Properties

Label 882.2.l.a.227.3
Level $882$
Weight $2$
Character 882.227
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 227.3
Root \(1.69547 - 0.354107i\) of defining polynomial
Character \(\chi\) \(=\) 882.227
Dual form 882.2.l.a.509.7

$q$-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 \(\left(\mathbb{Z}/882\mathbb{Z}\right)^\times\).

\(n\) \(199\) \(785\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 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 \(-0.702227\pi\)
0.993766 + 0.111485i \(0.0355607\pi\)
\(6\) −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 −0.152545 0.988297i \(-0.548747\pi\)
0.779617 + 0.626256i \(0.215414\pi\)
\(12\) −0.541068 + 1.64537i −0.156193 + 0.474978i
\(13\) 4.23601 2.44566i 1.17486 0.678305i 0.220039 0.975491i \(-0.429382\pi\)
0.954820 + 0.297186i \(0.0960482\pi\)
\(14\) 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 \(-0.686748\pi\)
0.998011 + 0.0630460i \(0.0200815\pi\)
\(18\) −1.78052 + 2.41449i −0.419672 + 0.569101i
\(19\) −2.61281 + 1.50851i −0.599419 + 0.346075i −0.768813 0.639474i \(-0.779152\pi\)
0.169394 + 0.985548i \(0.445819\pi\)
\(20\) −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 0.119775 0.992801i \(-0.461783\pi\)
−0.799904 + 0.600128i \(0.795116\pi\)
\(24\) 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 −0.131045 0.991376i \(-0.541833\pi\)
−0.924080 + 0.382200i \(0.875167\pi\)
\(30\) −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 −0.937715 0.347405i \(-0.887063\pi\)
0.167996 0.985788i \(-0.446271\pi\)
\(38\) 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 0.987330 + 0.158683i \(0.0507248\pi\)
−0.356241 + 0.934394i \(0.615942\pi\)
\(42\) 0 0
\(43\) −3.48127 + 6.02973i −0.530888 + 0.919526i 0.468462 + 0.883484i \(0.344808\pi\)
−0.999350 + 0.0360419i \(0.988525\pi\)
\(44\) −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 \(-0.377785\pi\)
0.374584 + 0.927193i \(0.377785\pi\)
\(48\) 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 \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(54\) 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 \(-0.101359\pi\)
0.949729 + 0.313073i \(0.101359\pi\)
\(60\) 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 \(0.115115\pi\)
−0.935317 + 0.353811i \(0.884885\pi\)
\(72\) 1.78052 2.41449i 0.209836 0.284550i
\(73\) −10.7226 6.19070i −1.25499 0.724567i −0.282891 0.959152i \(-0.591294\pi\)
−0.972096 + 0.234585i \(0.924627\pi\)
\(74\) −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 −0.169651 0.985504i \(-0.554264\pi\)
0.938297 0.345830i \(-0.112403\pi\)
\(84\) 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 \(-0.230331\pi\)
−0.948100 + 0.317973i \(0.896998\pi\)
\(90\) 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 \(-0.423592\pi\)
−0.722323 + 0.691556i \(0.756926\pi\)
\(98\) 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 \(-0.162702\pi\)
−0.859731 + 0.510747i \(0.829369\pi\)
\(102\) −4.73205 + 4.23048i −0.468543 + 0.418880i
\(103\) 0.145433 + 0.0839657i 0.0143299 + 0.00827339i 0.507148 0.861859i \(-0.330700\pi\)
−0.492818 + 0.870132i \(0.664033\pi\)
\(104\) 2.44566 + 4.23601i 0.239817 + 0.415375i
\(105\) 0 0
\(106\) 0 0
\(107\) −6.92024 + 3.99540i −0.669004 + 0.386250i −0.795699 0.605692i \(-0.792896\pi\)
0.126695 + 0.991942i \(0.459563\pi\)
\(108\) 4.23601 3.00935i 0.407611 0.289575i
\(109\) 9.47667 16.4141i 0.907700 1.57218i 0.0904491 0.995901i \(-0.471170\pi\)
0.817251 0.576282i \(-0.195497\pi\)
\(110\) −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 −0.546488 0.837467i \(-0.684036\pi\)
0.452023 + 0.892006i \(0.350702\pi\)
\(114\) 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 \(-0.681779\pi\)
0.998873 + 0.0474597i \(0.0151126\pi\)
\(132\) 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 −0.315093 0.949061i \(-0.602036\pi\)
0.664365 + 0.747409i \(0.268702\pi\)
\(138\) 4.34791 + 4.86340i 0.370119 + 0.414000i
\(139\) 2.04707 1.18187i 0.173630 0.100245i −0.410666 0.911786i \(-0.634704\pi\)
0.584296 + 0.811540i \(0.301371\pi\)
\(140\) 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 0.967433 0.253126i \(-0.0814587\pi\)
0.264503 + 0.964385i \(0.414792\pi\)
\(150\) −0.635497 3.04277i −0.0518881 0.248441i
\(151\) 5.61639 + 9.72787i 0.457055 + 0.791643i 0.998804 0.0488977i \(-0.0155708\pi\)
−0.541749 + 0.840541i \(0.682238\pi\)
\(152\) −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 0.938350 0.345686i \(-0.112354\pi\)
−0.768548 + 0.639792i \(0.779020\pi\)
\(164\) −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 \(-0.00717435\pi\)
−0.519391 + 0.854537i \(0.673841\pi\)
\(168\) 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 \(-0.269649\pi\)
0.662139 + 0.749381i \(0.269649\pi\)
\(174\) 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 0.0110562 0.999939i \(-0.496481\pi\)
−0.860444 + 0.509544i \(0.829814\pi\)
\(180\) 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 \(0.108660\pi\)
−0.942299 + 0.334774i \(0.891340\pi\)
\(192\) −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 \(-0.853275\pi\)
0.895630 0.444799i \(-0.146725\pi\)
\(198\) −0.803848 + 7.15953i −0.0571270 + 0.508805i
\(199\) 0.155144 + 0.0895727i 0.0109979 + 0.00634964i 0.505489 0.862833i \(-0.331312\pi\)
−0.494491 + 0.869183i \(0.664645\pi\)
\(200\) −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 0.999715 + 0.0238622i \(0.00759629\pi\)
−0.479192 + 0.877710i \(0.659070\pi\)
\(212\) 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 \(-0.242636\pi\)
−0.236406 + 0.971654i \(0.575970\pi\)
\(224\) 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 \(-0.192313\pi\)
−0.903458 + 0.428677i \(0.858980\pi\)
\(228\) −1.06834 5.11524i −0.0707528 0.338765i
\(229\) 1.74915 + 1.00987i 0.115587 + 0.0667344i 0.556679 0.830728i \(-0.312075\pi\)
−0.441092 + 0.897462i \(0.645409\pi\)
\(230\) 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 −0.0933759 0.995631i \(-0.529766\pi\)
0.815554 + 0.578681i \(0.196432\pi\)
\(234\) −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 0.0759814 0.997109i \(-0.475791\pi\)
0.901513 + 0.432753i \(0.142458\pi\)
\(240\) −2.06678 2.31181i −0.133410 0.149227i
\(241\) 9.90142 5.71659i 0.637807 0.368238i −0.145963 0.989290i \(-0.546628\pi\)
0.783769 + 0.621052i \(0.213295\pi\)
\(242\) 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 \(-0.168364\pi\)
0.863347 + 0.504611i \(0.168364\pi\)
\(252\) 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 \(-0.868117\pi\)
0.806330 + 0.591466i \(0.201451\pi\)
\(258\) 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 −0.219901 0.975522i \(-0.570573\pi\)
0.734877 + 0.678201i \(0.237240\pi\)
\(264\) 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 \(-0.900904\pi\)
0.741242 + 0.671238i \(0.234237\pi\)
\(270\) 9.26178 0.873992i 0.563654 0.0531895i
\(271\) −17.8672 + 10.3156i −1.08535 + 0.626629i −0.932335 0.361595i \(-0.882232\pi\)
−0.153017 + 0.988224i \(0.548899\pi\)
\(272\) 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 0.999250 0.0387296i \(-0.0123311\pi\)
−0.533166 + 0.846011i \(0.678998\pi\)
\(278\) −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 0.808275 0.588805i \(-0.200401\pi\)
−0.105783 + 0.994389i \(0.533735\pi\)
\(282\) −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 −0.963133 0.269026i \(-0.913298\pi\)
0.248583 0.968610i \(-0.420035\pi\)
\(294\) 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 \(-0.600103\pi\)
−0.309325 + 0.950956i \(0.600103\pi\)
\(312\) 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 \(-0.820350\pi\)
0.844917 0.534897i \(-0.179650\pi\)
\(318\) 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 0.894829 0.446408i \(-0.147297\pi\)
−0.834016 + 0.551741i \(0.813964\pi\)
\(338\) −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 \(0.326232\pi\)
−0.519195 + 0.854656i \(0.673768\pi\)
\(348\) 8.47203 7.57405i 0.454148 0.406012i
\(349\) 12.7613 + 7.36772i 0.683095 + 0.394385i 0.801020 0.598637i \(-0.204291\pi\)
−0.117925 + 0.993022i \(0.537624\pi\)
\(350\) 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 \(-0.148363\pi\)
−0.835858 + 0.548945i \(0.815030\pi\)
\(354\) −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 −0.999959 0.00905364i \(-0.997118\pi\)
−0.492139 + 0.870517i \(0.663785\pi\)
\(360\) −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 \(-0.384330\pi\)
0.987194 + 0.159527i \(0.0509969\pi\)
\(368\) −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 −0.838739 0.544534i \(-0.816707\pi\)
0.890950 + 0.454102i \(0.150040\pi\)
\(374\) −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 \(-0.826530\pi\)
0.876514 + 0.481377i \(0.159863\pi\)
\(384\) 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 −0.933552 0.358441i \(-0.883308\pi\)
−0.156357 + 0.987701i \(0.549975\pi\)
\(390\) −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 \(-0.642409\pi\)
0.564482 + 0.825445i \(0.309076\pi\)
\(398\) 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 0.189822 0.981819i \(-0.439209\pi\)
−0.755369 + 0.655300i \(0.772542\pi\)
\(402\) −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 \(-0.297853\pi\)
−0.993794 + 0.111234i \(0.964520\pi\)
\(420\) 0 0
\(421\) −7.72892 + 13.3869i −0.376684 + 0.652437i −0.990578 0.136952i \(-0.956269\pi\)
0.613893 + 0.789389i \(0.289603\pi\)
\(422\) 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 −0.123024 0.992404i \(-0.539259\pi\)
−0.920959 + 0.389660i \(0.872593\pi\)
\(432\) −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 \(0.00910938\pi\)
−0.999591 + 0.0286141i \(0.990891\pi\)
\(444\) 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 \(-0.782055\pi\)
0.774612 0.632436i \(-0.217945\pi\)
\(450\) −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 \(-0.869024\pi\)
0.804641 + 0.593761i \(0.202358\pi\)
\(462\) 0 0
\(463\) 10.5194 + 18.2201i 0.488877 + 0.846760i 0.999918 0.0127960i \(-0.00407321\pi\)
−0.511041 + 0.859556i \(0.670740\pi\)
\(464\) −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 \(-0.123650\pi\)
−0.790765 + 0.612120i \(0.790317\pi\)
\(468\) 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 −0.990239 0.139382i \(-0.955488\pi\)
0.374411 0.927263i \(-0.377845\pi\)
\(480\) −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 −0.669344 0.742953i \(-0.733425\pi\)
0.978088 + 0.208193i \(0.0667581\pi\)
\(488\) −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 −0.523162 + 0.852234i \(0.675248\pi\)
−0.999637 + 0.0269544i \(0.991419\pi\)
\(492\) −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 0.413045 + 0.910711i \(0.364465\pi\)
−0.995221 + 0.0976483i \(0.968868\pi\)
\(500\) −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 \(-0.575407\pi\)
−0.234689 + 0.972070i \(0.575407\pi\)
\(504\) 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 \(-0.839957\pi\)
0.855434 + 0.517911i \(0.173290\pi\)
\(510\) 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 0.00128461 + 0.999999i \(0.499591\pi\)
−0.866667 + 0.498887i \(0.833742\pi\)
\(522\) 18.0377 7.87817i 0.789489 0.344818i
\(523\) 21.0697 12.1646i 0.921315 0.531922i 0.0372609 0.999306i \(-0.488137\pi\)
0.884054 + 0.467384i \(0.154803\pi\)
\(524\) −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 −0.801677 0.597758i \(-0.796058\pi\)
−0.116835 0.993151i \(-0.537275\pi\)
\(542\) 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 0.475949 + 0.879473i \(0.342105\pi\)
−0.999620 + 0.0275530i \(0.991229\pi\)
\(548\) −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 0.452592 0.891718i \(-0.350499\pi\)
−0.545954 + 0.837815i \(0.683833\pi\)
\(558\) −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 \(-0.608143\pi\)
−0.333243 + 0.942841i \(0.608143\pi\)
\(564\) −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 \(0.0427170\pi\)
−0.991009 + 0.133797i \(0.957283\pi\)
\(570\) 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 \(-0.236991\pi\)
−0.219137 + 0.975694i \(0.570324\pi\)
\(578\) 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 \(-0.802070\pi\)
0.910881 + 0.412670i \(0.135404\pi\)
\(588\) 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 \(-0.143243\pi\)
−0.826921 + 0.562318i \(0.809910\pi\)
\(594\) 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 \(-0.900414\pi\)
0.951457 0.307780i \(-0.0995862\pi\)
\(600\) 0.635497 + 3.04277i 0.0259440 + 0.124220i
\(601\) 19.8704 + 11.4722i 0.810530 + 0.467960i 0.847140 0.531370i \(-0.178322\pi\)
−0.0366096 + 0.999330i \(0.511656\pi\)
\(602\) 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 \(-0.167816\pi\)
−0.00360990 + 0.999993i \(0.501149\pi\)
\(608\) 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 −0.857002 0.515313i \(-0.827676\pi\)
0.874775 + 0.484529i \(0.161009\pi\)
\(614\) 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 −0.717690 0.696362i \(-0.754801\pi\)
0.244222 + 0.969719i \(0.421467\pi\)
\(618\) −0.193860 0.216844i −0.00779818 0.00872274i
\(619\) −30.7325 + 17.7434i −1.23524 + 0.713169i −0.968118 0.250493i \(-0.919407\pi\)
−0.267126 + 0.963662i \(0.586074\pi\)
\(620\) −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 −0.518308 0.855194i \(-0.673438\pi\)
0.481466 + 0.876465i \(0.340105\pi\)
\(642\) 13.5481 2.82960i 0.534702 0.111675i
\(643\) −33.3126 + 19.2330i −1.31372 + 0.758477i −0.982710 0.185150i \(-0.940723\pi\)
−0.331010 + 0.943627i \(0.607389\pi\)
\(644\) 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 \(-0.889640\pi\)
0.764525 + 0.644594i \(0.222973\pi\)
\(648\) −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 0.680350 0.732887i \(-0.261828\pi\)
−0.294524 + 0.955644i \(0.595161\pi\)
\(654\) −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 0.965900 0.258915i \(-0.0833650\pi\)
0.258723 + 0.965952i \(0.416698\pi\)
\(660\) 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 −0.758939 0.651161i \(-0.774282\pi\)
0.943392 + 0.331680i \(0.107615\pi\)
\(674\) 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 \(-0.402907\pi\)
0.300320 + 0.953839i \(0.402907\pi\)
\(678\) 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 0.672961 0.739678i \(-0.265022\pi\)
−0.304099 + 0.952640i \(0.598355\pi\)
\(684\) −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 \(-0.604054\pi\)
0.321103 0.947044i \(-0.395946\pi\)
\(702\) 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 −0.985457 0.169924i \(-0.945648\pi\)
0.345571 0.938393i \(-0.387685\pi\)
\(720\) −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 \(-0.470262\pi\)
−0.815604 + 0.578610i \(0.803595\pi\)
\(728\) 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 \(-0.137980\pi\)
0.0899987 + 0.995942i \(0.471314\pi\)
\(734\) −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 −0.901155 0.433497i \(-0.857279\pi\)
0.825997 + 0.563675i \(0.190613\pi\)
\(740\) 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 −0.532340 0.846531i \(-0.678687\pi\)
0.466947 + 0.884285i \(0.345354\pi\)
\(744\) −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 −0.997249 0.0741262i \(-0.976383\pi\)
0.562820 + 0.826580i \(0.309717\pi\)
\(752\) 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 0.494775 + 0.869021i \(0.335250\pi\)
−0.999982 + 0.00602283i \(0.998083\pi\)
\(762\) −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 \(-0.625385\pi\)
0.607800 + 0.794090i \(0.292052\pi\)
\(770\) 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 \(-0.845595\pi\)
0.846127 + 0.532982i \(0.178929\pi\)
\(774\) −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
\(781\) 7.15953