Properties

Label 1050.2.bc.h.607.4
Level $1050$
Weight $2$
Character 1050.607
Analytic conductor $8.384$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1050.bc (of order \(12\), degree \(4\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(8.38429221223\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(4\) over \(\Q(\zeta_{12})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
Defining polynomial: \(x^{16} - 4 x^{15} + 12 x^{14} - 48 x^{13} + 67 x^{12} - 24 x^{11} + 118 x^{10} - 176 x^{9} + 351 x^{8} - 180 x^{7} + 358 x^{6} - 336 x^{5} + 390 x^{4} - 344 x^{3} + 164 x^{2} - 40 x + 4\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 210)
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 607.4
Root \(-1.09227 + 0.838128i\) of defining polynomial
Character \(\chi\) \(=\) 1050.607
Dual form 1050.2.bc.h.493.4

$q$-expansion

\(f(q)\) \(=\) \(q+(0.965926 - 0.258819i) q^{2} +(0.258819 - 0.965926i) q^{3} +(0.866025 - 0.500000i) q^{4} -1.00000i q^{6} +(2.64131 - 0.153213i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-0.866025 - 0.500000i) q^{9} +O(q^{10})\) \(q+(0.965926 - 0.258819i) q^{2} +(0.258819 - 0.965926i) q^{3} +(0.866025 - 0.500000i) q^{4} -1.00000i q^{6} +(2.64131 - 0.153213i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-0.866025 - 0.500000i) q^{9} +(2.27722 + 3.94427i) q^{11} +(-0.258819 - 0.965926i) q^{12} +(1.77772 + 1.77772i) q^{13} +(2.51166 - 0.831614i) q^{14} +(0.500000 - 0.866025i) q^{16} +(3.98386 + 1.06747i) q^{17} +(-0.965926 - 0.258819i) q^{18} +(-1.88956 + 3.27281i) q^{19} +(0.535629 - 2.59097i) q^{21} +(3.22048 + 3.22048i) q^{22} +(-2.08426 - 7.77857i) q^{23} +(-0.500000 - 0.866025i) q^{24} +(2.17725 + 1.25704i) q^{26} +(-0.707107 + 0.707107i) q^{27} +(2.21084 - 1.45334i) q^{28} +1.55563i q^{29} +(3.37208 - 1.94687i) q^{31} +(0.258819 - 0.965926i) q^{32} +(4.39926 - 1.17878i) q^{33} +4.12440 q^{34} -1.00000 q^{36} +(-11.0461 + 2.95980i) q^{37} +(-0.978107 + 3.65035i) q^{38} +(2.17725 - 1.25704i) q^{39} -11.3796i q^{41} +(-0.153213 - 2.64131i) q^{42} +(-0.367260 + 0.367260i) q^{43} +(3.94427 + 2.27722i) q^{44} +(-4.02648 - 6.97408i) q^{46} +(-1.30713 - 4.87829i) q^{47} +(-0.707107 - 0.707107i) q^{48} +(6.95305 - 0.809365i) q^{49} +(2.06220 - 3.57183i) q^{51} +(2.42841 + 0.650691i) q^{52} +(-8.14732 - 2.18307i) q^{53} +(-0.500000 + 0.866025i) q^{54} +(1.75935 - 1.97603i) q^{56} +(2.67224 + 2.67224i) q^{57} +(0.402626 + 1.50262i) q^{58} +(0.221511 + 0.383668i) q^{59} +(7.09442 + 4.09597i) q^{61} +(2.75329 - 2.75329i) q^{62} +(-2.36405 - 1.18797i) q^{63} -1.00000i q^{64} +(3.94427 - 2.27722i) q^{66} +(-2.41103 + 8.99808i) q^{67} +(3.98386 - 1.06747i) q^{68} -8.05297 q^{69} -6.68403 q^{71} +(-0.965926 + 0.258819i) q^{72} +(1.12560 - 4.20080i) q^{73} +(-9.90370 + 5.71790i) q^{74} +3.77912i q^{76} +(6.61917 + 10.0691i) q^{77} +(1.77772 - 1.77772i) q^{78} +(4.08283 + 2.35722i) q^{79} +(0.500000 + 0.866025i) q^{81} +(-2.94527 - 10.9919i) q^{82} +(-3.21718 - 3.21718i) q^{83} +(-0.831614 - 2.51166i) q^{84} +(-0.259692 + 0.449799i) q^{86} +(1.50262 + 0.402626i) q^{87} +(4.39926 + 1.17878i) q^{88} +(-3.02425 + 5.23816i) q^{89} +(4.96788 + 4.42314i) q^{91} +(-5.69431 - 5.69431i) q^{92} +(-1.00777 - 3.76106i) q^{93} +(-2.52519 - 4.37376i) q^{94} +(-0.866025 - 0.500000i) q^{96} +(0.462652 - 0.462652i) q^{97} +(6.50665 - 2.58137i) q^{98} -4.55445i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q + 8q^{7} + O(q^{10}) \) \( 16q + 8q^{7} + 4q^{11} + 16q^{13} + 16q^{14} + 8q^{16} + 12q^{17} - 8q^{19} + 8q^{21} - 4q^{22} - 32q^{23} - 8q^{24} - 12q^{26} + 8q^{28} - 24q^{31} - 8q^{33} + 16q^{34} - 16q^{36} + 8q^{37} + 28q^{38} - 12q^{39} + 4q^{42} + 24q^{43} - 4q^{46} + 24q^{47} + 52q^{49} + 8q^{51} + 8q^{52} - 44q^{53} - 8q^{54} + 8q^{56} + 8q^{57} - 48q^{58} + 8q^{59} + 24q^{61} - 8q^{62} - 4q^{63} - 36q^{67} + 12q^{68} - 8q^{69} - 32q^{71} + 40q^{73} - 24q^{74} + 44q^{77} + 16q^{78} + 12q^{79} + 8q^{81} - 12q^{82} + 16q^{83} + 4q^{84} - 8q^{86} - 12q^{87} - 8q^{88} - 16q^{89} + 8q^{91} - 8q^{92} - 40q^{93} + 8q^{94} - 44q^{97} + 8q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(451\) \(701\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(e\left(\frac{5}{6}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.965926 0.258819i 0.683013 0.183013i
\(3\) 0.258819 0.965926i 0.149429 0.557678i
\(4\) 0.866025 0.500000i 0.433013 0.250000i
\(5\) 0 0
\(6\) 1.00000i 0.408248i
\(7\) 2.64131 0.153213i 0.998322 0.0579090i
\(8\) 0.707107 0.707107i 0.250000 0.250000i
\(9\) −0.866025 0.500000i −0.288675 0.166667i
\(10\) 0 0
\(11\) 2.27722 + 3.94427i 0.686609 + 1.18924i 0.972928 + 0.231107i \(0.0742348\pi\)
−0.286319 + 0.958134i \(0.592432\pi\)
\(12\) −0.258819 0.965926i −0.0747146 0.278839i
\(13\) 1.77772 + 1.77772i 0.493051 + 0.493051i 0.909266 0.416215i \(-0.136644\pi\)
−0.416215 + 0.909266i \(0.636644\pi\)
\(14\) 2.51166 0.831614i 0.671268 0.222258i
\(15\) 0 0
\(16\) 0.500000 0.866025i 0.125000 0.216506i
\(17\) 3.98386 + 1.06747i 0.966228 + 0.258900i 0.707234 0.706979i \(-0.249943\pi\)
0.258993 + 0.965879i \(0.416609\pi\)
\(18\) −0.965926 0.258819i −0.227671 0.0610042i
\(19\) −1.88956 + 3.27281i −0.433494 + 0.750834i −0.997171 0.0751610i \(-0.976053\pi\)
0.563677 + 0.825995i \(0.309386\pi\)
\(20\) 0 0
\(21\) 0.535629 2.59097i 0.116884 0.565395i
\(22\) 3.22048 + 3.22048i 0.686609 + 0.686609i
\(23\) −2.08426 7.77857i −0.434599 1.62194i −0.742025 0.670372i \(-0.766134\pi\)
0.307426 0.951572i \(-0.400532\pi\)
\(24\) −0.500000 0.866025i −0.102062 0.176777i
\(25\) 0 0
\(26\) 2.17725 + 1.25704i 0.426995 + 0.246525i
\(27\) −0.707107 + 0.707107i −0.136083 + 0.136083i
\(28\) 2.21084 1.45334i 0.417809 0.274656i
\(29\) 1.55563i 0.288873i 0.989514 + 0.144436i \(0.0461369\pi\)
−0.989514 + 0.144436i \(0.953863\pi\)
\(30\) 0 0
\(31\) 3.37208 1.94687i 0.605643 0.349668i −0.165615 0.986190i \(-0.552961\pi\)
0.771258 + 0.636522i \(0.219628\pi\)
\(32\) 0.258819 0.965926i 0.0457532 0.170753i
\(33\) 4.39926 1.17878i 0.765813 0.205199i
\(34\) 4.12440 0.707328
\(35\) 0 0
\(36\) −1.00000 −0.166667
\(37\) −11.0461 + 2.95980i −1.81597 + 0.486589i −0.996277 0.0862078i \(-0.972525\pi\)
−0.819697 + 0.572797i \(0.805858\pi\)
\(38\) −0.978107 + 3.65035i −0.158670 + 0.592164i
\(39\) 2.17725 1.25704i 0.348640 0.201287i
\(40\) 0 0
\(41\) 11.3796i 1.77720i −0.458682 0.888600i \(-0.651678\pi\)
0.458682 0.888600i \(-0.348322\pi\)
\(42\) −0.153213 2.64131i −0.0236412 0.407563i
\(43\) −0.367260 + 0.367260i −0.0560066 + 0.0560066i −0.734555 0.678549i \(-0.762609\pi\)
0.678549 + 0.734555i \(0.262609\pi\)
\(44\) 3.94427 + 2.27722i 0.594621 + 0.343304i
\(45\) 0 0
\(46\) −4.02648 6.97408i −0.593673 1.02827i
\(47\) −1.30713 4.87829i −0.190665 0.711572i −0.993347 0.115164i \(-0.963261\pi\)
0.802681 0.596408i \(-0.203406\pi\)
\(48\) −0.707107 0.707107i −0.102062 0.102062i
\(49\) 6.95305 0.809365i 0.993293 0.115624i
\(50\) 0 0
\(51\) 2.06220 3.57183i 0.288765 0.500156i
\(52\) 2.42841 + 0.650691i 0.336760 + 0.0902346i
\(53\) −8.14732 2.18307i −1.11912 0.299868i −0.348593 0.937274i \(-0.613341\pi\)
−0.770528 + 0.637407i \(0.780007\pi\)
\(54\) −0.500000 + 0.866025i −0.0680414 + 0.117851i
\(55\) 0 0
\(56\) 1.75935 1.97603i 0.235103 0.264058i
\(57\) 2.67224 + 2.67224i 0.353947 + 0.353947i
\(58\) 0.402626 + 1.50262i 0.0528674 + 0.197304i
\(59\) 0.221511 + 0.383668i 0.0288383 + 0.0499493i 0.880084 0.474817i \(-0.157486\pi\)
−0.851246 + 0.524767i \(0.824153\pi\)
\(60\) 0 0
\(61\) 7.09442 + 4.09597i 0.908348 + 0.524435i 0.879899 0.475160i \(-0.157610\pi\)
0.0284488 + 0.999595i \(0.490943\pi\)
\(62\) 2.75329 2.75329i 0.349668 0.349668i
\(63\) −2.36405 1.18797i −0.297842 0.149670i
\(64\) 1.00000i 0.125000i
\(65\) 0 0
\(66\) 3.94427 2.27722i 0.485506 0.280307i
\(67\) −2.41103 + 8.99808i −0.294554 + 1.09929i 0.647017 + 0.762476i \(0.276016\pi\)
−0.941571 + 0.336815i \(0.890650\pi\)
\(68\) 3.98386 1.06747i 0.483114 0.129450i
\(69\) −8.05297 −0.969464
\(70\) 0 0
\(71\) −6.68403 −0.793248 −0.396624 0.917981i \(-0.629818\pi\)
−0.396624 + 0.917981i \(0.629818\pi\)
\(72\) −0.965926 + 0.258819i −0.113835 + 0.0305021i
\(73\) 1.12560 4.20080i 0.131742 0.491666i −0.868249 0.496130i \(-0.834754\pi\)
0.999990 + 0.00446349i \(0.00142078\pi\)
\(74\) −9.90370 + 5.71790i −1.15128 + 0.664693i
\(75\) 0 0
\(76\) 3.77912i 0.433494i
\(77\) 6.61917 + 10.0691i 0.754324 + 1.14748i
\(78\) 1.77772 1.77772i 0.201287 0.201287i
\(79\) 4.08283 + 2.35722i 0.459354 + 0.265208i 0.711773 0.702410i \(-0.247893\pi\)
−0.252418 + 0.967618i \(0.581226\pi\)
\(80\) 0 0
\(81\) 0.500000 + 0.866025i 0.0555556 + 0.0962250i
\(82\) −2.94527 10.9919i −0.325250 1.21385i
\(83\) −3.21718 3.21718i −0.353131 0.353131i 0.508142 0.861273i \(-0.330332\pi\)
−0.861273 + 0.508142i \(0.830332\pi\)
\(84\) −0.831614 2.51166i −0.0907365 0.274044i
\(85\) 0 0
\(86\) −0.259692 + 0.449799i −0.0280033 + 0.0485031i
\(87\) 1.50262 + 0.402626i 0.161098 + 0.0431660i
\(88\) 4.39926 + 1.17878i 0.468963 + 0.125658i
\(89\) −3.02425 + 5.23816i −0.320570 + 0.555244i −0.980606 0.195990i \(-0.937208\pi\)
0.660035 + 0.751234i \(0.270541\pi\)
\(90\) 0 0
\(91\) 4.96788 + 4.42314i 0.520775 + 0.463671i
\(92\) −5.69431 5.69431i −0.593673 0.593673i
\(93\) −1.00777 3.76106i −0.104501 0.390004i
\(94\) −2.52519 4.37376i −0.260453 0.451118i
\(95\) 0 0
\(96\) −0.866025 0.500000i −0.0883883 0.0510310i
\(97\) 0.462652 0.462652i 0.0469752 0.0469752i −0.683229 0.730204i \(-0.739425\pi\)
0.730204 + 0.683229i \(0.239425\pi\)
\(98\) 6.50665 2.58137i 0.657271 0.260758i
\(99\) 4.55445i 0.457739i
\(100\) 0 0
\(101\) −4.85151 + 2.80102i −0.482743 + 0.278712i −0.721559 0.692353i \(-0.756574\pi\)
0.238816 + 0.971065i \(0.423241\pi\)
\(102\) 1.06747 3.98386i 0.105695 0.394461i
\(103\) 5.36863 1.43852i 0.528987 0.141742i 0.0155666 0.999879i \(-0.495045\pi\)
0.513420 + 0.858137i \(0.328378\pi\)
\(104\) 2.51408 0.246525
\(105\) 0 0
\(106\) −8.43473 −0.819253
\(107\) 7.23514 1.93865i 0.699447 0.187416i 0.108464 0.994100i \(-0.465407\pi\)
0.590983 + 0.806684i \(0.298740\pi\)
\(108\) −0.258819 + 0.965926i −0.0249049 + 0.0929463i
\(109\) −1.27034 + 0.733433i −0.121677 + 0.0702501i −0.559603 0.828761i \(-0.689046\pi\)
0.437926 + 0.899011i \(0.355713\pi\)
\(110\) 0 0
\(111\) 11.4358i 1.08544i
\(112\) 1.18797 2.36405i 0.112253 0.223382i
\(113\) −7.08834 + 7.08834i −0.666815 + 0.666815i −0.956977 0.290163i \(-0.906291\pi\)
0.290163 + 0.956977i \(0.406291\pi\)
\(114\) 3.27281 + 1.88956i 0.306527 + 0.176973i
\(115\) 0 0
\(116\) 0.777814 + 1.34721i 0.0722182 + 0.125086i
\(117\) −0.650691 2.42841i −0.0601564 0.224507i
\(118\) 0.313264 + 0.313264i 0.0288383 + 0.0288383i
\(119\) 10.6862 + 2.20915i 0.979599 + 0.202512i
\(120\) 0 0
\(121\) −4.87150 + 8.43768i −0.442863 + 0.767062i
\(122\) 7.91280 + 2.12023i 0.716391 + 0.191957i
\(123\) −10.9919 2.94527i −0.991105 0.265566i
\(124\) 1.94687 3.37208i 0.174834 0.302821i
\(125\) 0 0
\(126\) −2.59097 0.535629i −0.230822 0.0477177i
\(127\) −12.9176 12.9176i −1.14625 1.14625i −0.987283 0.158971i \(-0.949182\pi\)
−0.158971 0.987283i \(-0.550818\pi\)
\(128\) −0.258819 0.965926i −0.0228766 0.0853766i
\(129\) 0.259692 + 0.449799i 0.0228646 + 0.0396026i
\(130\) 0 0
\(131\) 0.323655 + 0.186862i 0.0282779 + 0.0163262i 0.514072 0.857747i \(-0.328136\pi\)
−0.485794 + 0.874073i \(0.661470\pi\)
\(132\) 3.22048 3.22048i 0.280307 0.280307i
\(133\) −4.48947 + 8.93402i −0.389287 + 0.774677i
\(134\) 9.31550i 0.804737i
\(135\) 0 0
\(136\) 3.57183 2.06220i 0.306282 0.176832i
\(137\) 0.688094 2.56800i 0.0587878 0.219399i −0.930282 0.366844i \(-0.880438\pi\)
0.989070 + 0.147445i \(0.0471049\pi\)
\(138\) −7.77857 + 2.08426i −0.662156 + 0.177424i
\(139\) −4.58070 −0.388530 −0.194265 0.980949i \(-0.562232\pi\)
−0.194265 + 0.980949i \(0.562232\pi\)
\(140\) 0 0
\(141\) −5.05038 −0.425319
\(142\) −6.45627 + 1.72995i −0.541798 + 0.145174i
\(143\) −2.96354 + 11.0601i −0.247823 + 0.924889i
\(144\) −0.866025 + 0.500000i −0.0721688 + 0.0416667i
\(145\) 0 0
\(146\) 4.34898i 0.359925i
\(147\) 1.01780 6.92561i 0.0839463 0.571215i
\(148\) −8.08634 + 8.08634i −0.664693 + 0.664693i
\(149\) −14.9338 8.62203i −1.22342 0.706344i −0.257778 0.966204i \(-0.582990\pi\)
−0.965646 + 0.259860i \(0.916324\pi\)
\(150\) 0 0
\(151\) 2.78385 + 4.82177i 0.226546 + 0.392390i 0.956782 0.290805i \(-0.0939231\pi\)
−0.730236 + 0.683195i \(0.760590\pi\)
\(152\) 0.978107 + 3.65035i 0.0793350 + 0.296082i
\(153\) −2.91639 2.91639i −0.235776 0.235776i
\(154\) 8.99971 + 8.01287i 0.725217 + 0.645696i
\(155\) 0 0
\(156\) 1.25704 2.17725i 0.100644 0.174320i
\(157\) 3.99014 + 1.06916i 0.318448 + 0.0853279i 0.414503 0.910048i \(-0.363956\pi\)
−0.0960544 + 0.995376i \(0.530622\pi\)
\(158\) 4.55381 + 1.22019i 0.362281 + 0.0970730i
\(159\) −4.21737 + 7.30469i −0.334459 + 0.579300i
\(160\) 0 0
\(161\) −6.69696 20.2263i −0.527795 1.59406i
\(162\) 0.707107 + 0.707107i 0.0555556 + 0.0555556i
\(163\) 5.62644 + 20.9982i 0.440697 + 1.64470i 0.727054 + 0.686580i \(0.240889\pi\)
−0.286357 + 0.958123i \(0.592444\pi\)
\(164\) −5.68982 9.85506i −0.444300 0.769551i
\(165\) 0 0
\(166\) −3.94022 2.27489i −0.305821 0.176566i
\(167\) −17.4949 + 17.4949i −1.35380 + 1.35380i −0.472425 + 0.881371i \(0.656621\pi\)
−0.881371 + 0.472425i \(0.843379\pi\)
\(168\) −1.45334 2.21084i −0.112128 0.170570i
\(169\) 6.67942i 0.513802i
\(170\) 0 0
\(171\) 3.27281 1.88956i 0.250278 0.144498i
\(172\) −0.134426 + 0.501686i −0.0102499 + 0.0382532i
\(173\) 16.0017 4.28763i 1.21658 0.325982i 0.407241 0.913321i \(-0.366491\pi\)
0.809342 + 0.587338i \(0.199824\pi\)
\(174\) 1.55563 0.117932
\(175\) 0 0
\(176\) 4.55445 0.343304
\(177\) 0.427926 0.114663i 0.0321649 0.00861856i
\(178\) −1.56547 + 5.84241i −0.117337 + 0.437907i
\(179\) 11.0222 6.36367i 0.823837 0.475643i −0.0279007 0.999611i \(-0.508882\pi\)
0.851738 + 0.523968i \(0.175549\pi\)
\(180\) 0 0
\(181\) 9.09951i 0.676361i 0.941081 + 0.338180i \(0.109811\pi\)
−0.941081 + 0.338180i \(0.890189\pi\)
\(182\) 5.94340 + 2.98665i 0.440554 + 0.221385i
\(183\) 5.79257 5.79257i 0.428199 0.428199i
\(184\) −6.97408 4.02648i −0.514136 0.296836i
\(185\) 0 0
\(186\) −1.94687 3.37208i −0.142751 0.247253i
\(187\) 4.86175 + 18.1443i 0.355526 + 1.32684i
\(188\) −3.57116 3.57116i −0.260453 0.260453i
\(189\) −1.75935 + 1.97603i −0.127974 + 0.143735i
\(190\) 0 0
\(191\) −9.10308 + 15.7670i −0.658676 + 1.14086i 0.322283 + 0.946643i \(0.395550\pi\)
−0.980959 + 0.194216i \(0.937784\pi\)
\(192\) −0.965926 0.258819i −0.0697097 0.0186787i
\(193\) −9.72810 2.60664i −0.700244 0.187630i −0.108904 0.994052i \(-0.534734\pi\)
−0.591340 + 0.806422i \(0.701401\pi\)
\(194\) 0.327144 0.566631i 0.0234876 0.0406817i
\(195\) 0 0
\(196\) 5.61684 4.17746i 0.401203 0.298390i
\(197\) −16.2439 16.2439i −1.15733 1.15733i −0.985048 0.172283i \(-0.944886\pi\)
−0.172283 0.985048i \(-0.555114\pi\)
\(198\) −1.17878 4.39926i −0.0837721 0.312642i
\(199\) 12.6984 + 21.9943i 0.900168 + 1.55914i 0.827275 + 0.561797i \(0.189890\pi\)
0.0728933 + 0.997340i \(0.476777\pi\)
\(200\) 0 0
\(201\) 8.06746 + 4.65775i 0.569035 + 0.328532i
\(202\) −3.96124 + 3.96124i −0.278712 + 0.278712i
\(203\) 0.238342 + 4.10890i 0.0167283 + 0.288388i
\(204\) 4.12440i 0.288765i
\(205\) 0 0
\(206\) 4.81338 2.77901i 0.335364 0.193623i
\(207\) −2.08426 + 7.77857i −0.144866 + 0.540648i
\(208\) 2.42841 0.650691i 0.168380 0.0451173i
\(209\) −17.2118 −1.19056
\(210\) 0 0
\(211\) −13.6182 −0.937517 −0.468759 0.883326i \(-0.655299\pi\)
−0.468759 + 0.883326i \(0.655299\pi\)
\(212\) −8.14732 + 2.18307i −0.559560 + 0.149934i
\(213\) −1.72995 + 6.45627i −0.118534 + 0.442377i
\(214\) 6.48684 3.74518i 0.443432 0.256015i
\(215\) 0 0
\(216\) 1.00000i 0.0680414i
\(217\) 8.60842 5.65893i 0.584378 0.384153i
\(218\) −1.03723 + 1.03723i −0.0702501 + 0.0702501i
\(219\) −3.76633 2.17449i −0.254505 0.146939i
\(220\) 0 0
\(221\) 5.18452 + 8.97985i 0.348749 + 0.604050i
\(222\) 2.95980 + 11.0461i 0.198649 + 0.741369i
\(223\) 15.8412 + 15.8412i 1.06081 + 1.06081i 0.998027 + 0.0627803i \(0.0199968\pi\)
0.0627803 + 0.998027i \(0.480003\pi\)
\(224\) 0.535629 2.59097i 0.0357883 0.173116i
\(225\) 0 0
\(226\) −5.01221 + 8.68141i −0.333407 + 0.577479i
\(227\) 10.5795 + 2.83476i 0.702184 + 0.188150i 0.592209 0.805785i \(-0.298256\pi\)
0.109976 + 0.993934i \(0.464923\pi\)
\(228\) 3.65035 + 0.978107i 0.241750 + 0.0647767i
\(229\) 14.4722 25.0665i 0.956347 1.65644i 0.225092 0.974338i \(-0.427732\pi\)
0.731255 0.682104i \(-0.238935\pi\)
\(230\) 0 0
\(231\) 11.4392 3.78754i 0.752645 0.249202i
\(232\) 1.09999 + 1.09999i 0.0722182 + 0.0722182i
\(233\) −0.365476 1.36397i −0.0239431 0.0893569i 0.952920 0.303220i \(-0.0980619\pi\)
−0.976864 + 0.213864i \(0.931395\pi\)
\(234\) −1.25704 2.17725i −0.0821751 0.142332i
\(235\) 0 0
\(236\) 0.383668 + 0.221511i 0.0249747 + 0.0144191i
\(237\) 3.33362 3.33362i 0.216542 0.216542i
\(238\) 10.8938 0.631910i 0.706141 0.0409606i
\(239\) 4.36430i 0.282303i 0.989988 + 0.141152i \(0.0450805\pi\)
−0.989988 + 0.141152i \(0.954920\pi\)
\(240\) 0 0
\(241\) −2.65862 + 1.53496i −0.171257 + 0.0988752i −0.583178 0.812344i \(-0.698191\pi\)
0.411922 + 0.911219i \(0.364858\pi\)
\(242\) −2.52167 + 9.41101i −0.162099 + 0.604963i
\(243\) 0.965926 0.258819i 0.0619642 0.0166032i
\(244\) 8.19194 0.524435
\(245\) 0 0
\(246\) −11.3796 −0.725539
\(247\) −9.17725 + 2.45904i −0.583934 + 0.156465i
\(248\) 1.00777 3.76106i 0.0639937 0.238828i
\(249\) −3.94022 + 2.27489i −0.249701 + 0.144165i
\(250\) 0 0
\(251\) 1.25355i 0.0791234i −0.999217 0.0395617i \(-0.987404\pi\)
0.999217 0.0395617i \(-0.0125962\pi\)
\(252\) −2.64131 + 0.153213i −0.166387 + 0.00965150i
\(253\) 25.9344 25.9344i 1.63048 1.63048i
\(254\) −15.8208 9.13414i −0.992685 0.573127i
\(255\) 0 0
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) −1.82683 6.81783i −0.113955 0.425285i 0.885252 0.465112i \(-0.153986\pi\)
−0.999207 + 0.0398273i \(0.987319\pi\)
\(258\) 0.367260 + 0.367260i 0.0228646 + 0.0228646i
\(259\) −28.7228 + 9.51018i −1.78475 + 0.590934i
\(260\) 0 0
\(261\) 0.777814 1.34721i 0.0481455 0.0833904i
\(262\) 0.360990 + 0.0967271i 0.0223021 + 0.00597582i
\(263\) −5.49409 1.47214i −0.338780 0.0907758i 0.0854182 0.996345i \(-0.472777\pi\)
−0.424198 + 0.905569i \(0.639444\pi\)
\(264\) 2.27722 3.94427i 0.140153 0.242753i
\(265\) 0 0
\(266\) −2.02421 + 9.79156i −0.124112 + 0.600359i
\(267\) 4.27694 + 4.27694i 0.261745 + 0.261745i
\(268\) 2.41103 + 8.99808i 0.147277 + 0.549645i
\(269\) −3.85391 6.67517i −0.234977 0.406992i 0.724289 0.689496i \(-0.242168\pi\)
−0.959266 + 0.282504i \(0.908835\pi\)
\(270\) 0 0
\(271\) −15.4900 8.94316i −0.940951 0.543258i −0.0506925 0.998714i \(-0.516143\pi\)
−0.890258 + 0.455456i \(0.849476\pi\)
\(272\) 2.91639 2.91639i 0.176832 0.176832i
\(273\) 5.55821 3.65381i 0.336398 0.221139i
\(274\) 2.65859i 0.160611i
\(275\) 0 0
\(276\) −6.97408 + 4.02648i −0.419790 + 0.242366i
\(277\) −3.81664 + 14.2439i −0.229319 + 0.855832i 0.751308 + 0.659951i \(0.229423\pi\)
−0.980628 + 0.195881i \(0.937244\pi\)
\(278\) −4.42461 + 1.18557i −0.265371 + 0.0711059i
\(279\) −3.89374 −0.233112
\(280\) 0 0
\(281\) 0.587402 0.0350415 0.0175207 0.999847i \(-0.494423\pi\)
0.0175207 + 0.999847i \(0.494423\pi\)
\(282\) −4.87829 + 1.30713i −0.290498 + 0.0778387i
\(283\) −4.81795 + 17.9809i −0.286398 + 1.06885i 0.661414 + 0.750021i \(0.269957\pi\)
−0.947812 + 0.318830i \(0.896710\pi\)
\(284\) −5.78854 + 3.34201i −0.343486 + 0.198312i
\(285\) 0 0
\(286\) 11.4502i 0.677066i
\(287\) −1.74351 30.0572i −0.102916 1.77422i
\(288\) −0.707107 + 0.707107i −0.0416667 + 0.0416667i
\(289\) 0.00921092 + 0.00531793i 0.000541819 + 0.000312819i
\(290\) 0 0
\(291\) −0.327144 0.566631i −0.0191775 0.0332165i
\(292\) −1.12560 4.20080i −0.0658708 0.245833i
\(293\) −20.6736 20.6736i −1.20777 1.20777i −0.971749 0.236018i \(-0.924158\pi\)
−0.236018 0.971749i \(-0.575842\pi\)
\(294\) −0.809365 6.95305i −0.0472031 0.405510i
\(295\) 0 0
\(296\) −5.71790 + 9.90370i −0.332346 + 0.575641i
\(297\) −4.39926 1.17878i −0.255271 0.0683996i
\(298\) −16.6565 4.46309i −0.964884 0.258540i
\(299\) 10.1229 17.5334i 0.585422 1.01398i
\(300\) 0 0
\(301\) −0.913778 + 1.02632i −0.0526693 + 0.0591559i
\(302\) 3.93696 + 3.93696i 0.226546 + 0.226546i
\(303\) 1.44991 + 5.41115i 0.0832954 + 0.310863i
\(304\) 1.88956 + 3.27281i 0.108374 + 0.187709i
\(305\) 0 0
\(306\) −3.57183 2.06220i −0.204188 0.117888i
\(307\) −1.63464 + 1.63464i −0.0932937 + 0.0932937i −0.752213 0.658920i \(-0.771014\pi\)
0.658920 + 0.752213i \(0.271014\pi\)
\(308\) 10.7669 + 5.41055i 0.613503 + 0.308294i
\(309\) 5.55802i 0.316185i
\(310\) 0 0
\(311\) 12.0239 6.94197i 0.681810 0.393643i −0.118727 0.992927i \(-0.537881\pi\)
0.800537 + 0.599284i \(0.204548\pi\)
\(312\) 0.650691 2.42841i 0.0368381 0.137482i
\(313\) −13.0307 + 3.49157i −0.736540 + 0.197355i −0.607540 0.794289i \(-0.707843\pi\)
−0.129000 + 0.991645i \(0.541177\pi\)
\(314\) 4.13090 0.233120
\(315\) 0 0
\(316\) 4.71445 0.265208
\(317\) 13.2497 3.55024i 0.744175 0.199401i 0.133242 0.991083i \(-0.457461\pi\)
0.610933 + 0.791682i \(0.290794\pi\)
\(318\) −2.18307 + 8.14732i −0.122420 + 0.456879i
\(319\) −6.13581 + 3.54251i −0.343539 + 0.198343i
\(320\) 0 0
\(321\) 7.49036i 0.418071i
\(322\) −11.7037 17.8038i −0.652223 0.992167i
\(323\) −11.0214 + 11.0214i −0.613245 + 0.613245i
\(324\) 0.866025 + 0.500000i 0.0481125 + 0.0277778i
\(325\) 0 0
\(326\) 10.8694 + 18.8264i 0.602003 + 1.04270i
\(327\) 0.379653 + 1.41688i 0.0209948 + 0.0783538i
\(328\) −8.04662 8.04662i −0.444300 0.444300i
\(329\) −4.19996 12.6848i −0.231552 0.699336i
\(330\) 0 0
\(331\) −16.6194 + 28.7856i −0.913483 + 1.58220i −0.104375 + 0.994538i \(0.533284\pi\)
−0.809108 + 0.587660i \(0.800049\pi\)
\(332\) −4.39475 1.17757i −0.241193 0.0646275i
\(333\) 11.0461 + 2.95980i 0.605325 + 0.162196i
\(334\) −12.3708 + 21.4268i −0.676898 + 1.17242i
\(335\) 0 0
\(336\) −1.97603 1.75935i −0.107801 0.0959805i
\(337\) 17.0329 + 17.0329i 0.927842 + 0.927842i 0.997566 0.0697246i \(-0.0222121\pi\)
−0.0697246 + 0.997566i \(0.522212\pi\)
\(338\) −1.72876 6.45183i −0.0940323 0.350933i
\(339\) 5.01221 + 8.68141i 0.272226 + 0.471509i
\(340\) 0 0
\(341\) 15.3579 + 8.86691i 0.831679 + 0.480170i
\(342\) 2.67224 2.67224i 0.144498 0.144498i
\(343\) 18.2412 3.20308i 0.984931 0.172950i
\(344\) 0.519384i 0.0280033i
\(345\) 0 0
\(346\) 14.3467 8.28306i 0.771283 0.445300i
\(347\) −0.532414 + 1.98700i −0.0285815 + 0.106668i −0.978743 0.205090i \(-0.934251\pi\)
0.950162 + 0.311758i \(0.100918\pi\)
\(348\) 1.50262 0.402626i 0.0805489 0.0215830i
\(349\) 11.7250 0.627627 0.313814 0.949485i \(-0.398393\pi\)
0.313814 + 0.949485i \(0.398393\pi\)
\(350\) 0 0
\(351\) −2.51408 −0.134191
\(352\) 4.39926 1.17878i 0.234481 0.0628291i
\(353\) 2.95640 11.0334i 0.157353 0.587250i −0.841539 0.540196i \(-0.818350\pi\)
0.998892 0.0470542i \(-0.0149833\pi\)
\(354\) 0.383668 0.221511i 0.0203917 0.0117732i
\(355\) 0 0
\(356\) 6.04851i 0.320570i
\(357\) 4.89966 9.75027i 0.259317 0.516039i
\(358\) 8.99958 8.99958i 0.475643 0.475643i
\(359\) −2.08846 1.20577i −0.110225 0.0636383i 0.443874 0.896089i \(-0.353604\pi\)
−0.554099 + 0.832451i \(0.686937\pi\)
\(360\) 0 0
\(361\) 2.35914 + 4.08615i 0.124165 + 0.215061i
\(362\) 2.35513 + 8.78945i 0.123783 + 0.461963i
\(363\) 6.88934 + 6.88934i 0.361596 + 0.361596i
\(364\) 6.51388 + 1.34661i 0.341420 + 0.0705817i
\(365\) 0 0
\(366\) 4.09597 7.09442i 0.214100 0.370832i
\(367\) −5.03135 1.34815i −0.262635 0.0703727i 0.125099 0.992144i \(-0.460075\pi\)
−0.387733 + 0.921772i \(0.626742\pi\)
\(368\) −7.77857 2.08426i −0.405486 0.108650i
\(369\) −5.68982 + 9.85506i −0.296200 + 0.513034i
\(370\) 0 0
\(371\) −21.8541 4.51789i −1.13461 0.234557i
\(372\) −2.75329 2.75329i −0.142751 0.142751i
\(373\) 0.0379573 + 0.141659i 0.00196535 + 0.00733480i 0.966902 0.255150i \(-0.0821248\pi\)
−0.964936 + 0.262485i \(0.915458\pi\)
\(374\) 9.39217 + 16.2677i 0.485658 + 0.841184i
\(375\) 0 0
\(376\) −4.37376 2.52519i −0.225559 0.130227i
\(377\) −2.76547 + 2.76547i −0.142429 + 0.142429i
\(378\) −1.18797 + 2.36405i −0.0611026 + 0.121594i
\(379\) 18.5438i 0.952530i −0.879302 0.476265i \(-0.841990\pi\)
0.879302 0.476265i \(-0.158010\pi\)
\(380\) 0 0
\(381\) −15.8208 + 9.13414i −0.810524 + 0.467956i
\(382\) −4.71210 + 17.5858i −0.241092 + 0.899768i
\(383\) 3.71843 0.996351i 0.190003 0.0509112i −0.162563 0.986698i \(-0.551976\pi\)
0.352566 + 0.935787i \(0.385309\pi\)
\(384\) −1.00000 −0.0510310
\(385\) 0 0
\(386\) −10.0713 −0.512614
\(387\) 0.501686 0.134426i 0.0255021 0.00683328i
\(388\) 0.169342 0.631994i 0.00859706 0.0320847i
\(389\) 15.4340 8.91085i 0.782537 0.451798i −0.0547917 0.998498i \(-0.517449\pi\)
0.837329 + 0.546700i \(0.184116\pi\)
\(390\) 0 0
\(391\) 33.2136i 1.67969i
\(392\) 4.34424 5.48886i 0.219417 0.277229i
\(393\) 0.264263 0.264263i 0.0133303 0.0133303i
\(394\) −19.8946 11.4862i −1.00228 0.578665i
\(395\) 0 0
\(396\) −2.27722 3.94427i −0.114435 0.198207i
\(397\) −6.63778 24.7725i −0.333141 1.24330i −0.905871 0.423554i \(-0.860782\pi\)
0.572730 0.819744i \(-0.305884\pi\)
\(398\) 17.9583 + 17.9583i 0.900168 + 0.900168i
\(399\) 7.46764 + 6.64879i 0.373849 + 0.332856i
\(400\) 0 0
\(401\) 2.63060 4.55632i 0.131366 0.227532i −0.792838 0.609433i \(-0.791397\pi\)
0.924203 + 0.381901i \(0.124730\pi\)
\(402\) 8.99808 + 2.41103i 0.448784 + 0.120251i
\(403\) 9.45560 + 2.53362i 0.471017 + 0.126209i
\(404\) −2.80102 + 4.85151i −0.139356 + 0.241371i
\(405\) 0 0
\(406\) 1.29368 + 3.90720i 0.0642043 + 0.193911i
\(407\) −36.8288 36.8288i −1.82554 1.82554i
\(408\) −1.06747 3.98386i −0.0528477 0.197230i
\(409\) 4.18773 + 7.25336i 0.207070 + 0.358655i 0.950790 0.309835i \(-0.100274\pi\)
−0.743720 + 0.668491i \(0.766941\pi\)
\(410\) 0 0
\(411\) −2.30241 1.32929i −0.113569 0.0655693i
\(412\) 3.93011 3.93011i 0.193623 0.193623i
\(413\) 0.643862 + 0.979449i 0.0316824 + 0.0481955i
\(414\) 8.05297i 0.395782i
\(415\) 0 0
\(416\) 2.17725 1.25704i 0.106749 0.0616313i
\(417\) −1.18557 + 4.42461i −0.0580577 + 0.216674i
\(418\) −16.6253 + 4.45474i −0.813170 + 0.217888i
\(419\) 9.53078 0.465609 0.232805 0.972524i \(-0.425210\pi\)
0.232805 + 0.972524i \(0.425210\pi\)
\(420\) 0 0
\(421\) 16.8461 0.821027 0.410514 0.911854i \(-0.365349\pi\)
0.410514 + 0.911854i \(0.365349\pi\)
\(422\) −13.1542 + 3.52466i −0.640336 + 0.171578i
\(423\) −1.30713 + 4.87829i −0.0635550 + 0.237191i
\(424\) −7.30469 + 4.21737i −0.354747 + 0.204813i
\(425\) 0 0
\(426\) 6.68403i 0.323842i
\(427\) 19.3661 + 9.73177i 0.937193 + 0.470953i
\(428\) 5.29649 5.29649i 0.256015 0.256015i
\(429\) 9.91619 + 5.72511i 0.478758 + 0.276411i
\(430\) 0 0
\(431\) −10.7791 18.6699i −0.519209 0.899297i −0.999751 0.0223251i \(-0.992893\pi\)
0.480541 0.876972i \(-0.340440\pi\)
\(432\) 0.258819 + 0.965926i 0.0124524 + 0.0464731i
\(433\) −25.8823 25.8823i −1.24382 1.24382i −0.958402 0.285422i \(-0.907866\pi\)
−0.285422 0.958402i \(-0.592134\pi\)
\(434\) 6.85045 7.69413i 0.328832 0.369330i
\(435\) 0 0
\(436\) −0.733433 + 1.27034i −0.0351251 + 0.0608384i
\(437\) 29.3961 + 7.87667i 1.40621 + 0.376792i
\(438\) −4.20080 1.12560i −0.200722 0.0537832i
\(439\) 10.5899 18.3422i 0.505426 0.875424i −0.494554 0.869147i \(-0.664669\pi\)
0.999980 0.00627716i \(-0.00199809\pi\)
\(440\) 0 0
\(441\) −6.42620 2.77559i −0.306010 0.132171i
\(442\) 7.33202 + 7.33202i 0.348749 + 0.348749i
\(443\) 1.07420 + 4.00895i 0.0510366 + 0.190471i 0.986738 0.162322i \(-0.0518985\pi\)
−0.935701 + 0.352794i \(0.885232\pi\)
\(444\) 5.71790 + 9.90370i 0.271360 + 0.470009i
\(445\) 0 0
\(446\) 19.4015 + 11.2014i 0.918686 + 0.530404i
\(447\) −12.1934 + 12.1934i −0.576728 + 0.576728i
\(448\) −0.153213 2.64131i −0.00723862 0.124790i
\(449\) 29.3795i 1.38651i −0.720694 0.693253i \(-0.756177\pi\)
0.720694 0.693253i \(-0.243823\pi\)
\(450\) 0 0
\(451\) 44.8843 25.9140i 2.11352 1.22024i
\(452\) −2.59451 + 9.68285i −0.122036 + 0.455443i
\(453\) 5.37799 1.44103i 0.252680 0.0677053i
\(454\) 10.9527 0.514035
\(455\) 0 0
\(456\) 3.77912 0.176973
\(457\) −0.455291 + 0.121995i −0.0212976 + 0.00570668i −0.269452 0.963014i \(-0.586843\pi\)
0.248155 + 0.968720i \(0.420176\pi\)
\(458\) 7.49134 27.9581i 0.350047 1.30639i
\(459\) −3.57183 + 2.06220i −0.166719 + 0.0962551i
\(460\) 0 0
\(461\) 26.3199i 1.22584i −0.790145 0.612920i \(-0.789995\pi\)
0.790145 0.612920i \(-0.210005\pi\)
\(462\) 10.0691 6.61917i 0.468459 0.307952i
\(463\) 1.02619 1.02619i 0.0476909 0.0476909i −0.682859 0.730550i \(-0.739264\pi\)
0.730550 + 0.682859i \(0.239264\pi\)
\(464\) 1.34721 + 0.777814i 0.0625428 + 0.0361091i
\(465\) 0 0
\(466\) −0.706045 1.22291i −0.0327069 0.0566500i
\(467\) 8.02693 + 29.9569i 0.371442 + 1.38624i 0.858475 + 0.512856i \(0.171413\pi\)
−0.487033 + 0.873384i \(0.661921\pi\)
\(468\) −1.77772 1.77772i −0.0821751 0.0821751i
\(469\) −4.98966 + 24.1361i −0.230401 + 1.11450i
\(470\) 0 0
\(471\) 2.06545 3.57747i 0.0951709 0.164841i
\(472\) 0.427926 + 0.114663i 0.0196969 + 0.00527777i
\(473\) −2.28490 0.612238i −0.105060 0.0281507i
\(474\) 2.35722 4.08283i 0.108271 0.187531i
\(475\) 0 0
\(476\) 10.3591 3.42990i 0.474807 0.157209i
\(477\) 5.96425 + 5.96425i 0.273084 + 0.273084i
\(478\) 1.12956 + 4.21559i 0.0516650 + 0.192817i
\(479\) 16.6760 + 28.8837i 0.761945 + 1.31973i 0.941847 + 0.336043i \(0.109089\pi\)
−0.179901 + 0.983685i \(0.557578\pi\)
\(480\) 0 0
\(481\) −24.8987 14.3752i −1.13528 0.655455i
\(482\) −2.17075 + 2.17075i −0.0988752 + 0.0988752i
\(483\) −21.2704 + 1.23382i −0.967837 + 0.0561407i
\(484\) 9.74299i 0.442863i
\(485\) 0 0
\(486\) 0.866025 0.500000i 0.0392837 0.0226805i
\(487\) 0.855056 3.19111i 0.0387463 0.144603i −0.943843 0.330395i \(-0.892818\pi\)
0.982589 + 0.185791i \(0.0594849\pi\)
\(488\) 7.91280 2.12023i 0.358196 0.0959783i
\(489\) 21.7389 0.983067
\(490\) 0 0
\(491\) 3.61649 0.163210 0.0816051 0.996665i \(-0.473995\pi\)
0.0816051 + 0.996665i \(0.473995\pi\)
\(492\) −10.9919 + 2.94527i −0.495552 + 0.132783i
\(493\) −1.66059 + 6.19740i −0.0747891 + 0.279117i
\(494\) −8.22809 + 4.75049i −0.370199 + 0.213735i
\(495\) 0 0
\(496\) 3.89374i 0.174834i
\(497\) −17.6546 + 1.02408i −0.791917 + 0.0459362i
\(498\) −3.21718 + 3.21718i −0.144165 + 0.144165i
\(499\) −0.561004 0.323896i −0.0251140 0.0144996i 0.487390 0.873184i \(-0.337949\pi\)
−0.512504 + 0.858685i \(0.671282\pi\)
\(500\) 0 0
\(501\) 12.3708 + 21.4268i 0.552685 + 0.957278i
\(502\) −0.324443 1.21084i −0.0144806 0.0540423i
\(503\) 12.9189 + 12.9189i 0.576027 + 0.576027i 0.933806 0.357779i \(-0.116466\pi\)
−0.357779 + 0.933806i \(0.616466\pi\)
\(504\) −2.51166 + 0.831614i −0.111878 + 0.0370430i
\(505\) 0 0
\(506\) 18.3384 31.7631i 0.815242 1.41204i
\(507\) −6.45183 1.72876i −0.286536 0.0767770i
\(508\) −17.6458 4.72818i −0.782906 0.209779i
\(509\) −10.1554 + 17.5896i −0.450128 + 0.779645i −0.998394 0.0566595i \(-0.981955\pi\)
0.548265 + 0.836304i \(0.315288\pi\)
\(510\) 0 0
\(511\) 2.32944 11.2681i 0.103049 0.498470i
\(512\) −0.707107 0.707107i −0.0312500 0.0312500i
\(513\) −0.978107 3.65035i −0.0431845 0.161167i
\(514\) −3.52917 6.11270i −0.155665 0.269620i
\(515\) 0 0
\(516\) 0.449799 + 0.259692i 0.0198013 + 0.0114323i
\(517\) 16.2646 16.2646i 0.715318 0.715318i
\(518\) −25.2827 + 16.6201i −1.11086 + 0.730247i
\(519\) 16.5661i 0.727172i
\(520\) 0 0
\(521\) 1.07875 0.622814i 0.0472607 0.0272860i −0.476183 0.879346i \(-0.657980\pi\)
0.523444 + 0.852060i \(0.324647\pi\)
\(522\) 0.402626 1.50262i 0.0176225 0.0657679i
\(523\) −19.6016 + 5.25224i −0.857119 + 0.229664i −0.660509 0.750818i \(-0.729660\pi\)
−0.196609 + 0.980482i \(0.562993\pi\)
\(524\) 0.373725 0.0163262
\(525\) 0 0
\(526\) −5.68790 −0.248004
\(527\) 15.5121 4.15646i 0.675718 0.181058i
\(528\) 1.17878 4.39926i 0.0512997 0.191453i
\(529\) −36.2434 + 20.9252i −1.57580 + 0.909790i
\(530\) 0 0
\(531\) 0.443022i 0.0192255i
\(532\) 0.579009 + 9.98182i 0.0251032 + 0.432767i
\(533\) 20.2298 20.2298i 0.876250 0.876250i
\(534\) 5.23816 + 3.02425i 0.226677 + 0.130872i
\(535\) 0 0
\(536\) 4.65775 + 8.06746i 0.201184 + 0.348461i
\(537\) −3.29408 12.2937i −0.142150 0.530510i
\(538\) −5.45025 5.45025i −0.234977 0.234977i
\(539\) 19.0260 + 25.5816i 0.819508 + 1.10188i
\(540\) 0 0
\(541\) 17.0068 29.4566i 0.731178 1.26644i −0.225202 0.974312i \(-0.572304\pi\)
0.956380 0.292126i \(-0.0943625\pi\)
\(542\) −17.2769 4.62932i −0.742104 0.198846i
\(543\) 8.78945 + 2.35513i 0.377191 + 0.101068i
\(544\) 2.06220 3.57183i 0.0884160 0.153141i
\(545\) 0 0
\(546\) 4.42314 4.96788i 0.189293 0.212606i
\(547\) −27.8171 27.8171i −1.18937 1.18937i −0.977241 0.212132i \(-0.931959\pi\)
−0.212132 0.977241i \(-0.568041\pi\)
\(548\) −0.688094 2.56800i −0.0293939 0.109700i
\(549\) −4.09597 7.09442i −0.174812 0.302783i
\(550\) 0 0
\(551\) −5.09127 2.93945i −0.216896 0.125225i
\(552\) −5.69431 + 5.69431i −0.242366 + 0.242366i
\(553\) 11.1452 + 5.60062i 0.473941 + 0.238163i
\(554\) 14.7464i 0.626512i
\(555\) 0 0
\(556\) −3.96700 + 2.29035i −0.168238 + 0.0971324i
\(557\) −0.365782 + 1.36512i −0.0154987 + 0.0578419i −0.973242 0.229782i \(-0.926199\pi\)
0.957743 + 0.287624i \(0.0928653\pi\)
\(558\) −3.76106 + 1.00777i −0.159218 + 0.0426625i
\(559\) −1.30577 −0.0552282
\(560\) 0 0
\(561\) 18.7843 0.793076
\(562\) 0.567387 0.152031i 0.0239338 0.00641303i
\(563\) −9.90152 + 36.9530i −0.417299 + 1.55738i 0.362886 + 0.931834i \(0.381791\pi\)
−0.780185 + 0.625548i \(0.784875\pi\)
\(564\) −4.37376 + 2.52519i −0.184168 + 0.106330i
\(565\) 0 0
\(566\) 18.6151i 0.782453i
\(567\) 1.45334 + 2.21084i 0.0610346 + 0.0928464i
\(568\) −4.72632 + 4.72632i −0.198312 + 0.198312i
\(569\) 31.1820 + 18.0029i 1.30722 + 0.754723i 0.981631 0.190789i \(-0.0611047\pi\)
0.325587 + 0.945512i \(0.394438\pi\)
\(570\) 0 0
\(571\) 17.1990 + 29.7895i 0.719756 + 1.24665i 0.961096 + 0.276213i \(0.0890795\pi\)
−0.241341 + 0.970440i \(0.577587\pi\)
\(572\) 2.96354 + 11.0601i 0.123912 + 0.462445i
\(573\) 12.8737 + 12.8737i 0.537806 + 0.537806i
\(574\) −9.46346 28.5817i −0.394997 1.19298i
\(575\) 0 0
\(576\) −0.500000 + 0.866025i −0.0208333 + 0.0360844i
\(577\) 43.1900 + 11.5727i 1.79802 + 0.481779i 0.993666 0.112370i \(-0.0358442\pi\)
0.804355 + 0.594148i \(0.202511\pi\)
\(578\) 0.0102734 + 0.00275276i 0.000427319 + 0.000114500i
\(579\) −5.03564 + 8.72198i −0.209274 + 0.362473i
\(580\) 0 0
\(581\) −8.99048 8.00466i −0.372988 0.332089i
\(582\) −0.462652 0.462652i −0.0191775 0.0191775i
\(583\) −9.94267 37.1066i −0.411783 1.53680i
\(584\) −2.17449 3.76633i −0.0899811 0.155852i
\(585\) 0 0
\(586\) −25.3199 14.6185i −1.04596 0.603883i
\(587\) 19.7182 19.7182i 0.813859 0.813859i −0.171351 0.985210i \(-0.554813\pi\)
0.985210 + 0.171351i \(0.0548132\pi\)
\(588\) −2.58137 6.50665i −0.106454 0.268330i
\(589\) 14.7149i 0.606316i
\(590\) 0 0
\(591\) −19.8946 + 11.4862i −0.818356 + 0.472478i
\(592\) −2.95980 + 11.0461i −0.121647 + 0.453994i
\(593\) 9.62724 2.57961i 0.395343 0.105932i −0.0556699 0.998449i \(-0.517729\pi\)
0.451013 + 0.892517i \(0.351063\pi\)
\(594\) −4.55445 −0.186871
\(595\) 0 0
\(596\) −17.2441 −0.706344
\(597\) 24.5315 6.57319i 1.00401 0.269023i
\(598\) 5.23999 19.5559i 0.214279 0.799701i
\(599\) −14.2556 + 8.23048i −0.582469 + 0.336288i −0.762114 0.647443i \(-0.775838\pi\)
0.179645 + 0.983731i \(0.442505\pi\)
\(600\) 0 0
\(601\) 34.0216i 1.38777i 0.720086 + 0.693885i \(0.244102\pi\)
−0.720086 + 0.693885i \(0.755898\pi\)
\(602\) −0.617012 + 1.22785i −0.0251475 + 0.0500434i
\(603\) 6.58705 6.58705i 0.268246 0.268246i
\(604\) 4.82177 + 2.78385i 0.196195 + 0.113273i
\(605\) 0 0
\(606\) 2.80102 + 4.85151i 0.113784 + 0.197079i
\(607\) −9.31678 34.7707i −0.378156 1.41130i −0.848678 0.528910i \(-0.822601\pi\)
0.470521 0.882389i \(-0.344066\pi\)
\(608\) 2.67224 + 2.67224i 0.108374 + 0.108374i
\(609\) 4.03058 + 0.833240i 0.163327 + 0.0337646i
\(610\) 0 0
\(611\) 6.34852 10.9960i 0.256833 0.444849i
\(612\) −3.98386 1.06747i −0.161038 0.0431500i
\(613\) −31.8017 8.52125i −1.28446 0.344170i −0.448906 0.893579i \(-0.648186\pi\)
−0.835554 + 0.549409i \(0.814853\pi\)
\(614\) −1.15586 + 2.00201i −0.0466469 + 0.0807947i
\(615\) 0 0
\(616\) 11.8004 + 2.43950i 0.475452 + 0.0982901i
\(617\) 10.3705 + 10.3705i 0.417499 + 0.417499i 0.884341 0.466842i \(-0.154608\pi\)
−0.466842 + 0.884341i \(0.654608\pi\)
\(618\) −1.43852 5.36863i −0.0578658 0.215958i
\(619\) 2.58828 + 4.48304i 0.104032 + 0.180188i 0.913342 0.407193i \(-0.133492\pi\)
−0.809310 + 0.587381i \(0.800159\pi\)
\(620\) 0 0
\(621\) 6.97408 + 4.02648i 0.279860 + 0.161577i
\(622\) 9.81743 9.81743i 0.393643 0.393643i
\(623\) −7.18544 + 14.2990i −0.287879 + 0.572876i
\(624\) 2.51408i 0.100644i
\(625\) 0 0
\(626\) −11.6830 + 6.74520i −0.466948 + 0.269592i
\(627\) −4.45474 + 16.6253i −0.177905 + 0.663951i
\(628\) 3.99014 1.06916i 0.159224 0.0426640i
\(629\) −47.1658 −1.88062
\(630\) 0 0
\(631\) 14.5385 0.578769 0.289384 0.957213i \(-0.406549\pi\)
0.289384 + 0.957213i \(0.406549\pi\)
\(632\) 4.55381 1.22019i 0.181141 0.0485365i
\(633\) −3.52466 + 13.1542i −0.140093 + 0.522832i
\(634\) 11.8793 6.85853i 0.471788 0.272387i
\(635\) 0 0
\(636\) 8.43473i 0.334459i
\(637\) 13.7994 + 10.9218i 0.546752 + 0.432736i
\(638\) −5.00987 + 5.00987i −0.198343 + 0.198343i
\(639\) 5.78854 + 3.34201i 0.228991 + 0.132208i
\(640\) 0 0
\(641\) −20.8743 36.1553i −0.824484 1.42805i −0.902313 0.431082i \(-0.858132\pi\)
0.0778281 0.996967i \(-0.475201\pi\)
\(642\) −1.93865 7.23514i −0.0765124 0.285548i
\(643\) −15.5128 15.5128i −0.611766 0.611766i 0.331640 0.943406i \(-0.392398\pi\)
−0.943406 + 0.331640i \(0.892398\pi\)
\(644\) −15.9129 14.1680i −0.627056 0.558298i
\(645\) 0 0
\(646\) −7.79328 + 13.4984i −0.306623 + 0.531086i
\(647\) 13.8141 + 3.70148i 0.543089 + 0.145520i 0.519926 0.854211i \(-0.325960\pi\)
0.0231633 + 0.999732i \(0.492626\pi\)
\(648\) 0.965926 + 0.258819i 0.0379452 + 0.0101674i
\(649\) −1.00886 + 1.74740i −0.0396012 + 0.0685913i
\(650\) 0 0
\(651\) −3.23809 9.77973i −0.126911 0.383298i
\(652\) 15.3717 + 15.3717i 0.602003 + 0.602003i
\(653\) −3.95094 14.7451i −0.154612 0.577021i −0.999138 0.0415062i \(-0.986784\pi\)
0.844526 0.535515i \(-0.179882\pi\)
\(654\) 0.733433 + 1.27034i 0.0286795 + 0.0496743i
\(655\) 0 0
\(656\) −9.85506 5.68982i −0.384775 0.222150i
\(657\) −3.07520 + 3.07520i −0.119975 + 0.119975i
\(658\) −7.33993 11.1656i −0.286140 0.435279i
\(659\) 18.9116i 0.736690i −0.929689 0.368345i \(-0.879924\pi\)
0.929689 0.368345i \(-0.120076\pi\)
\(660\) 0 0
\(661\) 19.5815 11.3054i 0.761632 0.439728i −0.0682495 0.997668i \(-0.521741\pi\)
0.829881 + 0.557940i \(0.188408\pi\)
\(662\) −8.60281 + 32.1061i −0.334358 + 1.24784i
\(663\) 10.0157 2.68371i 0.388979 0.104226i
\(664\) −4.54978 −0.176566
\(665\) 0 0
\(666\) 11.4358 0.443129
\(667\) 12.1006 3.24233i 0.468535 0.125544i
\(668\) −6.40358 + 23.8985i −0.247762 + 0.924660i
\(669\) 19.4015 11.2014i 0.750104 0.433073i
\(670\) 0 0
\(671\) 37.3097i 1.44033i
\(672\) −2.36405 1.18797i −0.0911952 0.0458269i
\(673\) 24.2623 24.2623i 0.935243 0.935243i −0.0627838 0.998027i \(-0.519998\pi\)
0.998027 + 0.0627838i \(0.0199978\pi\)
\(674\) 20.8610 + 12.0441i 0.803534 + 0.463921i
\(675\) 0 0
\(676\) −3.33971 5.78455i −0.128450 0.222483i
\(677\) −2.30402 8.59870i −0.0885505 0.330475i 0.907412 0.420241i \(-0.138055\pi\)
−0.995963 + 0.0897664i \(0.971388\pi\)
\(678\) 7.08834 + 7.08834i 0.272226 + 0.272226i
\(679\) 1.15112 1.29289i 0.0441761 0.0496166i
\(680\) 0 0
\(681\) 5.47634 9.48530i 0.209854 0.363477i
\(682\) 17.1296 + 4.58985i 0.655925 + 0.175755i
\(683\) 46.2697 + 12.3979i 1.77046 + 0.474394i 0.988792 0.149299i \(-0.0477018\pi\)
0.781669 + 0.623693i \(0.214368\pi\)
\(684\) 1.88956 3.27281i 0.0722491 0.125139i
\(685\) 0 0
\(686\) 16.7906 7.81510i 0.641068 0.298382i
\(687\) −20.4667 20.4667i −0.780854 0.780854i
\(688\) 0.134426 + 0.501686i 0.00512496 + 0.0191266i
\(689\) −10.6028 18.3645i −0.403934 0.699633i
\(690\) 0 0
\(691\) −22.3848 12.9239i −0.851559 0.491648i 0.00961738 0.999954i \(-0.496939\pi\)
−0.861177 + 0.508306i \(0.830272\pi\)
\(692\) 11.7140 11.7140i 0.445300 0.445300i
\(693\) −0.697800 12.0297i −0.0265072 0.456971i
\(694\) 2.05709i 0.0780861i
\(695\) 0 0
\(696\) 1.34721 0.777814i 0.0510660 0.0294829i
\(697\) 12.1474 45.3349i 0.460117 1.71718i
\(698\) 11.3255 3.03467i 0.428677 0.114864i
\(699\) −1.41209 −0.0534102
\(700\) 0 0
\(701\) 3.95788 0.149487 0.0747435 0.997203i \(-0.476186\pi\)
0.0747435 + 0.997203i \(0.476186\pi\)
\(702\) −2.42841 + 0.650691i −0.0916544 + 0.0245587i
\(703\) 11.1854 41.7447i 0.421867 1.57443i
\(704\) 3.94427 2.27722i 0.148655 0.0858261i
\(705\) 0 0
\(706\) 11.4227i 0.429897i
\(707\) −12.3852 + 8.14167i −0.465793 + 0.306199i
\(708\) 0.313264 0.313264i 0.0117732 0.0117732i
\(709\) 25.1665 + 14.5299i 0.945148 + 0.545682i 0.891570 0.452882i \(-0.149604\pi\)
0.0535778 + 0.998564i \(0.482937\pi\)
\(710\) 0 0
\(711\) −2.35722 4.08283i −0.0884028 0.153118i
\(712\) 1.56547 + 5.84241i 0.0586684 + 0.218954i
\(713\) −22.1722 22.1722i −0.830354 0.830354i
\(714\) 2.20915 10.6862i 0.0826753 0.399920i
\(715\) 0 0
\(716\) 6.36367 11.0222i 0.237821 0.411919i
\(717\) 4.21559 + 1.12956i 0.157434 + 0.0421843i
\(718\) −2.32938 0.624155i −0.0869316 0.0232932i
\(719\) 10.1319 17.5490i 0.377857 0.654467i −0.612893 0.790166i \(-0.709995\pi\)
0.990750 + 0.135699i \(0.0433279\pi\)
\(720\) 0 0
\(721\) 13.9598 4.62212i 0.519891 0.172137i
\(722\) 3.33633 + 3.33633i 0.124165 + 0.124165i
\(723\) 0.794551 + 2.96531i 0.0295497 + 0.110281i
\(724\) 4.54975 + 7.88040i 0.169090 + 0.292873i
\(725\) 0 0
\(726\) 8.43768 + 4.87150i 0.313152 + 0.180798i
\(727\) −2.80940 + 2.80940i −0.104195 + 0.104195i −0.757282 0.653088i \(-0.773473\pi\)
0.653088 + 0.757282i \(0.273473\pi\)
\(728\) 6.64046 0.385189i 0.246112 0.0142760i
\(729\) 1.00000i 0.0370370i
\(730\) 0 0
\(731\) −1.85515 + 1.07107i −0.0686152 + 0.0396150i
\(732\) 2.12023 7.91280i 0.0783659 0.292466i
\(733\) 1.68418 0.451275i 0.0622066 0.0166682i −0.227582 0.973759i \(-0.573082\pi\)
0.289788 + 0.957091i \(0.406415\pi\)
\(734\) −5.20884 −0.192262
\(735\) 0 0
\(736\) −8.05297 −0.296836
\(737\) −40.9813 + 10.9809i −1.50957 + 0.404487i
\(738\) −2.94527 + 10.9919i −0.108417 + 0.404617i
\(739\) 20.2692 11.7024i 0.745615 0.430481i −0.0784926 0.996915i \(-0.525011\pi\)
0.824107 + 0.566434i \(0.191677\pi\)
\(740\) 0 0
\(741\) 9.50098i 0.349027i
\(742\) −22.2787 + 1.29231i −0.817879 + 0.0474421i
\(743\) −1.84057 + 1.84057i −0.0675240 + 0.0675240i −0.740062 0.672538i \(-0.765204\pi\)
0.672538 + 0.740062i \(0.265204\pi\)
\(744\) −3.37208 1.94687i −0.123626 0.0713757i
\(745\) 0 0
\(746\) 0.0733279 + 0.127008i 0.00268472 + 0.00465008i
\(747\) 1.17757 + 4.39475i 0.0430850 + 0.160795i
\(748\) 13.2825 + 13.2825i 0.485658 + 0.485658i
\(749\) 18.8132 6.22909i 0.687420 0.227606i
\(750\) 0 0
\(751\) −21.1862 + 36.6956i −0.773096 + 1.33904i 0.162762 + 0.986665i \(0.447960\pi\)
−0.935858 + 0.352376i \(0.885374\pi\)
\(752\) −4.87829 1.30713i −0.177893 0.0476663i
\(753\) −1.21084 0.324443i −0.0441254 0.0118234i
\(754\) −1.95548 + 3.38699i −0.0712145 + 0.123347i
\(755\) 0 0
\(756\) −0.535629 + 2.59097i −0.0194807 + 0.0942325i
\(757\) −10.2470 10.2470i −0.372434 0.372434i 0.495929 0.868363i \(-0.334828\pi\)
−0.868363 + 0.495929i \(0.834828\pi\)
\(758\) −4.79948 17.9119i −0.174325 0.650590i
\(759\) −18.3384 31.7631i −0.665642 1.15293i
\(760\) 0 0
\(761\) 13.4082 + 7.74124i 0.486048 + 0.280620i 0.722933 0.690918i \(-0.242793\pi\)
−0.236886 + 0.971538i \(0.576127\pi\)
\(762\) −12.9176 + 12.9176i −0.467956 + 0.467956i
\(763\) −3.24300 + 2.13186i −0.117404 + 0.0771784i
\(764\) 18.2062i 0.658676i
\(765\) 0 0
\(766\) 3.33386 1.92480i 0.120457 0.0695460i
\(767\) −0.288270 + 1.07584i −0.0104088 + 0.0388463i
\(768\) −0.965926 + 0.258819i −0.0348548 + 0.00933933i
\(769\) −15.9644 −0.575691 −0.287846 0.957677i \(-0.592939\pi\)
−0.287846 + 0.957677i \(0.592939\pi\)
\(770\) 0 0
\(771\) −7.05834 −0.254200
\(772\) −9.72810 + 2.60664i −0.350122 + 0.0938149i
\(773\) −5.99662 + 22.3797i −0.215683 + 0.804941i 0.770241 + 0.637752i \(0.220136\pi\)
−0.985925 + 0.167189i \(0.946531\pi\)
\(774\) 0.449799 0.259692i 0.0161677 0.00933443i
\(775\) 0 0
\(776\) 0.654289i 0.0234876i
\(777\) 1.75211 + 30.2055i 0.0628567 + 1.08362i
\(778\) 12.6018 12.6018i 0.451798 0.451798i
\(779\) 37.2434 + 21.5025i 1.33438 + 0.770406i
\(780\) 0 0
\(781\) −15.2210 26.3636i −0.544651 0.943363i