Properties

Label 637.2.x.b.80.1
Level $637$
Weight $2$
Character 637.80
Analytic conductor $5.086$
Analytic rank $0$
Dimension $32$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 637 = 7^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 637.x (of order \(12\), degree \(4\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.08647060876\)
Analytic rank: \(0\)
Dimension: \(32\)
Relative dimension: \(8\) over \(\Q(\zeta_{12})\)
Twist minimal: no (minimal twist has level 91)
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 80.1
Character \(\chi\) \(=\) 637.80
Dual form 637.2.x.b.215.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.433802 - 1.61897i) q^{2} -0.637748i q^{3} +(-0.700831 + 0.404625i) q^{4} +(0.520288 - 1.94174i) q^{5} +(-1.03250 + 0.276656i) q^{6} +(-1.41124 - 1.41124i) q^{8} +2.59328 q^{9} +O(q^{10})\) \(q+(-0.433802 - 1.61897i) q^{2} -0.637748i q^{3} +(-0.700831 + 0.404625i) q^{4} +(0.520288 - 1.94174i) q^{5} +(-1.03250 + 0.276656i) q^{6} +(-1.41124 - 1.41124i) q^{8} +2.59328 q^{9} -3.36932 q^{10} +(0.694217 + 0.694217i) q^{11} +(0.258049 + 0.446954i) q^{12} +(1.60977 - 3.22624i) q^{13} +(-1.23834 - 0.331813i) q^{15} +(-2.48181 + 4.29862i) q^{16} +(-2.99281 - 5.18370i) q^{17} +(-1.12497 - 4.19844i) q^{18} +(1.98532 + 1.98532i) q^{19} +(0.421043 + 1.57135i) q^{20} +(0.822765 - 1.42507i) q^{22} +(-2.58851 - 1.49448i) q^{23} +(-0.900016 + 0.900016i) q^{24} +(0.830467 + 0.479471i) q^{25} +(-5.92151 - 1.20663i) q^{26} -3.56710i q^{27} +(3.65708 + 6.33425i) q^{29} +2.14878i q^{30} +(-8.34708 + 2.23659i) q^{31} +(4.18037 + 1.12013i) q^{32} +(0.442736 - 0.442736i) q^{33} +(-7.09397 + 7.09397i) q^{34} +(-1.81745 + 1.04931i) q^{36} +(4.63309 - 1.24143i) q^{37} +(2.35294 - 4.07541i) q^{38} +(-2.05753 - 1.02663i) q^{39} +(-3.47451 + 2.00601i) q^{40} +(0.886060 - 3.30682i) q^{41} +(-0.748633 - 0.432224i) q^{43} +(-0.767427 - 0.205631i) q^{44} +(1.34925 - 5.03547i) q^{45} +(-1.29661 + 4.83903i) q^{46} +(-2.96429 - 0.794280i) q^{47} +(2.74144 + 1.58277i) q^{48} +(0.415990 - 1.55250i) q^{50} +(-3.30589 + 1.90866i) q^{51} +(0.177238 + 2.91241i) q^{52} +(-3.16223 + 5.47715i) q^{53} +(-5.77504 + 1.54742i) q^{54} +(1.70918 - 0.986797i) q^{55} +(1.26614 - 1.26614i) q^{57} +(8.66852 - 8.66852i) q^{58} +(-0.491481 - 0.131692i) q^{59} +(1.00213 - 0.268520i) q^{60} +13.0284i q^{61} +(7.24196 + 12.5434i) q^{62} +2.67342i q^{64} +(-5.42698 - 4.80434i) q^{65} +(-0.908836 - 0.524717i) q^{66} +(0.606011 - 0.606011i) q^{67} +(4.19491 + 2.42193i) q^{68} +(-0.953100 + 1.65082i) q^{69} +(-3.01121 - 11.2380i) q^{71} +(-3.65973 - 3.65973i) q^{72} +(0.377014 + 1.40704i) q^{73} +(-4.01968 - 6.96230i) q^{74} +(0.305782 - 0.529629i) q^{75} +(-2.19469 - 0.588064i) q^{76} +(-0.769526 + 3.77644i) q^{78} +(5.80137 + 10.0483i) q^{79} +(7.05555 + 7.05555i) q^{80} +5.50492 q^{81} -5.73802 q^{82} +(1.23779 + 1.23779i) q^{83} +(-11.6225 + 3.11424i) q^{85} +(-0.374999 + 1.39951i) q^{86} +(4.03966 - 2.33230i) q^{87} -1.95941i q^{88} +(-2.07729 - 7.75255i) q^{89} -8.73759 q^{90} +2.41881 q^{92} +(1.42638 + 5.32334i) q^{93} +5.14367i q^{94} +(4.88792 - 2.82204i) q^{95} +(0.714359 - 2.66602i) q^{96} +(12.0756 - 3.23566i) q^{97} +(1.80030 + 1.80030i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32q + 4q^{2} + 12q^{4} - 16q^{8} - 16q^{9} + O(q^{10}) \) \( 32q + 4q^{2} + 12q^{4} - 16q^{8} - 16q^{9} + 20q^{11} - 8q^{15} + 12q^{16} - 64q^{18} + 4q^{22} + 12q^{23} + 4q^{29} + 64q^{32} + 4q^{37} + 36q^{39} - 48q^{43} - 84q^{44} - 108q^{46} - 44q^{50} + 12q^{51} - 36q^{53} - 92q^{57} + 44q^{58} + 28q^{60} + 28q^{65} + 64q^{67} + 84q^{71} + 4q^{72} - 24q^{74} + 148q^{78} + 40q^{79} - 56q^{81} + 36q^{85} + 108q^{86} + 24q^{92} - 24q^{93} + 84q^{95} - 60q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/637\mathbb{Z}\right)^\times\).

\(n\) \(197\) \(248\)
\(\chi(n)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{1}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.433802 1.61897i −0.306744 1.14479i −0.931433 0.363912i \(-0.881441\pi\)
0.624689 0.780873i \(-0.285226\pi\)
\(3\) 0.637748i 0.368204i −0.982907 0.184102i \(-0.941062\pi\)
0.982907 0.184102i \(-0.0589377\pi\)
\(4\) −0.700831 + 0.404625i −0.350416 + 0.202313i
\(5\) 0.520288 1.94174i 0.232680 0.868373i −0.746501 0.665384i \(-0.768268\pi\)
0.979181 0.202989i \(-0.0650656\pi\)
\(6\) −1.03250 + 0.276656i −0.421515 + 0.112945i
\(7\) 0 0
\(8\) −1.41124 1.41124i −0.498948 0.498948i
\(9\) 2.59328 0.864426
\(10\) −3.36932 −1.06547
\(11\) 0.694217 + 0.694217i 0.209314 + 0.209314i 0.803976 0.594662i \(-0.202714\pi\)
−0.594662 + 0.803976i \(0.702714\pi\)
\(12\) 0.258049 + 0.446954i 0.0744924 + 0.129025i
\(13\) 1.60977 3.22624i 0.446471 0.894798i
\(14\) 0 0
\(15\) −1.23834 0.331813i −0.319739 0.0856737i
\(16\) −2.48181 + 4.29862i −0.620452 + 1.07465i
\(17\) −2.99281 5.18370i −0.725863 1.25723i −0.958618 0.284696i \(-0.908107\pi\)
0.232755 0.972535i \(-0.425226\pi\)
\(18\) −1.12497 4.19844i −0.265158 0.989582i
\(19\) 1.98532 + 1.98532i 0.455464 + 0.455464i 0.897163 0.441699i \(-0.145624\pi\)
−0.441699 + 0.897163i \(0.645624\pi\)
\(20\) 0.421043 + 1.57135i 0.0941481 + 0.351366i
\(21\) 0 0
\(22\) 0.822765 1.42507i 0.175414 0.303826i
\(23\) −2.58851 1.49448i −0.539742 0.311620i 0.205233 0.978713i \(-0.434205\pi\)
−0.744974 + 0.667093i \(0.767538\pi\)
\(24\) −0.900016 + 0.900016i −0.183715 + 0.183715i
\(25\) 0.830467 + 0.479471i 0.166093 + 0.0958941i
\(26\) −5.92151 1.20663i −1.16130 0.236639i
\(27\) 3.56710i 0.686489i
\(28\) 0 0
\(29\) 3.65708 + 6.33425i 0.679103 + 1.17624i 0.975251 + 0.221099i \(0.0709645\pi\)
−0.296148 + 0.955142i \(0.595702\pi\)
\(30\) 2.14878i 0.392312i
\(31\) −8.34708 + 2.23659i −1.49918 + 0.401704i −0.912825 0.408351i \(-0.866104\pi\)
−0.586354 + 0.810055i \(0.699437\pi\)
\(32\) 4.18037 + 1.12013i 0.738992 + 0.198012i
\(33\) 0.442736 0.442736i 0.0770704 0.0770704i
\(34\) −7.09397 + 7.09397i −1.21661 + 1.21661i
\(35\) 0 0
\(36\) −1.81745 + 1.04931i −0.302908 + 0.174884i
\(37\) 4.63309 1.24143i 0.761675 0.204090i 0.142984 0.989725i \(-0.454330\pi\)
0.618690 + 0.785635i \(0.287664\pi\)
\(38\) 2.35294 4.07541i 0.381697 0.661119i
\(39\) −2.05753 1.02663i −0.329468 0.164393i
\(40\) −3.47451 + 2.00601i −0.549369 + 0.317178i
\(41\) 0.886060 3.30682i 0.138379 0.516439i −0.861582 0.507619i \(-0.830526\pi\)
0.999961 0.00881984i \(-0.00280748\pi\)
\(42\) 0 0
\(43\) −0.748633 0.432224i −0.114165 0.0659135i 0.441830 0.897099i \(-0.354329\pi\)
−0.555995 + 0.831185i \(0.687663\pi\)
\(44\) −0.767427 0.205631i −0.115694 0.0310001i
\(45\) 1.34925 5.03547i 0.201134 0.750644i
\(46\) −1.29661 + 4.83903i −0.191175 + 0.713476i
\(47\) −2.96429 0.794280i −0.432387 0.115858i 0.0360596 0.999350i \(-0.488519\pi\)
−0.468446 + 0.883492i \(0.655186\pi\)
\(48\) 2.74144 + 1.58277i 0.395692 + 0.228453i
\(49\) 0 0
\(50\) 0.415990 1.55250i 0.0588299 0.219556i
\(51\) −3.30589 + 1.90866i −0.462918 + 0.267266i
\(52\) 0.177238 + 2.91241i 0.0245784 + 0.403878i
\(53\) −3.16223 + 5.47715i −0.434366 + 0.752344i −0.997244 0.0741963i \(-0.976361\pi\)
0.562878 + 0.826540i \(0.309694\pi\)
\(54\) −5.77504 + 1.54742i −0.785883 + 0.210577i
\(55\) 1.70918 0.986797i 0.230466 0.133060i
\(56\) 0 0
\(57\) 1.26614 1.26614i 0.167704 0.167704i
\(58\) 8.66852 8.66852i 1.13823 1.13823i
\(59\) −0.491481 0.131692i −0.0639854 0.0171448i 0.226684 0.973968i \(-0.427211\pi\)
−0.290670 + 0.956823i \(0.593878\pi\)
\(60\) 1.00213 0.268520i 0.129374 0.0346657i
\(61\) 13.0284i 1.66811i 0.551679 + 0.834057i \(0.313988\pi\)
−0.551679 + 0.834057i \(0.686012\pi\)
\(62\) 7.24196 + 12.5434i 0.919729 + 1.59302i
\(63\) 0 0
\(64\) 2.67342i 0.334178i
\(65\) −5.42698 4.80434i −0.673134 0.595905i
\(66\) −0.908836 0.524717i −0.111870 0.0645882i
\(67\) 0.606011 0.606011i 0.0740361 0.0740361i −0.669119 0.743155i \(-0.733328\pi\)
0.743155 + 0.669119i \(0.233328\pi\)
\(68\) 4.19491 + 2.42193i 0.508707 + 0.293702i
\(69\) −0.953100 + 1.65082i −0.114740 + 0.198735i
\(70\) 0 0
\(71\) −3.01121 11.2380i −0.357365 1.33370i −0.877482 0.479609i \(-0.840778\pi\)
0.520117 0.854095i \(-0.325888\pi\)
\(72\) −3.65973 3.65973i −0.431304 0.431304i
\(73\) 0.377014 + 1.40704i 0.0441262 + 0.164681i 0.984473 0.175536i \(-0.0561660\pi\)
−0.940347 + 0.340217i \(0.889499\pi\)
\(74\) −4.01968 6.96230i −0.467279 0.809350i
\(75\) 0.305782 0.529629i 0.0353086 0.0611563i
\(76\) −2.19469 0.588064i −0.251748 0.0674556i
\(77\) 0 0
\(78\) −0.769526 + 3.77644i −0.0871316 + 0.427597i
\(79\) 5.80137 + 10.0483i 0.652705 + 1.13052i 0.982464 + 0.186454i \(0.0596994\pi\)
−0.329758 + 0.944065i \(0.606967\pi\)
\(80\) 7.05555 + 7.05555i 0.788834 + 0.788834i
\(81\) 5.50492 0.611657
\(82\) −5.73802 −0.633658
\(83\) 1.23779 + 1.23779i 0.135865 + 0.135865i 0.771768 0.635904i \(-0.219372\pi\)
−0.635904 + 0.771768i \(0.719372\pi\)
\(84\) 0 0
\(85\) −11.6225 + 3.11424i −1.26064 + 0.337787i
\(86\) −0.374999 + 1.39951i −0.0404372 + 0.150914i
\(87\) 4.03966 2.33230i 0.433097 0.250049i
\(88\) 1.95941i 0.208874i
\(89\) −2.07729 7.75255i −0.220192 0.821769i −0.984274 0.176649i \(-0.943474\pi\)
0.764082 0.645120i \(-0.223193\pi\)
\(90\) −8.73759 −0.921023
\(91\) 0 0
\(92\) 2.41881 0.252179
\(93\) 1.42638 + 5.32334i 0.147909 + 0.552004i
\(94\) 5.14367i 0.530529i
\(95\) 4.88792 2.82204i 0.501490 0.289535i
\(96\) 0.714359 2.66602i 0.0729090 0.272100i
\(97\) 12.0756 3.23566i 1.22609 0.328531i 0.413037 0.910714i \(-0.364468\pi\)
0.813058 + 0.582183i \(0.197801\pi\)
\(98\) 0 0
\(99\) 1.80030 + 1.80030i 0.180937 + 0.180937i
\(100\) −0.776023 −0.0776023
\(101\) 7.99635 0.795667 0.397833 0.917458i \(-0.369762\pi\)
0.397833 + 0.917458i \(0.369762\pi\)
\(102\) 4.52417 + 4.52417i 0.447959 + 0.447959i
\(103\) 5.16928 + 8.95345i 0.509344 + 0.882210i 0.999941 + 0.0108235i \(0.00344528\pi\)
−0.490597 + 0.871386i \(0.663221\pi\)
\(104\) −6.82477 + 2.28122i −0.669224 + 0.223692i
\(105\) 0 0
\(106\) 10.2391 + 2.74356i 0.994511 + 0.266479i
\(107\) −6.52593 + 11.3032i −0.630885 + 1.09273i 0.356486 + 0.934301i \(0.383975\pi\)
−0.987371 + 0.158425i \(0.949358\pi\)
\(108\) 1.44334 + 2.49994i 0.138885 + 0.240557i
\(109\) −3.03074 11.3109i −0.290292 1.08339i −0.944885 0.327403i \(-0.893826\pi\)
0.654592 0.755982i \(-0.272840\pi\)
\(110\) −2.33904 2.33904i −0.223019 0.223019i
\(111\) −0.791721 2.95474i −0.0751468 0.280452i
\(112\) 0 0
\(113\) 4.05748 7.02777i 0.381696 0.661117i −0.609609 0.792702i \(-0.708674\pi\)
0.991305 + 0.131586i \(0.0420069\pi\)
\(114\) −2.59909 1.50058i −0.243427 0.140543i
\(115\) −4.24866 + 4.24866i −0.396189 + 0.396189i
\(116\) −5.12600 2.95950i −0.475937 0.274782i
\(117\) 4.17459 8.36653i 0.385941 0.773486i
\(118\) 0.852822i 0.0785086i
\(119\) 0 0
\(120\) 1.27933 + 2.21587i 0.116786 + 0.202280i
\(121\) 10.0361i 0.912375i
\(122\) 21.0926 5.65174i 1.90963 0.511684i
\(123\) −2.10892 0.565083i −0.190155 0.0509518i
\(124\) 4.94491 4.94491i 0.444066 0.444066i
\(125\) 8.47036 8.47036i 0.757612 0.757612i
\(126\) 0 0
\(127\) 6.81853 3.93668i 0.605047 0.349324i −0.165977 0.986130i \(-0.553078\pi\)
0.771024 + 0.636805i \(0.219745\pi\)
\(128\) 12.6889 3.39999i 1.12155 0.300519i
\(129\) −0.275650 + 0.477440i −0.0242696 + 0.0420362i
\(130\) −5.42385 + 10.8702i −0.475703 + 0.953384i
\(131\) 17.2856 9.97987i 1.51025 0.871945i 0.510325 0.859982i \(-0.329525\pi\)
0.999928 0.0119634i \(-0.00380815\pi\)
\(132\) −0.131141 + 0.489425i −0.0114144 + 0.0425990i
\(133\) 0 0
\(134\) −1.24400 0.718226i −0.107466 0.0620452i
\(135\) −6.92639 1.85592i −0.596129 0.159732i
\(136\) −3.09187 + 11.5390i −0.265125 + 0.989461i
\(137\) −2.78324 + 10.3872i −0.237788 + 0.887437i 0.739084 + 0.673613i \(0.235259\pi\)
−0.976872 + 0.213824i \(0.931408\pi\)
\(138\) 3.08608 + 0.826913i 0.262705 + 0.0703915i
\(139\) −14.1096 8.14616i −1.19676 0.690949i −0.236927 0.971527i \(-0.576140\pi\)
−0.959831 + 0.280579i \(0.909474\pi\)
\(140\) 0 0
\(141\) −0.506551 + 1.89047i −0.0426593 + 0.159207i
\(142\) −16.8877 + 9.75012i −1.41719 + 0.818212i
\(143\) 3.35724 1.12218i 0.280747 0.0938413i
\(144\) −6.43601 + 11.1475i −0.536334 + 0.928959i
\(145\) 14.2022 3.80547i 1.17943 0.316027i
\(146\) 2.11440 1.22075i 0.174989 0.101030i
\(147\) 0 0
\(148\) −2.74470 + 2.74470i −0.225613 + 0.225613i
\(149\) 13.2274 13.2274i 1.08363 1.08363i 0.0874634 0.996168i \(-0.472124\pi\)
0.996168 0.0874634i \(-0.0278761\pi\)
\(150\) −0.990103 0.265297i −0.0808416 0.0216614i
\(151\) 0.0351934 0.00943004i 0.00286400 0.000767406i −0.257387 0.966308i \(-0.582861\pi\)
0.260251 + 0.965541i \(0.416195\pi\)
\(152\) 5.60353i 0.454506i
\(153\) −7.76118 13.4428i −0.627454 1.08678i
\(154\) 0 0
\(155\) 17.3715i 1.39532i
\(156\) 1.85738 0.113033i 0.148710 0.00904988i
\(157\) −6.22554 3.59432i −0.496852 0.286858i 0.230560 0.973058i \(-0.425944\pi\)
−0.727413 + 0.686200i \(0.759277\pi\)
\(158\) 13.7512 13.7512i 1.09399 1.09399i
\(159\) 3.49304 + 2.01671i 0.277016 + 0.159935i
\(160\) 4.34999 7.53441i 0.343897 0.595647i
\(161\) 0 0
\(162\) −2.38804 8.91230i −0.187622 0.700216i
\(163\) −11.6359 11.6359i −0.911397 0.911397i 0.0849855 0.996382i \(-0.472916\pi\)
−0.996382 + 0.0849855i \(0.972916\pi\)
\(164\) 0.717044 + 2.67605i 0.0559918 + 0.208964i
\(165\) −0.629328 1.09003i −0.0489932 0.0848586i
\(166\) 1.46699 2.54090i 0.113860 0.197212i
\(167\) 6.49344 + 1.73991i 0.502478 + 0.134638i 0.501150 0.865361i \(-0.332911\pi\)
0.00132801 + 0.999999i \(0.499577\pi\)
\(168\) 0 0
\(169\) −7.81725 10.3870i −0.601327 0.799003i
\(170\) 10.0837 + 17.4656i 0.773388 + 1.33955i
\(171\) 5.14849 + 5.14849i 0.393715 + 0.393715i
\(172\) 0.699554 0.0533405
\(173\) 9.51731 0.723587 0.361794 0.932258i \(-0.382164\pi\)
0.361794 + 0.932258i \(0.382164\pi\)
\(174\) −5.52834 5.52834i −0.419102 0.419102i
\(175\) 0 0
\(176\) −4.70709 + 1.26126i −0.354810 + 0.0950711i
\(177\) −0.0839864 + 0.313441i −0.00631280 + 0.0235597i
\(178\) −11.6500 + 6.72614i −0.873206 + 0.504146i
\(179\) 6.00707i 0.448989i −0.974475 0.224495i \(-0.927927\pi\)
0.974475 0.224495i \(-0.0720731\pi\)
\(180\) 1.09188 + 4.07496i 0.0813841 + 0.303729i
\(181\) 6.05960 0.450407 0.225203 0.974312i \(-0.427695\pi\)
0.225203 + 0.974312i \(0.427695\pi\)
\(182\) 0 0
\(183\) 8.30883 0.614207
\(184\) 1.54394 + 5.76207i 0.113821 + 0.424786i
\(185\) 9.64216i 0.708905i
\(186\) 7.99956 4.61855i 0.586556 0.338648i
\(187\) 1.52095 5.67627i 0.111223 0.415090i
\(188\) 2.39886 0.642771i 0.174955 0.0468789i
\(189\) 0 0
\(190\) −6.68919 6.68919i −0.485285 0.485285i
\(191\) 21.6273 1.56490 0.782449 0.622715i \(-0.213970\pi\)
0.782449 + 0.622715i \(0.213970\pi\)
\(192\) 1.70497 0.123046
\(193\) 6.85258 + 6.85258i 0.493260 + 0.493260i 0.909332 0.416072i \(-0.136594\pi\)
−0.416072 + 0.909332i \(0.636594\pi\)
\(194\) −10.4769 18.1465i −0.752195 1.30284i
\(195\) −3.06396 + 3.46105i −0.219415 + 0.247851i
\(196\) 0 0
\(197\) −4.47322 1.19859i −0.318704 0.0853964i 0.0959210 0.995389i \(-0.469420\pi\)
−0.414624 + 0.909993i \(0.636087\pi\)
\(198\) 2.13366 3.69560i 0.151632 0.262635i
\(199\) 10.7801 + 18.6717i 0.764182 + 1.32360i 0.940678 + 0.339300i \(0.110190\pi\)
−0.176496 + 0.984301i \(0.556476\pi\)
\(200\) −0.495341 1.84864i −0.0350259 0.130718i
\(201\) −0.386483 0.386483i −0.0272604 0.0272604i
\(202\) −3.46883 12.9459i −0.244066 0.910868i
\(203\) 0 0
\(204\) 1.54458 2.67530i 0.108142 0.187308i
\(205\) −5.95998 3.44100i −0.416263 0.240330i
\(206\) 12.2529 12.2529i 0.853702 0.853702i
\(207\) −6.71272 3.87559i −0.466566 0.269372i
\(208\) 9.87322 + 14.9267i 0.684585 + 1.03498i
\(209\) 2.75649i 0.190670i
\(210\) 0 0
\(211\) 7.39505 + 12.8086i 0.509096 + 0.881780i 0.999945 + 0.0105352i \(0.00335353\pi\)
−0.490848 + 0.871245i \(0.663313\pi\)
\(212\) 5.11807i 0.351511i
\(213\) −7.16701 + 1.92039i −0.491076 + 0.131583i
\(214\) 21.1306 + 5.66192i 1.44446 + 0.387041i
\(215\) −1.22877 + 1.22877i −0.0838015 + 0.0838015i
\(216\) −5.03404 + 5.03404i −0.342523 + 0.342523i
\(217\) 0 0
\(218\) −16.9972 + 9.81336i −1.15120 + 0.664644i
\(219\) 0.897335 0.240440i 0.0606363 0.0162474i
\(220\) −0.798566 + 1.38316i −0.0538393 + 0.0932524i
\(221\) −21.5416 + 1.31094i −1.44904 + 0.0881832i
\(222\) −4.44019 + 2.56355i −0.298006 + 0.172054i
\(223\) −5.52568 + 20.6221i −0.370027 + 1.38096i 0.490450 + 0.871469i \(0.336832\pi\)
−0.860477 + 0.509490i \(0.829834\pi\)
\(224\) 0 0
\(225\) 2.15363 + 1.24340i 0.143575 + 0.0828933i
\(226\) −13.1379 3.52029i −0.873919 0.234166i
\(227\) 3.49849 13.0566i 0.232203 0.866594i −0.747186 0.664615i \(-0.768596\pi\)
0.979390 0.201980i \(-0.0647375\pi\)
\(228\) −0.375037 + 1.39966i −0.0248374 + 0.0926946i
\(229\) −6.94692 1.86142i −0.459066 0.123006i 0.0218726 0.999761i \(-0.493037\pi\)
−0.480938 + 0.876755i \(0.659704\pi\)
\(230\) 8.72153 + 5.03538i 0.575081 + 0.332023i
\(231\) 0 0
\(232\) 3.77813 14.1002i 0.248046 0.925721i
\(233\) −20.0959 + 11.6024i −1.31653 + 0.760097i −0.983168 0.182702i \(-0.941515\pi\)
−0.333359 + 0.942800i \(0.608182\pi\)
\(234\) −15.3561 3.12912i −1.00386 0.204557i
\(235\) −3.08457 + 5.34264i −0.201215 + 0.348515i
\(236\) 0.397731 0.106572i 0.0258901 0.00693723i
\(237\) 6.40827 3.69982i 0.416262 0.240329i
\(238\) 0 0
\(239\) −2.77302 + 2.77302i −0.179372 + 0.179372i −0.791082 0.611710i \(-0.790482\pi\)
0.611710 + 0.791082i \(0.290482\pi\)
\(240\) 4.49966 4.49966i 0.290452 0.290452i
\(241\) 3.08037 + 0.825382i 0.198424 + 0.0531675i 0.356662 0.934233i \(-0.383915\pi\)
−0.158238 + 0.987401i \(0.550581\pi\)
\(242\) −16.2482 + 4.35369i −1.04447 + 0.279866i
\(243\) 14.2121i 0.911704i
\(244\) −5.27161 9.13070i −0.337480 0.584533i
\(245\) 0 0
\(246\) 3.65941i 0.233316i
\(247\) 9.60104 3.20920i 0.610900 0.204197i
\(248\) 14.9361 + 8.62336i 0.948443 + 0.547584i
\(249\) 0.789397 0.789397i 0.0500260 0.0500260i
\(250\) −17.3877 10.0388i −1.09970 0.634910i
\(251\) −5.89697 + 10.2138i −0.372213 + 0.644692i −0.989906 0.141727i \(-0.954734\pi\)
0.617692 + 0.786420i \(0.288068\pi\)
\(252\) 0 0
\(253\) −0.759496 2.83448i −0.0477491 0.178202i
\(254\) −9.33127 9.33127i −0.585496 0.585496i
\(255\) 1.98610 + 7.41224i 0.124375 + 0.464173i
\(256\) −8.33554 14.4376i −0.520971 0.902349i
\(257\) −8.34519 + 14.4543i −0.520559 + 0.901634i 0.479156 + 0.877730i \(0.340943\pi\)
−0.999714 + 0.0239041i \(0.992390\pi\)
\(258\) 0.892538 + 0.239155i 0.0555670 + 0.0148891i
\(259\) 0 0
\(260\) 5.74735 + 1.17114i 0.356436 + 0.0726310i
\(261\) 9.48383 + 16.4265i 0.587034 + 1.01677i
\(262\) −23.6557 23.6557i −1.46145 1.46145i
\(263\) 9.51537 0.586743 0.293371 0.955999i \(-0.405223\pi\)
0.293371 + 0.955999i \(0.405223\pi\)
\(264\) −1.24961 −0.0769083
\(265\) 8.98993 + 8.98993i 0.552247 + 0.552247i
\(266\) 0 0
\(267\) −4.94418 + 1.32479i −0.302579 + 0.0810758i
\(268\) −0.179504 + 0.669919i −0.0109650 + 0.0409218i
\(269\) 0.275945 0.159317i 0.0168247 0.00971373i −0.491564 0.870841i \(-0.663575\pi\)
0.508389 + 0.861128i \(0.330241\pi\)
\(270\) 12.0187i 0.731437i
\(271\) 6.94654 + 25.9248i 0.421972 + 1.57482i 0.770447 + 0.637504i \(0.220033\pi\)
−0.348475 + 0.937318i \(0.613300\pi\)
\(272\) 29.7103 1.80145
\(273\) 0 0
\(274\) 18.0239 1.08886
\(275\) 0.243668 + 0.909381i 0.0146937 + 0.0548378i
\(276\) 1.54259i 0.0928532i
\(277\) 13.1218 7.57587i 0.788412 0.455190i −0.0509909 0.998699i \(-0.516238\pi\)
0.839403 + 0.543509i \(0.182905\pi\)
\(278\) −7.06764 + 26.3768i −0.423889 + 1.58198i
\(279\) −21.6463 + 5.80010i −1.29593 + 0.347243i
\(280\) 0 0
\(281\) 5.40600 + 5.40600i 0.322495 + 0.322495i 0.849724 0.527228i \(-0.176769\pi\)
−0.527228 + 0.849724i \(0.676769\pi\)
\(282\) 3.28036 0.195343
\(283\) −1.79244 −0.106549 −0.0532746 0.998580i \(-0.516966\pi\)
−0.0532746 + 0.998580i \(0.516966\pi\)
\(284\) 6.65752 + 6.65752i 0.395051 + 0.395051i
\(285\) −1.79975 3.11726i −0.106608 0.184651i
\(286\) −3.27315 4.94848i −0.193546 0.292610i
\(287\) 0 0
\(288\) 10.8409 + 2.90480i 0.638803 + 0.171167i
\(289\) −9.41380 + 16.3052i −0.553753 + 0.959128i
\(290\) −12.3219 21.3422i −0.723567 1.25325i
\(291\) −2.06353 7.70122i −0.120967 0.451453i
\(292\) −0.833545 0.833545i −0.0487796 0.0487796i
\(293\) 6.85691 + 25.5903i 0.400585 + 1.49500i 0.812055 + 0.583580i \(0.198349\pi\)
−0.411471 + 0.911423i \(0.634985\pi\)
\(294\) 0 0
\(295\) −0.511424 + 0.885812i −0.0297762 + 0.0515739i
\(296\) −8.29035 4.78644i −0.481867 0.278206i
\(297\) 2.47634 2.47634i 0.143692 0.143692i
\(298\) −27.1529 15.6767i −1.57292 0.908127i
\(299\) −8.98846 + 5.94538i −0.519816 + 0.343830i
\(300\) 0.494908i 0.0285735i
\(301\) 0 0
\(302\) −0.0305339 0.0528863i −0.00175703 0.00304327i
\(303\) 5.09966i 0.292968i
\(304\) −13.4613 + 3.60695i −0.772059 + 0.206873i
\(305\) 25.2978 + 6.77851i 1.44855 + 0.388136i
\(306\) −18.3966 + 18.3966i −1.05166 + 1.05166i
\(307\) −1.54710 + 1.54710i −0.0882978 + 0.0882978i −0.749876 0.661578i \(-0.769887\pi\)
0.661578 + 0.749876i \(0.269887\pi\)
\(308\) 0 0
\(309\) 5.71005 3.29670i 0.324833 0.187543i
\(310\) 28.1240 7.53581i 1.59734 0.428005i
\(311\) −14.6672 + 25.4043i −0.831699 + 1.44055i 0.0649904 + 0.997886i \(0.479298\pi\)
−0.896690 + 0.442660i \(0.854035\pi\)
\(312\) 1.45484 + 4.35249i 0.0823644 + 0.246411i
\(313\) −24.2354 + 13.9923i −1.36987 + 0.790893i −0.990911 0.134521i \(-0.957050\pi\)
−0.378957 + 0.925414i \(0.623717\pi\)
\(314\) −3.11844 + 11.6382i −0.175984 + 0.656781i
\(315\) 0 0
\(316\) −8.13157 4.69476i −0.457436 0.264101i
\(317\) −7.59654 2.03549i −0.426664 0.114324i 0.0390957 0.999235i \(-0.487552\pi\)
−0.465760 + 0.884911i \(0.654219\pi\)
\(318\) 1.74970 6.52998i 0.0981185 0.366183i
\(319\) −1.85854 + 6.93616i −0.104058 + 0.388350i
\(320\) 5.19109 + 1.39095i 0.290191 + 0.0777564i
\(321\) 7.20862 + 4.16190i 0.402346 + 0.232295i
\(322\) 0 0
\(323\) 4.34961 16.2330i 0.242019 0.903227i
\(324\) −3.85802 + 2.22743i −0.214334 + 0.123746i
\(325\) 2.88375 1.90745i 0.159962 0.105806i
\(326\) −13.7905 + 23.8859i −0.763788 + 1.32292i
\(327\) −7.21349 + 1.93285i −0.398907 + 0.106887i
\(328\) −5.91716 + 3.41627i −0.326720 + 0.188632i
\(329\) 0 0
\(330\) −1.49172 + 1.49172i −0.0821165 + 0.0821165i
\(331\) 11.5133 11.5133i 0.632826 0.632826i −0.315950 0.948776i \(-0.602323\pi\)
0.948776 + 0.315950i \(0.102323\pi\)
\(332\) −1.36832 0.366640i −0.0750963 0.0201220i
\(333\) 12.0149 3.21938i 0.658411 0.176421i
\(334\) 11.2675i 0.616529i
\(335\) −0.861417 1.49202i −0.0470642 0.0815176i
\(336\) 0 0
\(337\) 11.0114i 0.599827i 0.953966 + 0.299913i \(0.0969578\pi\)
−0.953966 + 0.299913i \(0.903042\pi\)
\(338\) −13.4252 + 17.1618i −0.730233 + 0.933480i
\(339\) −4.48195 2.58765i −0.243426 0.140542i
\(340\) 6.88532 6.88532i 0.373409 0.373409i
\(341\) −7.34737 4.24200i −0.397882 0.229717i
\(342\) 6.10183 10.5687i 0.329949 0.571488i
\(343\) 0 0
\(344\) 0.446530 + 1.66647i 0.0240753 + 0.0898501i
\(345\) 2.70957 + 2.70957i 0.145879 + 0.145879i
\(346\) −4.12863 15.4082i −0.221956 0.828352i
\(347\) −2.36362 4.09391i −0.126886 0.219772i 0.795583 0.605845i \(-0.207165\pi\)
−0.922468 + 0.386073i \(0.873831\pi\)
\(348\) −1.88741 + 3.26910i −0.101176 + 0.175242i
\(349\) −22.4353 6.01151i −1.20093 0.321789i −0.397734 0.917501i \(-0.630203\pi\)
−0.803198 + 0.595712i \(0.796870\pi\)
\(350\) 0 0
\(351\) −11.5083 5.74223i −0.614269 0.306498i
\(352\) 2.12447 + 3.67970i 0.113235 + 0.196128i
\(353\) −9.29908 9.29908i −0.494940 0.494940i 0.414919 0.909859i \(-0.363810\pi\)
−0.909859 + 0.414919i \(0.863810\pi\)
\(354\) 0.543886 0.0289072
\(355\) −23.3880 −1.24130
\(356\) 4.59271 + 4.59271i 0.243413 + 0.243413i
\(357\) 0 0
\(358\) −9.72526 + 2.60588i −0.513996 + 0.137725i
\(359\) 2.43301 9.08010i 0.128409 0.479229i −0.871529 0.490344i \(-0.836871\pi\)
0.999938 + 0.0111144i \(0.00353790\pi\)
\(360\) −9.01037 + 5.20214i −0.474888 + 0.274177i
\(361\) 11.1170i 0.585105i
\(362\) −2.62867 9.81032i −0.138160 0.515619i
\(363\) −6.40052 −0.335940
\(364\) 0 0
\(365\) 2.92826 0.153272
\(366\) −3.60439 13.4518i −0.188404 0.703135i
\(367\) 7.31961i 0.382081i −0.981582 0.191040i \(-0.938814\pi\)
0.981582 0.191040i \(-0.0611861\pi\)
\(368\) 12.8484 7.41801i 0.669767 0.386690i
\(369\) 2.29780 8.57550i 0.119619 0.446423i
\(370\) −15.6104 + 4.18279i −0.811544 + 0.217453i
\(371\) 0 0
\(372\) −3.15361 3.15361i −0.163507 0.163507i
\(373\) −1.08512 −0.0561856 −0.0280928 0.999605i \(-0.508943\pi\)
−0.0280928 + 0.999605i \(0.508943\pi\)
\(374\) −9.84951 −0.509306
\(375\) −5.40196 5.40196i −0.278956 0.278956i
\(376\) 3.06241 + 5.30425i 0.157932 + 0.273546i
\(377\) 26.3229 1.60191i 1.35570 0.0825025i
\(378\) 0 0
\(379\) −25.1695 6.74414i −1.29287 0.346423i −0.454119 0.890941i \(-0.650046\pi\)
−0.838749 + 0.544518i \(0.816713\pi\)
\(380\) −2.28374 + 3.95555i −0.117153 + 0.202915i
\(381\) −2.51061 4.34851i −0.128623 0.222781i
\(382\) −9.38197 35.0140i −0.480023 1.79147i
\(383\) 3.76918 + 3.76918i 0.192596 + 0.192596i 0.796817 0.604221i \(-0.206516\pi\)
−0.604221 + 0.796817i \(0.706516\pi\)
\(384\) −2.16834 8.09234i −0.110652 0.412961i
\(385\) 0 0
\(386\) 8.12146 14.0668i 0.413372 0.715981i
\(387\) −1.94141 1.12088i −0.0986876 0.0569773i
\(388\) −7.15375 + 7.15375i −0.363177 + 0.363177i
\(389\) −2.97841 1.71958i −0.151011 0.0871864i 0.422590 0.906321i \(-0.361121\pi\)
−0.573602 + 0.819134i \(0.694454\pi\)
\(390\) 6.93249 + 3.45905i 0.351040 + 0.175156i
\(391\) 17.8907i 0.904773i
\(392\) 0 0
\(393\) −6.36465 11.0239i −0.321054 0.556082i
\(394\) 7.76196i 0.391042i
\(395\) 22.5295 6.03677i 1.13358 0.303743i
\(396\) −1.99015 0.533259i −0.100009 0.0267973i
\(397\) 0.424872 0.424872i 0.0213237 0.0213237i −0.696365 0.717688i \(-0.745200\pi\)
0.717688 + 0.696365i \(0.245200\pi\)
\(398\) 25.5525 25.5525i 1.28083 1.28083i
\(399\) 0 0
\(400\) −4.12212 + 2.37991i −0.206106 + 0.118995i
\(401\) −11.5834 + 3.10377i −0.578448 + 0.154995i −0.536168 0.844111i \(-0.680129\pi\)
−0.0422800 + 0.999106i \(0.513462\pi\)
\(402\) −0.458047 + 0.793361i −0.0228453 + 0.0395693i
\(403\) −6.22113 + 30.5301i −0.309896 + 1.52081i
\(404\) −5.60409 + 3.23553i −0.278814 + 0.160973i
\(405\) 2.86414 10.6891i 0.142320 0.531147i
\(406\) 0 0
\(407\) 4.07819 + 2.35454i 0.202148 + 0.116710i
\(408\) 7.35898 + 1.97183i 0.364324 + 0.0976203i
\(409\) −3.00424 + 11.2120i −0.148550 + 0.554396i 0.851022 + 0.525131i \(0.175984\pi\)
−0.999572 + 0.0292657i \(0.990683\pi\)
\(410\) −2.98542 + 11.1418i −0.147440 + 0.550252i
\(411\) 6.62441 + 1.77501i 0.326758 + 0.0875546i
\(412\) −7.24558 4.18324i −0.356964 0.206093i
\(413\) 0 0
\(414\) −3.36248 + 12.5489i −0.165257 + 0.616747i
\(415\) 3.04747 1.75946i 0.149594 0.0863683i
\(416\) 10.3432 11.6837i 0.507119 0.572842i
\(417\) −5.19520 + 8.99836i −0.254410 + 0.440651i
\(418\) 4.46267 1.19577i 0.218276 0.0584870i
\(419\) −30.9881 + 17.8910i −1.51387 + 0.874032i −0.513999 + 0.857791i \(0.671836\pi\)
−0.999868 + 0.0162408i \(0.994830\pi\)
\(420\) 0 0
\(421\) −3.47255 + 3.47255i −0.169242 + 0.169242i −0.786646 0.617404i \(-0.788184\pi\)
0.617404 + 0.786646i \(0.288184\pi\)
\(422\) 17.5288 17.5288i 0.853287 0.853287i
\(423\) −7.68723 2.05979i −0.373766 0.100150i
\(424\) 12.1922 3.26690i 0.592107 0.158655i
\(425\) 5.73985i 0.278424i
\(426\) 6.21813 + 10.7701i 0.301269 + 0.521814i
\(427\) 0 0
\(428\) 10.5622i 0.510544i
\(429\) −0.715668 2.14108i −0.0345528 0.103372i
\(430\) 2.52239 + 1.45630i 0.121640 + 0.0702291i
\(431\) 0.347144 0.347144i 0.0167213 0.0167213i −0.698697 0.715418i \(-0.746236\pi\)
0.715418 + 0.698697i \(0.246236\pi\)
\(432\) 15.3336 + 8.85286i 0.737739 + 0.425934i
\(433\) 8.89347 15.4039i 0.427393 0.740266i −0.569248 0.822166i \(-0.692765\pi\)
0.996641 + 0.0818999i \(0.0260988\pi\)
\(434\) 0 0
\(435\) −2.42693 9.05744i −0.116363 0.434271i
\(436\) 6.70070 + 6.70070i 0.320905 + 0.320905i
\(437\) −2.17201 8.10604i −0.103901 0.387764i
\(438\) −0.778531 1.34846i −0.0371997 0.0644317i
\(439\) 14.3012 24.7704i 0.682559 1.18223i −0.291639 0.956529i \(-0.594200\pi\)
0.974197 0.225698i \(-0.0724662\pi\)
\(440\) −3.80467 1.01946i −0.181381 0.0486008i
\(441\) 0 0
\(442\) 11.4672 + 34.3065i 0.545437 + 1.63179i
\(443\) 3.68575 + 6.38391i 0.175115 + 0.303309i 0.940201 0.340620i \(-0.110637\pi\)
−0.765086 + 0.643928i \(0.777304\pi\)
\(444\) 1.75043 + 1.75043i 0.0830716 + 0.0830716i
\(445\) −16.1342 −0.764836
\(446\) 35.7837 1.69441
\(447\) −8.43576 8.43576i −0.398998 0.398998i
\(448\) 0 0
\(449\) 22.5220 6.03476i 1.06288 0.284798i 0.315315 0.948987i \(-0.397890\pi\)
0.747565 + 0.664189i \(0.231223\pi\)
\(450\) 1.07878 4.02606i 0.0508541 0.189790i
\(451\) 2.91077 1.68053i 0.137063 0.0791332i
\(452\) 6.56704i 0.308887i
\(453\) −0.00601399 0.0224445i −0.000282562 0.00105454i
\(454\) −22.6558 −1.06329
\(455\) 0 0
\(456\) −3.57364 −0.167351
\(457\) −1.16783 4.35841i −0.0546289 0.203878i 0.933217 0.359313i \(-0.116989\pi\)
−0.987846 + 0.155435i \(0.950322\pi\)
\(458\) 12.0544i 0.563263i
\(459\) −18.4908 + 10.6757i −0.863076 + 0.498297i
\(460\) 1.25848 4.69671i 0.0586769 0.218985i
\(461\) 32.1809 8.62285i 1.49882 0.401606i 0.586112 0.810230i \(-0.300658\pi\)
0.912703 + 0.408623i \(0.133991\pi\)
\(462\) 0 0
\(463\) 29.0991 + 29.0991i 1.35235 + 1.35235i 0.883028 + 0.469321i \(0.155501\pi\)
0.469321 + 0.883028i \(0.344499\pi\)
\(464\) −36.3047 −1.68540
\(465\) 11.0787 0.513761
\(466\) 27.5016 + 27.5016i 1.27399 + 1.27399i
\(467\) −2.85866 4.95135i −0.132283 0.229121i 0.792273 0.610167i \(-0.208897\pi\)
−0.924556 + 0.381045i \(0.875564\pi\)
\(468\) 0.459626 + 7.55267i 0.0212462 + 0.349122i
\(469\) 0 0
\(470\) 9.98767 + 2.67619i 0.460697 + 0.123443i
\(471\) −2.29227 + 3.97033i −0.105622 + 0.182943i
\(472\) 0.507749 + 0.879447i 0.0233710 + 0.0404798i
\(473\) −0.219657 0.819771i −0.0100998 0.0376931i
\(474\) −8.76981 8.76981i −0.402811 0.402811i
\(475\) 0.696841 + 2.60065i 0.0319733 + 0.119326i
\(476\) 0 0
\(477\) −8.20054 + 14.2038i −0.375477 + 0.650345i
\(478\) 5.69239 + 3.28650i 0.260364 + 0.150321i
\(479\) −23.5643 + 23.5643i −1.07668 + 1.07668i −0.0798746 + 0.996805i \(0.525452\pi\)
−0.996805 + 0.0798746i \(0.974548\pi\)
\(480\) −4.80506 2.77420i −0.219320 0.126624i
\(481\) 3.45307 16.9459i 0.157446 0.772665i
\(482\) 5.34507i 0.243461i
\(483\) 0 0
\(484\) 4.06087 + 7.03363i 0.184585 + 0.319711i
\(485\) 25.1312i 1.14115i
\(486\) −23.0089 + 6.16522i −1.04371 + 0.279660i
\(487\) 14.6038 + 3.91309i 0.661763 + 0.177319i 0.574041 0.818826i \(-0.305375\pi\)
0.0877214 + 0.996145i \(0.472041\pi\)
\(488\) 18.3862 18.3862i 0.832303 0.832303i
\(489\) −7.42080 + 7.42080i −0.335580 + 0.335580i
\(490\) 0 0
\(491\) −3.79911 + 2.19342i −0.171451 + 0.0989875i −0.583270 0.812278i \(-0.698227\pi\)
0.411819 + 0.911266i \(0.364894\pi\)
\(492\) 1.70664 0.457294i 0.0769415 0.0206164i
\(493\) 21.8899 37.9144i 0.985871 1.70758i
\(494\) −9.36056 14.1516i −0.421151 0.636713i
\(495\) 4.43238 2.55904i 0.199221 0.115020i
\(496\) 11.1016 41.4317i 0.498476 1.86034i
\(497\) 0 0
\(498\) −1.62045 0.935569i −0.0726142 0.0419238i
\(499\) −19.3575 5.18682i −0.866560 0.232194i −0.201960 0.979394i \(-0.564731\pi\)
−0.664599 + 0.747200i \(0.731398\pi\)
\(500\) −2.50897 + 9.36361i −0.112205 + 0.418753i
\(501\) 1.10963 4.14118i 0.0495745 0.185014i
\(502\) 19.0940 + 5.11623i 0.852209 + 0.228349i
\(503\) −0.917016 0.529439i −0.0408877 0.0236065i 0.479417 0.877587i \(-0.340848\pi\)
−0.520305 + 0.853981i \(0.674182\pi\)
\(504\) 0 0
\(505\) 4.16041 15.5268i 0.185136 0.690936i
\(506\) −4.25947 + 2.45920i −0.189356 + 0.109325i
\(507\) −6.62432 + 4.98544i −0.294196 + 0.221411i
\(508\) −3.18576 + 5.51790i −0.141345 + 0.244817i
\(509\) −10.8606 + 2.91008i −0.481387 + 0.128987i −0.491348 0.870963i \(-0.663496\pi\)
0.00996149 + 0.999950i \(0.496829\pi\)
\(510\) 11.1386 6.43089i 0.493227 0.284765i
\(511\) 0 0
\(512\) −1.18017 + 1.18017i −0.0521565 + 0.0521565i
\(513\) 7.08184 7.08184i 0.312671 0.312671i
\(514\) 27.0212 + 7.24032i 1.19186 + 0.319357i
\(515\) 20.0748 5.37903i 0.884601 0.237028i
\(516\) 0.446140i 0.0196402i
\(517\) −1.50646 2.60927i −0.0662541 0.114755i
\(518\) 0 0
\(519\) 6.06965i 0.266428i
\(520\) 0.878691 + 14.4388i 0.0385332 + 0.633185i
\(521\) −14.6510 8.45874i −0.641871 0.370584i 0.143464 0.989656i \(-0.454176\pi\)
−0.785335 + 0.619071i \(0.787509\pi\)
\(522\) 22.4799 22.4799i 0.983917 0.983917i
\(523\) 0.268849 + 0.155220i 0.0117560 + 0.00678731i 0.505866 0.862612i \(-0.331173\pi\)
−0.494111 + 0.869399i \(0.664506\pi\)
\(524\) −8.07621 + 13.9884i −0.352811 + 0.611086i
\(525\) 0 0
\(526\) −4.12779 15.4051i −0.179980 0.671695i
\(527\) 36.5750 + 36.5750i 1.59323 + 1.59323i
\(528\) 0.804367 + 3.00194i 0.0350056 + 0.130643i
\(529\) −7.03308 12.1816i −0.305786 0.529637i
\(530\) 10.6546 18.4543i 0.462806 0.801603i
\(531\) −1.27455 0.341514i −0.0553106 0.0148204i
\(532\) 0 0
\(533\) −9.24224 8.18188i −0.400326 0.354396i
\(534\) 4.28959 + 7.42978i 0.185629 + 0.321518i
\(535\) 18.5526 + 18.5526i 0.802099 + 0.802099i
\(536\) −1.71045 −0.0738803
\(537\) −3.83100 −0.165320
\(538\) −0.377635 0.377635i −0.0162810 0.0162810i
\(539\) 0 0
\(540\) 5.60519 1.50190i 0.241209 0.0646317i
\(541\) −8.05676 + 30.0682i −0.346387 + 1.29273i 0.544597 + 0.838698i \(0.316683\pi\)
−0.890984 + 0.454036i \(0.849984\pi\)
\(542\) 38.9581 22.4925i 1.67340 0.966135i
\(543\) 3.86450i 0.165842i
\(544\) −6.70465 25.0221i −0.287459 1.07281i
\(545\) −23.5396 −1.00833
\(546\) 0 0
\(547\) −13.8672 −0.592920 −0.296460 0.955045i \(-0.595806\pi\)
−0.296460 + 0.955045i \(0.595806\pi\)
\(548\) −2.25234 8.40583i −0.0962150 0.359079i
\(549\) 33.7862i 1.44196i
\(550\) 1.36656 0.788983i 0.0582702 0.0336423i
\(551\) −5.31504 + 19.8360i −0.226428 + 0.845042i
\(552\) 3.67475 0.984647i 0.156408 0.0419094i
\(553\) 0 0
\(554\) −17.9574 17.9574i −0.762936 0.762936i
\(555\) −6.14927 −0.261022
\(556\) 13.1846 0.559150
\(557\) −16.0453 16.0453i −0.679860 0.679860i 0.280108 0.959968i \(-0.409630\pi\)
−0.959968 + 0.280108i \(0.909630\pi\)
\(558\) 18.7804 + 32.5286i 0.795038 + 1.37705i
\(559\) −2.59959 + 1.71949i −0.109951 + 0.0727266i
\(560\) 0 0
\(561\) −3.62003 0.969985i −0.152838 0.0409528i
\(562\) 6.40703 11.0973i 0.270264 0.468111i
\(563\) 11.2217 + 19.4366i 0.472940 + 0.819156i 0.999520 0.0309690i \(-0.00985932\pi\)
−0.526580 + 0.850125i \(0.676526\pi\)
\(564\) −0.409927 1.52987i −0.0172610 0.0644190i
\(565\) −11.5350 11.5350i −0.485283 0.485283i
\(566\) 0.777562 + 2.90190i 0.0326834 + 0.121976i
\(567\) 0 0
\(568\) −11.6100 + 20.1090i −0.487143 + 0.843756i
\(569\) 11.1921 + 6.46175i 0.469196 + 0.270891i 0.715903 0.698200i \(-0.246015\pi\)
−0.246707 + 0.969090i \(0.579349\pi\)
\(570\) −4.26602 + 4.26602i −0.178684 + 0.178684i
\(571\) 15.1053 + 8.72106i 0.632138 + 0.364965i 0.781580 0.623805i \(-0.214414\pi\)
−0.149442 + 0.988771i \(0.547748\pi\)
\(572\) −1.89880 + 2.14488i −0.0793928 + 0.0896821i
\(573\) 13.7928i 0.576202i
\(574\) 0 0
\(575\) −1.43312 2.48223i −0.0597650 0.103516i
\(576\) 6.93292i 0.288872i
\(577\) 13.9338 3.73355i 0.580071 0.155430i 0.0431598 0.999068i \(-0.486258\pi\)
0.536912 + 0.843639i \(0.319591\pi\)
\(578\) 30.4813 + 8.16745i 1.26786 + 0.339721i
\(579\) 4.37022 4.37022i 0.181620 0.181620i
\(580\) −8.41357 + 8.41357i −0.349354 + 0.349354i
\(581\) 0 0
\(582\) −11.5729 + 6.68160i −0.479711 + 0.276961i
\(583\) −5.99760 + 1.60705i −0.248395 + 0.0665573i
\(584\) 1.45361 2.51772i 0.0601507 0.104184i
\(585\) −14.0737 12.4590i −0.581874 0.515116i
\(586\) 38.4555 22.2023i 1.58858 0.917167i
\(587\) 4.97130 18.5532i 0.205188 0.765771i −0.784205 0.620502i \(-0.786929\pi\)
0.989392 0.145268i \(-0.0464046\pi\)
\(588\) 0 0
\(589\) −21.0120 12.1313i −0.865783 0.499860i
\(590\) 1.65596 + 0.443713i 0.0681748 + 0.0182674i
\(591\) −0.764402 + 2.85279i −0.0314433 + 0.117348i
\(592\) −6.16199 + 22.9969i −0.253256 + 0.945165i
\(593\) −2.51561 0.674056i −0.103304 0.0276802i 0.206797 0.978384i \(-0.433696\pi\)
−0.310101 + 0.950704i \(0.600363\pi\)
\(594\) −5.08337 2.93489i −0.208573 0.120420i
\(595\) 0 0
\(596\) −3.91804 + 14.6223i −0.160489 + 0.598954i
\(597\) 11.9078 6.87500i 0.487356 0.281375i
\(598\) 13.5246 + 11.9729i 0.553063 + 0.489610i
\(599\) −12.4050 + 21.4861i −0.506855 + 0.877898i 0.493114 + 0.869965i \(0.335859\pi\)
−0.999969 + 0.00793343i \(0.997475\pi\)
\(600\) −1.17896 + 0.315903i −0.0481310 + 0.0128967i
\(601\) 15.2889 8.82708i 0.623649 0.360064i −0.154639 0.987971i \(-0.549422\pi\)
0.778288 + 0.627907i \(0.216088\pi\)
\(602\) 0 0
\(603\) 1.57155 1.57155i 0.0639987 0.0639987i
\(604\) −0.0208490 + 0.0208490i −0.000848334 + 0.000848334i
\(605\) −19.4876 5.22168i −0.792282 0.212291i
\(606\) −8.25620 + 2.21224i −0.335385 + 0.0898662i
\(607\) 15.0740i 0.611835i 0.952058 + 0.305917i \(0.0989631\pi\)
−0.952058 + 0.305917i \(0.901037\pi\)
\(608\) 6.07556 + 10.5232i 0.246397 + 0.426771i
\(609\) 0 0
\(610\) 43.8969i 1.77733i
\(611\) −7.33438 + 8.28491i −0.296717 + 0.335172i
\(612\) 10.8786 + 6.28074i 0.439740 + 0.253884i
\(613\) −24.8050 + 24.8050i −1.00186 + 1.00186i −0.00186450 + 0.999998i \(0.500593\pi\)
−0.999998 + 0.00186450i \(0.999407\pi\)
\(614\) 3.17585 + 1.83358i 0.128167 + 0.0739972i
\(615\) −2.19449 + 3.80097i −0.0884904 + 0.153270i
\(616\) 0 0
\(617\) 9.01921 + 33.6601i 0.363100 + 1.35511i 0.869979 + 0.493089i \(0.164132\pi\)
−0.506879 + 0.862017i \(0.669201\pi\)
\(618\) −7.81429 7.81429i −0.314337 0.314337i
\(619\) −2.05655 7.67515i −0.0826597 0.308490i 0.912201 0.409743i \(-0.134382\pi\)
−0.994861 + 0.101253i \(0.967715\pi\)
\(620\) −7.02896 12.1745i −0.282290 0.488940i
\(621\) −5.33095 + 9.23348i −0.213924 + 0.370527i
\(622\) 47.4915 + 12.7253i 1.90423 + 0.510238i
\(623\) 0 0
\(624\) 9.51949 6.29663i 0.381084 0.252067i
\(625\) −9.64286 16.7019i −0.385715 0.668077i
\(626\) 33.1665 + 33.1665i 1.32560 + 1.32560i
\(627\) 1.75795 0.0702056
\(628\) 5.81741 0.232140
\(629\) −20.3011 20.3011i −0.809460 0.809460i
\(630\) 0 0
\(631\) 40.9973 10.9852i 1.63208 0.437314i 0.677559 0.735469i \(-0.263038\pi\)
0.954517 + 0.298155i \(0.0963713\pi\)
\(632\) 5.99339 22.3676i 0.238404 0.889737i
\(633\) 8.16866 4.71618i 0.324675 0.187451i
\(634\) 13.1816i 0.523507i
\(635\) −4.09642 15.2880i −0.162561 0.606687i
\(636\) −3.26404 −0.129428
\(637\) 0 0
\(638\) 12.0357 0.476497
\(639\) −7.80890 29.1432i −0.308915 1.15289i
\(640\) 26.4076i 1.04385i
\(641\) 17.7415 10.2431i 0.700748 0.404577i −0.106878 0.994272i \(-0.534085\pi\)
0.807626 + 0.589695i \(0.200752\pi\)
\(642\) 3.61088 13.4760i 0.142510 0.531855i
\(643\) −20.9593 + 5.61604i −0.826556 + 0.221475i −0.647211 0.762311i \(-0.724065\pi\)
−0.179345 + 0.983786i \(0.557398\pi\)
\(644\) 0 0
\(645\) 0.783647 + 0.783647i 0.0308561 + 0.0308561i
\(646\) −28.1676 −1.10824
\(647\) −39.1337 −1.53850 −0.769252 0.638945i \(-0.779371\pi\)
−0.769252 + 0.638945i \(0.779371\pi\)
\(648\) −7.76875 7.76875i −0.305185 0.305185i
\(649\) −0.249772 0.432618i −0.00980440 0.0169817i
\(650\) −4.33908 3.84126i −0.170193 0.150666i
\(651\) 0 0
\(652\) 12.8630 + 3.44664i 0.503755 + 0.134981i
\(653\) 14.8092 25.6503i 0.579528 1.00377i −0.416005 0.909362i \(-0.636570\pi\)
0.995533 0.0944103i \(-0.0300966\pi\)
\(654\) 6.25845 + 10.8400i 0.244725 + 0.423876i
\(655\) −10.3848 38.7566i −0.405768 1.51435i
\(656\) 12.0157 + 12.0157i 0.469135 + 0.469135i
\(657\) 0.977702 + 3.64883i 0.0381438 + 0.142355i
\(658\) 0 0
\(659\) 1.87682 3.25074i 0.0731104 0.126631i −0.827153 0.561977i \(-0.810041\pi\)
0.900263 + 0.435346i \(0.143374\pi\)
\(660\) 0.882106 + 0.509284i 0.0343359 + 0.0198239i
\(661\) 30.7260 30.7260i 1.19510 1.19510i 0.219487 0.975615i \(-0.429562\pi\)
0.975615 0.219487i \(-0.0704385\pi\)
\(662\) −23.6341 13.6452i −0.918566 0.530334i
\(663\) 0.836048 + 13.7381i 0.0324694 + 0.533544i
\(664\) 3.49363i 0.135579i
\(665\) 0 0
\(666\) −10.4242 18.0552i −0.403928 0.699623i
\(667\) 21.8617i 0.846488i
\(668\) −5.25482 + 1.40802i −0.203315 + 0.0544781i
\(669\) 13.1517 + 3.52399i 0.508475 + 0.136245i
\(670\) −2.04185 + 2.04185i −0.0788835 + 0.0788835i
\(671\) −9.04453 + 9.04453i −0.349160 + 0.349160i
\(672\) 0 0
\(673\) 23.1880 13.3876i 0.893833 0.516055i 0.0186390 0.999826i \(-0.494067\pi\)
0.875194 + 0.483771i \(0.160733\pi\)
\(674\) 17.8271 4.77675i 0.686673 0.183993i
\(675\) 1.71032 2.96236i 0.0658303 0.114021i
\(676\) 9.68143 + 4.11651i 0.372363 + 0.158327i
\(677\) −18.0711 + 10.4333i −0.694527 + 0.400985i −0.805306 0.592860i \(-0.797999\pi\)
0.110779 + 0.993845i \(0.464666\pi\)
\(678\) −2.24506 + 8.37867i −0.0862209 + 0.321781i
\(679\) 0 0
\(680\) 20.7971 + 12.0072i 0.797532 + 0.460456i
\(681\) −8.32680 2.23116i −0.319084 0.0854982i
\(682\) −3.68038 + 13.7354i −0.140929 + 0.525954i
\(683\) 8.48852 31.6796i 0.324804 1.21219i −0.589704 0.807619i \(-0.700756\pi\)
0.914509 0.404567i \(-0.132578\pi\)
\(684\) −5.69143 1.52501i −0.217617 0.0583103i
\(685\) 18.7211 + 10.8087i 0.715298 + 0.412977i
\(686\) 0 0
\(687\) −1.18712 + 4.43039i −0.0452914 + 0.169030i
\(688\) 3.71593 2.14539i 0.141668 0.0817923i
\(689\) 12.5801 + 19.0191i 0.479264 + 0.724570i
\(690\) 3.21130 5.56214i 0.122252 0.211747i
\(691\) −43.4491 + 11.6421i −1.65288 + 0.442888i −0.960418 0.278564i \(-0.910141\pi\)
−0.692464 + 0.721453i \(0.743475\pi\)
\(692\) −6.67003 + 3.85094i −0.253556 + 0.146391i
\(693\) 0 0
\(694\) −5.60257 + 5.60257i −0.212671 + 0.212671i
\(695\) −23.1588 + 23.1588i −0.878463 + 0.878463i
\(696\) −8.99236 2.40950i −0.340855 0.0913317i
\(697\) −19.7934 + 5.30361i −0.749727 + 0.200889i
\(698\) 38.9298i 1.47352i
\(699\) 7.39940 + 12.8161i 0.279871 + 0.484751i
\(700\) 0 0
\(701\) 38.7293i 1.46279i 0.681956 + 0.731393i \(0.261129\pi\)
−0.681956 + 0.731393i \(0.738871\pi\)
\(702\) −4.30417 + 21.1226i −0.162450 + 0.797223i
\(703\) 11.6628 + 6.73352i 0.439871 + 0.253960i
\(704\) −1.85593 + 1.85593i −0.0699482 + 0.0699482i
\(705\) 3.40726 + 1.96718i 0.128325 + 0.0740884i
\(706\) −11.0210 + 19.0889i −0.414780 + 0.718420i
\(707\) 0 0
\(708\) −0.0679660 0.253653i −0.00255432 0.00953285i
\(709\) 20.8624 + 20.8624i 0.783504 + 0.783504i 0.980420 0.196917i \(-0.0630928\pi\)
−0.196917 + 0.980420i \(0.563093\pi\)
\(710\) 10.1457 + 37.8644i 0.380763 + 1.42103i
\(711\) 15.0446 + 26.0580i 0.564215 + 0.977250i
\(712\) −8.00915 + 13.8723i −0.300156 + 0.519885i
\(713\) 24.9490 + 6.68507i 0.934348 + 0.250358i
\(714\) 0 0
\(715\) −0.432246 7.10276i −0.0161651 0.265628i
\(716\) 2.43061 + 4.20994i 0.0908362 + 0.157333i
\(717\) 1.76849 + 1.76849i 0.0660455 + 0.0660455i
\(718\) −15.7559 −0.588003
\(719\) −8.46228 −0.315590 −0.157795 0.987472i \(-0.550438\pi\)
−0.157795 + 0.987472i \(0.550438\pi\)
\(720\) 18.2970 + 18.2970i 0.681888 + 0.681888i
\(721\) 0 0
\(722\) −17.9981 + 4.82258i −0.669820 + 0.179478i
\(723\) 0.526386 1.96450i 0.0195765 0.0730605i
\(724\) −4.24676 + 2.45187i −0.157830 + 0.0911229i
\(725\) 7.01385i 0.260488i
\(726\) 2.77656 + 10.3623i 0.103048 + 0.384580i
\(727\) 3.27056 0.121299 0.0606493 0.998159i \(-0.480683\pi\)
0.0606493 + 0.998159i \(0.480683\pi\)
\(728\) 0 0
\(729\) 7.45103 0.275964
\(730\) −1.27028 4.74076i −0.0470153 0.175463i
\(731\) 5.17425i 0.191376i
\(732\) −5.82309 + 3.36196i −0.215228 + 0.124262i
\(733\) 3.57318 13.3353i 0.131979 0.492551i −0.868014 0.496541i \(-0.834603\pi\)
0.999992 + 0.00399003i \(0.00127007\pi\)
\(734\) −11.8502 + 3.17526i −0.437400 + 0.117201i
\(735\) 0 0
\(736\) −9.14692 9.14692i −0.337160 0.337160i
\(737\) 0.841407 0.0309936
\(738\) −14.8803 −0.547750
\(739\) 30.0608 + 30.0608i 1.10580 + 1.10580i 0.993696 + 0.112109i \(0.0357605\pi\)
0.112109 + 0.993696i \(0.464240\pi\)
\(740\) 3.90146 + 6.75753i 0.143420 + 0.248412i
\(741\) −2.04666 6.12305i −0.0751861 0.224936i
\(742\) 0 0
\(743\) −47.1919 12.6450i −1.73130 0.463901i −0.750820 0.660507i \(-0.770341\pi\)
−0.980482 + 0.196606i \(0.937008\pi\)
\(744\) 5.49953 9.52547i 0.201623 0.349221i
\(745\) −18.8021 32.5663i −0.688857 1.19314i
\(746\) 0.470729 + 1.75678i 0.0172346 + 0.0643204i
\(747\) 3.20993 + 3.20993i 0.117445 + 0.117445i
\(748\) 1.23083 + 4.59352i 0.0450036 + 0.167956i
\(749\) 0 0
\(750\) −6.40223 + 11.0890i −0.233776 + 0.404913i
\(751\) 9.96838 + 5.75525i 0.363751 + 0.210012i 0.670725 0.741706i \(-0.265983\pi\)
−0.306974 + 0.951718i \(0.599316\pi\)
\(752\) 10.7711 10.7711i 0.392782 0.392782i
\(753\) 6.51387 + 3.76078i 0.237379 + 0.137051i
\(754\) −14.0124 41.9211i −0.510300 1.52668i
\(755\) 0.0732428i 0.00266558i
\(756\) 0 0
\(757\) −8.97468 15.5446i −0.326190 0.564978i 0.655562 0.755141i \(-0.272432\pi\)
−0.981753 + 0.190163i \(0.939098\pi\)
\(758\) 43.6743i 1.58632i
\(759\) −1.80768 + 0.484368i −0.0656148 + 0.0175814i
\(760\) −10.8806 2.91545i −0.394681 0.105754i
\(761\) −7.83029 + 7.83029i −0.283848 + 0.283848i −0.834641 0.550794i \(-0.814325\pi\)
0.550794 + 0.834641i \(0.314325\pi\)
\(762\) −5.95100 + 5.95100i −0.215582 + 0.215582i
\(763\) 0 0
\(764\) −15.1571 + 8.75096i −0.548365 + 0.316599i
\(765\) −30.1404 + 8.07610i −1.08973 + 0.291992i
\(766\) 4.46711 7.73726i 0.161403 0.279559i
\(767\) −1.21604 + 1.37364i −0.0439088 + 0.0495993i
\(768\) −9.20755 + 5.31598i −0.332249 + 0.191824i
\(769\) −2.87361 + 10.7245i −0.103625 + 0.386734i −0.998186 0.0602130i \(-0.980822\pi\)
0.894561 + 0.446947i \(0.147489\pi\)
\(770\) 0 0
\(771\) 9.21820 + 5.32213i 0.331986 + 0.191672i
\(772\) −7.57523 2.02978i −0.272638 0.0730533i
\(773\) −0.718001 + 2.67962i −0.0258247 + 0.0963792i −0.977635 0.210307i \(-0.932554\pi\)
0.951811 + 0.306686i \(0.0992203\pi\)
\(774\) −0.972476 + 3.62933i −0.0349549 + 0.130454i
\(775\) −8.00436 2.14476i −0.287525 0.0770421i
\(776\) −21.6079 12.4753i −0.775678 0.447838i
\(777\) 0 0
\(778\) −1.49192 + 5.56791i −0.0534879 + 0.199619i
\(779\) 8.32421 4.80599i 0.298246 0.172192i
\(780\) 0.746893 3.66537i 0.0267431 0.131241i