879i \(0.128175\pi\)
\(504\) 25.4528 + 10.5429i 1.13376 + 0.469618i
\(505\) −6.15599 14.8619i −0.273938 0.661345i
\(506\) 4.22945i 0.188022i
\(507\) −25.8135 + 10.6923i −1.14642 + 0.474863i
\(508\) 10.7616 + 10.7616i 0.477469 + 0.477469i
\(509\) −35.7666 −1.58533 −0.792663 0.609660i \(-0.791306\pi\)
−0.792663 + 0.609660i \(0.791306\pi\)
\(510\) −22.4424 + 2.54153i −0.993767 + 0.112541i
\(511\) −38.7387 −1.71370
\(512\) 9.97613 + 9.97613i 0.440887 + 0.440887i
\(513\) −0.516151 + 0.213797i −0.0227886 + 0.00943936i
\(514\) 0.539852i 0.0238118i
\(515\) 22.6363 + 54.6488i 0.997473 + 2.40811i
\(516\) 3.33269 + 1.38045i 0.146714 + 0.0607708i
\(517\) −1.57503 + 3.80245i −0.0692697 + 0.167232i
\(518\) −2.28319 + 2.28319i −0.100317 + 0.100317i
\(519\) −37.3623 + 37.3623i −1.64002 + 1.64002i
\(520\) −15.3585 + 37.0787i −0.673515 + 1.62601i
\(521\) −3.54688 1.46917i −0.155392 0.0643653i 0.303632 0.952789i \(-0.401801\pi\)
−0.459024 + 0.888424i \(0.651801\pi\)
\(522\) −0.786446 1.89865i −0.0344218 0.0831016i
\(523\) 13.3596i 0.584176i 0.956391 + 0.292088i \(0.0943500\pi\)
−0.956391 + 0.292088i \(0.905650\pi\)
\(524\) 2.33522 0.967281i 0.102015 0.0422559i
\(525\) −41.2492 41.2492i −1.80026 1.80026i
\(526\) −11.4225 −0.498044
\(527\) 3.33329 + 6.02307i 0.145201 + 0.262369i
\(528\) −2.71107 −0.117984
\(529\) 18.5085 + 18.5085i 0.804717 + 0.804717i
\(530\) 2.12821 0.881535i 0.0924437 0.0382914i
\(531\) 20.1936i 0.876327i
\(532\) 1.79634 + 4.33676i 0.0778814 + 0.188022i
\(533\) 16.4137 + 6.79878i 0.710957 + 0.294488i
\(534\) 4.03629 9.74447i 0.174668 0.421685i
\(535\) 44.3206 44.3206i 1.91615 1.91615i
\(536\) 24.9264 24.9264i 1.07666 1.07666i
\(537\) −21.5985 + 52.1433i −0.932043 + 2.25015i
\(538\) −7.88475 3.26597i −0.339936 0.140806i
\(539\) −3.48537 8.41443i −0.150126 0.362435i
\(540\) 3.75748i 0.161696i
\(541\) 18.3423 7.59763i 0.788597 0.326647i 0.0482175 0.998837i \(-0.484646\pi\)
0.740379 + 0.672189i \(0.234646\pi\)
\(542\) −14.2951 14.2951i −0.614026 0.614026i
\(543\) −26.5840 −1.14083
\(544\) −14.9530 + 18.7723i −0.641105 + 0.804856i
\(545\) 42.7004 1.82908
\(546\) 24.4919 + 24.4919i 1.04816 + 1.04816i
\(547\) −8.97745 + 3.71858i −0.383848 + 0.158995i −0.566259 0.824227i \(-0.691610\pi\)
0.182411 + 0.983222i \(0.441610\pi\)
\(548\) 30.4386i 1.30027i
\(549\) −1.23744 2.98745i −0.0528128 0.127501i
\(550\) −3.25585 1.34862i −0.138830 0.0575053i
\(551\) 0.311116 0.751100i 0.0132540 0.0319980i
\(552\) 28.9790 28.9790i 1.23343 1.23343i
\(553\) −17.4227 + 17.4227i −0.740887 + 0.740887i
\(554\) 8.39417 20.2653i 0.356634 0.860991i
\(555\) −8.01419 3.31959i −0.340184 0.140909i
\(556\) −7.92741 19.1385i −0.336197 0.811652i
\(557\) 4.15170i 0.175913i 0.996124 + 0.0879566i \(0.0280337\pi\)
−0.996124 + 0.0879566i \(0.971966\pi\)
\(558\) −2.88854 + 1.19647i −0.122282 + 0.0506507i
\(559\) 3.51566 + 3.51566i 0.148697 + 0.148697i
\(560\) −18.1422 −0.766649
\(561\) −0.956064 8.44230i −0.0403651 0.356434i
\(562\) −7.83187 −0.330367
\(563\) −2.29138 2.29138i −0.0965700 0.0965700i 0.657171 0.753741i \(-0.271753\pi\)
−0.753741 + 0.657171i \(0.771753\pi\)
\(564\) 15.8692 6.57324i 0.668214 0.276783i
\(565\) 2.64066i 0.111093i
\(566\) 0.832903 + 2.01081i 0.0350095 + 0.0845205i
\(567\) −38.1051 15.7836i −1.60026 0.662851i
\(568\) 9.72622 23.4812i 0.408103 0.985248i
\(569\) 26.5233 26.5233i 1.11191 1.11191i 0.119022 0.992892i \(-0.462024\pi\)
0.992892 0.119022i \(-0.0379759\pi\)
\(570\) 2.86948 2.86948i 0.120189 0.120189i
\(571\) 6.02699 14.5504i 0.252222 0.608917i −0.746161 0.665766i \(-0.768105\pi\)
0.998383 + 0.0568482i \(0.0181051\pi\)
\(572\) −6.00748 2.48838i −0.251185 0.104044i
\(573\) 18.7420 + 45.2472i 0.782958 + 1.89023i
\(574\) 10.4417i 0.435828i
\(575\) −37.8551 + 15.6801i −1.57867 + 0.653906i
\(576\) −2.71441 2.71441i −0.113100 0.113100i
\(577\) −13.2294 −0.550748 −0.275374 0.961337i \(-0.588802\pi\)
−0.275374 + 0.961337i \(0.588802\pi\)
\(578\) −10.0513 6.29978i −0.418079 0.262036i
\(579\) 48.8246 2.02908
\(580\) 3.86637 + 3.86637i 0.160542 + 0.160542i
\(581\) −38.5971 + 15.9875i −1.60128 + 0.663271i
\(582\) 3.94672i 0.163597i
\(583\) 0.331612 + 0.800583i 0.0137340 + 0.0331568i
\(584\) 20.9505 + 8.67797i 0.866937 + 0.359097i
\(585\) −16.8138 + 40.5921i −0.695165 + 1.67828i
\(586\) −9.25833 + 9.25833i −0.382458 + 0.382458i
\(587\) 17.8849 17.8849i 0.738188 0.738188i −0.234039 0.972227i \(-0.575194\pi\)
0.972227 + 0.234039i \(0.0751943\pi\)
\(588\) −14.5459 + 35.1169i −0.599862 + 1.44820i
\(589\) −1.14270 0.473321i −0.0470841 0.0195029i
\(590\) −6.61640 15.9734i −0.272393 0.657615i
\(591\) 27.2841i 1.12232i
\(592\) −1.34310 + 0.556328i −0.0552009 + 0.0228650i
\(593\) −7.46590 7.46590i −0.306588 0.306588i 0.536997 0.843584i \(-0.319559\pi\)
−0.843584 + 0.536997i \(0.819559\pi\)
\(594\) −0.454850 −0.0186627
\(595\) −6.39790 56.4951i −0.262288 2.31608i
\(596\) −18.8146 −0.770676
\(597\) −40.1166 40.1166i −1.64186 1.64186i
\(598\) 22.4767 9.31014i 0.919139 0.380720i
\(599\) 4.54677i 0.185776i −0.995677 0.0928880i \(-0.970390\pi\)
0.995677 0.0928880i \(-0.0296098\pi\)
\(600\) 13.0678 + 31.5486i 0.533493 + 1.28797i
\(601\) −2.14879 0.890056i −0.0876508 0.0363061i 0.338427 0.940993i \(-0.390105\pi\)
−0.426078 + 0.904686i \(0.640105\pi\)
\(602\) 1.11826 2.69971i 0.0455767 0.110032i
\(603\) 27.2883 27.2883i 1.11127 1.11127i
\(604\) 8.55854 8.55854i 0.348242 0.348242i
\(605\) −12.9200 + 31.1916i −0.525272 + 1.26812i
\(606\) 7.50820 + 3.11000i 0.305000 + 0.126335i
\(607\) 0.331060 + 0.799249i 0.0134373 + 0.0324405i 0.930456 0.366404i \(-0.119411\pi\)
−0.917018 + 0.398845i \(0.869411\pi\)
\(608\) 4.31210i 0.174879i
\(609\) 10.1225 4.19286i 0.410183 0.169903i
\(610\) −1.95767 1.95767i −0.0792638 0.0792638i
\(611\) 23.6745 0.957769
\(612\) −10.4313 + 13.0957i −0.421662 + 0.529362i
\(613\) 0.635418 0.0256643 0.0128322 0.999918i \(-0.495915\pi\)
0.0128322 + 0.999918i \(0.495915\pi\)
\(614\) −13.9613 13.9613i −0.563433 0.563433i
\(615\) 25.9164 10.7349i 1.04505 0.432874i
\(616\) 8.87320i 0.357511i
\(617\) −0.591191 1.42726i −0.0238005 0.0574594i 0.911532 0.411228i \(-0.134900\pi\)
−0.935333 + 0.353769i \(0.884900\pi\)
\(618\) −27.6085 11.4358i −1.11058 0.460015i
\(619\) −11.2387 + 27.1327i −0.451723 + 1.09056i 0.519943 + 0.854201i \(0.325953\pi\)
−0.971667 + 0.236356i \(0.924047\pi\)
\(620\) 5.88216 5.88216i 0.236233 0.236233i
\(621\) −3.73950 + 3.73950i −0.150061 + 0.150061i
\(622\) −5.89623 + 14.2348i −0.236417 + 0.570762i
\(623\) 24.5301 + 10.1607i 0.982779 + 0.407080i
\(624\) 5.96778 + 14.4075i 0.238902 + 0.576761i
\(625\) 20.0742i 0.802968i
\(626\) 5.28402 2.18871i 0.211192 0.0874786i
\(627\) 1.07943 + 1.07943i 0.0431082 + 0.0431082i
\(628\) −18.4242 −0.735206
\(629\) −2.20606 3.98623i −0.0879614 0.158941i
\(630\) 25.8229 1.02881
\(631\) 2.30075 + 2.30075i 0.0915915 + 0.0915915i 0.751418 0.659827i \(-0.229370\pi\)
−0.659827 + 0.751418i \(0.729370\pi\)
\(632\) 13.3254 5.51954i 0.530054 0.219556i
\(633\) 3.72438i 0.148031i
\(634\) 3.09873 + 7.48099i 0.123066 + 0.297108i
\(635\) 30.5997 + 12.6748i 1.21431 + 0.502984i
\(636\) 1.38395 3.34116i 0.0548774 0.132486i
\(637\) −37.0448 + 37.0448i −1.46777 + 1.46777i
\(638\) 0.468031 0.468031i 0.0185295 0.0185295i
\(639\) 10.6478 25.7061i 0.421221 1.01692i
\(640\) 32.3799 + 13.4122i 1.27993 + 0.530163i
\(641\) −3.86829 9.33888i −0.152788 0.368864i 0.828889 0.559413i \(-0.188973\pi\)
−0.981678 + 0.190549i \(0.938973\pi\)
\(642\) 31.6652i 1.24973i
\(643\) −17.2467 + 7.14382i −0.680144 + 0.281725i −0.695887 0.718151i \(-0.744989\pi\)
0.0157431 + 0.999876i \(0.494989\pi\)
\(644\) 31.4197 + 31.4197i 1.23811 + 1.23811i
\(645\) 7.85036 0.309108
\(646\) 2.11780 0.239835i 0.0833238 0.00943616i
\(647\) −2.66177 −0.104645 −0.0523225 0.998630i \(-0.516662\pi\)
−0.0523225 + 0.998630i \(0.516662\pi\)
\(648\) 17.0721 + 17.0721i 0.670655 + 0.670655i
\(649\) 6.00881 2.48893i 0.235867 0.0976991i
\(650\) 20.2713i 0.795107i
\(651\) −6.37887 15.4000i −0.250008 0.603572i
\(652\) −31.3542 12.9873i −1.22793 0.508623i
\(653\) 7.53266 18.1855i 0.294776 0.711652i −0.705221 0.708988i \(-0.749152\pi\)
0.999996 0.00266397i \(-0.000847968\pi\)
\(654\) −15.2538 + 15.2538i −0.596471 + 0.596471i
\(655\) 3.88962 3.88962i 0.151980 0.151980i
\(656\) 1.79906 4.34332i 0.0702416 0.169578i
\(657\) 22.9356 + 9.50024i 0.894803 + 0.370640i
\(658\) −5.32477 12.8551i −0.207581 0.501145i
\(659\) 30.6816i 1.19519i 0.801800 + 0.597593i \(0.203876\pi\)
−0.801800 + 0.597593i \(0.796124\pi\)
\(660\) −9.48549 + 3.92902i −0.369222 + 0.152937i
\(661\) 21.9308 + 21.9308i 0.853008 + 0.853008i 0.990503 0.137494i \(-0.0439049\pi\)
−0.137494 + 0.990503i \(0.543905\pi\)
\(662\) −3.88932 −0.151163
\(663\) −42.7606 + 23.6646i −1.66068 + 0.919056i
\(664\) 24.4553 0.949051
\(665\) 7.22344 + 7.22344i 0.280113 + 0.280113i
\(666\) 1.91171 0.791856i 0.0740772 0.0306838i
\(667\) 7.69572i 0.297980i
\(668\) 11.1350 + 26.8822i 0.430825 + 1.04010i
\(669\) −59.9724 24.8414i −2.31867 0.960424i
\(670\) 12.6445 30.5264i 0.488498 1.17934i
\(671\) 0.736429 0.736429i 0.0284295 0.0284295i
\(672\) 41.0924 41.0924i 1.58518 1.58518i
\(673\) −15.1828 + 36.6546i −0.585256 + 1.41293i 0.302737 + 0.953074i \(0.402100\pi\)
−0.887992 + 0.459858i \(0.847900\pi\)
\(674\) −3.92439 1.62554i −0.151162 0.0626133i
\(675\) −1.68629 4.07108i −0.0649055 0.156696i
\(676\) 17.7331i 0.682041i
\(677\) 44.8187 18.5645i 1.72252 0.713492i 0.722772 0.691086i \(-0.242868\pi\)
0.999749 0.0224055i \(-0.00713248\pi\)
\(678\) 0.943320 + 0.943320i 0.0362280 + 0.0362280i
\(679\) 9.93524 0.381279
\(680\) −9.19557 + 31.9867i −0.352634 + 1.22663i
\(681\) 5.36971 0.205768
\(682\) −0.712045 0.712045i −0.0272656 0.0272656i
\(683\) −0.319156 + 0.132199i −0.0122122 + 0.00505845i −0.388781 0.921330i \(-0.627104\pi\)
0.376569 + 0.926389i \(0.377104\pi\)
\(684\) 3.00815i 0.115020i
\(685\) −25.3497 61.1996i −0.968563 2.33832i
\(686\) 9.54909 + 3.95536i 0.364586 + 0.151016i
\(687\) 4.87002 11.7573i 0.185803 0.448568i
\(688\) 0.930297 0.930297i 0.0354673 0.0354673i
\(689\) 3.52459 3.52459i 0.134276 0.134276i
\(690\) 14.7002 35.4895i 0.559628 1.35106i
\(691\) 22.6800 + 9.39437i 0.862789 + 0.357379i 0.769798 0.638288i \(-0.220357\pi\)
0.0929913 + 0.995667i \(0.470357\pi\)
\(692\) 12.8333 + 30.9824i 0.487851 + 1.17778i
\(693\) 9.71397i 0.369003i
\(694\) −16.1683 + 6.69711i −0.613739 + 0.254219i
\(695\) −31.8776 31.8776i −1.20919 1.20919i
\(696\) −6.41364 −0.243108
\(697\) 14.1596 + 4.07062i 0.536333 + 0.154186i
\(698\) −18.1259 −0.686076
\(699\) −24.8136 24.8136i −0.938535 0.938535i
\(700\) −34.2056 + 14.1684i −1.29285 + 0.535516i
\(701\) 2.57726i 0.0973418i −0.998815 0.0486709i \(-0.984501\pi\)
0.998815 0.0486709i \(-0.0154985\pi\)
\(702\) 1.00125 + 2.41722i 0.0377896 + 0.0912321i
\(703\) 0.756268 + 0.313256i 0.0285232 + 0.0118147i
\(704\) 0.473140 1.14226i 0.0178321 0.0430506i
\(705\) 26.4323 26.4323i 0.995496 0.995496i
\(706\) −0.646206 + 0.646206i −0.0243203 + 0.0243203i
\(707\) −7.82891 + 18.9007i −0.294437 + 0.710833i
\(708\) −25.0772 10.3873i −0.942461 0.390380i
\(709\) 16.0701 + 38.7967i 0.603527 + 1.45704i 0.869927 + 0.493180i \(0.164166\pi\)
−0.266401 + 0.963862i \(0.585834\pi\)
\(710\) 23.8226i 0.894047i
\(711\) 14.5880 6.04254i 0.547092 0.226613i
\(712\) −10.9901 10.9901i −0.411873 0.411873i
\(713\) −11.7080 −0.438468
\(714\) 22.4672 + 17.8962i 0.840815 + 0.669748i
\(715\) −14.1510 −0.529216
\(716\) 25.3291 + 25.3291i 0.946593 + 0.946593i
\(717\) −24.8884 + 10.3091i −0.929473 + 0.385000i
\(718\) 16.2268i 0.605580i
\(719\) 8.87506 + 21.4263i 0.330984 + 0.799066i 0.998515 + 0.0544838i \(0.0173513\pi\)
−0.667531 + 0.744582i \(0.732649\pi\)
\(720\) 10.7413 + 4.44919i 0.400304 + 0.165811i
\(721\) 28.7878 69.4998i 1.07211 2.58831i
\(722\) 9.10401 9.10401i 0.338816 0.338816i
\(723\) 23.5846 23.5846i 0.877119 0.877119i
\(724\) −6.45672 + 15.5879i −0.239962 + 0.579320i
\(725\) 5.92421 + 2.45389i 0.220020 + 0.0911351i
\(726\) −6.52715 15.7579i −0.242245 0.584832i
\(727\) 42.6594i 1.58215i 0.611721 + 0.791074i \(0.290478\pi\)
−0.611721 + 0.791074i \(0.709522\pi\)
\(728\) 47.1551 19.5323i 1.74768 0.723914i
\(729\) 14.8758 + 14.8758i 0.550954 + 0.550954i
\(730\) 21.2551 0.786688
\(731\) 3.22503 + 2.56889i 0.119282 + 0.0950137i
\(732\) −4.34647 −0.160650
\(733\) −24.6931 24.6931i −0.912061 0.912061i 0.0843732 0.996434i \(-0.473111\pi\)
−0.996434 + 0.0843732i \(0.973111\pi\)
\(734\) 1.62896 0.674736i 0.0601259 0.0249050i
\(735\) 82.7199i 3.05117i
\(736\) −15.6205 37.7113i −0.575780 1.39006i
\(737\) 11.4833 + 4.75654i 0.422993 + 0.175209i
\(738\) −2.56071 + 6.18211i −0.0942612 + 0.227567i
\(739\) 5.28062 5.28062i 0.194251 0.194251i −0.603279 0.797530i \(-0.706140\pi\)
0.797530 + 0.603279i \(0.206140\pi\)
\(740\) −3.89297 + 3.89297i −0.143108 + 0.143108i
\(741\) 3.36032 8.11254i 0.123445 0.298022i
\(742\) −2.70657 1.12110i −0.0993612 0.0411568i
\(743\) 20.2083 + 48.7872i 0.741372 + 1.78983i 0.600208 + 0.799844i \(0.295084\pi\)
0.141163 + 0.989986i \(0.454916\pi\)
\(744\) 9.75748i 0.357727i
\(745\) −37.8286 + 15.6691i −1.38593 + 0.574072i
\(746\) 1.32921 + 1.32921i 0.0486660 + 0.0486660i
\(747\) 26.7726 0.979557
\(748\) −5.18246 1.48986i −0.189490 0.0544747i
\(749\) −79.7121 −2.91261
\(750\) 3.26540 + 3.26540i 0.119236 + 0.119236i
\(751\) −21.4631 + 8.89031i −0.783200 + 0.324412i −0.738206 0.674575i \(-0.764327\pi\)
−0.0449937 + 0.998987i \(0.514327\pi\)
\(752\) 6.26464i 0.228448i
\(753\) 20.3006 + 49.0100i 0.739796 + 1.78602i
\(754\) −3.51753 1.45701i −0.128101 0.0530611i
\(755\) 10.0801 24.3354i 0.366851 0.885657i
\(756\) −3.37898 + 3.37898i −0.122892 + 0.122892i
\(757\) −3.46078 + 3.46078i −0.125784 + 0.125784i −0.767196 0.641412i \(-0.778349\pi\)
0.641412 + 0.767196i \(0.278349\pi\)
\(758\) −8.80444 + 21.2558i −0.319792 + 0.772045i
\(759\) 13.3503 + 5.52987i 0.484585 + 0.200722i
\(760\) −2.28840 5.52470i −0.0830091 0.200402i
\(761\) 3.85748i 0.139833i 0.997553 +