Properties

Label 637.2.x.b.215.1
Level $637$
Weight $2$
Character 637.215
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 215.1
Character \(\chi\) \(=\) 637.215
Dual form 637.2.x.b.80.2

$q$-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 \(\left(\mathbb{Z}/637\mathbb{Z}\right)^\times\).

\(n\) \(197\) \(248\)
\(\chi(n)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{5}{6}\right)\)

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 0.624689 + 0.780873i \(0.285226\pi\)
−0.931433 + 0.363912i \(0.881441\pi\)
\(3\) 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 −0.979181 0.202989i \(-0.934934\pi\)
0.746501 0.665384i \(-0.231732\pi\)
\(6\) 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 −0.594662 0.803976i \(-0.702714\pi\)
0.803976 + 0.594662i \(0.202714\pi\)
\(12\) −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 −0.232755 0.972535i \(-0.574774\pi\)
0.958618 0.284696i \(-0.0918925\pi\)
\(18\) −1.12497 + 4.19844i −0.265158 + 0.989582i
\(19\) −1.98532 + 1.98532i −0.455464 + 0.455464i −0.897163 0.441699i \(-0.854376\pi\)
0.441699 + 0.897163i \(0.354376\pi\)
\(20\) −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 −0.744974 0.667093i \(-0.767538\pi\)
0.205233 + 0.978713i \(0.434205\pi\)
\(24\) 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 −0.296148 0.955142i \(-0.595702\pi\)
0.975251 0.221099i \(-0.0709645\pi\)
\(30\) 2.14878i 0.392312i
\(31\) 8.34708 + 2.23659i 1.49918 + 0.401704i 0.912825 0.408351i \(-0.133896\pi\)
0.586354 + 0.810055i \(0.300563\pi\)
\(32\) 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 0.618690 0.785635i \(-0.287664\pi\)
0.142984 + 0.989725i \(0.454330\pi\)
\(38\) −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 −0.999961 0.00881984i \(-0.997193\pi\)
0.861582 0.507619i \(-0.169474\pi\)
\(42\) 0 0
\(43\) −0.748633 + 0.432224i −0.114165 + 0.0659135i −0.555995 0.831185i \(-0.687663\pi\)
0.441830 + 0.897099i \(0.354329\pi\)
\(44\) −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 \(-0.511481\pi\)
0.468446 + 0.883492i \(0.344814\pi\)
\(48\) −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 0.562878 0.826540i \(-0.309694\pi\)
−0.997244 + 0.0741963i \(0.976361\pi\)
\(54\) 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 \(-0.572789\pi\)
0.290670 + 0.956823i \(0.406122\pi\)
\(60\) 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 0.743155 0.669119i \(-0.233328\pi\)
−0.669119 + 0.743155i \(0.733328\pi\)
\(68\) −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 0.520117 + 0.854095i \(0.325888\pi\)
−0.877482 + 0.479609i \(0.840778\pi\)
\(72\) −3.65973 + 3.65973i −0.431304 + 0.431304i
\(73\) −0.377014 + 1.40704i −0.0441262 + 0.164681i −0.984473 0.175536i \(-0.943834\pi\)
0.940347 + 0.340217i \(0.110501\pi\)
\(74\) −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 −0.329758 0.944065i \(-0.606967\pi\)
0.982464 0.186454i \(-0.0596994\pi\)
\(80\) −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 \(-0.780628\pi\)
0.635904 + 0.771768i \(0.280628\pi\)
\(84\) 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 −0.764082 0.645120i \(-0.776807\pi\)
0.984274 0.176649i \(-0.0565258\pi\)
\(90\) 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 \(-0.635532\pi\)
−0.813058 + 0.582183i \(0.802199\pi\)
\(98\) 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 \(-0.630238\pi\)
−0.397833 + 0.917458i \(0.630238\pi\)
\(102\) 4.52417 4.52417i 0.447959 0.447959i
\(103\) −5.16928 + 8.95345i −0.509344 + 0.882210i 0.490597 + 0.871386i \(0.336779\pi\)
−0.999941 + 0.0108235i \(0.996555\pi\)
\(104\) 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 −0.987371 0.158425i \(-0.949358\pi\)
0.356486 0.934301i \(-0.383975\pi\)
\(108\) −1.44334 + 2.49994i −0.138885 + 0.240557i
\(109\) −3.03074 + 11.3109i −0.290292 + 1.08339i 0.654592 + 0.755982i \(0.272840\pi\)
−0.944885 + 0.327403i \(0.893826\pi\)
\(110\) 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 0.991305 0.131586i \(-0.0420069\pi\)
−0.609609 + 0.792702i \(0.708674\pi\)
\(114\) −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 0.771024 0.636805i \(-0.219745\pi\)
−0.165977 + 0.986130i \(0.553078\pi\)
\(128\) 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 −0.999928 0.0119634i \(-0.996192\pi\)
−0.510325 0.859982i \(-0.670475\pi\)
\(132\) 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 −0.976872 0.213824i \(-0.931408\pi\)
0.739084 0.673613i \(-0.235259\pi\)
\(138\) −3.08608 + 0.826913i −0.262705 + 0.0703915i
\(139\) 14.1096 8.14616i 1.19676 0.690949i 0.236927 0.971527i \(-0.423860\pi\)
0.959831 + 0.280579i \(0.0905264\pi\)
\(140\) 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 0.996168 + 0.0874634i \(0.0278761\pi\)
0.0874634 + 0.996168i \(0.472124\pi\)
\(150\) 0.990103 0.265297i 0.0808416 0.0216614i
\(151\) 0.0351934 + 0.00943004i 0.00286400 + 0.000767406i 0.260251 0.965541i \(-0.416195\pi\)
−0.257387 + 0.966308i \(0.582861\pi\)
\(152\) 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 \(-0.574056\pi\)
0.727413 + 0.686200i \(0.240723\pi\)
\(158\) 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 −0.996382 0.0849855i \(-0.972916\pi\)
0.0849855 + 0.996382i \(0.472916\pi\)
\(164\) −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 \(-0.667089\pi\)
−0.00132801 + 0.999999i \(0.500423\pi\)
\(168\) 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 \(-0.617836\pi\)
−0.361794 + 0.932258i \(0.617836\pi\)
\(174\) 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 \(0.0720731\pi\)
−0.974475 + 0.224495i \(0.927927\pi\)
\(180\) −1.09188 + 4.07496i −0.0813841 + 0.303729i
\(181\) −6.05960 −0.450407 −0.225203 0.974312i \(-0.572305\pi\)
−0.225203 + 0.974312i \(0.572305\pi\)
\(182\) 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 −0.416072 0.909332i \(-0.636594\pi\)
0.909332 + 0.416072i \(0.136594\pi\)
\(194\) 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 −0.414624 0.909993i \(-0.636087\pi\)
0.0959210 + 0.995389i \(0.469420\pi\)
\(198\) 2.13366 + 3.69560i 0.151632 + 0.262635i
\(199\) −10.7801 + 18.6717i −0.764182 + 1.32360i 0.176496 + 0.984301i \(0.443524\pi\)
−0.940678 + 0.339300i \(0.889810\pi\)
\(200\) −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 −0.490848 0.871245i \(-0.663313\pi\)
0.999945 0.0105352i \(-0.00335353\pi\)
\(212\) 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 0.860477 + 0.509490i \(0.170166\pi\)
−0.490450 + 0.871469i \(0.663168\pi\)
\(224\) 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 −0.979390 0.201980i \(-0.935262\pi\)
0.747186 0.664615i \(-0.231404\pi\)
\(228\) −0.375037 1.39966i −0.0248374 0.0926946i
\(229\) 6.94692 1.86142i 0.459066 0.123006i −0.0218726 0.999761i \(-0.506963\pi\)
0.480938 + 0.876755i \(0.340296\pi\)
\(230\) −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 −0.333359 0.942800i \(-0.608182\pi\)
−0.983168 + 0.182702i \(0.941515\pi\)
\(234\) 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 0.611710 0.791082i \(-0.290482\pi\)
−0.791082 + 0.611710i \(0.790482\pi\)
\(240\) 4.49966 + 4.49966i 0.290452 + 0.290452i
\(241\) −3.08037 + 0.825382i −0.198424 + 0.0531675i −0.356662 0.934233i \(-0.616085\pi\)
0.158238 + 0.987401i \(0.449419\pi\)
\(242\) −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 \(-0.0452656\pi\)
−0.617692 + 0.786420i \(0.711932\pi\)
\(252\) 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 0.999714 + 0.0239041i \(0.00760964\pi\)
−0.479156 + 0.877730i \(0.659057\pi\)
\(258\) −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 \(-0.336425\pi\)
−0.508389 + 0.861128i \(0.669759\pi\)
\(270\) 12.0187i 0.731437i
\(271\) −6.94654 + 25.9248i −0.421972 + 1.57482i 0.348475 + 0.937318i \(0.386700\pi\)
−0.770447 + 0.637504i \(0.779967\pi\)
\(272\) −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 0.839403 0.543509i \(-0.182905\pi\)
−0.0509909 + 0.998699i \(0.516238\pi\)
\(278\) 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 −0.527228 0.849724i \(-0.676769\pi\)
0.849724 + 0.527228i \(0.176769\pi\)
\(282\) 3.28036 0.195343
\(283\) 1.79244 0.106549 0.0532746 0.998580i \(-0.483034\pi\)
0.0532746 + 0.998580i \(0.483034\pi\)
\(284\) 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 0.411471 + 0.911423i \(0.365015\pi\)
−0.812055 + 0.583580i \(0.801651\pi\)
\(294\) 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 \(-0.230113\pi\)
−0.661578 + 0.749876i \(0.730113\pi\)
\(308\) 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 0.896690 + 0.442660i \(0.145965\pi\)
−0.0649904 + 0.997886i \(0.520702\pi\)
\(312\) 1.45484 4.35249i 0.0823644 0.246411i
\(313\) 24.2354 + 13.9923i 1.36987 + 0.790893i 0.990911 0.134521i \(-0.0429497\pi\)
0.378957 + 0.925414i \(0.376283\pi\)
\(314\) 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 −0.465760 0.884911i \(-0.654219\pi\)
0.0390957 + 0.999235i \(0.487552\pi\)
\(318\) −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 0.948776 0.315950i \(-0.102323\pi\)
−0.315950 + 0.948776i \(0.602323\pi\)
\(332\) 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 \(-0.903042\pi\)
0.953966 0.299913i \(-0.0969578\pi\)
\(338\) −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 −0.922468 0.386073i \(-0.873831\pi\)
0.795583 + 0.605845i \(0.207165\pi\)
\(348\) 1.88741 + 3.26910i 0.101176 + 0.175242i
\(349\) 22.4353 6.01151i 1.20093 0.321789i 0.397734 0.917501i \(-0.369797\pi\)
0.803198 + 0.595712i \(0.203130\pi\)
\(350\) 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 \(-0.636190\pi\)
0.909859 + 0.414919i \(0.136190\pi\)
\(354\) 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 0.999938 0.0111144i \(-0.00353790\pi\)
−0.871529 + 0.490344i \(0.836871\pi\)
\(360\) 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 −0.838749 0.544518i \(-0.816713\pi\)
−0.454119 + 0.890941i \(0.650046\pi\)
\(380\) −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 \(-0.793484\pi\)
0.604221 + 0.796817i \(0.293484\pi\)
\(384\) 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 −0.573602 0.819134i \(-0.694454\pi\)
0.422590 + 0.906321i \(0.361121\pi\)
\(390\) −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 \(-0.254800\pi\)
−0.717688 + 0.696365i \(0.754800\pi\)
\(398\) −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 −0.0422800 0.999106i \(-0.513462\pi\)
−0.536168 + 0.844111i \(0.680129\pi\)
\(402\) 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 0.999572 + 0.0292657i \(0.00931689\pi\)
−0.851022 + 0.525131i \(0.824016\pi\)
\(410\) −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 0.999868 + 0.0162408i \(0.00516982\pi\)
0.513999 + 0.857791i \(0.328164\pi\)
\(420\) 0 0
\(421\) −3.47255 3.47255i −0.169242 0.169242i 0.617404 0.786646i \(-0.288184\pi\)
−0.786646 + 0.617404i \(0.788184\pi\)
\(422\) 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 0.715418 0.698697i \(-0.246236\pi\)
−0.698697 + 0.715418i \(0.746236\pi\)
\(432\) −15.3336 + 8.85286i −0.737739 + 0.425934i
\(433\) −8.89347 15.4039i −0.427393 0.740266i 0.569248 0.822166i \(-0.307235\pi\)
−0.996641 + 0.0818999i \(0.973901\pi\)
\(434\) 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 −0.974197 0.225698i \(-0.927534\pi\)
0.291639 0.956529i \(-0.405800\pi\)
\(440\) 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 −0.765086 0.643928i \(-0.777304\pi\)
0.940201 + 0.340620i \(0.110637\pi\)
\(444\) −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 0.747565 0.664189i \(-0.231223\pi\)
0.315315 + 0.948987i \(0.397890\pi\)
\(450\) 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 −0.987846 0.155435i \(-0.950322\pi\)
0.933217 + 0.359313i \(0.116989\pi\)
\(458\) 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 \(-0.699342\pi\)
−0.912703 + 0.408623i \(0.866009\pi\)
\(462\) 0 0
\(463\) 29.0991 29.0991i 1.35235 1.35235i 0.469321 0.883028i \(-0.344499\pi\)
0.883028 0.469321i \(-0.155501\pi\)
\(464\) −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 \(-0.791103\pi\)
0.924556 + 0.381045i \(0.124436\pi\)
\(468\) −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 0.996805 + 0.0798746i \(0.0254520\pi\)
0.0798746 + 0.996805i \(0.474548\pi\)
\(480\) −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 0.0877214 0.996145i \(-0.472041\pi\)
0.574041 + 0.818826i \(0.305375\pi\)
\(488\) −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 0.411819 0.911266i \(-0.364894\pi\)
−0.583270 + 0.812278i \(0.698227\pi\)
\(492\) 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 −0.664599 0.747200i \(-0.731398\pi\)
−0.201960 + 0.979394i \(0.564731\pi\)
\(500\) 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 \(-0.659152\pi\)
0.520305 + 0.853981i \(0.325818\pi\)
\(504\) 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 \(-0.336504\pi\)
−0.00996149 + 0.999950i \(0.503171\pi\)
\(510\) −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 \(-0.545824\pi\)
0.785335 + 0.619071i \(0.212491\pi\)
\(522\) 22.4799 + 22.4799i 0.983917 + 0.983917i
\(523\) −0.268849 + 0.155220i −0.0117560 + 0.00678731i −0.505866 0.862612i \(-0.668827\pi\)
0.494111 + 0.869399i \(0.335494\pi\)
\(524\) 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 −0.890984 0.454036i \(-0.849984\pi\)
0.544597 0.838698i \(-0.316683\pi\)
\(542\) −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 −0.959968 0.280108i \(-0.909630\pi\)
0.280108 + 0.959968i \(0.409630\pi\)
\(558\) −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 \(-0.990141\pi\)
0.526580 + 0.850125i \(0.323474\pi\)
\(564\) −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 −0.246707 0.969090i \(-0.579349\pi\)
0.715903 + 0.698200i \(0.246015\pi\)
\(570\) 4.26602 + 4.26602i 0.178684 + 0.178684i
\(571\) 15.1053 8.72106i 0.632138 0.364965i −0.149442 0.988771i \(-0.547748\pi\)
0.781580 + 0.623805i \(0.214414\pi\)
\(572\) 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 \(-0.513742\pi\)
−0.536912 + 0.843639i \(0.680409\pi\)
\(578\) 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 −0.989392 0.145268i \(-0.953595\pi\)
0.784205 0.620502i \(-0.213071\pi\)
\(588\) 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 \(-0.566304\pi\)
0.310101 + 0.950704i \(0.399637\pi\)
\(594\) 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 −0.999969 0.00793343i \(-0.997475\pi\)
0.493114 0.869965i \(-0.335859\pi\)
\(600\) 1.17896 + 0.315903i 0.0481310 + 0.0128967i
\(601\) −15.2889 8.82708i −0.623649 0.360064i 0.154639 0.987971i \(-0.450578\pi\)
−0.778288 + 0.627907i \(0.783912\pi\)
\(602\) 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 −0.999998 0.00186450i \(-0.999407\pi\)
−0.00186450 0.999998i \(-0.500593\pi\)
\(614\) −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 −0.506879 0.862017i \(-0.669201\pi\)
0.869979 0.493089i \(-0.164132\pi\)
\(618\) −7.81429 + 7.81429i −0.314337 + 0.314337i
\(619\) 2.05655 7.67515i 0.0826597 0.308490i −0.912201 0.409743i \(-0.865618\pi\)
0.994861 + 0.101253i \(0.0322851\pi\)
\(620\) −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 0.954517 0.298155i \(-0.0963713\pi\)
0.677559 + 0.735469i \(0.263038\pi\)
\(632\) 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 0.807626 0.589695i \(-0.200752\pi\)
−0.106878 + 0.994272i \(0.534085\pi\)
\(642\) −3.61088 13.4760i −0.142510 0.531855i
\(643\) 20.9593 + 5.61604i 0.826556 + 0.221475i 0.647211 0.762311i \(-0.275935\pi\)
0.179345 + 0.983786i \(0.442602\pi\)
\(644\) 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 \(-0.220629\pi\)
0.769252 + 0.638945i \(0.220629\pi\)
\(648\) −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 0.995533 + 0.0944103i \(0.0300966\pi\)
−0.416005 + 0.909362i \(0.636570\pi\)
\(654\) −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 0.900263 0.435346i \(-0.143374\pi\)
−0.827153 + 0.561977i \(0.810041\pi\)
\(660\) 0.882106 0.509284i 0.0343359 0.0198239i
\(661\) −30.7260 30.7260i −1.19510 1.19510i −0.975615 0.219487i \(-0.929562\pi\)
−0.219487 0.975615i \(-0.570438\pi\)
\(662\) −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 0.875194 0.483771i \(-0.160733\pi\)
0.0186390 + 0.999826i \(0.494067\pi\)
\(674\) 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 \(-0.202001\pi\)
−0.110779 + 0.993845i \(0.535334\pi\)
\(678\) 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 0.914509 + 0.404567i \(0.132578\pi\)
−0.589704 + 0.807619i \(0.700756\pi\)
\(684\) 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 \(-0.0898586\pi\)
0.692464 + 0.721453i \(0.256525\pi\)
\(692\) 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 \(-0.738871\pi\)
0.681956 0.731393i \(-0.261129\pi\)
\(702\) −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 −0.196917 0.980420i \(-0.563093\pi\)
0.980420 + 0.196917i \(0.0630928\pi\)
\(710\) −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 \(-0.449562\pi\)
0.157795 + 0.987472i \(0.449562\pi\)
\(720\) −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 \(-0.519317\pi\)
−0.0606493 + 0.998159i \(0.519317\pi\)
\(728\) 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 \(-0.165397\pi\)
−0.999992 + 0.00399003i \(0.998730\pi\)
\(734\) 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 0.112109 0.993696i \(-0.464240\pi\)
0.993696 0.112109i \(-0.0357605\pi\)
\(740\) −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 −0.980482 0.196606i \(-0.937008\pi\)
−0.750820 + 0.660507i \(0.770341\pi\)
\(744\) 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 −0.306974 0.951718i \(-0.599316\pi\)
0.670725 + 0.741706i \(0.265983\pi\)
\(752\) −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 −0.981753 0.190163i \(-0.939098\pi\)
0.655562 + 0.755141i \(0.272432\pi\)
\(758\) 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 \(-0.185675\pi\)
−0.550794 + 0.834641i \(0.685675\pi\)
\(762\) 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 \(-0.0191780\pi\)
−0.894561 + 0.446947i \(0.852511\pi\)
\(770\) 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 \(-0.0674464\pi\)
−0.951811 + 0.306686i \(0.900780\pi\)
\(774\) −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