Properties

Label 882.2.l.a.509.6
Level $882$
Weight $2$
Character 882.509
Analytic conductor $7.043$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 882 = 2 \cdot 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 882.l (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(7.04280545828\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
Defining polynomial: \(x^{16} - 6 x^{14} + 9 x^{12} + 54 x^{10} - 288 x^{8} + 486 x^{6} + 729 x^{4} - 4374 x^{2} + 6561\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{2}\cdot 3^{2} \)
Twist minimal: no (minimal twist has level 126)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 509.6
Root \(-1.69547 - 0.354107i\) of defining polynomial
Character \(\chi\) \(=\) 882.509
Dual form 882.2.l.a.227.2

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000i q^{2} +(-0.541068 - 1.64537i) q^{3} -1.00000 q^{4} +(-0.895175 - 1.55049i) q^{5} +(1.64537 - 0.541068i) q^{6} -1.00000i q^{8} +(-2.41449 + 1.78052i) q^{9} +O(q^{10})\) \(q+1.00000i q^{2} +(-0.541068 - 1.64537i) q^{3} -1.00000 q^{4} +(-0.895175 - 1.55049i) q^{5} +(1.64537 - 0.541068i) q^{6} -1.00000i q^{8} +(-2.41449 + 1.78052i) q^{9} +(1.55049 - 0.895175i) q^{10} +(2.07976 + 1.20075i) q^{11} +(0.541068 + 1.64537i) q^{12} +(-4.23601 - 2.44566i) q^{13} +(-2.06678 + 2.31181i) q^{15} +1.00000 q^{16} +(-1.83233 - 3.17369i) q^{17} +(-1.78052 - 2.41449i) q^{18} +(2.61281 + 1.50851i) q^{19} +(0.895175 + 1.55049i) q^{20} +(-1.20075 + 2.07976i) q^{22} +(-3.26178 + 1.88319i) q^{23} +(-1.64537 + 0.541068i) q^{24} +(0.897324 - 1.55421i) q^{25} +(2.44566 - 4.23601i) q^{26} +(4.23601 + 3.00935i) q^{27} +(-5.68202 + 3.28052i) q^{29} +(-2.31181 - 2.06678i) q^{30} +4.64661i q^{31} +1.00000i q^{32} +(0.850388 - 4.07167i) q^{33} +(3.17369 - 1.83233i) q^{34} +(2.41449 - 1.78052i) q^{36} +(-4.68202 + 8.10950i) q^{37} +(-1.50851 + 2.61281i) q^{38} +(-1.73205 + 8.29308i) q^{39} +(-1.55049 + 0.895175i) q^{40} +(-4.04094 + 6.99911i) q^{41} +(-3.48127 - 6.02973i) q^{43} +(-2.07976 - 1.20075i) q^{44} +(4.92206 + 2.14977i) q^{45} +(-1.88319 - 3.26178i) q^{46} -5.13604 q^{47} +(-0.541068 - 1.64537i) q^{48} +(1.55421 + 0.897324i) q^{50} +(-4.23048 + 4.73205i) q^{51} +(4.23601 + 2.44566i) q^{52} +(-3.00935 + 4.23601i) q^{54} -4.29953i q^{55} +(1.06834 - 5.11524i) q^{57} +(-3.28052 - 5.68202i) q^{58} -14.5900 q^{59} +(2.06678 - 2.31181i) q^{60} +11.3283i q^{61} -4.64661 q^{62} -1.00000 q^{64} +8.75718i q^{65} +(4.07167 + 0.850388i) q^{66} +0.570231 q^{67} +(1.83233 + 3.17369i) q^{68} +(4.86340 + 4.34791i) q^{69} -5.96254i q^{71} +(1.78052 + 2.41449i) q^{72} +(10.7226 - 6.19070i) q^{73} +(-8.10950 - 4.68202i) q^{74} +(-3.04277 - 0.635497i) q^{75} +(-2.61281 - 1.50851i) q^{76} +(-8.29308 - 1.73205i) q^{78} +3.03663 q^{79} +(-0.895175 - 1.55049i) q^{80} +(2.65953 - 8.59808i) q^{81} +(-6.99911 - 4.04094i) q^{82} +(-7.00270 - 12.1290i) q^{83} +(-3.28052 + 5.68202i) q^{85} +(6.02973 - 3.48127i) q^{86} +(8.47203 + 7.57405i) q^{87} +(1.20075 - 2.07976i) q^{88} +(1.87432 - 3.24641i) q^{89} +(-2.14977 + 4.92206i) q^{90} +(3.26178 - 1.88319i) q^{92} +(7.64539 - 2.51413i) q^{93} -5.13604i q^{94} -5.40150i q^{95} +(1.64537 - 0.541068i) q^{96} +(4.77256 - 2.75544i) q^{97} +(-7.15953 + 0.803848i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q - 16 q^{4} - 12 q^{9} + O(q^{10}) \) \( 16 q - 16 q^{4} - 12 q^{9} + 12 q^{11} + 16 q^{16} + 12 q^{18} + 48 q^{23} - 8 q^{25} - 12 q^{29} + 12 q^{30} + 12 q^{36} + 4 q^{37} + 4 q^{43} - 12 q^{44} - 12 q^{46} + 60 q^{50} + 24 q^{51} + 48 q^{57} - 12 q^{58} - 16 q^{64} + 56 q^{67} - 12 q^{72} - 36 q^{74} - 24 q^{78} + 8 q^{79} - 12 q^{85} + 24 q^{86} - 48 q^{92} + 84 q^{93} - 72 q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/882\mathbb{Z}\right)^\times\).

\(n\) \(199\) \(785\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{5}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000i 0.707107i
\(3\) −0.541068 1.64537i −0.312386 0.949955i
\(4\) −1.00000 −0.500000
\(5\) −0.895175 1.55049i −0.400334 0.693399i 0.593432 0.804884i \(-0.297773\pi\)
−0.993766 + 0.111485i \(0.964439\pi\)
\(6\) 1.64537 0.541068i 0.671720 0.220890i
\(7\) 0 0
\(8\) 1.00000i 0.353553i
\(9\) −2.41449 + 1.78052i −0.804830 + 0.593505i
\(10\) 1.55049 0.895175i 0.490307 0.283079i
\(11\) 2.07976 + 1.20075i 0.627072 + 0.362040i 0.779617 0.626256i \(-0.215414\pi\)
−0.152545 + 0.988297i \(0.548747\pi\)
\(12\) 0.541068 + 1.64537i 0.156193 + 0.474978i
\(13\) −4.23601 2.44566i −1.17486 0.678305i −0.220039 0.975491i \(-0.570618\pi\)
−0.954820 + 0.297186i \(0.903952\pi\)
\(14\) 0 0
\(15\) −2.06678 + 2.31181i −0.533640 + 0.596908i
\(16\) 1.00000 0.250000
\(17\) −1.83233 3.17369i −0.444406 0.769734i 0.553605 0.832780i \(-0.313252\pi\)
−0.998011 + 0.0630460i \(0.979919\pi\)
\(18\) −1.78052 2.41449i −0.419672 0.569101i
\(19\) 2.61281 + 1.50851i 0.599419 + 0.346075i 0.768813 0.639474i \(-0.220848\pi\)
−0.169394 + 0.985548i \(0.554181\pi\)
\(20\) 0.895175 + 1.55049i 0.200167 + 0.346700i
\(21\) 0 0
\(22\) −1.20075 + 2.07976i −0.256001 + 0.443407i
\(23\) −3.26178 + 1.88319i −0.680129 + 0.392673i −0.799904 0.600128i \(-0.795116\pi\)
0.119775 + 0.992801i \(0.461783\pi\)
\(24\) −1.64537 + 0.541068i −0.335860 + 0.110445i
\(25\) 0.897324 1.55421i 0.179465 0.310842i
\(26\) 2.44566 4.23601i 0.479634 0.830750i
\(27\) 4.23601 + 3.00935i 0.815221 + 0.579150i
\(28\) 0 0
\(29\) −5.68202 + 3.28052i −1.05512 + 0.609176i −0.924080 0.382200i \(-0.875167\pi\)
−0.131045 + 0.991376i \(0.541833\pi\)
\(30\) −2.31181 2.06678i −0.422078 0.377340i
\(31\) 4.64661i 0.834556i 0.908779 + 0.417278i \(0.137016\pi\)
−0.908779 + 0.417278i \(0.862984\pi\)
\(32\) 1.00000i 0.176777i
\(33\) 0.850388 4.07167i 0.148034 0.708787i
\(34\) 3.17369 1.83233i 0.544284 0.314242i
\(35\) 0 0
\(36\) 2.41449 1.78052i 0.402415 0.296753i
\(37\) −4.68202 + 8.10950i −0.769719 + 1.33319i 0.167996 + 0.985788i \(0.446271\pi\)
−0.937715 + 0.347405i \(0.887063\pi\)
\(38\) −1.50851 + 2.61281i −0.244712 + 0.423853i
\(39\) −1.73205 + 8.29308i −0.277350 + 1.32796i
\(40\) −1.55049 + 0.895175i −0.245154 + 0.141540i
\(41\) −4.04094 + 6.99911i −0.631088 + 1.09308i 0.356241 + 0.934394i \(0.384058\pi\)
−0.987330 + 0.158683i \(0.949275\pi\)
\(42\) 0 0
\(43\) −3.48127 6.02973i −0.530888 0.919526i −0.999350 0.0360419i \(-0.988525\pi\)
0.468462 0.883484i \(-0.344808\pi\)
\(44\) −2.07976 1.20075i −0.313536 0.181020i
\(45\) 4.92206 + 2.14977i 0.733737 + 0.320468i
\(46\) −1.88319 3.26178i −0.277661 0.480924i
\(47\) −5.13604 −0.749169 −0.374584 0.927193i \(-0.622215\pi\)
−0.374584 + 0.927193i \(0.622215\pi\)
\(48\) −0.541068 1.64537i −0.0780965 0.237489i
\(49\) 0 0
\(50\) 1.55421 + 0.897324i 0.219799 + 0.126901i
\(51\) −4.23048 + 4.73205i −0.592386 + 0.662620i
\(52\) 4.23601 + 2.44566i 0.587429 + 0.339152i
\(53\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(54\) −3.00935 + 4.23601i −0.409521 + 0.576448i
\(55\) 4.29953i 0.579749i
\(56\) 0 0
\(57\) 1.06834 5.11524i 0.141506 0.677530i
\(58\) −3.28052 5.68202i −0.430753 0.746086i
\(59\) −14.5900 −1.89946 −0.949729 0.313073i \(-0.898641\pi\)
−0.949729 + 0.313073i \(0.898641\pi\)
\(60\) 2.06678 2.31181i 0.266820 0.298454i
\(61\) 11.3283i 1.45044i 0.688518 + 0.725219i \(0.258262\pi\)
−0.688518 + 0.725219i \(0.741738\pi\)
\(62\) −4.64661 −0.590120
\(63\) 0 0
\(64\) −1.00000 −0.125000
\(65\) 8.75718i 1.08619i
\(66\) 4.07167 + 0.850388i 0.501188 + 0.104676i
\(67\) 0.570231 0.0696648 0.0348324 0.999393i \(-0.488910\pi\)
0.0348324 + 0.999393i \(0.488910\pi\)
\(68\) 1.83233 + 3.17369i 0.222203 + 0.384867i
\(69\) 4.86340 + 4.34791i 0.585484 + 0.523427i
\(70\) 0 0
\(71\) 5.96254i 0.707623i −0.935317 0.353811i \(-0.884885\pi\)
0.935317 0.353811i \(-0.115115\pi\)
\(72\) 1.78052 + 2.41449i 0.209836 + 0.284550i
\(73\) 10.7226 6.19070i 1.25499 0.724567i 0.282891 0.959152i \(-0.408706\pi\)
0.972096 + 0.234585i \(0.0753731\pi\)
\(74\) −8.10950 4.68202i −0.942710 0.544274i
\(75\) −3.04277 0.635497i −0.351348 0.0733808i
\(76\) −2.61281 1.50851i −0.299710 0.173037i
\(77\) 0 0
\(78\) −8.29308 1.73205i −0.939007 0.196116i
\(79\) 3.03663 0.341647 0.170824 0.985302i \(-0.445357\pi\)
0.170824 + 0.985302i \(0.445357\pi\)
\(80\) −0.895175 1.55049i −0.100084 0.173350i
\(81\) 2.65953 8.59808i 0.295503 0.955342i
\(82\) −6.99911 4.04094i −0.772922 0.446247i
\(83\) −7.00270 12.1290i −0.768646 1.33133i −0.938297 0.345830i \(-0.887597\pi\)
0.169651 0.985504i \(-0.445736\pi\)
\(84\) 0 0
\(85\) −3.28052 + 5.68202i −0.355822 + 0.616302i
\(86\) 6.02973 3.48127i 0.650203 0.375395i
\(87\) 8.47203 + 7.57405i 0.908296 + 0.812023i
\(88\) 1.20075 2.07976i 0.128001 0.221704i
\(89\) 1.87432 3.24641i 0.198677 0.344119i −0.749423 0.662092i \(-0.769669\pi\)
0.948100 + 0.317973i \(0.103002\pi\)
\(90\) −2.14977 + 4.92206i −0.226605 + 0.518831i
\(91\) 0 0
\(92\) 3.26178 1.88319i 0.340064 0.196336i
\(93\) 7.64539 2.51413i 0.792791 0.260703i
\(94\) 5.13604i 0.529742i
\(95\) 5.40150i 0.554183i
\(96\) 1.64537 0.541068i 0.167930 0.0552225i
\(97\) 4.77256 2.75544i 0.484580 0.279772i −0.237743 0.971328i \(-0.576408\pi\)
0.722323 + 0.691556i \(0.243074\pi\)
\(98\) 0 0
\(99\) −7.15953 + 0.803848i −0.719560 + 0.0807897i
\(100\) −0.897324 + 1.55421i −0.0897324 + 0.155421i
\(101\) −0.125162 + 0.216787i −0.0124541 + 0.0215711i −0.872185 0.489176i \(-0.837298\pi\)
0.859731 + 0.510747i \(0.170631\pi\)
\(102\) −4.73205 4.23048i −0.468543 0.418880i
\(103\) −0.145433 + 0.0839657i −0.0143299 + 0.00827339i −0.507148 0.861859i \(-0.669300\pi\)
0.492818 + 0.870132i \(0.335967\pi\)
\(104\) −2.44566 + 4.23601i −0.239817 + 0.415375i
\(105\) 0 0
\(106\) 0 0
\(107\) −6.92024 3.99540i −0.669004 0.386250i 0.126695 0.991942i \(-0.459563\pi\)
−0.795699 + 0.605692i \(0.792896\pi\)
\(108\) −4.23601 3.00935i −0.407611 0.289575i
\(109\) 9.47667 + 16.4141i 0.907700 + 1.57218i 0.817251 + 0.576282i \(0.195497\pi\)
0.0904491 + 0.995901i \(0.471170\pi\)
\(110\) 4.29953 0.409944
\(111\) 15.8764 + 3.31587i 1.50692 + 0.314728i
\(112\) 0 0
\(113\) −1.00418 0.579764i −0.0944653 0.0545396i 0.452023 0.892006i \(-0.350702\pi\)
−0.546488 + 0.837467i \(0.684036\pi\)
\(114\) 5.11524 + 1.06834i 0.479086 + 0.100060i
\(115\) 5.83973 + 3.37157i 0.544558 + 0.314401i
\(116\) 5.68202 3.28052i 0.527562 0.304588i
\(117\) 14.5824 1.63726i 1.34814 0.151365i
\(118\) 14.5900i 1.34312i
\(119\) 0 0
\(120\) 2.31181 + 2.06678i 0.211039 + 0.188670i
\(121\) −2.61639 4.53172i −0.237854 0.411974i
\(122\) −11.3283 −1.02561
\(123\) 13.7026 + 2.86185i 1.23552 + 0.258044i
\(124\) 4.64661i 0.417278i
\(125\) −12.1648 −1.08805
\(126\) 0 0
\(127\) 1.40150 0.124363 0.0621817 0.998065i \(-0.480194\pi\)
0.0621817 + 0.998065i \(0.480194\pi\)
\(128\) 1.00000i 0.0883883i
\(129\) −8.03754 + 8.99047i −0.707666 + 0.791567i
\(130\) −8.75718 −0.768056
\(131\) −5.24589 9.08614i −0.458335 0.793860i 0.540538 0.841320i \(-0.318221\pi\)
−0.998873 + 0.0474597i \(0.984887\pi\)
\(132\) −0.850388 + 4.07167i −0.0740168 + 0.354393i
\(133\) 0 0
\(134\) 0.570231i 0.0492604i
\(135\) 0.873992 9.26178i 0.0752213 0.797127i
\(136\) −3.17369 + 1.83233i −0.272142 + 0.157121i
\(137\) 4.08812 + 2.36028i 0.349272 + 0.201652i 0.664365 0.747409i \(-0.268702\pi\)
−0.315093 + 0.949061i \(0.602036\pi\)
\(138\) −4.34791 + 4.86340i −0.370119 + 0.414000i
\(139\) −2.04707 1.18187i −0.173630 0.100245i 0.410666 0.911786i \(-0.365296\pi\)
−0.584296 + 0.811540i \(0.698629\pi\)
\(140\) 0 0
\(141\) 2.77895 + 8.45070i 0.234030 + 0.711677i
\(142\) 5.96254 0.500365
\(143\) −5.87327 10.1728i −0.491148 0.850692i
\(144\) −2.41449 + 1.78052i −0.201208 + 0.148376i
\(145\) 10.1728 + 5.87327i 0.844805 + 0.487749i
\(146\) 6.19070 + 10.7226i 0.512346 + 0.887410i
\(147\) 0 0
\(148\) 4.68202 8.10950i 0.384860 0.666597i
\(149\) 15.0377 8.68202i 1.23194 0.711259i 0.264503 0.964385i \(-0.414792\pi\)
0.967433 + 0.253126i \(0.0814587\pi\)
\(150\) 0.635497 3.04277i 0.0518881 0.248441i
\(151\) 5.61639 9.72787i 0.457055 0.791643i −0.541749 0.840541i \(-0.682238\pi\)
0.998804 + 0.0488977i \(0.0155708\pi\)
\(152\) 1.50851 2.61281i 0.122356 0.211927i
\(153\) 10.0750 + 4.40035i 0.814512 + 0.355748i
\(154\) 0 0
\(155\) 7.20451 4.15953i 0.578680 0.334101i
\(156\) 1.73205 8.29308i 0.138675 0.663978i
\(157\) 13.8431i 1.10480i −0.833580 0.552399i \(-0.813713\pi\)
0.833580 0.552399i \(-0.186287\pi\)
\(158\) 3.03663i 0.241581i
\(159\) 0 0
\(160\) 1.55049 0.895175i 0.122577 0.0707698i
\(161\) 0 0
\(162\) 8.59808 + 2.65953i 0.675529 + 0.208952i
\(163\) 2.16789 3.75489i 0.169802 0.294106i −0.768548 0.639792i \(-0.779020\pi\)
0.938350 + 0.345686i \(0.112354\pi\)
\(164\) 4.04094 6.99911i 0.315544 0.546539i
\(165\) −7.07432 + 2.32634i −0.550735 + 0.181105i
\(166\) 12.1290 7.00270i 0.941395 0.543515i
\(167\) −6.20756 + 10.7518i −0.480355 + 0.832000i −0.999746 0.0225370i \(-0.992826\pi\)
0.519391 + 0.854537i \(0.326159\pi\)
\(168\) 0 0
\(169\) 5.46254 + 9.46139i 0.420195 + 0.727799i
\(170\) −5.68202 3.28052i −0.435791 0.251604i
\(171\) −8.99452 + 1.00987i −0.687828 + 0.0772270i
\(172\) 3.48127 + 6.02973i 0.265444 + 0.459763i
\(173\) −17.4182 −1.32428 −0.662139 0.749381i \(-0.730351\pi\)
−0.662139 + 0.749381i \(0.730351\pi\)
\(174\) −7.57405 + 8.47203i −0.574187 + 0.642263i
\(175\) 0 0
\(176\) 2.07976 + 1.20075i 0.156768 + 0.0905101i
\(177\) 7.89419 + 24.0060i 0.593364 + 1.80440i
\(178\) 3.24641 + 1.87432i 0.243329 + 0.140486i
\(179\) −11.3640 + 6.56103i −0.849388 + 0.490395i −0.860444 0.509544i \(-0.829814\pi\)
0.0110562 + 0.999939i \(0.496481\pi\)
\(180\) −4.92206 2.14977i −0.366869 0.160234i
\(181\) 13.3577i 0.992873i −0.868073 0.496437i \(-0.834641\pi\)
0.868073 0.496437i \(-0.165359\pi\)
\(182\) 0 0
\(183\) 18.6392 6.12937i 1.37785 0.453096i
\(184\) 1.88319 + 3.26178i 0.138831 + 0.240462i
\(185\) 16.7649 1.23258
\(186\) 2.51413 + 7.64539i 0.184345 + 0.560588i
\(187\) 8.80071i 0.643572i
\(188\) 5.13604 0.374584
\(189\) 0 0
\(190\) 5.40150 0.391866
\(191\) 9.25333i 0.669547i −0.942299 0.334774i \(-0.891340\pi\)
0.942299 0.334774i \(-0.108660\pi\)
\(192\) 0.541068 + 1.64537i 0.0390482 + 0.118744i
\(193\) −24.5602 −1.76788 −0.883941 0.467599i \(-0.845119\pi\)
−0.883941 + 0.467599i \(0.845119\pi\)
\(194\) 2.75544 + 4.77256i 0.197829 + 0.342650i
\(195\) 14.4088 4.73823i 1.03184 0.339312i
\(196\) 0 0
\(197\) 12.4861i 0.889598i 0.895630 + 0.444799i \(0.146725\pi\)
−0.895630 + 0.444799i \(0.853275\pi\)
\(198\) −0.803848 7.15953i −0.0571270 0.508805i
\(199\) −0.155144 + 0.0895727i −0.0109979 + 0.00634964i −0.505489 0.862833i \(-0.668688\pi\)
0.494491 + 0.869183i \(0.335355\pi\)
\(200\) −1.55421 0.897324i −0.109899 0.0634504i
\(201\) −0.308534 0.938241i −0.0217623 0.0661784i
\(202\) −0.216787 0.125162i −0.0152531 0.00880637i
\(203\) 0 0
\(204\) 4.23048 4.73205i 0.296193 0.331310i
\(205\) 14.4694 1.01059
\(206\) −0.0839657 0.145433i −0.00585017 0.0101328i
\(207\) 4.52249 10.3546i 0.314335 0.719695i
\(208\) −4.23601 2.44566i −0.293715 0.169576i
\(209\) 3.62268 + 6.27467i 0.250586 + 0.434028i
\(210\) 0 0
\(211\) 7.56103 13.0961i 0.520523 0.901572i −0.479192 0.877710i \(-0.659070\pi\)
0.999715 0.0238622i \(-0.00759629\pi\)
\(212\) 0 0
\(213\) −9.81058 + 3.22614i −0.672210 + 0.221051i
\(214\) 3.99540 6.92024i 0.273120 0.473058i
\(215\) −6.23269 + 10.7953i −0.425066 + 0.736235i
\(216\) 3.00935 4.23601i 0.204760 0.288224i
\(217\) 0 0
\(218\) −16.4141 + 9.47667i −1.11170 + 0.641841i
\(219\) −15.9877 14.2931i −1.08035 0.965837i
\(220\) 4.29953i 0.289874i
\(221\) 17.9251i 1.20577i
\(222\) −3.31587 + 15.8764i −0.222547 + 1.06556i
\(223\) −7.27049 + 4.19762i −0.486868 + 0.281093i −0.723274 0.690561i \(-0.757364\pi\)
0.236406 + 0.971654i \(0.424030\pi\)
\(224\) 0 0
\(225\) 0.600717 + 5.35033i 0.0400478 + 0.356688i
\(226\) 0.579764 1.00418i 0.0385653 0.0667971i
\(227\) 1.21261 2.10030i 0.0804836 0.139402i −0.822974 0.568079i \(-0.807687\pi\)
0.903458 + 0.428677i \(0.141020\pi\)
\(228\) −1.06834 + 5.11524i −0.0707528 + 0.338765i
\(229\) −1.74915 + 1.00987i −0.115587 + 0.0667344i −0.556679 0.830728i \(-0.687925\pi\)
0.441092 + 0.897462i \(0.354591\pi\)
\(230\) −3.37157 + 5.83973i −0.222315 + 0.385061i
\(231\) 0 0
\(232\) 3.28052 + 5.68202i 0.215376 + 0.373043i
\(233\) 11.0236 + 6.36446i 0.722178 + 0.416950i 0.815554 0.578681i \(-0.196432\pi\)
−0.0933759 + 0.995631i \(0.529766\pi\)
\(234\) 1.63726 + 14.5824i 0.107031 + 0.953278i
\(235\) 4.59766 + 7.96337i 0.299918 + 0.519473i
\(236\) 14.5900 0.949729
\(237\) −1.64302 4.99637i −0.106726 0.324549i
\(238\) 0 0
\(239\) 15.1117 + 8.72474i 0.977494 + 0.564356i 0.901513 0.432753i \(-0.142458\pi\)
0.0759814 + 0.997109i \(0.475791\pi\)
\(240\) −2.06678 + 2.31181i −0.133410 + 0.149227i
\(241\) −9.90142 5.71659i −0.637807 0.368238i 0.145963 0.989290i \(-0.453372\pi\)
−0.783769 + 0.621052i \(0.786705\pi\)
\(242\) 4.53172 2.61639i 0.291310 0.168188i
\(243\) −15.5860 + 0.276237i −0.999843 + 0.0177206i
\(244\) 11.3283i 0.725219i
\(245\) 0 0
\(246\) −2.86185 + 13.7026i −0.182465 + 0.873643i
\(247\) −7.37859 12.7801i −0.469489 0.813178i
\(248\) 4.64661 0.295060
\(249\) −16.1678 + 18.0847i −1.02459 + 1.14607i
\(250\) 12.1648i 0.769369i
\(251\) −27.3560 −1.72669 −0.863347 0.504611i \(-0.831636\pi\)
−0.863347 + 0.504611i \(0.831636\pi\)
\(252\) 0 0
\(253\) −9.04499 −0.568653
\(254\) 1.40150i 0.0879382i
\(255\) 11.1240 + 2.32330i 0.696613 + 0.145491i
\(256\) 1.00000 0.0625000
\(257\) 1.74837 + 3.02826i 0.109060 + 0.188898i 0.915390 0.402569i \(-0.131883\pi\)
−0.806330 + 0.591466i \(0.798549\pi\)
\(258\) −8.99047 8.03754i −0.559722 0.500396i
\(259\) 0 0
\(260\) 8.75718i 0.543097i
\(261\) 7.87817 18.0377i 0.487647 1.11651i
\(262\) 9.08614 5.24589i 0.561344 0.324092i
\(263\) 8.35150 + 4.82174i 0.514976 + 0.297321i 0.734877 0.678201i \(-0.237240\pi\)
−0.219901 + 0.975522i \(0.570573\pi\)
\(264\) −4.07167 0.850388i −0.250594 0.0523378i
\(265\) 0 0
\(266\) 0 0
\(267\) −6.35568 1.32741i −0.388961 0.0812365i
\(268\) −0.570231 −0.0348324
\(269\) 3.45554 + 5.98517i 0.210688 + 0.364922i 0.951930 0.306316i \(-0.0990963\pi\)
−0.741242 + 0.671238i \(0.765763\pi\)
\(270\) 9.26178 + 0.873992i 0.563654 + 0.0531895i
\(271\) 17.8672 + 10.3156i 1.08535 + 0.626629i 0.932335 0.361595i \(-0.117768\pi\)
0.153017 + 0.988224i \(0.451101\pi\)
\(272\) −1.83233 3.17369i −0.111101 0.192433i
\(273\) 0 0
\(274\) −2.36028 + 4.08812i −0.142590 + 0.246973i
\(275\) 3.73244 2.15493i 0.225075 0.129947i
\(276\) −4.86340 4.34791i −0.292742 0.261713i
\(277\) 7.75718 13.4358i 0.466084 0.807281i −0.533166 0.846011i \(-0.678998\pi\)
0.999250 + 0.0387296i \(0.0123311\pi\)
\(278\) 1.18187 2.04707i 0.0708841 0.122775i
\(279\) −8.27336 11.2192i −0.495313 0.671675i
\(280\) 0 0
\(281\) 11.7759 6.79883i 0.702492 0.405584i −0.105783 0.994389i \(-0.533735\pi\)
0.808275 + 0.588805i \(0.200401\pi\)
\(282\) −8.45070 + 2.77895i −0.503232 + 0.165484i
\(283\) 5.44783i 0.323840i 0.986804 + 0.161920i \(0.0517687\pi\)
−0.986804 + 0.161920i \(0.948231\pi\)
\(284\) 5.96254i 0.353811i
\(285\) −8.88748 + 2.92258i −0.526449 + 0.173119i
\(286\) 10.1728 5.87327i 0.601530 0.347294i
\(287\) 0 0
\(288\) −1.78052 2.41449i −0.104918 0.142275i
\(289\) 1.78512 3.09191i 0.105007 0.181877i
\(290\) −5.87327 + 10.1728i −0.344890 + 0.597368i
\(291\) −7.11600 6.36175i −0.417147 0.372932i
\(292\) −10.7226 + 6.19070i −0.627493 + 0.362284i
\(293\) 12.2311 21.1849i 0.714550 1.23764i −0.248583 0.968610i \(-0.579965\pi\)
0.963133 0.269026i \(-0.0867017\pi\)
\(294\) 0 0
\(295\) 13.0606 + 22.6216i 0.760418 + 1.31708i
\(296\) 8.10950 + 4.68202i 0.471355 + 0.272137i
\(297\) 5.19642 + 11.3451i 0.301527 + 0.658312i
\(298\) 8.68202 + 15.0377i 0.502936 + 0.871111i
\(299\) 18.4226 1.06541
\(300\) 3.04277 + 0.635497i 0.175674 + 0.0366904i
\(301\) 0 0
\(302\) 9.72787 + 5.61639i 0.559776 + 0.323187i
\(303\) 0.424416 + 0.0886415i 0.0243821 + 0.00509232i
\(304\) 2.61281 + 1.50851i 0.149855 + 0.0865187i
\(305\) 17.5644 10.1408i 1.00573 0.580660i
\(306\) −4.40035 + 10.0750i −0.251552 + 0.575947i
\(307\) 31.2223i 1.78195i 0.454053 + 0.890975i \(0.349978\pi\)
−0.454053 + 0.890975i \(0.650022\pi\)
\(308\) 0 0
\(309\) 0.216844 + 0.193860i 0.0123358 + 0.0110283i
\(310\) 4.15953 + 7.20451i 0.236245 + 0.409189i
\(311\) 10.9100 0.618651 0.309325 0.950956i \(-0.399897\pi\)
0.309325 + 0.950956i \(0.399897\pi\)
\(312\) 8.29308 + 1.73205i 0.469503 + 0.0980581i
\(313\) 3.42405i 0.193539i 0.995307 + 0.0967694i \(0.0308509\pi\)
−0.995307 + 0.0967694i \(0.969149\pi\)
\(314\) 13.8431 0.781210
\(315\) 0 0
\(316\) −3.03663 −0.170824
\(317\) 19.0471i 1.06979i 0.844917 + 0.534897i \(0.179650\pi\)
−0.844917 + 0.534897i \(0.820350\pi\)
\(318\) 0 0
\(319\) −15.7563 −0.882186
\(320\) 0.895175 + 1.55049i 0.0500418 + 0.0866749i
\(321\) −2.82960 + 13.5481i −0.157933 + 0.756183i
\(322\) 0 0
\(323\) 11.0563i 0.615191i
\(324\) −2.65953 + 8.59808i −0.147752 + 0.477671i
\(325\) −7.60215 + 4.38910i −0.421692 + 0.243464i
\(326\) 3.75489 + 2.16789i 0.207964 + 0.120068i
\(327\) 21.8797 24.4738i 1.20995 1.35340i
\(328\) 6.99911 + 4.04094i 0.386461 + 0.223123i
\(329\) 0 0
\(330\) −2.32634 7.07432i −0.128061 0.389429i
\(331\) 0.0732502 0.00402620 0.00201310 0.999998i \(-0.499359\pi\)
0.00201310 + 0.999998i \(0.499359\pi\)
\(332\) 7.00270 + 12.1290i 0.384323 + 0.665667i
\(333\) −3.13439 27.9167i −0.171764 1.52983i
\(334\) −10.7518 6.20756i −0.588313 0.339663i
\(335\) −0.510456 0.884136i −0.0278892 0.0483055i
\(336\) 0 0
\(337\) 1.11639 1.93364i 0.0608136 0.105332i −0.834016 0.551741i \(-0.813964\pi\)
0.894829 + 0.446408i \(0.147297\pi\)
\(338\) −9.46139 + 5.46254i −0.514632 + 0.297123i
\(339\) −0.410596 + 1.96594i −0.0223005 + 0.106775i
\(340\) 3.28052 5.68202i 0.177911 0.308151i
\(341\) −5.57943 + 9.66385i −0.302143 + 0.523327i
\(342\) −1.00987 8.99452i −0.0546077 0.486368i
\(343\) 0 0
\(344\) −6.02973 + 3.48127i −0.325101 + 0.187697i
\(345\) 2.38779 11.4328i 0.128554 0.615520i
\(346\) 17.4182i 0.936406i
\(347\) 31.8409i 1.70931i −0.519195 0.854656i \(-0.673768\pi\)
0.519195 0.854656i \(-0.326232\pi\)
\(348\) −8.47203 7.57405i −0.454148 0.406012i
\(349\) −12.7613 + 7.36772i −0.683095 + 0.394385i −0.801020 0.598637i \(-0.795709\pi\)
0.117925 + 0.993022i \(0.462376\pi\)
\(350\) 0 0
\(351\) −10.5839 23.1075i −0.564929 1.23339i
\(352\) −1.20075 + 2.07976i −0.0640003 + 0.110852i
\(353\) −1.07979 + 1.87025i −0.0574713 + 0.0995431i −0.893330 0.449402i \(-0.851637\pi\)
0.835858 + 0.548945i \(0.184970\pi\)
\(354\) −24.0060 + 7.89419i −1.27590 + 0.419572i
\(355\) −9.24484 + 5.33751i −0.490665 + 0.283286i
\(356\) −1.87432 + 3.24641i −0.0993385 + 0.172059i
\(357\) 0 0
\(358\) −6.56103 11.3640i −0.346761 0.600608i
\(359\) −28.2712 16.3224i −1.49210 0.861463i −0.492139 0.870517i \(-0.663785\pi\)
−0.999959 + 0.00905364i \(0.997118\pi\)
\(360\) 2.14977 4.92206i 0.113303 0.259415i
\(361\) −4.94882 8.57161i −0.260464 0.451138i
\(362\) 13.3577 0.702067
\(363\) −6.04071 + 6.75690i −0.317055 + 0.354645i
\(364\) 0 0
\(365\) −19.1972 11.0835i −1.00483 0.580138i
\(366\) 6.12937 + 18.6392i 0.320388 + 0.974288i
\(367\) −25.7212 14.8501i −1.34264 0.775171i −0.355442 0.934698i \(-0.615670\pi\)
−0.987194 + 0.159527i \(0.949003\pi\)
\(368\) −3.26178 + 1.88319i −0.170032 + 0.0981682i
\(369\) −2.70522 24.0942i −0.140828 1.25430i
\(370\) 16.7649i 0.871566i
\(371\) 0 0
\(372\) −7.64539 + 2.51413i −0.396395 + 0.130352i
\(373\) 1.00836 + 1.74653i 0.0522109 + 0.0904320i 0.890950 0.454102i \(-0.150040\pi\)
−0.838739 + 0.544534i \(0.816707\pi\)
\(374\) 8.80071 0.455074
\(375\) 6.58198 + 20.0156i 0.339892 + 1.03360i
\(376\) 5.13604i 0.264871i
\(377\) 32.0921 1.65283
\(378\) 0 0
\(379\) −18.8709 −0.969332 −0.484666 0.874699i \(-0.661059\pi\)
−0.484666 + 0.874699i \(0.661059\pi\)
\(380\) 5.40150i 0.277091i
\(381\) −0.758309 2.30599i −0.0388494 0.118140i
\(382\) 9.25333 0.473441
\(383\) −0.418256 0.724440i −0.0213719 0.0370172i 0.855142 0.518394i \(-0.173470\pi\)
−0.876514 + 0.481377i \(0.840137\pi\)
\(384\) −1.64537 + 0.541068i −0.0839650 + 0.0276113i
\(385\) 0 0
\(386\) 24.5602i 1.25008i
\(387\) 19.1415 + 8.36028i 0.973018 + 0.424977i
\(388\) −4.77256 + 2.75544i −0.242290 + 0.139886i
\(389\) −21.4964 12.4109i −1.08991 0.629260i −0.156357 0.987701i \(-0.549975\pi\)
−0.933552 + 0.358441i \(0.883308\pi\)
\(390\) 4.73823 + 14.4088i 0.239930 + 0.729619i
\(391\) 11.9533 + 6.90127i 0.604507 + 0.349012i
\(392\) 0 0
\(393\) −12.1117 + 13.5477i −0.610954 + 0.683389i
\(394\) −12.4861 −0.629041
\(395\) −2.71831 4.70825i −0.136773 0.236898i
\(396\) 7.15953 0.803848i 0.359780 0.0403949i
\(397\) −2.62744 1.51695i −0.131867 0.0761336i 0.432615 0.901579i \(-0.357591\pi\)
−0.564482 + 0.825445i \(0.690924\pi\)
\(398\) −0.0895727 0.155144i −0.00448987 0.00777669i
\(399\) 0 0
\(400\) 0.897324 1.55421i 0.0448662 0.0777105i
\(401\) −11.3251 + 6.53854i −0.565548 + 0.326519i −0.755369 0.655300i \(-0.772542\pi\)
0.189822 + 0.981819i \(0.439209\pi\)
\(402\) 0.938241 0.308534i 0.0467952 0.0153883i
\(403\) 11.3640 19.6831i 0.566083 0.980485i
\(404\) 0.125162 0.216787i 0.00622705 0.0107856i
\(405\) −15.7120 + 3.57322i −0.780733 + 0.177555i
\(406\) 0 0
\(407\) −19.4750 + 11.2439i −0.965339 + 0.557339i
\(408\) 4.73205 + 4.23048i 0.234271 + 0.209440i
\(409\) 5.56709i 0.275275i −0.990483 0.137637i \(-0.956049\pi\)
0.990483 0.137637i \(-0.0439508\pi\)
\(410\) 14.4694i 0.714592i
\(411\) 1.67158 8.00355i 0.0824530 0.394786i
\(412\) 0.145433 0.0839657i 0.00716496 0.00413669i
\(413\) 0 0
\(414\) 10.3546 + 4.52249i 0.508901 + 0.222268i
\(415\) −12.5373 + 21.7152i −0.615431 + 1.06596i
\(416\) 2.44566 4.23601i 0.119908 0.207688i
\(417\) −0.837019 + 4.00766i −0.0409890 + 0.196256i
\(418\) −6.27467 + 3.62268i −0.306904 + 0.177191i
\(419\) 8.19938 14.2017i 0.400566 0.693800i −0.593228 0.805034i \(-0.702147\pi\)
0.993794 + 0.111234i \(0.0354802\pi\)
\(420\) 0 0
\(421\) −7.72892 13.3869i −0.376684 0.652437i 0.613893 0.789389i \(-0.289603\pi\)
−0.990578 + 0.136952i \(0.956269\pi\)
\(422\) 13.0961 + 7.56103i 0.637508 + 0.368065i
\(423\) 12.4009 9.14481i 0.602954 0.444636i
\(424\) 0 0
\(425\) −6.57678 −0.319021
\(426\) −3.22614 9.81058i −0.156307 0.475324i
\(427\) 0 0
\(428\) 6.92024 + 3.99540i 0.334502 + 0.193125i
\(429\) −13.5602 + 15.1679i −0.654692 + 0.732313i
\(430\) −10.7953 6.23269i −0.520597 0.300567i
\(431\) −21.6737 + 12.5133i −1.04398 + 0.602744i −0.920959 0.389660i \(-0.872593\pi\)
−0.123024 + 0.992404i \(0.539259\pi\)
\(432\) 4.23601 + 3.00935i 0.203805 + 0.144787i
\(433\) 2.25168i 0.108209i 0.998535 + 0.0541044i \(0.0172304\pi\)
−0.998535 + 0.0541044i \(0.982770\pi\)
\(434\) 0 0
\(435\) 4.15953 19.9159i 0.199434 0.954893i
\(436\) −9.47667 16.4141i −0.453850 0.786091i
\(437\) −11.3632 −0.543576
\(438\) 14.2931 15.9877i 0.682950 0.763920i
\(439\) 18.7400i 0.894412i 0.894431 + 0.447206i \(0.147581\pi\)
−0.894431 + 0.447206i \(0.852419\pi\)
\(440\) −4.29953 −0.204972
\(441\) 0 0
\(442\) −17.9251 −0.852609
\(443\) 1.20451i 0.0572281i −0.999591 0.0286141i \(-0.990891\pi\)
0.999591 0.0286141i \(-0.00910938\pi\)
\(444\) −15.8764 3.31587i −0.753462 0.157364i
\(445\) −6.71136 −0.318149
\(446\) −4.19762 7.27049i −0.198763 0.344268i
\(447\) −22.4216 20.0450i −1.06050 0.948097i
\(448\) 0 0
\(449\) 26.8022i 1.26487i 0.774612 + 0.632436i \(0.217945\pi\)
−0.774612 + 0.632436i \(0.782055\pi\)
\(450\) −5.35033 + 0.600717i −0.252217 + 0.0283181i
\(451\) −16.8084 + 9.70433i −0.791476 + 0.456959i
\(452\) 1.00418 + 0.579764i 0.0472327 + 0.0272698i
\(453\) −19.0448 3.97760i −0.894803 0.186884i
\(454\) 2.10030 + 1.21261i 0.0985719 + 0.0569105i
\(455\) 0 0
\(456\) −5.11524 1.06834i −0.239543 0.0500298i
\(457\) 13.8488 0.647821 0.323911 0.946088i \(-0.395002\pi\)
0.323911 + 0.946088i \(0.395002\pi\)
\(458\) −1.00987 1.74915i −0.0471883 0.0817326i
\(459\) 1.78897 18.9579i 0.0835022 0.884881i
\(460\) −5.83973 3.37157i −0.272279 0.157200i
\(461\) 2.40241 + 4.16110i 0.111892 + 0.193802i 0.916533 0.399959i \(-0.130976\pi\)
−0.804641 + 0.593761i \(0.797642\pi\)
\(462\) 0 0
\(463\) 10.5194 18.2201i 0.488877 0.846760i −0.511041 0.859556i \(-0.670740\pi\)
0.999918 + 0.0127960i \(0.00407321\pi\)
\(464\) −5.68202 + 3.28052i −0.263781 + 0.152294i
\(465\) −10.7421 9.60351i −0.498153 0.445352i
\(466\) −6.36446 + 11.0236i −0.294828 + 0.510657i
\(467\) −2.91151 + 5.04288i −0.134729 + 0.233357i −0.925494 0.378763i \(-0.876350\pi\)
0.790765 + 0.612120i \(0.209683\pi\)
\(468\) −14.5824 + 1.63726i −0.674070 + 0.0756823i
\(469\) 0 0
\(470\) −7.96337 + 4.59766i −0.367323 + 0.212074i
\(471\) −22.7770 + 7.49005i −1.04951 + 0.345123i
\(472\) 14.5900i 0.671560i
\(473\) 16.7206i 0.768812i
\(474\) 4.99637 1.64302i 0.229491 0.0754665i
\(475\) 4.68907 2.70724i 0.215149 0.124217i
\(476\) 0 0
\(477\) 0 0
\(478\) −8.72474 + 15.1117i −0.399060 + 0.691193i
\(479\) 13.4781 23.3447i 0.615828 1.06665i −0.374411 0.927263i \(-0.622155\pi\)
0.990239 0.139382i \(-0.0445117\pi\)
\(480\) −2.31181 2.06678i −0.105519 0.0943351i
\(481\) 39.6662 22.9013i 1.80862 1.04421i
\(482\) 5.71659 9.90142i 0.260383 0.450997i
\(483\) 0 0
\(484\) 2.61639 + 4.53172i 0.118927 + 0.205987i
\(485\) −8.54455 4.93320i −0.387988 0.224005i
\(486\) −0.276237 15.5860i −0.0125304 0.706996i
\(487\) 6.81338 + 11.8011i 0.308744 + 0.534760i 0.978088 0.208193i \(-0.0667581\pi\)
−0.669344 + 0.742953i \(0.733425\pi\)
\(488\) 11.3283 0.512807
\(489\) −7.35116 1.53533i −0.332431 0.0694299i
\(490\) 0 0
\(491\) −33.7430 19.4815i −1.52280 0.879188i −0.999637 0.0269544i \(-0.991419\pi\)
−0.523162 0.852234i \(-0.675248\pi\)
\(492\) −13.7026 2.86185i −0.617759 0.129022i
\(493\) 20.8227 + 12.0220i 0.937807 + 0.541443i
\(494\) 12.7801 7.37859i 0.575004 0.331979i
\(495\) 7.65538 + 10.3812i 0.344084 + 0.466599i
\(496\) 4.64661i 0.208639i
\(497\) 0 0
\(498\) −18.0847 16.1678i −0.810393 0.724497i
\(499\) −13.0048 22.5250i −0.582176 1.00836i −0.995221 0.0976483i \(-0.968868\pi\)
0.413045 0.910711i \(-0.364465\pi\)
\(500\) 12.1648 0.544026
\(501\) 21.0494 + 4.39628i 0.940419 + 0.196411i
\(502\) 27.3560i 1.22096i
\(503\) 10.5271 0.469378 0.234689 0.972070i \(-0.424593\pi\)
0.234689 + 0.972070i \(0.424593\pi\)
\(504\) 0 0
\(505\) 0.448168 0.0199432
\(506\) 9.04499i 0.402099i
\(507\) 12.6119 14.1072i 0.560114 0.626521i
\(508\) −1.40150 −0.0621817
\(509\) 0.469435 + 0.813086i 0.0208074 + 0.0360394i 0.876242 0.481872i \(-0.160043\pi\)
−0.855434 + 0.517911i \(0.826710\pi\)
\(510\) −2.32330 + 11.1240i −0.102878 + 0.492580i
\(511\) 0 0
\(512\) 1.00000i 0.0441942i
\(513\) 6.52826 + 14.2529i 0.288230 + 0.629281i
\(514\) −3.02826 + 1.74837i −0.133571 + 0.0771172i
\(515\) 0.260376 + 0.150328i 0.0114735 + 0.00662424i
\(516\) 8.03754 8.99047i 0.353833 0.395784i
\(517\) −10.6818 6.16711i −0.469783 0.271229i
\(518\) 0 0
\(519\) 9.42442 + 28.6593i 0.413686 + 1.25801i
\(520\) 8.75718 0.384028
\(521\) 19.7527 + 34.2127i 0.865382 + 1.49889i 0.866667 + 0.498887i \(0.166258\pi\)
−0.00128461 + 0.999999i \(0.500409\pi\)
\(522\) 18.0377 + 7.87817i 0.789489 + 0.344818i
\(523\) −21.0697 12.1646i −0.921315 0.531922i −0.0372609 0.999306i \(-0.511863\pi\)
−0.884054 + 0.467384i \(0.845197\pi\)
\(524\) 5.24589 + 9.08614i 0.229168 + 0.396930i
\(525\) 0 0
\(526\) −4.82174 + 8.35150i −0.210238 + 0.364143i
\(527\) 14.7469 8.51413i 0.642385 0.370881i
\(528\) 0.850388 4.07167i 0.0370084 0.177197i
\(529\) −4.40718 + 7.63346i −0.191616 + 0.331889i
\(530\) 0 0
\(531\) 35.2274 25.9777i 1.52874 1.12734i
\(532\) 0 0
\(533\) 34.2349 19.7655i 1.48288 0.856141i
\(534\) 1.32741 6.35568i 0.0574429 0.275037i
\(535\) 14.3063i 0.618516i
\(536\) 0.570231i 0.0246302i
\(537\) 16.9441 + 15.1481i 0.731190 + 0.653689i
\(538\) −5.98517 + 3.45554i −0.258039 + 0.148979i
\(539\) 0 0
\(540\) −0.873992 + 9.26178i −0.0376106 + 0.398564i
\(541\) −21.3640 + 37.0036i −0.918512 + 1.59091i −0.116835 + 0.993151i \(0.537275\pi\)
−0.801677 + 0.597758i \(0.796058\pi\)
\(542\) −10.3156 + 17.8672i −0.443093 + 0.767460i
\(543\) −21.9784 + 7.22745i −0.943185 + 0.310160i
\(544\) 3.17369 1.83233i 0.136071 0.0785606i
\(545\) 16.9665 29.3869i 0.726767 1.25880i
\(546\) 0 0
\(547\) −12.2477 21.2136i −0.523672 0.907026i −0.999620 0.0275530i \(-0.991229\pi\)
0.475949 0.879473i \(-0.342105\pi\)
\(548\) −4.08812 2.36028i −0.174636 0.100826i
\(549\) −20.1702 27.3520i −0.860843 1.16736i
\(550\) 2.15493 + 3.73244i 0.0918864 + 0.159152i
\(551\) −19.7947 −0.843283
\(552\) 4.34791 4.86340i 0.185059 0.207000i
\(553\) 0 0
\(554\) 13.4358 + 7.75718i 0.570834 + 0.329571i
\(555\) −9.07096 27.5845i −0.385041 1.17090i
\(556\) 2.04707 + 1.18187i 0.0868150 + 0.0501227i
\(557\) −2.20344 + 1.27216i −0.0933627 + 0.0539030i −0.545954 0.837815i \(-0.683833\pi\)
0.452592 + 0.891718i \(0.350499\pi\)
\(558\) 11.2192 8.27336i 0.474946 0.350239i
\(559\) 34.0560i 1.44042i
\(560\) 0 0
\(561\) −14.4804 + 4.76178i −0.611364 + 0.201043i
\(562\) 6.79883 + 11.7759i 0.286791 + 0.496737i
\(563\) 15.8141 0.666487 0.333243 0.942841i \(-0.391857\pi\)
0.333243 + 0.942841i \(0.391857\pi\)
\(564\) −2.77895 8.45070i −0.117015 0.355838i
\(565\) 2.07596i 0.0873363i
\(566\) −5.44783 −0.228990
\(567\) 0 0
\(568\) −5.96254 −0.250182
\(569\) 6.38311i 0.267594i −0.991009 0.133797i \(-0.957283\pi\)
0.991009 0.133797i \(-0.0427170\pi\)
\(570\) −2.92258 8.88748i −0.122414 0.372255i
\(571\) −7.82375 −0.327414 −0.163707 0.986509i \(-0.552345\pi\)
−0.163707 + 0.986509i \(0.552345\pi\)
\(572\) 5.87327 + 10.1728i 0.245574 + 0.425346i
\(573\) −15.2252 + 5.00668i −0.636040 + 0.209157i
\(574\) 0 0
\(575\) 6.75933i 0.281884i
\(576\) 2.41449 1.78052i 0.100604 0.0741882i
\(577\) −12.4012 + 7.15986i −0.516270 + 0.298069i −0.735407 0.677625i \(-0.763009\pi\)
0.219137 + 0.975694i \(0.429676\pi\)
\(578\) 3.09191 + 1.78512i 0.128607 + 0.0742510i
\(579\) 13.2887 + 40.4106i 0.552261 + 1.67941i
\(580\) −10.1728 5.87327i −0.422403 0.243874i
\(581\) 0 0
\(582\) 6.36175 7.11600i 0.263703 0.294968i
\(583\) 0 0
\(584\) −6.19070 10.7226i −0.256173 0.443705i
\(585\) −15.5923 21.1441i −0.644662 0.874202i
\(586\) 21.1849 + 12.2311i 0.875141 + 0.505263i
\(587\) −2.37575 4.11492i −0.0980577 0.169841i 0.812823 0.582511i \(-0.197930\pi\)
−0.910881 + 0.412670i \(0.864596\pi\)
\(588\) 0 0
\(589\) −7.00943 + 12.1407i −0.288819 + 0.500249i
\(590\) −22.6216 + 13.0606i −0.931318 + 0.537697i
\(591\) 20.5443 6.75583i 0.845078 0.277898i
\(592\) −4.68202 + 8.10950i −0.192430 + 0.333298i
\(593\) −1.79035 + 3.10098i −0.0735208 + 0.127342i −0.900442 0.434976i \(-0.856757\pi\)
0.826921 + 0.562318i \(0.190090\pi\)
\(594\) −11.3451 + 5.19642i −0.465497 + 0.213212i
\(595\) 0 0
\(596\) −15.0377 + 8.68202i −0.615968 + 0.355629i
\(597\) 0.231324 + 0.206805i 0.00946746 + 0.00846398i
\(598\) 18.4226i 0.753357i
\(599\) 15.0655i 0.615561i 0.951457 + 0.307780i \(0.0995862\pi\)
−0.951457 + 0.307780i \(0.900414\pi\)
\(600\) −0.635497 + 3.04277i −0.0259440 + 0.124220i
\(601\) −19.8704 + 11.4722i −0.810530 + 0.467960i −0.847140 0.531370i \(-0.821678\pi\)
0.0366096 + 0.999330i \(0.488344\pi\)
\(602\) 0 0
\(603\) −1.37682 + 1.01531i −0.0560683 + 0.0413464i
\(604\) −5.61639 + 9.72787i −0.228528 + 0.395821i
\(605\) −4.68425 + 8.11336i −0.190442 + 0.329855i
\(606\) −0.0886415 + 0.424416i −0.00360081 + 0.0172407i
\(607\) −21.2030 + 12.2416i −0.860605 + 0.496870i −0.864215 0.503123i \(-0.832184\pi\)
0.00360990 + 0.999993i \(0.498851\pi\)
\(608\) −1.50851 + 2.61281i −0.0611780 + 0.105963i
\(609\) 0 0
\(610\) 10.1408 + 17.5644i 0.410589 + 0.711161i
\(611\) 21.7563 + 12.5610i 0.880167 + 0.508165i
\(612\) −10.0750 4.40035i −0.407256 0.177874i
\(613\) 0.440043 + 0.762177i 0.0177732 + 0.0307840i 0.874775 0.484529i \(-0.161009\pi\)
−0.857002 + 0.515313i \(0.827676\pi\)
\(614\) −31.2223 −1.26003
\(615\) −7.82892 23.8075i −0.315693 0.960011i
\(616\) 0 0
\(617\) −11.7607 6.79005i −0.473468 0.273357i 0.244222 0.969719i \(-0.421467\pi\)
−0.717690 + 0.696362i \(0.754801\pi\)
\(618\) −0.193860 + 0.216844i −0.00779818 + 0.00872274i
\(619\) 30.7325 + 17.7434i 1.23524 + 0.713169i 0.968118 0.250493i \(-0.0805926\pi\)
0.267126 + 0.963662i \(0.413926\pi\)
\(620\) −7.20451 + 4.15953i −0.289340 + 0.167051i
\(621\) −19.4841 1.83863i −0.781872 0.0737817i
\(622\) 10.9100i 0.437452i
\(623\) 0 0
\(624\) −1.73205 + 8.29308i −0.0693375 + 0.331989i
\(625\) 6.40300 + 11.0903i 0.256120 + 0.443613i
\(626\) −3.42405 −0.136853
\(627\) 8.36404 9.35568i 0.334028 0.373630i
\(628\) 13.8431i 0.552399i
\(629\) 34.3161 1.36827
\(630\) 0 0
\(631\) 26.9822 1.07415 0.537073 0.843536i \(-0.319530\pi\)
0.537073 + 0.843536i \(0.319530\pi\)
\(632\) 3.03663i 0.120790i
\(633\) −25.6390 5.35482i −1.01906 0.212835i
\(634\) −19.0471 −0.756458
\(635\) −1.25459 2.17302i −0.0497869 0.0862335i
\(636\) 0 0
\(637\) 0 0
\(638\) 15.7563i 0.623800i
\(639\) 10.6164 + 14.3965i 0.419978 + 0.569516i
\(640\) −1.55049 + 0.895175i −0.0612884 + 0.0353849i
\(641\) −0.932777 0.538539i −0.0368425 0.0212710i 0.481466 0.876465i \(-0.340105\pi\)
−0.518308 + 0.855194i \(0.673438\pi\)
\(642\) −13.5481 2.82960i −0.534702 0.111675i
\(643\) 33.3126 + 19.2330i 1.31372 + 0.758477i 0.982710 0.185150i \(-0.0592773\pi\)
0.331010 + 0.943627i \(0.392611\pi\)
\(644\) 0 0
\(645\) 21.1346 + 4.41407i 0.832175 + 0.173804i
\(646\) 11.0563 0.435006
\(647\) 4.47605 + 7.75275i 0.175972 + 0.304792i 0.940497 0.339802i \(-0.110360\pi\)
−0.764525 + 0.644594i \(0.777027\pi\)
\(648\) −8.59808 2.65953i −0.337764 0.104476i
\(649\) −30.3438 17.5190i −1.19110 0.687680i
\(650\) −4.38910 7.60215i −0.172155 0.298181i
\(651\) 0 0
\(652\) −2.16789 + 3.75489i −0.0849010 + 0.147053i
\(653\) 9.85934 5.69229i 0.385826 0.222757i −0.294524 0.955644i \(-0.595161\pi\)
0.680350 + 0.732887i \(0.261828\pi\)
\(654\) 24.4738 + 21.8797i 0.957000 + 0.855564i
\(655\) −9.39197 + 16.2674i −0.366975 + 0.635619i
\(656\) −4.04094 + 6.99911i −0.157772 + 0.273269i
\(657\) −14.8670 + 34.0392i −0.580017 + 1.32799i
\(658\) 0 0
\(659\) 31.4373 18.1503i 1.22462 0.707036i 0.258723 0.965952i \(-0.416698\pi\)
0.965900 + 0.258915i \(0.0833650\pi\)
\(660\) 7.07432 2.32634i 0.275368 0.0905527i
\(661\) 36.0758i 1.40319i 0.712578 + 0.701593i \(0.247527\pi\)
−0.712578 + 0.701593i \(0.752473\pi\)
\(662\) 0.0732502i 0.00284695i
\(663\) 29.4934 9.69869i 1.14543 0.376666i
\(664\) −12.1290 + 7.00270i −0.470698 + 0.271757i
\(665\) 0 0
\(666\) 27.9167 3.13439i 1.08175 0.121455i
\(667\) 12.3557 21.4007i 0.478414 0.828637i
\(668\) 6.20756 10.7518i 0.240178 0.416000i
\(669\) 10.8405 + 9.69145i 0.419117 + 0.374693i
\(670\) 0.884136 0.510456i 0.0341572 0.0197206i
\(671\) −13.6025 + 23.5602i −0.525117 + 0.909530i
\(672\) 0 0
\(673\) 4.78512 + 8.28806i 0.184453 + 0.319481i 0.943392 0.331680i \(-0.107615\pi\)
−0.758939 + 0.651161i \(0.774282\pi\)
\(674\) 1.93364 + 1.11639i 0.0744811 + 0.0430017i
\(675\) 8.47824 3.88329i 0.326328 0.149468i
\(676\) −5.46254 9.46139i −0.210098 0.363900i
\(677\) −15.6282 −0.600639 −0.300320 0.953839i \(-0.597093\pi\)
−0.300320 + 0.953839i \(0.597093\pi\)
\(678\) −1.96594 0.410596i −0.0755015 0.0157689i
\(679\) 0 0
\(680\) 5.68202 + 3.28052i 0.217896 + 0.125802i
\(681\) −4.11188 0.858785i −0.157567 0.0329087i
\(682\) −9.66385 5.57943i −0.370048 0.213647i
\(683\) 9.63996 5.56563i 0.368863 0.212963i −0.304099 0.952640i \(-0.598355\pi\)
0.672961 + 0.739678i \(0.265022\pi\)
\(684\) 8.99452 1.00987i 0.343914 0.0386135i
\(685\) 8.45145i 0.322913i
\(686\) 0 0
\(687\) 2.60803 + 2.33159i 0.0995025 + 0.0889559i
\(688\) −3.48127 6.02973i −0.132722 0.229881i
\(689\) 0 0
\(690\) 11.4328 + 2.38779i 0.435238 + 0.0909017i
\(691\) 3.02419i 0.115046i 0.998344 + 0.0575228i \(0.0183202\pi\)
−0.998344 + 0.0575228i \(0.981680\pi\)
\(692\) 17.4182 0.662139
\(693\) 0 0
\(694\) 31.8409 1.20867
\(695\) 4.23194i 0.160527i
\(696\) 7.57405 8.47203i 0.287094 0.321131i
\(697\) 29.6174 1.12184
\(698\) −7.36772 12.7613i −0.278872 0.483021i
\(699\) 4.50739 21.5815i 0.170485 0.816286i
\(700\) 0 0
\(701\) 50.1486i 1.89409i 0.321103 + 0.947044i \(0.395946\pi\)
−0.321103 + 0.947044i \(0.604054\pi\)
\(702\) 23.1075 10.5839i 0.872137 0.399465i
\(703\) −24.4664 + 14.1257i −0.922769 + 0.532761i
\(704\) −2.07976 1.20075i −0.0783840 0.0452550i
\(705\) 10.6151 11.8736i 0.399786 0.447185i
\(706\) −1.87025 1.07979i −0.0703876 0.0406383i
\(707\) 0 0
\(708\) −7.89419 24.0060i −0.296682 0.902200i
\(709\) −3.60770 −0.135490 −0.0677449 0.997703i \(-0.521580\pi\)
−0.0677449 + 0.997703i \(0.521580\pi\)
\(710\) −5.33751 9.24484i −0.200313 0.346953i
\(711\) −7.33190 + 5.40676i −0.274968 + 0.202769i
\(712\) −3.24641 1.87432i −0.121664 0.0702429i
\(713\) −8.75046 15.1562i −0.327707 0.567605i
\(714\) 0 0
\(715\) −10.5152 + 18.2129i −0.393246 + 0.681123i
\(716\) 11.3640 6.56103i 0.424694 0.245197i
\(717\) 6.17898 29.5850i 0.230758 1.10487i
\(718\) 16.3224 28.2712i 0.609146 1.05507i
\(719\) 17.1580 29.7186i 0.639887 1.10832i −0.345571 0.938393i \(-0.612315\pi\)
0.985457 0.169924i \(-0.0543521\pi\)
\(720\) 4.92206 + 2.14977i 0.183434 + 0.0801171i
\(721\) 0 0
\(722\) 8.57161 4.94882i 0.319002 0.184176i
\(723\) −4.04856 + 19.3846i −0.150568 + 0.720920i
\(724\) 13.3577i 0.496437i
\(725\) 11.7747i 0.437303i
\(726\) −6.75690 6.04071i −0.250772 0.224192i
\(727\) 19.4757 11.2443i 0.722315 0.417029i −0.0932892 0.995639i \(-0.529738\pi\)
0.815604 + 0.578610i \(0.196405\pi\)
\(728\) 0 0
\(729\) 8.88761 + 25.4953i 0.329171 + 0.944270i
\(730\) 11.0835 19.1972i 0.410220 0.710521i
\(731\) −12.7577 + 22.0970i −0.471860 + 0.817285i
\(732\) −18.6392 + 6.12937i −0.688926 + 0.226548i
\(733\) −27.0065 + 15.5922i −0.997509 + 0.575912i −0.907510 0.420030i \(-0.862020\pi\)
−0.0899987 + 0.995942i \(0.528686\pi\)
\(734\) 14.8501 25.7212i 0.548129 0.949387i
\(735\) 0 0
\(736\) −1.88319 3.26178i −0.0694154 0.120231i
\(737\) 1.18595 + 0.684706i 0.0436849 + 0.0252215i
\(738\) 24.0942 2.70522i 0.886921 0.0995805i
\(739\) −2.04314 3.53882i −0.0751581 0.130178i 0.825997 0.563675i \(-0.190613\pi\)
−0.901155 + 0.433497i \(0.857279\pi\)
\(740\) −16.7649 −0.616290
\(741\) −17.0357 + 19.0554i −0.625821 + 0.700018i
\(742\) 0 0
\(743\) −1.78246 1.02910i −0.0653921 0.0377542i 0.466947 0.884285i \(-0.345354\pi\)
−0.532340 + 0.846531i \(0.678687\pi\)
\(744\) −2.51413 7.64539i −0.0921726 0.280294i
\(745\) −26.9227 15.5439i −0.986373 0.569483i
\(746\) −1.74653 + 1.00836i −0.0639450 + 0.0369187i
\(747\) 38.5039 + 16.8170i 1.40878 + 0.615302i
\(748\) 8.80071i 0.321786i
\(749\) 0 0
\(750\) −20.0156 + 6.58198i −0.730866 + 0.240340i
\(751\) −11.9053 20.6205i −0.434429 0.752454i 0.562820 0.826580i \(-0.309717\pi\)
−0.997249 + 0.0741262i \(0.976383\pi\)
\(752\) −5.13604 −0.187292
\(753\) 14.8014 + 45.0107i 0.539395 + 1.64028i
\(754\) 32.0921i 1.16873i
\(755\) −20.1106 −0.731900
\(756\) 0 0
\(757\) 10.0754 0.366197 0.183098 0.983095i \(-0.441387\pi\)
0.183098 + 0.983095i \(0.441387\pi\)
\(758\) 18.8709i 0.685421i
\(759\) 4.89395 + 14.8824i 0.177639 + 0.540195i
\(760\) −5.40150 −0.195933
\(761\) 13.9368 + 24.1392i 0.505207 + 0.875044i 0.999982 + 0.00602283i \(0.00191714\pi\)
−0.494775 + 0.869021i \(0.664750\pi\)
\(762\) 2.30599 0.758309i 0.0835374 0.0274707i
\(763\) 0 0
\(764\) 9.25333i 0.334774i
\(765\) −2.19615 19.5602i −0.0794021 0.707200i
\(766\) 0.724440 0.418256i 0.0261751 0.0151122i
\(767\) 61.8035 + 35.6823i 2.23159 + 1.28841i
\(768\) −0.541068 1.64537i −0.0195241 0.0593722i
\(769\) −6.21166 3.58631i −0.223998 0.129326i 0.383802 0.923415i \(-0.374615\pi\)
−0.607800 + 0.794090i \(0.707948\pi\)
\(770\) 0 0
\(771\) 4.03663 4.51521i 0.145376 0.162611i
\(772\) 24.5602 0.883941
\(773\) 1.07077 + 1.85462i 0.0385128 + 0.0667061i 0.884639 0.466276i \(-0.154405\pi\)
−0.846127 + 0.532982i \(0.821071\pi\)
\(774\) −8.36028 + 19.1415i −0.300504 + 0.688028i
\(775\) 7.22181 + 4.16951i 0.259415 + 0.149773i
\(776\) −2.75544 4.77256i −0.0989144 0.171325i
\(777\) 0 0
\(778\) 12.4109 21.4964i 0.444954 0.770682i
\(779\) −21.1164 + 12.1916i −0.756573 + 0.436808i
\(780\) −14.4088 + 4.73823i −0.515918 + 0.169656i
\(7