Properties

Label 731.2.j.a.135.18
Level 731
Weight 2
Character 731.135
Analytic conductor 5.837
Analytic rank 0
Dimension 128
CM no
Inner twists 4

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Newspace parameters

Level: \( N \) = \( 731 = 17 \cdot 43 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 731.j (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.83706438776\)
Analytic rank: \(0\)
Dimension: \(128\)
Relative dimension: \(64\) over \(\Q(\zeta_{6})\)
Coefficient ring index: multiple of None
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 135.18
Character \(\chi\) = 731.135
Dual form 731.2.j.a.509.18

$q$-expansion

\(f(q)\) \(=\) \(q-1.28957 q^{2} +(0.316022 + 0.182455i) q^{3} -0.337012 q^{4} +(-3.24573 - 1.87392i) q^{5} +(-0.407532 - 0.235289i) q^{6} +(-2.23124 + 1.28820i) q^{7} +3.01374 q^{8} +(-1.43342 - 2.48276i) q^{9} +O(q^{10})\) \(q-1.28957 q^{2} +(0.316022 + 0.182455i) q^{3} -0.337012 q^{4} +(-3.24573 - 1.87392i) q^{5} +(-0.407532 - 0.235289i) q^{6} +(-2.23124 + 1.28820i) q^{7} +3.01374 q^{8} +(-1.43342 - 2.48276i) q^{9} +(4.18560 + 2.41656i) q^{10} +2.13325i q^{11} +(-0.106503 - 0.0614895i) q^{12} +(-0.772737 - 1.33842i) q^{13} +(2.87733 - 1.66123i) q^{14} +(-0.683815 - 1.18440i) q^{15} -3.21240 q^{16} +(-3.98504 - 1.05805i) q^{17} +(1.84849 + 3.20169i) q^{18} +(0.244239 - 0.423034i) q^{19} +(1.09385 + 0.631535i) q^{20} -0.940158 q^{21} -2.75097i q^{22} +(-1.32968 - 0.767692i) q^{23} +(0.952406 + 0.549872i) q^{24} +(4.52319 + 7.83439i) q^{25} +(0.996498 + 1.72599i) q^{26} -2.14087i q^{27} +(0.751952 - 0.434140i) q^{28} +(1.70110 - 0.982131i) q^{29} +(0.881826 + 1.52737i) q^{30} +(4.62044 + 2.66761i) q^{31} -1.88486 q^{32} +(-0.389222 + 0.674152i) q^{33} +(5.13898 + 1.36443i) q^{34} +9.65599 q^{35} +(0.483079 + 0.836718i) q^{36} +(7.15392 + 4.13032i) q^{37} +(-0.314963 + 0.545532i) q^{38} -0.563960i q^{39} +(-9.78179 - 5.64752i) q^{40} +5.61023i q^{41} +1.21240 q^{42} +(6.10384 + 2.39648i) q^{43} -0.718929i q^{44} +10.7445i q^{45} +(1.71472 + 0.989992i) q^{46} +8.49880 q^{47} +(-1.01519 - 0.586119i) q^{48} +(-0.181059 + 0.313603i) q^{49} +(-5.83297 - 10.1030i) q^{50} +(-1.06631 - 1.06146i) q^{51} +(0.260421 + 0.451063i) q^{52} +(4.24221 - 7.34772i) q^{53} +2.76080i q^{54} +(3.99754 - 6.92395i) q^{55} +(-6.72436 + 3.88231i) q^{56} +(0.154370 - 0.0891253i) q^{57} +(-2.19369 + 1.26653i) q^{58} -6.25216 q^{59} +(0.230453 + 0.399157i) q^{60} +(-8.76186 + 5.05866i) q^{61} +(-5.95837 - 3.44007i) q^{62} +(6.39660 + 3.69308i) q^{63} +8.85546 q^{64} +5.79221i q^{65} +(0.501929 - 0.869366i) q^{66} +(-2.34135 + 4.05534i) q^{67} +(1.34300 + 0.356577i) q^{68} +(-0.280139 - 0.485215i) q^{69} -12.4521 q^{70} +(5.29001 - 3.05419i) q^{71} +(-4.31995 - 7.48238i) q^{72} +(-9.25020 + 5.34061i) q^{73} +(-9.22548 - 5.32633i) q^{74} +3.30112i q^{75} +(-0.0823113 + 0.142567i) q^{76} +(-2.74806 - 4.75978i) q^{77} +0.727265i q^{78} +(2.76606 - 1.59699i) q^{79} +(10.4266 + 6.01980i) q^{80} +(-3.90965 + 6.77171i) q^{81} -7.23479i q^{82} +(2.49609 - 4.32336i) q^{83} +0.316844 q^{84} +(10.9517 + 10.9018i) q^{85} +(-7.87132 - 3.09043i) q^{86} +0.716780 q^{87} +6.42905i q^{88} +(3.88291 - 6.72540i) q^{89} -13.8558i q^{90} +(3.44832 + 1.99089i) q^{91} +(0.448118 + 0.258721i) q^{92} +(0.973439 + 1.68605i) q^{93} -10.9598 q^{94} +(-1.58547 + 0.915371i) q^{95} +(-0.595658 - 0.343903i) q^{96} +2.15392i q^{97} +(0.233488 - 0.404412i) q^{98} +(5.29633 - 3.05784i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 128q - 4q^{2} + 116q^{4} - 12q^{8} + 70q^{9} + O(q^{10}) \) \( 128q - 4q^{2} + 116q^{4} - 12q^{8} + 70q^{9} + 4q^{13} - 12q^{15} + 76q^{16} + 2q^{17} - 16q^{18} - 2q^{19} - 20q^{21} + 60q^{25} - 2q^{26} - 28q^{30} - 48q^{32} + 22q^{33} - 18q^{34} - 112q^{35} + 36q^{36} - 40q^{38} + 36q^{42} + 10q^{43} + 36q^{47} + 52q^{49} + 16q^{50} + 10q^{51} + 10q^{52} + 24q^{55} - 12q^{59} - 78q^{60} + 36q^{64} + 14q^{66} + 10q^{67} - q^{68} - 64q^{70} - 68q^{72} - 22q^{76} - 28q^{77} - 20q^{81} - 6q^{83} + 32q^{84} + 6q^{85} - 58q^{86} + 32q^{87} + 36q^{89} + 6q^{93} + 132q^{94} - 48q^{98} + O(q^{100}) \)

Character values

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

\(n\) \(173\) \(562\)
\(\chi(n)\) \(-1\) \(e\left(\frac{2}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.28957 −0.911863 −0.455932 0.890015i \(-0.650694\pi\)
−0.455932 + 0.890015i \(0.650694\pi\)
\(3\) 0.316022 + 0.182455i 0.182455 + 0.105341i 0.588446 0.808537i \(-0.299740\pi\)
−0.405991 + 0.913877i \(0.633073\pi\)
\(4\) −0.337012 −0.168506
\(5\) −3.24573 1.87392i −1.45154 0.838045i −0.452967 0.891527i \(-0.649635\pi\)
−0.998569 + 0.0534824i \(0.982968\pi\)
\(6\) −0.407532 0.235289i −0.166374 0.0960561i
\(7\) −2.23124 + 1.28820i −0.843328 + 0.486896i −0.858394 0.512991i \(-0.828537\pi\)
0.0150662 + 0.999886i \(0.495204\pi\)
\(8\) 3.01374 1.06552
\(9\) −1.43342 2.48276i −0.477807 0.827586i
\(10\) 4.18560 + 2.41656i 1.32360 + 0.764182i
\(11\) 2.13325i 0.643198i 0.946876 + 0.321599i \(0.104220\pi\)
−0.946876 + 0.321599i \(0.895780\pi\)
\(12\) −0.106503 0.0614895i −0.0307448 0.0177505i
\(13\) −0.772737 1.33842i −0.214319 0.371211i 0.738743 0.673987i \(-0.235420\pi\)
−0.953062 + 0.302776i \(0.902086\pi\)
\(14\) 2.87733 1.66123i 0.768999 0.443982i
\(15\) −0.683815 1.18440i −0.176560 0.305811i
\(16\) −3.21240 −0.803100
\(17\) −3.98504 1.05805i −0.966513 0.256616i
\(18\) 1.84849 + 3.20169i 0.435694 + 0.754645i
\(19\) 0.244239 0.423034i 0.0560322 0.0970507i −0.836649 0.547740i \(-0.815488\pi\)
0.892681 + 0.450689i \(0.148822\pi\)
\(20\) 1.09385 + 0.631535i 0.244592 + 0.141215i
\(21\) −0.940158 −0.205159
\(22\) 2.75097i 0.586509i
\(23\) −1.32968 0.767692i −0.277258 0.160075i 0.354923 0.934895i \(-0.384507\pi\)
−0.632181 + 0.774820i \(0.717840\pi\)
\(24\) 0.952406 + 0.549872i 0.194409 + 0.112242i
\(25\) 4.52319 + 7.83439i 0.904638 + 1.56688i
\(26\) 0.996498 + 1.72599i 0.195429 + 0.338494i
\(27\) 2.14087i 0.412011i
\(28\) 0.751952 0.434140i 0.142106 0.0820447i
\(29\) 1.70110 0.982131i 0.315886 0.182377i −0.333671 0.942690i \(-0.608287\pi\)
0.649558 + 0.760312i \(0.274954\pi\)
\(30\) 0.881826 + 1.52737i 0.160999 + 0.278858i
\(31\) 4.62044 + 2.66761i 0.829855 + 0.479117i 0.853803 0.520596i \(-0.174290\pi\)
−0.0239480 + 0.999713i \(0.507624\pi\)
\(32\) −1.88486 −0.333200
\(33\) −0.389222 + 0.674152i −0.0677548 + 0.117355i
\(34\) 5.13898 + 1.36443i 0.881328 + 0.233999i
\(35\) 9.65599 1.63216
\(36\) 0.483079 + 0.836718i 0.0805132 + 0.139453i
\(37\) 7.15392 + 4.13032i 1.17610 + 0.679020i 0.955109 0.296256i \(-0.0957382\pi\)
0.220989 + 0.975276i \(0.429071\pi\)
\(38\) −0.314963 + 0.545532i −0.0510937 + 0.0884969i
\(39\) 0.563960i 0.0903058i
\(40\) −9.78179 5.64752i −1.54664 0.892951i
\(41\) 5.61023i 0.876171i 0.898933 + 0.438086i \(0.144343\pi\)
−0.898933 + 0.438086i \(0.855657\pi\)
\(42\) 1.21240 0.187077
\(43\) 6.10384 + 2.39648i 0.930827 + 0.365460i
\(44\) 0.718929i 0.108383i
\(45\) 10.7445i 1.60169i
\(46\) 1.71472 + 0.989992i 0.252821 + 0.145966i
\(47\) 8.49880 1.23968 0.619839 0.784729i \(-0.287198\pi\)
0.619839 + 0.784729i \(0.287198\pi\)
\(48\) −1.01519 0.586119i −0.146530 0.0845990i
\(49\) −0.181059 + 0.313603i −0.0258655 + 0.0448004i
\(50\) −5.83297 10.1030i −0.824906 1.42878i
\(51\) −1.06631 1.06146i −0.149313 0.148634i
\(52\) 0.260421 + 0.451063i 0.0361140 + 0.0625512i
\(53\) 4.24221 7.34772i 0.582712 1.00929i −0.412444 0.910983i \(-0.635325\pi\)
0.995156 0.0983046i \(-0.0313419\pi\)
\(54\) 2.76080i 0.375697i
\(55\) 3.99754 6.92395i 0.539029 0.933625i
\(56\) −6.72436 + 3.88231i −0.898580 + 0.518796i
\(57\) 0.154370 0.0891253i 0.0204467 0.0118049i
\(58\) −2.19369 + 1.26653i −0.288045 + 0.166303i
\(59\) −6.25216 −0.813962 −0.406981 0.913437i \(-0.633418\pi\)
−0.406981 + 0.913437i \(0.633418\pi\)
\(60\) 0.230453 + 0.399157i 0.0297514 + 0.0515310i
\(61\) −8.76186 + 5.05866i −1.12184 + 0.647695i −0.941870 0.335977i \(-0.890934\pi\)
−0.179971 + 0.983672i \(0.557600\pi\)
\(62\) −5.95837 3.44007i −0.756714 0.436889i
\(63\) 6.39660 + 3.69308i 0.805895 + 0.465284i
\(64\) 8.85546 1.10693
\(65\) 5.79221i 0.718435i
\(66\) 0.501929 0.869366i 0.0617831 0.107012i
\(67\) −2.34135 + 4.05534i −0.286041 + 0.495438i −0.972861 0.231390i \(-0.925673\pi\)
0.686820 + 0.726828i \(0.259006\pi\)
\(68\) 1.34300 + 0.356577i 0.162863 + 0.0432413i
\(69\) −0.280139 0.485215i −0.0337248 0.0584130i
\(70\) −12.4521 −1.48831
\(71\) 5.29001 3.05419i 0.627809 0.362466i −0.152094 0.988366i \(-0.548602\pi\)
0.779903 + 0.625900i \(0.215268\pi\)
\(72\) −4.31995 7.48238i −0.509111 0.881807i
\(73\) −9.25020 + 5.34061i −1.08265 + 0.625071i −0.931611 0.363457i \(-0.881597\pi\)
−0.151043 + 0.988527i \(0.548263\pi\)
\(74\) −9.22548 5.32633i −1.07244 0.619173i
\(75\) 3.30112i 0.381180i
\(76\) −0.0823113 + 0.142567i −0.00944176 + 0.0163536i
\(77\) −2.74806 4.75978i −0.313170 0.542427i
\(78\) 0.727265i 0.0823465i
\(79\) 2.76606 1.59699i 0.311206 0.179675i −0.336260 0.941769i \(-0.609162\pi\)
0.647466 + 0.762094i \(0.275829\pi\)
\(80\) 10.4266 + 6.01980i 1.16573 + 0.673034i
\(81\) −3.90965 + 6.77171i −0.434405 + 0.752412i
\(82\) 7.23479i 0.798948i
\(83\) 2.49609 4.32336i 0.273982 0.474550i −0.695896 0.718142i \(-0.744993\pi\)
0.969878 + 0.243592i \(0.0783259\pi\)
\(84\) 0.316844 0.0345705
\(85\) 10.9517 + 10.9018i 1.18787 + 1.18247i
\(86\) −7.87132 3.09043i −0.848787 0.333250i
\(87\) 0.716780 0.0768468
\(88\) 6.42905i 0.685339i
\(89\) 3.88291 6.72540i 0.411588 0.712891i −0.583476 0.812131i \(-0.698308\pi\)
0.995064 + 0.0992395i \(0.0316410\pi\)
\(90\) 13.8558i 1.46053i
\(91\) 3.44832 + 1.99089i 0.361482 + 0.208702i
\(92\) 0.448118 + 0.258721i 0.0467196 + 0.0269736i
\(93\) 0.973439 + 1.68605i 0.100941 + 0.174835i
\(94\) −10.9598 −1.13042
\(95\) −1.58547 + 0.915371i −0.162666 + 0.0939150i
\(96\) −0.595658 0.343903i −0.0607941 0.0350995i
\(97\) 2.15392i 0.218698i 0.994003 + 0.109349i \(0.0348766\pi\)
−0.994003 + 0.109349i \(0.965123\pi\)
\(98\) 0.233488 0.404412i 0.0235858 0.0408518i
\(99\) 5.29633 3.05784i 0.532301 0.307324i
\(100\) −1.52437 2.64028i −0.152437 0.264028i
\(101\) 5.01543 + 8.68698i 0.499054 + 0.864387i 0.999999 0.00109196i \(-0.000347580\pi\)
−0.500945 + 0.865479i \(0.667014\pi\)
\(102\) 1.37508 + 1.36882i 0.136153 + 0.135534i
\(103\) 8.37047 + 14.4981i 0.824767 + 1.42854i 0.902097 + 0.431533i \(0.142027\pi\)
−0.0773305 + 0.997006i \(0.524640\pi\)
\(104\) −2.32883 4.03365i −0.228360 0.395532i
\(105\) 3.05150 + 1.76179i 0.297796 + 0.171933i
\(106\) −5.47062 + 9.47540i −0.531354 + 0.920332i
\(107\) 13.9033i 1.34409i −0.740512 0.672043i \(-0.765417\pi\)
0.740512 0.672043i \(-0.234583\pi\)
\(108\) 0.721498i 0.0694262i
\(109\) −2.64500 1.52709i −0.253345 0.146269i 0.367950 0.929846i \(-0.380060\pi\)
−0.621295 + 0.783577i \(0.713393\pi\)
\(110\) −5.15511 + 8.92891i −0.491520 + 0.851338i
\(111\) 1.50720 + 2.61054i 0.143057 + 0.247782i
\(112\) 7.16762 4.13823i 0.677277 0.391026i
\(113\) 6.92478i 0.651429i −0.945468 0.325714i \(-0.894395\pi\)
0.945468 0.325714i \(-0.105605\pi\)
\(114\) −0.199070 + 0.114933i −0.0186446 + 0.0107645i
\(115\) 2.87720 + 4.98345i 0.268300 + 0.464709i
\(116\) −0.573291 + 0.330990i −0.0532287 + 0.0307316i
\(117\) −2.21531 + 3.83704i −0.204806 + 0.354734i
\(118\) 8.06259 0.742222
\(119\) 10.2545 2.77277i 0.940033 0.254180i
\(120\) −2.06084 3.56948i −0.188128 0.325847i
\(121\) 6.44926 0.586296
\(122\) 11.2990 6.52349i 1.02297 0.590609i
\(123\) −1.02362 + 1.77296i −0.0922964 + 0.159862i
\(124\) −1.55714 0.899016i −0.139835 0.0807340i
\(125\) 15.1652i 1.35642i
\(126\) −8.24885 4.76248i −0.734866 0.424275i
\(127\) 5.17067 0.458823 0.229412 0.973330i \(-0.426320\pi\)
0.229412 + 0.973330i \(0.426320\pi\)
\(128\) −7.65000 −0.676171
\(129\) 1.49170 + 1.87102i 0.131336 + 0.164734i
\(130\) 7.46945i 0.655114i
\(131\) 3.91055i 0.341666i 0.985300 + 0.170833i \(0.0546459\pi\)
−0.985300 + 0.170833i \(0.945354\pi\)
\(132\) 0.131172 0.227197i 0.0114171 0.0197750i
\(133\) 1.25852i 0.109127i
\(134\) 3.01933 5.22964i 0.260831 0.451772i
\(135\) −4.01183 + 6.94870i −0.345283 + 0.598048i
\(136\) −12.0099 3.18870i −1.02984 0.273429i
\(137\) −13.3848 −1.14354 −0.571769 0.820415i \(-0.693742\pi\)
−0.571769 + 0.820415i \(0.693742\pi\)
\(138\) 0.361258 + 0.625718i 0.0307524 + 0.0532647i
\(139\) −12.3851 7.15054i −1.05049 0.606501i −0.127703 0.991812i \(-0.540761\pi\)
−0.922786 + 0.385312i \(0.874094\pi\)
\(140\) −3.25418 −0.275029
\(141\) 2.68581 + 1.55065i 0.226186 + 0.130588i
\(142\) −6.82183 + 3.93859i −0.572476 + 0.330519i
\(143\) 2.85518 1.64844i 0.238762 0.137849i
\(144\) 4.60472 + 7.97561i 0.383727 + 0.664634i
\(145\) −7.36176 −0.611361
\(146\) 11.9288 6.88708i 0.987232 0.569979i
\(147\) −0.114437 + 0.0660701i −0.00943859 + 0.00544937i
\(148\) −2.41096 1.39197i −0.198179 0.114419i
\(149\) −1.47152 + 2.54875i −0.120552 + 0.208802i −0.919985 0.391953i \(-0.871800\pi\)
0.799434 + 0.600754i \(0.205133\pi\)
\(150\) 4.25702i 0.347584i
\(151\) −4.19588 −0.341456 −0.170728 0.985318i \(-0.554612\pi\)
−0.170728 + 0.985318i \(0.554612\pi\)
\(152\) 0.736072 1.27491i 0.0597033 0.103409i
\(153\) 3.08534 + 11.4105i 0.249435 + 0.922485i
\(154\) 3.54381 + 6.13806i 0.285568 + 0.494619i
\(155\) −9.99780 17.3167i −0.803043 1.39091i
\(156\) 0.190061i 0.0152171i
\(157\) 3.48687 + 6.03944i 0.278283 + 0.482000i 0.970958 0.239250i \(-0.0769015\pi\)
−0.692675 + 0.721249i \(0.743568\pi\)
\(158\) −3.56703 + 2.05942i −0.283778 + 0.163839i
\(159\) 2.68126 1.54803i 0.212638 0.122766i
\(160\) 6.11777 + 3.53209i 0.483652 + 0.279237i
\(161\) 3.95578 0.311759
\(162\) 5.04176 8.73259i 0.396118 0.686097i
\(163\) −4.10641 + 2.37084i −0.321639 + 0.185698i −0.652123 0.758113i \(-0.726121\pi\)
0.330484 + 0.943812i \(0.392788\pi\)
\(164\) 1.89071i 0.147640i
\(165\) 2.52662 1.45875i 0.196697 0.113563i
\(166\) −3.21888 + 5.57527i −0.249834 + 0.432725i
\(167\) 11.6993 + 6.75461i 0.905322 + 0.522688i 0.878923 0.476964i \(-0.158263\pi\)
0.0263986 + 0.999651i \(0.491596\pi\)
\(168\) −2.83339 −0.218601
\(169\) 5.30575 9.18984i 0.408135 0.706910i
\(170\) −14.1229 14.0587i −1.08318 1.07825i
\(171\) −1.40039 −0.107090
\(172\) −2.05707 0.807642i −0.156850 0.0615822i
\(173\) 11.4250i 0.868628i −0.900762 0.434314i \(-0.856991\pi\)
0.900762 0.434314i \(-0.143009\pi\)
\(174\) −0.924337 −0.0700738
\(175\) −20.1846 11.6536i −1.52581 0.880928i
\(176\) 6.85284i 0.516552i
\(177\) −1.97582 1.14074i −0.148512 0.0857432i
\(178\) −5.00728 + 8.67287i −0.375312 + 0.650059i
\(179\) −2.73043 4.72924i −0.204082 0.353480i 0.745758 0.666217i \(-0.232088\pi\)
−0.949840 + 0.312737i \(0.898754\pi\)
\(180\) 3.62102i 0.269895i
\(181\) −18.8008 + 10.8546i −1.39745 + 0.806819i −0.994125 0.108237i \(-0.965479\pi\)
−0.403326 + 0.915056i \(0.632146\pi\)
\(182\) −4.44684 2.56739i −0.329622 0.190307i
\(183\) −3.69192 −0.272914
\(184\) −4.00731 2.31362i −0.295423 0.170563i
\(185\) −15.4798 26.8118i −1.13810 1.97124i
\(186\) −1.25532 2.17427i −0.0920443 0.159425i
\(187\) 2.25709 8.50107i 0.165055 0.621660i
\(188\) −2.86420 −0.208893
\(189\) 2.75788 + 4.77679i 0.200606 + 0.347460i
\(190\) 2.04457 1.18043i 0.148329 0.0856377i
\(191\) −8.49089 + 14.7067i −0.614379 + 1.06414i 0.376114 + 0.926574i \(0.377260\pi\)
−0.990493 + 0.137563i \(0.956073\pi\)
\(192\) 2.79852 + 1.61572i 0.201966 + 0.116605i
\(193\) 4.75676i 0.342399i 0.985236 + 0.171200i \(0.0547643\pi\)
−0.985236 + 0.171200i \(0.945236\pi\)
\(194\) 2.77763i 0.199422i
\(195\) −1.05682 + 1.83046i −0.0756803 + 0.131082i
\(196\) 0.0610188 0.105688i 0.00435849 0.00754912i
\(197\) 20.5487 11.8638i 1.46404 0.845262i 0.464842 0.885394i \(-0.346111\pi\)
0.999194 + 0.0401322i \(0.0127779\pi\)
\(198\) −6.82999 + 3.94329i −0.485386 + 0.280238i
\(199\) 6.37500i 0.451912i −0.974138 0.225956i \(-0.927449\pi\)
0.974138 0.225956i \(-0.0725505\pi\)
\(200\) 13.6317 + 23.6108i 0.963907 + 1.66954i
\(201\) −1.47983 + 0.854383i −0.104379 + 0.0602635i
\(202\) −6.46774 11.2025i −0.455069 0.788203i
\(203\) −2.53037 + 4.38273i −0.177597 + 0.307607i
\(204\) 0.359359 + 0.357724i 0.0251602 + 0.0250457i
\(205\) 10.5132 18.2093i 0.734271 1.27179i
\(206\) −10.7943 18.6963i −0.752074 1.30263i
\(207\) 4.40170i 0.305940i
\(208\) 2.48234 + 4.29954i 0.172119 + 0.298119i
\(209\) 0.902436 + 0.521022i 0.0624228 + 0.0360398i
\(210\) −3.93512 2.27194i −0.271549 0.156779i
\(211\) 13.8580i 0.954024i −0.878897 0.477012i \(-0.841720\pi\)
0.878897 0.477012i \(-0.158280\pi\)
\(212\) −1.42967 + 2.47627i −0.0981904 + 0.170071i
\(213\) 2.22901 0.152729
\(214\) 17.9293i 1.22562i
\(215\) −15.3206 19.2165i −1.04486 1.31055i
\(216\) 6.45202i 0.439005i
\(217\) −13.7457 −0.933120
\(218\) 3.41090 + 1.96929i 0.231016 + 0.133377i
\(219\) −3.89768 −0.263381
\(220\) −1.34722 + 2.33345i −0.0908295 + 0.157321i
\(221\) 1.66327 + 6.15125i 0.111883 + 0.413778i
\(222\) −1.94363 3.36647i −0.130448 0.225943i
\(223\) −17.4944 −1.17151 −0.585755 0.810488i \(-0.699202\pi\)
−0.585755 + 0.810488i \(0.699202\pi\)
\(224\) 4.20558 2.42809i 0.280997 0.162234i
\(225\) 12.9673 22.4600i 0.864484 1.49733i
\(226\) 8.92998i 0.594014i
\(227\) 19.4961 + 11.2561i 1.29400 + 0.747092i 0.979361 0.202119i \(-0.0647829\pi\)
0.314640 + 0.949211i \(0.398116\pi\)
\(228\) −0.0520243 + 0.0300363i −0.00344540 + 0.00198920i
\(229\) 11.7425 + 20.3386i 0.775967 + 1.34401i 0.934249 + 0.356620i \(0.116071\pi\)
−0.158283 + 0.987394i \(0.550596\pi\)
\(230\) −3.71034 6.42650i −0.244653 0.423751i
\(231\) 2.00559i 0.131958i
\(232\) 5.12667 2.95989i 0.336583 0.194326i
\(233\) −8.43918 + 4.87236i −0.552869 + 0.319199i −0.750278 0.661122i \(-0.770080\pi\)
0.197409 + 0.980321i \(0.436747\pi\)
\(234\) 2.85680 4.94812i 0.186755 0.323469i
\(235\) −27.5848 15.9261i −1.79944 1.03891i
\(236\) 2.10705 0.137157
\(237\) 1.16551 0.0757083
\(238\) −13.2239 + 3.57568i −0.857181 + 0.231777i
\(239\) −9.45964 + 16.3846i −0.611893 + 1.05983i 0.379028 + 0.925385i \(0.376259\pi\)
−0.990921 + 0.134445i \(0.957075\pi\)
\(240\) 2.19669 + 3.80477i 0.141795 + 0.245597i
\(241\) 3.65263 2.10884i 0.235286 0.135843i −0.377722 0.925919i \(-0.623293\pi\)
0.613008 + 0.790076i \(0.289959\pi\)
\(242\) −8.31676 −0.534622
\(243\) −8.03321 + 4.63798i −0.515331 + 0.297526i
\(244\) 2.95285 1.70483i 0.189037 0.109140i
\(245\) 1.17534 0.678580i 0.0750894 0.0433529i
\(246\) 1.32002 2.28635i 0.0841617 0.145772i
\(247\) −0.754930 −0.0480350
\(248\) 13.9248 + 8.03948i 0.884225 + 0.510507i
\(249\) 1.57764 0.910849i 0.0999787 0.0577227i
\(250\) 19.5566i 1.23687i
\(251\) 13.4971 + 23.3777i 0.851932 + 1.47559i 0.879462 + 0.475969i \(0.157903\pi\)
−0.0275299 + 0.999621i \(0.508764\pi\)
\(252\) −2.15573 1.24461i −0.135798 0.0784031i
\(253\) 1.63768 2.83654i 0.102960 0.178332i
\(254\) −6.66794 −0.418384
\(255\) 1.47187 + 5.44340i 0.0921718 + 0.340879i
\(256\) −7.84572 −0.490357
\(257\) −19.4276 −1.21186 −0.605932 0.795517i \(-0.707200\pi\)
−0.605932 + 0.795517i \(0.707200\pi\)
\(258\) −1.92364 2.41281i −0.119761 0.150215i
\(259\) −21.2828 −1.32245
\(260\) 1.95204i 0.121060i
\(261\) −4.87678 2.81561i −0.301865 0.174282i
\(262\) 5.04293i 0.311553i
\(263\) 2.60211 4.50698i 0.160453 0.277913i −0.774578 0.632478i \(-0.782038\pi\)
0.935031 + 0.354565i \(0.115371\pi\)
\(264\) −1.17301 + 2.03172i −0.0721939 + 0.125044i
\(265\) −27.5382 + 15.8992i −1.69166 + 0.976678i
\(266\) 1.62295i 0.0995092i
\(267\) 2.45417 1.41691i 0.150193 0.0867138i
\(268\) 0.789062 1.36670i 0.0481996 0.0834842i
\(269\) 30.7504i 1.87488i 0.348144 + 0.937441i \(0.386812\pi\)
−0.348144 + 0.937441i \(0.613188\pi\)
\(270\) 5.17353 8.96082i 0.314851 0.545338i
\(271\) 7.36540 + 12.7572i 0.447416 + 0.774947i 0.998217 0.0596893i \(-0.0190110\pi\)
−0.550801 + 0.834637i \(0.685678\pi\)
\(272\) 12.8015 + 3.39889i 0.776207 + 0.206088i
\(273\) 0.726495 + 1.25833i 0.0439695 + 0.0761574i
\(274\) 17.2606 1.04275
\(275\) −16.7127 + 9.64908i −1.00781 + 0.581861i
\(276\) 0.0944101 + 0.163523i 0.00568282 + 0.00984293i
\(277\) 9.70983 + 5.60597i 0.583407 + 0.336830i 0.762486 0.647004i \(-0.223978\pi\)
−0.179079 + 0.983835i \(0.557312\pi\)
\(278\) 15.9714 + 9.22111i 0.957903 + 0.553045i
\(279\) 15.2952i 0.915701i
\(280\) 29.1006 1.73910
\(281\) 15.9073 27.5523i 0.948952 1.64363i 0.201312 0.979527i \(-0.435479\pi\)
0.747639 0.664105i \(-0.231187\pi\)
\(282\) −3.46353 1.99967i −0.206250 0.119079i
\(283\) 7.00308 4.04323i 0.416290 0.240345i −0.277199 0.960813i \(-0.589406\pi\)
0.693489 + 0.720467i \(0.256073\pi\)
\(284\) −1.78280 + 1.02930i −0.105789 + 0.0610776i
\(285\) −0.668056 −0.0395722
\(286\) −3.68195 + 2.12578i −0.217718 + 0.125700i
\(287\) −7.22713 12.5178i −0.426604 0.738900i
\(288\) 2.70180 + 4.67966i 0.159205 + 0.275752i
\(289\) 14.7610 + 8.43277i 0.868297 + 0.496045i
\(290\) 9.49350 0.557477
\(291\) −0.392994 + 0.680686i −0.0230377 + 0.0399025i
\(292\) 3.11743 1.79985i 0.182434 0.105328i
\(293\) 15.2821 0.892789 0.446394 0.894836i \(-0.352708\pi\)
0.446394 + 0.894836i \(0.352708\pi\)
\(294\) 0.147574 0.0852020i 0.00860670 0.00496908i
\(295\) 20.2928 + 11.7161i 1.18149 + 0.682136i
\(296\) 21.5600 + 12.4477i 1.25315 + 0.723508i
\(297\) 4.56701 0.265005
\(298\) 1.89763 3.28679i 0.109927 0.190399i
\(299\) 2.37290i 0.137228i
\(300\) 1.11251i 0.0642311i
\(301\) −16.7063 + 2.51588i −0.962933 + 0.145013i
\(302\) 5.41087 0.311361
\(303\) 3.66037i 0.210282i
\(304\) −0.784593 + 1.35895i −0.0449995 + 0.0779414i
\(305\) 37.9182 2.17119
\(306\) −3.97876 14.7146i −0.227451 0.841180i
\(307\) 11.9340 20.6703i 0.681108 1.17971i −0.293535 0.955948i \(-0.594832\pi\)
0.974643 0.223765i \(-0.0718349\pi\)
\(308\) 0.926128 + 1.60410i 0.0527710 + 0.0914021i
\(309\) 6.10894i 0.347526i
\(310\) 12.8929 + 22.3311i 0.732265 + 1.26832i
\(311\) 7.35380 + 4.24572i 0.416996 + 0.240753i 0.693791 0.720176i \(-0.255939\pi\)
−0.276795 + 0.960929i \(0.589272\pi\)
\(312\) 1.69963i 0.0962224i
\(313\) 14.0281 + 8.09911i 0.792913 + 0.457788i 0.840987 0.541055i \(-0.181975\pi\)
−0.0480741 + 0.998844i \(0.515308\pi\)
\(314\) −4.49656 7.78827i −0.253756 0.439518i
\(315\) −13.8411 23.9735i −0.779857 1.35075i
\(316\) −0.932195 + 0.538203i −0.0524401 + 0.0302763i
\(317\) 10.6195i 0.596452i −0.954495 0.298226i \(-0.903605\pi\)
0.954495 0.298226i \(-0.0963950\pi\)
\(318\) −3.45767 + 1.99629i −0.193897 + 0.111946i
\(319\) 2.09513 + 3.62887i 0.117305 + 0.203178i
\(320\) −28.7425 16.5945i −1.60675 0.927659i
\(321\) 2.53673 4.39375i 0.141587 0.245235i
\(322\) −5.10125 −0.284282
\(323\) −1.42089 + 1.42739i −0.0790607 + 0.0794220i
\(324\) 1.31760 2.28214i 0.0731998 0.126786i
\(325\) 6.99047 12.1079i 0.387762 0.671623i
\(326\) 5.29550 3.05736i 0.293290 0.169331i
\(327\) −0.557251 0.965186i −0.0308160 0.0533749i
\(328\) 16.9078i 0.933576i
\(329\) −18.9628 + 10.9482i −1.04545 + 0.603594i
\(330\) −3.25825 + 1.88115i −0.179361 + 0.103554i
\(331\) 14.2297 + 24.6465i 0.782134 + 1.35469i 0.930697 + 0.365792i \(0.119202\pi\)
−0.148563 + 0.988903i \(0.547465\pi\)
\(332\) −0.841212 + 1.45702i −0.0461675 + 0.0799644i
\(333\) 23.6819i 1.29776i
\(334\) −15.0871 8.71054i −0.825529 0.476620i
\(335\) 15.1988 8.77503i 0.830399 0.479431i
\(336\) 3.02016 0.164763
\(337\) 17.8804 10.3233i 0.974009 0.562345i 0.0735532 0.997291i \(-0.476566\pi\)
0.900456 + 0.434947i \(0.143233\pi\)
\(338\) −6.84214 + 11.8509i −0.372163 + 0.644606i
\(339\) 1.26346 2.18838i 0.0686218 0.118857i
\(340\) −3.69083 3.67404i −0.200164 0.199253i
\(341\) −5.69067 + 9.85653i −0.308167 + 0.533761i
\(342\) 1.80590 0.0976517
\(343\) 18.9678i 1.02417i
\(344\) 18.3954 + 7.22237i 0.991812 + 0.389404i
\(345\) 2.09984i 0.113051i
\(346\) 14.7333i 0.792070i
\(347\) −3.94448 2.27735i −0.211751 0.122254i 0.390374 0.920656i \(-0.372346\pi\)
−0.602125 + 0.798402i \(0.705679\pi\)
\(348\) −0.241563 −0.0129491
\(349\) −6.48218 + 11.2275i −0.346983 + 0.600992i −0.985712 0.168440i \(-0.946127\pi\)
0.638729 + 0.769432i \(0.279461\pi\)
\(350\) 26.0294 + 15.0281i 1.39133 + 0.803286i
\(351\) −2.86538 + 1.65433i −0.152943 + 0.0883016i
\(352\) 4.02088i 0.214314i
\(353\) −12.1183 20.9894i −0.644989 1.11715i −0.984304 0.176482i \(-0.943528\pi\)
0.339314 0.940673i \(-0.389805\pi\)
\(354\) 2.54795 + 1.47106i 0.135422 + 0.0781860i
\(355\) −22.8933 −1.21505
\(356\) −1.30859 + 2.26654i −0.0693549 + 0.120126i
\(357\) 3.74657 + 0.994739i 0.198289 + 0.0526472i
\(358\) 3.52108 + 6.09868i 0.186095 + 0.322325i
\(359\) 7.26285 + 12.5796i 0.383318 + 0.663927i 0.991534 0.129845i \(-0.0414479\pi\)
−0.608216 + 0.793772i \(0.708115\pi\)
\(360\) 32.3811i 1.70663i
\(361\) 9.38069 + 16.2478i 0.493721 + 0.855149i
\(362\) 24.2449 13.9978i 1.27428 0.735708i
\(363\) 2.03811 + 1.17670i 0.106973 + 0.0617608i
\(364\) −1.16212 0.670952i −0.0609118 0.0351674i
\(365\) 40.0316 2.09535
\(366\) 4.76098 0.248860
\(367\) −6.87953 3.97190i −0.359109 0.207332i 0.309581 0.950873i \(-0.399811\pi\)
−0.668690 + 0.743542i \(0.733145\pi\)
\(368\) 4.27147 + 2.46613i 0.222666 + 0.128556i
\(369\) 13.9288 8.04182i 0.725107 0.418641i
\(370\) 19.9623 + 34.5757i 1.03779 + 1.79751i
\(371\) 21.8593i 1.13488i
\(372\) −0.328060 0.568217i −0.0170091 0.0294607i
\(373\) 9.95269 + 17.2386i 0.515331 + 0.892579i 0.999842 + 0.0177939i \(0.00566429\pi\)
−0.484511 + 0.874785i \(0.661002\pi\)
\(374\) −2.91068 + 10.9627i −0.150507 + 0.566868i
\(375\) 2.76697 4.79254i 0.142886 0.247486i
\(376\) 25.6132 1.32090
\(377\) −2.62901 1.51786i −0.135401 0.0781737i
\(378\) −3.55648 6.16000i −0.182925 0.316836i
\(379\) 35.6656i 1.83202i 0.401154 + 0.916011i \(0.368609\pi\)
−0.401154 + 0.916011i \(0.631391\pi\)
\(380\) 0.534321 0.308491i 0.0274101 0.0158252i
\(381\) 1.63404 + 0.943416i 0.0837146 + 0.0483327i
\(382\) 10.9496 18.9653i 0.560230 0.970347i
\(383\) −24.8532 −1.26994 −0.634971 0.772536i \(-0.718988\pi\)
−0.634971 + 0.772536i \(0.718988\pi\)
\(384\) −2.41757 1.39578i −0.123371 0.0712282i
\(385\) 20.5986i 1.04980i
\(386\) 6.13417i 0.312221i
\(387\) −2.79949 18.5895i −0.142306 0.944958i
\(388\) 0.725897i 0.0368519i
\(389\) −17.4253 −0.883499 −0.441749 0.897138i \(-0.645642\pi\)
−0.441749 + 0.897138i \(0.645642\pi\)
\(390\) 1.36284 2.36051i 0.0690101 0.119529i
\(391\) 4.48657 + 4.46616i 0.226896 + 0.225863i
\(392\) −0.545663 + 0.945116i −0.0275601 + 0.0477356i
\(393\) −0.713500 + 1.23582i −0.0359913 + 0.0623388i
\(394\) −26.4990 + 15.2992i −1.33500 + 0.770763i
\(395\) −11.9705 −0.602303
\(396\) −1.78493 + 1.03053i −0.0896959 + 0.0517859i
\(397\) 22.5263 + 13.0056i 1.13056 + 0.652732i 0.944077 0.329726i \(-0.106956\pi\)
0.186487 + 0.982457i \(0.440290\pi\)
\(398\) 8.22100i 0.412082i
\(399\) −0.229623 + 0.397719i −0.0114955 + 0.0199109i
\(400\) −14.5303 25.1672i −0.726515 1.25836i
\(401\) −22.8429 + 13.1884i −1.14072 + 0.658596i −0.946609 0.322383i \(-0.895516\pi\)
−0.194113 + 0.980979i \(0.562183\pi\)
\(402\) 1.90835 1.10179i 0.0951798 0.0549521i
\(403\) 8.24545i 0.410735i
\(404\) −1.69026 2.92761i −0.0840935 0.145654i
\(405\) 25.3793 14.6528i 1.26111 0.728102i
\(406\) 3.26309 5.65183i 0.161944 0.280496i
\(407\) −8.81099 + 15.2611i −0.436745 + 0.756464i
\(408\) −3.21358 3.19896i −0.159096 0.158372i
\(409\) −6.60081 −0.326389 −0.163194 0.986594i \(-0.552180\pi\)
−0.163194 + 0.986594i \(0.552180\pi\)
\(410\) −13.5574 + 23.4822i −0.669554 + 1.15970i
\(411\) −4.22987 2.44212i −0.208644 0.120461i
\(412\) −2.82095 4.88602i −0.138978 0.240717i
\(413\) 13.9500 8.05406i 0.686437 0.396314i
\(414\) 5.67630i 0.278975i
\(415\) −16.2033 + 9.35497i −0.795388 + 0.459218i
\(416\) 1.45650 + 2.52274i 0.0714110 + 0.123688i
\(417\) −2.60930 4.51945i −0.127778 0.221318i
\(418\) −1.16375 0.671894i −0.0569211 0.0328634i
\(419\) 19.0091i 0.928654i 0.885664 + 0.464327i \(0.153704\pi\)
−0.885664 + 0.464327i \(0.846296\pi\)
\(420\) −1.02839 0.593742i −0.0501804 0.0289717i
\(421\) 18.4049 + 31.8781i 0.896998 + 1.55365i 0.831312 + 0.555806i \(0.187590\pi\)
0.0656856 + 0.997840i \(0.479077\pi\)
\(422\) 17.8709i 0.869939i
\(423\) −12.1824 21.1005i −0.592326 1.02594i
\(424\) 12.7849 22.1441i 0.620890 1.07541i
\(425\) −9.73586 36.0061i −0.472259 1.74655i
\(426\) −2.87446 −0.139268
\(427\) 13.0332 22.5741i 0.630720 1.09244i
\(428\) 4.68558i 0.226486i
\(429\) 1.20306 0.0580845
\(430\) 19.7570 + 24.7810i 0.952767 + 1.19504i
\(431\) 12.5914i 0.606507i 0.952910 + 0.303254i \(0.0980729\pi\)
−0.952910 + 0.303254i \(0.901927\pi\)
\(432\) 6.87733i 0.330886i
\(433\) −8.78875 + 15.2226i −0.422360 + 0.731549i −0.996170 0.0874394i \(-0.972132\pi\)
0.573810 + 0.818989i \(0.305465\pi\)
\(434\) 17.7260 0.850877
\(435\) −2.32648 1.34319i −0.111546 0.0644011i
\(436\) 0.891394 + 0.514647i 0.0426900 + 0.0246471i
\(437\) −0.649520 + 0.375001i −0.0310708 + 0.0179387i
\(438\) 5.02633 0.240168
\(439\) 5.31274 3.06731i 0.253563 0.146395i −0.367831 0.929892i \(-0.619900\pi\)
0.621395 + 0.783498i \(0.286566\pi\)
\(440\) 12.0476 20.8670i 0.574344 0.994794i
\(441\) 1.03813 0.0494349
\(442\) −2.14490 7.93246i −0.102022 0.377309i
\(443\) 8.55282 + 14.8139i 0.406357 + 0.703830i 0.994478 0.104942i \(-0.0334657\pi\)
−0.588122 + 0.808772i \(0.700132\pi\)
\(444\) −0.507943 0.879782i −0.0241059 0.0417526i
\(445\) −25.2058 + 14.5526i −1.19487 + 0.689858i
\(446\) 22.5602 1.06826
\(447\) −0.930066 + 0.536974i −0.0439906 + 0.0253980i
\(448\) −19.7586 + 11.4076i −0.933507 + 0.538961i
\(449\) −25.3882 14.6579i −1.19814 0.691749i −0.238003 0.971265i \(-0.576493\pi\)
−0.960141 + 0.279516i \(0.909826\pi\)
\(450\) −16.7222 + 28.9637i −0.788291 + 1.36536i
\(451\) −11.9680 −0.563552
\(452\) 2.33373i 0.109770i
\(453\) −1.32599 0.765559i −0.0623003 0.0359691i
\(454\) −25.1416 14.5155i −1.17995 0.681245i
\(455\) −7.46155 12.9238i −0.349803 0.605876i
\(456\) 0.465229 0.268600i 0.0217864 0.0125784i
\(457\) −12.8423 −0.600738 −0.300369 0.953823i \(-0.597110\pi\)
−0.300369 + 0.953823i \(0.597110\pi\)
\(458\) −15.1428 26.2281i −0.707575 1.22556i
\(459\) −2.26516 + 8.53145i −0.105729 + 0.398214i
\(460\) −0.969649 1.67948i −0.0452101 0.0783062i
\(461\) −5.07325 + 8.78713i −0.236285 + 0.409257i −0.959645 0.281213i \(-0.909263\pi\)
0.723360 + 0.690471i \(0.242597\pi\)
\(462\) 2.58635i 0.120328i
\(463\) 14.9677 25.9248i 0.695607 1.20483i −0.274369 0.961625i \(-0.588469\pi\)
0.969976 0.243202i \(-0.0781978\pi\)
\(464\) −5.46462 + 3.15500i −0.253688 + 0.146467i
\(465\) 7.29660i 0.338372i
\(466\) 10.8829 6.28324i 0.504141 0.291066i
\(467\) −6.45305 + 11.1770i −0.298612 + 0.517211i −0.975819 0.218582i \(-0.929857\pi\)
0.677207 + 0.735793i \(0.263190\pi\)
\(468\) 0.746587 1.29313i 0.0345110 0.0597748i
\(469\) 12.0645i 0.557089i
\(470\) 35.5726 + 20.5378i 1.64084 + 0.947339i
\(471\) 2.54479i 0.117258i
\(472\) −18.8424 −0.867290
\(473\) −5.11229 + 13.0210i −0.235063 + 0.598706i
\(474\) −1.50301 −0.0690356
\(475\) 4.41895 0.202756
\(476\) −3.45590 + 0.934457i −0.158401 + 0.0428308i
\(477\) −24.3235 −1.11370
\(478\) 12.1989 21.1290i 0.557963 0.966420i
\(479\) −13.7904 7.96188i −0.630099 0.363788i 0.150692 0.988581i \(-0.451850\pi\)
−0.780790 + 0.624793i \(0.785183\pi\)
\(480\) 1.28890 + 2.23244i 0.0588299 + 0.101896i
\(481\) 12.7666i 0.582107i
\(482\) −4.71031 + 2.71950i −0.214549 + 0.123870i
\(483\) 1.25011 + 0.721752i 0.0568821 + 0.0328409i
\(484\) −2.17348 −0.0987943
\(485\) 4.03629 6.99106i 0.183279 0.317448i
\(486\) 10.3594 5.98099i 0.469911 0.271303i
\(487\) 21.0347 12.1444i 0.953171 0.550314i 0.0591066 0.998252i \(-0.481175\pi\)
0.894065 + 0.447938i \(0.147841\pi\)
\(488\) −26.4060 + 15.2455i −1.19534 + 0.690131i
\(489\) −1.73028 −0.0782462
\(490\) −1.51568 + 0.875076i −0.0684713 + 0.0395319i
\(491\) −6.24663 10.8195i −0.281907 0.488277i 0.689948 0.723859i \(-0.257633\pi\)
−0.971854 + 0.235583i \(0.924300\pi\)
\(492\) 0.344971 0.597507i 0.0155525 0.0269377i
\(493\) −7.81810 + 2.11397i −0.352109 + 0.0952085i
\(494\) 0.973534 0.0438014
\(495\) −22.9206 −1.03021
\(496\) −14.8427 8.56943i −0.666457 0.384779i
\(497\) −7.86884 + 13.6292i −0.352966 + 0.611355i
\(498\) −2.03447 + 1.17460i −0.0911669 + 0.0526352i
\(499\) 12.8129 7.39752i 0.573584 0.331159i −0.184996 0.982739i \(-0.559227\pi\)
0.758579 + 0.651581i \(0.225894\pi\)
\(500\) 5.11086i 0.228564i
\(501\) 2.46483 + 4.26921i 0.110120 + 0.190734i
\(502\) −17.4055 30.1472i −0.776846 1.34554i
\(503\) 0.464569 0.268219i 0.0207141 0.0119593i −0.489607 0.871943i \(-0.662860\pi\)
0.510321 + 0.859984i \(0.329526\pi\)
\(504\) 19.2777 + 11.1300i 0.858695 + 0.495768i
\(505\) 37.5942i 1.67292i
\(506\) −2.11190 + 3.65791i −0.0938853 + 0.162614i
\(507\) 3.35347 1.93612i 0.148933 0.0859863i
\(508\) −1.74258 −0.0773144
\(509\) 9.28009 + 16.0736i 0.411333 + 0.712450i 0.995036 0.0995178i \(-0.0317300\pi\)
−0.583703 + 0.811967i \(0.698397\pi\)
\(510\) −1.89807 7.01964i −0.0840480 0.310835i
\(511\) 13.7596 23.8323i 0.608688 1.05428i
\(512\) 25.4176 1.12331
\(513\) −0.905661 0.522884i −0.0399859 0.0230859i
\(514\) 25.0533 1.10505
\(515\) 62.7425i 2.76477i
\(516\) −0.502719 0.630555i −0.0221310 0.0277586i
\(517\) 18.1300i 0.797358i
\(518\) 27.4456 1.20589
\(519\) 2.08455 3.61055i 0.0915017 0.158486i
\(520\) 17.4562i 0.765505i
\(521\) 15.4718 + 8.93266i 0.677832 + 0.391347i 0.799038 0.601281i \(-0.205343\pi\)
−0.121205 + 0.992627i \(0.538676\pi\)
\(522\) 6.28895 + 3.63093i 0.275260 + 0.158921i
\(523\) 19.0050 + 32.9176i 0.831030 + 1.43939i 0.897222 + 0.441580i \(0.145582\pi\)
−0.0661914 + 0.997807i \(0.521085\pi\)
\(524\) 1.31790i 0.0575728i
\(525\) −4.25251 7.36557i −0.185595 0.321460i
\(526\) −3.35560 + 5.81207i −0.146311 + 0.253418i
\(527\) −15.5901 15.5192i −0.679117 0.676027i
\(528\) 1.25034 2.16565i 0.0544139 0.0942476i
\(529\) −10.3213 17.8770i −0.448752 0.777261i
\(530\) 35.5124 20.5031i 1.54256 0.890597i
\(531\) 8.96197 + 15.5226i 0.388916 + 0.673623i
\(532\) 0.424135i 0.0183886i
\(533\) 7.50885 4.33524i 0.325244 0.187780i
\(534\) −3.16482 + 1.82721i −0.136955 + 0.0790711i
\(535\) −26.0538 + 45.1265i −1.12640 + 1.95099i
\(536\) −7.05621 + 12.2217i −0.304782 + 0.527898i
\(537\) 1.99272i 0.0859923i
\(538\) 39.6547i 1.70964i
\(539\) −0.668992 0.386243i −0.0288155 0.0166366i
\(540\) 1.35203 2.34179i 0.0581823 0.100775i
\(541\) 23.2199 13.4060i 0.998300 0.576369i 0.0905551 0.995891i \(-0.471136\pi\)
0.907745 + 0.419523i \(0.137803\pi\)
\(542\) −9.49819 16.4513i −0.407982 0.706646i
\(543\) −7.92194 −0.339963
\(544\) 7.51125 + 1.99429i 0.322042 + 0.0855044i
\(545\) 5.72330 + 9.91305i 0.245159 + 0.424628i
\(546\) −0.936866 1.62270i −0.0400942 0.0694451i
\(547\) −4.51484 2.60664i −0.193041 0.111452i 0.400365 0.916356i \(-0.368883\pi\)
−0.593405 + 0.804904i \(0.702217\pi\)
\(548\) 4.51082 0.192693
\(549\) 25.1189 + 14.5024i 1.07205 + 0.618946i
\(550\) 21.5522 12.4432i 0.918988 0.530578i
\(551\) 0.959498i 0.0408760i
\(552\) −0.844265 1.46231i −0.0359343 0.0622401i
\(553\) −4.11449 + 7.12651i −0.174966 + 0.303050i
\(554\) −12.5215 7.22929i −0.531988 0.307143i
\(555\) 11.2975i 0.479552i
\(556\) 4.17392 + 2.40981i 0.177014 + 0.102199i
\(557\) 40.0335 1.69627 0.848137 0.529776i \(-0.177724\pi\)
0.848137 + 0.529776i \(0.177724\pi\)
\(558\) 19.7243i 0.834994i
\(559\) −1.50917 10.0214i −0.0638309 0.423858i
\(560\) −31.0189 −1.31079
\(561\) 2.26435 2.27470i 0.0956011 0.0960380i
\(562\) −20.5136 + 35.5306i −0.865314 + 1.49877i
\(563\) −31.6552 −1.33411 −0.667054 0.745010i \(-0.732445\pi\)
−0.667054 + 0.745010i \(0.732445\pi\)
\(564\) −0.905148 0.522587i −0.0381136 0.0220049i
\(565\) −12.9765 + 22.4760i −0.545926 + 0.945572i
\(566\) −9.03096 + 5.21403i −0.379600 + 0.219162i
\(567\) 20.1457i 0.846040i
\(568\) 15.9427 9.20453i 0.668941 0.386213i
\(569\) −2.46993 + 4.27804i −0.103545 + 0.179345i −0.913143 0.407640i \(-0.866352\pi\)
0.809598 + 0.586985i \(0.199685\pi\)
\(570\) 0.861505 0.0360845
\(571\) −15.7910 9.11696i −0.660834 0.381533i 0.131760 0.991282i \(-0.457937\pi\)
−0.792595 + 0.609749i \(0.791270\pi\)
\(572\) −0.962229 + 0.555543i −0.0402328 + 0.0232284i
\(573\) −5.36661 + 3.09841i −0.224193 + 0.129438i
\(574\) 9.31988 + 16.1425i 0.389004 + 0.673775i
\(575\) 13.8897i 0.579239i
\(576\) −12.6936 21.9860i −0.528900 0.916082i
\(577\) 6.78065 + 11.7444i 0.282282 + 0.488927i 0.971946 0.235202i \(-0.0755752\pi\)
−0.689664 + 0.724129i \(0.742242\pi\)
\(578\) −19.0354 10.8746i −0.791768 0.452326i
\(579\) −0.867896 + 1.50324i −0.0360685 + 0.0624725i
\(580\) 2.48100 0.103018
\(581\) 12.8619i 0.533602i
\(582\) 0.506794 0.877792i 0.0210073 0.0363857i
\(583\) 15.6745 + 9.04968i 0.649172 + 0.374800i
\(584\) −27.8777 + 16.0952i −1.15359 + 0.666024i
\(585\) 14.3806 8.30267i 0.594566 0.343273i
\(586\) −19.7073 −0.814101
\(587\) −9.91887 17.1800i −0.409395 0.709094i 0.585427 0.810725i \(-0.300927\pi\)
−0.994822 + 0.101632i \(0.967594\pi\)
\(588\) 0.0385666 0.0222664i 0.00159046 0.000918251i
\(589\) 2.25698 1.30307i 0.0929973 0.0536920i
\(590\) −26.1690 15.1087i −1.07736 0.622015i
\(591\) 8.65846 0.356161
\(592\) −22.9813 13.2682i −0.944524 0.545321i
\(593\) −0.166983 0.289224i −0.00685719 0.0118770i 0.862576 0.505927i \(-0.168849\pi\)
−0.869434 + 0.494050i \(0.835516\pi\)
\(594\) −5.88947 −0.241648
\(595\) −38.4795 10.2166i −1.57751 0.418838i
\(596\) 0.495920 0.858959i 0.0203137 0.0351843i
\(597\) 1.16315 2.01464i 0.0476046 0.0824536i
\(598\) 3.06002i 0.125133i
\(599\) −14.0871 + 24.3995i −0.575582 + 0.996937i 0.420397 + 0.907340i \(0.361891\pi\)
−0.995978 + 0.0895962i \(0.971442\pi\)
\(600\) 9.94870i 0.406154i
\(601\) 14.6200i 0.596362i 0.954509 + 0.298181i \(0.0963799\pi\)
−0.954509 + 0.298181i \(0.903620\pi\)
\(602\) 21.5439 3.24440i 0.878063 0.132232i
\(603\) 13.4246 0.546690
\(604\) 1.41406 0.0575372
\(605\) −20.9326 12.0854i −0.851030 0.491342i
\(606\) 4.72029i 0.191749i
\(607\) −12.0077 6.93267i −0.487379 0.281389i 0.236107 0.971727i \(-0.424128\pi\)
−0.723487 + 0.690338i \(0.757462\pi\)
\(608\) −0.460357 + 0.797362i −0.0186699 + 0.0323373i
\(609\) −1.59930 + 0.923359i −0.0648071 + 0.0374164i
\(610\) −48.8982 −1.97983
\(611\) −6.56734 11.3750i −0.265686 0.460182i
\(612\) −1.03980 3.84548i −0.0420313 0.155444i
\(613\) −5.86167 −0.236751 −0.118375 0.992969i \(-0.537769\pi\)
−0.118375 + 0.992969i \(0.537769\pi\)
\(614\) −15.3897 + 26.6557i −0.621077 + 1.07574i
\(615\) 6.64477 3.83636i 0.267943 0.154697i
\(616\) −8.28193 14.3447i −0.333688 0.577965i
\(617\) 12.2806 7.09020i 0.494398 0.285441i −0.231999 0.972716i \(-0.574527\pi\)
0.726397 + 0.687275i \(0.241193\pi\)
\(618\) 7.87790i 0.316896i
\(619\) 33.7499 19.4855i 1.35652 0.783190i 0.367371 0.930074i \(-0.380258\pi\)
0.989154 + 0.146884i \(0.0469245\pi\)
\(620\) 3.36938 + 5.83593i 0.135317 + 0.234377i
\(621\) −1.64353 + 2.84668i −0.0659526 + 0.114233i
\(622\) −9.48324 5.47515i −0.380243 0.219534i
\(623\) 20.0079i 0.801601i
\(624\) 1.81166i 0.0725246i
\(625\) −5.80254 + 10.0503i −0.232102 + 0.402012i
\(626\) −18.0902 10.4444i −0.723028 0.417440i
\(627\) 0.190126 + 0.329308i 0.00759291 + 0.0131513i
\(628\) −1.17512 2.03536i −0.0468923 0.0812198i
\(629\) −24.1385 24.0287i −0.962467 0.958088i
\(630\) 17.8491 + 30.9155i 0.711123 + 1.23170i
\(631\) −6.26732 10.8553i −0.249498 0.432143i 0.713889 0.700259i \(-0.246932\pi\)
−0.963387 + 0.268116i \(0.913599\pi\)
\(632\) 8.33619 4.81290i 0.331596 0.191447i
\(633\) 2.52846 4.37943i 0.100497 0.174067i
\(634\) 13.6946i 0.543883i
\(635\) −16.7826 9.68946i −0.665998 0.384514i
\(636\) −0.903616 + 0.521703i −0.0358307 + 0.0206869i
\(637\) 0.559643 0.0221739
\(638\) −2.70181 4.67968i −0.106966 0.185270i
\(639\) −15.1656 8.75587i −0.599943 0.346377i
\(640\) 24.8299 + 14.3355i 0.981487 + 0.566662i
\(641\) 9.72936i 0.384287i 0.981367 + 0.192143i \(0.0615438\pi\)
−0.981367 + 0.192143i \(0.938456\pi\)
\(642\) −3.27129 + 5.66605i −0.129108 + 0.223621i
\(643\) 38.2988i 1.51036i −0.655519 0.755179i \(-0.727550\pi\)
0.655519 0.755179i \(-0.272450\pi\)
\(644\) −1.33314 −0.0525332
\(645\) −1.33550 8.86815i −0.0525852 0.349183i
\(646\) 1.83234 1.84072i 0.0720925 0.0724220i
\(647\) 25.0129 0.983359 0.491680 0.870776i \(-0.336383\pi\)
0.491680 + 0.870776i \(0.336383\pi\)
\(648\) −11.7827 + 20.4082i −0.462866 + 0.801708i
\(649\) 13.3374i 0.523539i
\(650\) −9.01470 + 15.6139i −0.353586 + 0.612428i
\(651\) −4.34394 2.50798i −0.170253 0.0982953i
\(652\) 1.38391 0.798999i 0.0541980 0.0312912i
\(653\) 5.64480i 0.220898i −0.993882 0.110449i \(-0.964771\pi\)
0.993882 0.110449i \(-0.0352289\pi\)
\(654\) 0.718613 + 1.24467i 0.0281000 + 0.0486706i
\(655\) 7.32808 12.6926i 0.286332 0.495941i
\(656\) 18.0223i 0.703653i
\(657\) 26.5188 + 15.3107i 1.03460 + 0.597326i
\(658\) 24.4539 14.1185i 0.953311 0.550395i
\(659\) −13.8745 24.0313i −0.540473 0.936126i −0.998877 0.0473822i \(-0.984912\pi\)
0.458404 0.888744i \(-0.348421\pi\)
\(660\) −0.851501 + 0.491614i −0.0331446 + 0.0191361i
\(661\) 49.1770 1.91276 0.956381 0.292122i \(-0.0943612\pi\)
0.956381 + 0.292122i \(0.0943612\pi\)
\(662\) −18.3501 31.7834i −0.713199 1.23530i
\(663\) −0.596700 + 2.24740i −0.0231739 + 0.0872818i
\(664\) 7.52256 13.0295i 0.291932 0.505641i
\(665\) 2.35837 4.08481i 0.0914536 0.158402i
\(666\) 30.5395i 1.18338i
\(667\) −3.01590 −0.116776
\(668\) −3.94281 2.27638i −0.152552 0.0880759i
\(669\) −5.52860 3.19194i −0.213748 0.123407i
\(670\) −19.5999 + 11.3160i −0.757210 + 0.437175i
\(671\) −10.7914 18.6912i −0.416596 0.721566i
\(672\) 1.77207 0.0683591
\(673\) −5.92857 + 3.42286i −0.228530 + 0.131942i −0.609894 0.792483i \(-0.708788\pi\)
0.381364 + 0.924425i \(0.375454\pi\)
\(674\) −23.0581 + 13.3126i −0.888163 + 0.512781i
\(675\) 16.7724 9.68356i 0.645571 0.372721i
\(676\) −1.78810 + 3.09708i −0.0687731 + 0.119119i
\(677\) 31.3269i 1.20399i 0.798499 + 0.601996i \(0.205628\pi\)
−0.798499 + 0.601996i \(0.794372\pi\)
\(678\) −1.62932 + 2.82207i −0.0625737 + 0.108381i
\(679\) −2.77469 4.80591i −0.106483 0.184434i
\(680\) 33.0054 + 32.8552i 1.26570 + 1.25994i
\(681\) 4.10746 + 7.11432i 0.157398 + 0.272622i
\(682\) 7.33851 12.7107i 0.281006 0.486717i
\(683\) −15.5768 8.99325i −0.596028 0.344117i 0.171449 0.985193i \(-0.445155\pi\)
−0.767478 + 0.641076i \(0.778488\pi\)
\(684\) 0.471947 0.0180453
\(685\) 43.4434 + 25.0820i 1.65989 + 0.958335i
\(686\) 24.4603i 0.933899i
\(687\) 8.56993i 0.326963i
\(688\) −19.6080 7.69846i −0.747547 0.293501i
\(689\) −13.1125 −0.499545
\(690\) 2.70788i 0.103087i
\(691\) −10.0380 5.79542i −0.381862 0.220468i 0.296766 0.954950i \(-0.404092\pi\)
−0.678628 + 0.734482i \(0.737425\pi\)
\(692\) 3.85036i 0.146369i
\(693\) −7.87824 + 13.6455i −0.299270 + 0.518350i
\(694\) 5.08668 + 2.93679i 0.193088 + 0.111479i
\(695\) 26.7991 + 46.4175i 1.01655 + 1.76071i
\(696\) 2.16019 0.0818816
\(697\) 5.93593 22.3570i 0.224840 0.846832i
\(698\) 8.35922 14.4786i 0.316401 0.548023i
\(699\) −3.55595 −0.134498
\(700\) 6.80245 + 3.92739i 0.257108 + 0.148442i
\(701\) −2.05082 3.55213i −0.0774585 0.134162i 0.824694 0.565579i \(-0.191347\pi\)
−0.902153 + 0.431417i \(0.858014\pi\)
\(702\) 3.69511 2.13337i 0.139463 0.0805190i
\(703\) 3.49453 2.01757i 0.131799 0.0760940i
\(704\) 18.8909i 0.711977i
\(705\) −5.81160 10.0660i −0.218878 0.379107i
\(706\) 15.6273 + 27.0673i 0.588142 + 1.01869i
\(707\) −22.3812 12.9218i −0.841732 0.485974i
\(708\) 0.665873 + 0.384442i 0.0250251 + 0.0144482i
\(709\) 37.2174i 1.39773i 0.715254 + 0.698864i \(0.246311\pi\)
−0.715254 + 0.698864i \(0.753689\pi\)
\(710\) 29.5225 1.10796
\(711\) −7.92986 4.57831i −0.297393 0.171700i
\(712\) 11.7021 20.2686i 0.438554 0.759598i
\(713\) −4.09581 7.09415i −0.153389 0.265678i
\(714\) −4.83145 1.28278i −0.180813 0.0480070i
\(715\) −12.3562 −0.462096
\(716\) 0.920186 + 1.59381i 0.0343890 + 0.0595634i
\(717\) −5.97890 + 3.45192i −0.223286 + 0.128914i
\(718\) −9.36594 16.2223i −0.349534 0.605410i
\(719\) −8.76939 5.06301i −0.327043 0.188818i 0.327484 0.944857i \(-0.393799\pi\)
−0.654528 + 0.756038i \(0.727132\pi\)
\(720\) 34.5156i 1.28632i
\(721\) −37.3530 21.5658i −1.39110 0.803151i
\(722\) −12.0971 20.9527i −0.450206 0.779779i
\(723\) 1.53908 0.0572389
\(724\) 6.33608 3.65814i 0.235479 0.135954i
\(725\) 15.3888 + 8.88473i 0.571526 + 0.329971i
\(726\) −2.62828 1.51744i −0.0975445 0.0563174i
\(727\) −48.6188 −1.80317 −0.901586 0.432599i \(-0.857597\pi\)
−0.901586 + 0.432599i \(0.857597\pi\)
\(728\) 10.3923 + 6.00001i 0.385165 + 0.222375i
\(729\) 20.0730 0.743444
\(730\) −51.6235 −1.91067
\(731\) −21.7884 16.0083i −0.805874 0.592087i
\(732\) 1.24422 0.0459877
\(733\) 24.6175 0.909267 0.454633 0.890679i \(-0.349770\pi\)
0.454633 + 0.890679i \(0.349770\pi\)
\(734\) 8.87163 + 5.12204i 0.327458 + 0.189058i
\(735\) 0.495242 0.0182673
\(736\) 2.50627 + 1.44700i 0.0923824 + 0.0533370i
\(737\) −8.65103 4.99468i −0.318665 0.183981i
\(738\) −17.9622 + 10.3705i −0.661198 + 0.381743i
\(739\) 30.3877 1.11783 0.558915 0.829225i \(-0.311218\pi\)
0.558915 + 0.829225i \(0.311218\pi\)
\(740\) 5.21688 + 9.03590i 0.191776 + 0.332166i
\(741\) −0.238574 0.137741i −0.00876424 0.00506004i
\(742\) 28.1891i 1.03486i
\(743\) 40.9289 + 23.6303i 1.50153 + 0.866911i 0.999998 + 0.00177412i \(0.000564720\pi\)
0.501536 + 0.865137i \(0.332769\pi\)
\(744\) 2.93369 + 5.08130i 0.107554 + 0.186289i
\(745\) 9.55234 5.51505i 0.349971 0.202056i
\(746\) −12.8347 22.2303i −0.469911 0.813910i
\(747\) −14.3118 −0.523641
\(748\) −0.760666 + 2.86496i −0.0278127 + 0.104753i
\(749\) 17.9103 + 31.0216i 0.654429 + 1.13350i
\(750\) −3.56820 + 6.18031i −0.130292 + 0.225673i
\(751\) −23.5979 13.6242i −0.861099 0.497156i 0.00328104 0.999995i \(-0.498956\pi\)
−0.864380 + 0.502839i \(0.832289\pi\)
\(752\) −27.3016 −0.995585
\(753\) 9.85050i 0.358972i
\(754\) 3.39029 + 1.95738i 0.123467 + 0.0712837i
\(755\) 13.6187 + 7.86276i 0.495635 + 0.286155i
\(756\) −0.929437 1.60983i −0.0338033 0.0585491i
\(757\) 1.40620 + 2.43562i 0.0511094 + 0.0885240i 0.890448 0.455085i \(-0.150391\pi\)
−0.839339 + 0.543609i \(0.817058\pi\)
\(758\) 45.9933i 1.67055i
\(759\) 1.03508 0.597605i 0.0375711 0.0216917i
\(760\) −4.77819 + 2.75869i −0.173323 + 0.100068i
\(761\) −4.01842 6.96011i −0.145668 0.252304i 0.783954 0.620819i \(-0.213200\pi\)
−0.929622 + 0.368515i \(0.879866\pi\)