Properties

Label 1183.2.e.g.508.5
Level $1183$
Weight $2$
Character 1183.508
Analytic conductor $9.446$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1183 = 7 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1183.e (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(9.44630255912\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
Defining polynomial: \(x^{12} - x^{11} + 7 x^{10} - 2 x^{9} + 33 x^{8} - 11 x^{7} + 55 x^{6} + 17 x^{5} + 47 x^{4} + x^{3} + 8 x^{2} + x + 1\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 91)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 508.5
Root \(-1.02197 + 1.77010i\) of defining polynomial
Character \(\chi\) \(=\) 1183.508
Dual form 1183.2.e.g.170.5

$q$-expansion

\(f(q)\) \(=\) \(q+(0.777343 + 1.34640i) q^{2} +(0.244626 - 0.423704i) q^{3} +(-0.208526 + 0.361177i) q^{4} +(-0.595756 - 1.03188i) q^{5} +0.760633 q^{6} +(-2.10390 + 1.60425i) q^{7} +2.46099 q^{8} +(1.38032 + 2.39078i) q^{9} +O(q^{10})\) \(q+(0.777343 + 1.34640i) q^{2} +(0.244626 - 0.423704i) q^{3} +(-0.208526 + 0.361177i) q^{4} +(-0.595756 - 1.03188i) q^{5} +0.760633 q^{6} +(-2.10390 + 1.60425i) q^{7} +2.46099 q^{8} +(1.38032 + 2.39078i) q^{9} +(0.926214 - 1.60425i) q^{10} +(1.05807 - 1.83263i) q^{11} +(0.102021 + 0.176706i) q^{12} +(-3.79541 - 1.58563i) q^{14} -0.582949 q^{15} +(2.33009 + 4.03583i) q^{16} +(0.453151 - 0.784881i) q^{17} +(-2.14596 + 3.71691i) q^{18} +(3.34514 + 5.79395i) q^{19} +0.496921 q^{20} +(0.165059 + 1.28387i) q^{21} +3.28993 q^{22} +(-1.79866 - 3.11538i) q^{23} +(0.602021 - 1.04273i) q^{24} +(1.79015 - 3.10063i) q^{25} +2.81840 q^{27} +(-0.140701 - 1.09441i) q^{28} +8.51545 q^{29} +(-0.453151 - 0.784881i) q^{30} +(-2.64390 + 4.57937i) q^{31} +(-1.16156 + 2.01189i) q^{32} +(-0.517662 - 0.896617i) q^{33} +1.40902 q^{34} +(2.90880 + 1.21523i) q^{35} -1.15133 q^{36} +(2.49579 + 4.32284i) q^{37} +(-5.20065 + 9.00778i) q^{38} +(-1.46615 - 2.53944i) q^{40} -1.53636 q^{41} +(-1.60029 + 1.22024i) q^{42} +5.43273 q^{43} +(0.441269 + 0.764301i) q^{44} +(1.64466 - 2.84864i) q^{45} +(2.79636 - 4.84344i) q^{46} +(-1.59337 - 2.75979i) q^{47} +2.28000 q^{48} +(1.85277 - 6.75035i) q^{49} +5.56625 q^{50} +(-0.221705 - 0.384004i) q^{51} +(1.41239 - 2.44632i) q^{53} +(2.19086 + 3.79469i) q^{54} -2.52140 q^{55} +(-5.17767 + 3.94804i) q^{56} +3.27323 q^{57} +(6.61943 + 11.4652i) q^{58} +(-5.12298 + 8.87327i) q^{59} +(0.121560 - 0.210548i) q^{60} +(4.13423 + 7.16069i) q^{61} -8.22088 q^{62} +(-6.73945 - 2.81558i) q^{63} +5.70861 q^{64} +(0.804802 - 1.39396i) q^{66} +(-1.87182 + 3.24208i) q^{67} +(0.188987 + 0.327336i) q^{68} -1.76000 q^{69} +(0.624956 + 4.86105i) q^{70} +2.53020 q^{71} +(3.39694 + 5.88368i) q^{72} +(-2.86522 + 4.96271i) q^{73} +(-3.88018 + 6.72066i) q^{74} +(-0.875834 - 1.51699i) q^{75} -2.79019 q^{76} +(0.713925 + 5.55307i) q^{77} +(-3.03620 - 5.25885i) q^{79} +(2.77632 - 4.80873i) q^{80} +(-3.45150 + 5.97817i) q^{81} +(-1.19428 - 2.06856i) q^{82} +11.6309 q^{83} +(-0.498124 - 0.208104i) q^{84} -1.07987 q^{85} +(4.22310 + 7.31462i) q^{86} +(2.08310 - 3.60803i) q^{87} +(2.60390 - 4.51008i) q^{88} +(-8.87557 - 15.3729i) q^{89} +5.11387 q^{90} +1.50027 q^{92} +(1.29353 + 2.24046i) q^{93} +(2.47719 - 4.29061i) q^{94} +(3.98577 - 6.90356i) q^{95} +(0.568297 + 0.984319i) q^{96} -6.20434 q^{97} +(10.5289 - 2.75277i) q^{98} +5.84188 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12q - 2q^{2} + q^{3} - 4q^{4} - q^{5} - 18q^{6} + 6q^{7} + 6q^{8} + 3q^{9} + O(q^{10}) \) \( 12q - 2q^{2} + q^{3} - 4q^{4} - q^{5} - 18q^{6} + 6q^{7} + 6q^{8} + 3q^{9} + 4q^{10} - 4q^{11} + 5q^{12} - 2q^{14} - 4q^{15} + 8q^{16} + 5q^{17} - 3q^{18} + q^{19} - 2q^{20} + 9q^{21} + 10q^{22} - q^{23} + 11q^{24} + 7q^{25} - 8q^{27} - 8q^{28} - 6q^{29} - 5q^{30} - 16q^{31} - 8q^{32} - 16q^{33} - 32q^{34} - 28q^{35} + 42q^{36} + 13q^{37} - 17q^{38} - 5q^{40} - 16q^{41} - 52q^{42} + 22q^{43} - 21q^{44} + 7q^{45} - 16q^{46} + q^{47} - 42q^{48} + 6q^{49} + 12q^{50} - 20q^{51} - 2q^{53} + 18q^{54} - 18q^{55} + 9q^{56} - 42q^{57} + 8q^{58} - 13q^{59} - 20q^{60} - 5q^{61} - 10q^{62} - 8q^{63} - 30q^{64} + 18q^{66} + 11q^{67} + 29q^{68} - 46q^{69} + 39q^{70} + 12q^{71} - 25q^{72} + 30q^{73} - 3q^{74} - 3q^{75} - 18q^{76} + 11q^{77} + 7q^{79} + 7q^{80} - 6q^{81} + q^{82} + 54q^{83} - 41q^{84} - 2q^{85} + 7q^{86} + 16q^{87} - 4q^{89} - 16q^{90} + 54q^{92} + 7q^{93} + 45q^{94} - 6q^{95} - 19q^{96} - 70q^{97} + 82q^{98} + 20q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1183\mathbb{Z}\right)^\times\).

\(n\) \(339\) \(1016\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.777343 + 1.34640i 0.549665 + 0.952047i 0.998297 + 0.0583310i \(0.0185779\pi\)
−0.448632 + 0.893716i \(0.648089\pi\)
\(3\) 0.244626 0.423704i 0.141235 0.244626i −0.786727 0.617301i \(-0.788226\pi\)
0.927962 + 0.372675i \(0.121559\pi\)
\(4\) −0.208526 + 0.361177i −0.104263 + 0.180588i
\(5\) −0.595756 1.03188i −0.266430 0.461470i 0.701507 0.712662i \(-0.252511\pi\)
−0.967937 + 0.251192i \(0.919177\pi\)
\(6\) 0.760633 0.310527
\(7\) −2.10390 + 1.60425i −0.795199 + 0.606349i
\(8\) 2.46099 0.870091
\(9\) 1.38032 + 2.39078i 0.460105 + 0.796926i
\(10\) 0.926214 1.60425i 0.292894 0.507308i
\(11\) 1.05807 1.83263i 0.319020 0.552559i −0.661264 0.750153i \(-0.729980\pi\)
0.980284 + 0.197595i \(0.0633130\pi\)
\(12\) 0.102021 + 0.176706i 0.0294511 + 0.0510107i
\(13\) 0 0
\(14\) −3.79541 1.58563i −1.01437 0.423778i
\(15\) −0.582949 −0.150517
\(16\) 2.33009 + 4.03583i 0.582521 + 1.00896i
\(17\) 0.453151 0.784881i 0.109905 0.190362i −0.805826 0.592152i \(-0.798279\pi\)
0.915732 + 0.401790i \(0.131612\pi\)
\(18\) −2.14596 + 3.71691i −0.505808 + 0.876084i
\(19\) 3.34514 + 5.79395i 0.767428 + 1.32922i 0.938953 + 0.344045i \(0.111797\pi\)
−0.171525 + 0.985180i \(0.554870\pi\)
\(20\) 0.496921 0.111115
\(21\) 0.165059 + 1.28387i 0.0360189 + 0.280164i
\(22\) 3.28993 0.701416
\(23\) −1.79866 3.11538i −0.375048 0.649601i 0.615287 0.788303i \(-0.289040\pi\)
−0.990334 + 0.138702i \(0.955707\pi\)
\(24\) 0.602021 1.04273i 0.122887 0.212847i
\(25\) 1.79015 3.10063i 0.358030 0.620126i
\(26\) 0 0
\(27\) 2.81840 0.542401
\(28\) −0.140701 1.09441i −0.0265900 0.206823i
\(29\) 8.51545 1.58128 0.790639 0.612282i \(-0.209748\pi\)
0.790639 + 0.612282i \(0.209748\pi\)
\(30\) −0.453151 0.784881i −0.0827337 0.143299i
\(31\) −2.64390 + 4.57937i −0.474859 + 0.822479i −0.999585 0.0287913i \(-0.990834\pi\)
0.524727 + 0.851271i \(0.324168\pi\)
\(32\) −1.16156 + 2.01189i −0.205337 + 0.355655i
\(33\) −0.517662 0.896617i −0.0901134 0.156081i
\(34\) 1.40902 0.241644
\(35\) 2.90880 + 1.21523i 0.491677 + 0.205411i
\(36\) −1.15133 −0.191888
\(37\) 2.49579 + 4.32284i 0.410306 + 0.710670i 0.994923 0.100639i \(-0.0320886\pi\)
−0.584617 + 0.811309i \(0.698755\pi\)
\(38\) −5.20065 + 9.00778i −0.843656 + 1.46126i
\(39\) 0 0
\(40\) −1.46615 2.53944i −0.231818 0.401521i
\(41\) −1.53636 −0.239939 −0.119970 0.992778i \(-0.538280\pi\)
−0.119970 + 0.992778i \(0.538280\pi\)
\(42\) −1.60029 + 1.22024i −0.246931 + 0.188288i
\(43\) 5.43273 0.828483 0.414242 0.910167i \(-0.364047\pi\)
0.414242 + 0.910167i \(0.364047\pi\)
\(44\) 0.441269 + 0.764301i 0.0665238 + 0.115223i
\(45\) 1.64466 2.84864i 0.245172 0.424650i
\(46\) 2.79636 4.84344i 0.412301 0.714126i
\(47\) −1.59337 2.75979i −0.232416 0.402557i 0.726102 0.687587i \(-0.241330\pi\)
−0.958519 + 0.285030i \(0.907997\pi\)
\(48\) 2.28000 0.329089
\(49\) 1.85277 6.75035i 0.264682 0.964336i
\(50\) 5.56625 0.787186
\(51\) −0.221705 0.384004i −0.0310449 0.0537714i
\(52\) 0 0
\(53\) 1.41239 2.44632i 0.194006 0.336029i −0.752568 0.658514i \(-0.771185\pi\)
0.946574 + 0.322486i \(0.104518\pi\)
\(54\) 2.19086 + 3.79469i 0.298139 + 0.516391i
\(55\) −2.52140 −0.339986
\(56\) −5.17767 + 3.94804i −0.691895 + 0.527579i
\(57\) 3.27323 0.433550
\(58\) 6.61943 + 11.4652i 0.869173 + 1.50545i
\(59\) −5.12298 + 8.87327i −0.666956 + 1.15520i 0.311795 + 0.950149i \(0.399070\pi\)
−0.978751 + 0.205052i \(0.934264\pi\)
\(60\) 0.121560 0.210548i 0.0156933 0.0271816i
\(61\) 4.13423 + 7.16069i 0.529333 + 0.916832i 0.999415 + 0.0342093i \(0.0108913\pi\)
−0.470081 + 0.882623i \(0.655775\pi\)
\(62\) −8.22088 −1.04405
\(63\) −6.73945 2.81558i −0.849091 0.354730i
\(64\) 5.70861 0.713576
\(65\) 0 0
\(66\) 0.804802 1.39396i 0.0990643 0.171584i
\(67\) −1.87182 + 3.24208i −0.228679 + 0.396083i −0.957417 0.288709i \(-0.906774\pi\)
0.728738 + 0.684793i \(0.240107\pi\)
\(68\) 0.188987 + 0.327336i 0.0229181 + 0.0396953i
\(69\) −1.76000 −0.211879
\(70\) 0.624956 + 4.86105i 0.0746965 + 0.581007i
\(71\) 2.53020 0.300280 0.150140 0.988665i \(-0.452028\pi\)
0.150140 + 0.988665i \(0.452028\pi\)
\(72\) 3.39694 + 5.88368i 0.400334 + 0.693398i
\(73\) −2.86522 + 4.96271i −0.335349 + 0.580841i −0.983552 0.180627i \(-0.942187\pi\)
0.648203 + 0.761468i \(0.275521\pi\)
\(74\) −3.88018 + 6.72066i −0.451061 + 0.781261i
\(75\) −0.875834 1.51699i −0.101133 0.175167i
\(76\) −2.79019 −0.320057
\(77\) 0.713925 + 5.55307i 0.0813593 + 0.632831i
\(78\) 0 0
\(79\) −3.03620 5.25885i −0.341599 0.591667i 0.643131 0.765756i \(-0.277635\pi\)
−0.984730 + 0.174089i \(0.944302\pi\)
\(80\) 2.77632 4.80873i 0.310402 0.537633i
\(81\) −3.45150 + 5.97817i −0.383500 + 0.664241i
\(82\) −1.19428 2.06856i −0.131886 0.228434i
\(83\) 11.6309 1.27665 0.638327 0.769766i \(-0.279627\pi\)
0.638327 + 0.769766i \(0.279627\pi\)
\(84\) −0.498124 0.208104i −0.0543498 0.0227060i
\(85\) −1.07987 −0.117128
\(86\) 4.22310 + 7.31462i 0.455388 + 0.788755i
\(87\) 2.08310 3.60803i 0.223331 0.386821i
\(88\) 2.60390 4.51008i 0.277576 0.480776i
\(89\) −8.87557 15.3729i −0.940808 1.62953i −0.763934 0.645295i \(-0.776735\pi\)
−0.176875 0.984233i \(-0.556599\pi\)
\(90\) 5.11387 0.539049
\(91\) 0 0
\(92\) 1.50027 0.156414
\(93\) 1.29353 + 2.24046i 0.134133 + 0.232325i
\(94\) 2.47719 4.29061i 0.255502 0.442543i
\(95\) 3.98577 6.90356i 0.408932 0.708291i
\(96\) 0.568297 + 0.984319i 0.0580015 + 0.100462i
\(97\) −6.20434 −0.629955 −0.314978 0.949099i \(-0.601997\pi\)
−0.314978 + 0.949099i \(0.601997\pi\)
\(98\) 10.5289 2.75277i 1.06358 0.278072i
\(99\) 5.84188 0.587131
\(100\) 0.746584 + 1.29312i 0.0746584 + 0.129312i
\(101\) 3.61133 6.25501i 0.359341 0.622397i −0.628510 0.777802i \(-0.716335\pi\)
0.987851 + 0.155405i \(0.0496682\pi\)
\(102\) 0.344682 0.597007i 0.0341286 0.0591125i
\(103\) −4.96322 8.59656i −0.489041 0.847044i 0.510879 0.859652i \(-0.329320\pi\)
−0.999921 + 0.0126084i \(0.995987\pi\)
\(104\) 0 0
\(105\) 1.22646 0.935195i 0.119691 0.0912657i
\(106\) 4.39164 0.426553
\(107\) 1.10003 + 1.90531i 0.106344 + 0.184193i 0.914287 0.405068i \(-0.132752\pi\)
−0.807942 + 0.589261i \(0.799419\pi\)
\(108\) −0.587708 + 1.01794i −0.0565523 + 0.0979514i
\(109\) 6.87291 11.9042i 0.658305 1.14022i −0.322749 0.946485i \(-0.604607\pi\)
0.981054 0.193734i \(-0.0620598\pi\)
\(110\) −1.96000 3.39481i −0.186878 0.323683i
\(111\) 2.44214 0.231798
\(112\) −11.3767 4.75293i −1.07500 0.449110i
\(113\) −16.0947 −1.51406 −0.757032 0.653378i \(-0.773351\pi\)
−0.757032 + 0.653378i \(0.773351\pi\)
\(114\) 2.54442 + 4.40707i 0.238307 + 0.412760i
\(115\) −2.14313 + 3.71201i −0.199848 + 0.346147i
\(116\) −1.77569 + 3.07558i −0.164869 + 0.285561i
\(117\) 0 0
\(118\) −15.9293 −1.46641
\(119\) 0.305761 + 2.37828i 0.0280290 + 0.218016i
\(120\) −1.43463 −0.130963
\(121\) 3.26098 + 5.64818i 0.296453 + 0.513471i
\(122\) −6.42743 + 11.1326i −0.581912 + 1.00790i
\(123\) −0.375834 + 0.650963i −0.0338878 + 0.0586954i
\(124\) −1.10264 1.90983i −0.0990202 0.171508i
\(125\) −10.2235 −0.914420
\(126\) −1.44797 11.2627i −0.128996 1.00336i
\(127\) −15.6784 −1.39123 −0.695617 0.718413i \(-0.744869\pi\)
−0.695617 + 0.718413i \(0.744869\pi\)
\(128\) 6.76067 + 11.7098i 0.597565 + 1.03501i
\(129\) 1.32899 2.30187i 0.117011 0.202668i
\(130\) 0 0
\(131\) 4.76884 + 8.25988i 0.416656 + 0.721669i 0.995601 0.0936976i \(-0.0298687\pi\)
−0.578945 + 0.815367i \(0.696535\pi\)
\(132\) 0.431783 0.0375819
\(133\) −16.3328 6.82345i −1.41623 0.591668i
\(134\) −5.82018 −0.502787
\(135\) −1.67908 2.90825i −0.144512 0.250302i
\(136\) 1.11520 1.93158i 0.0956277 0.165632i
\(137\) −1.38231 + 2.39422i −0.118098 + 0.204552i −0.919014 0.394225i \(-0.871013\pi\)
0.800916 + 0.598777i \(0.204346\pi\)
\(138\) −1.36812 2.36966i −0.116462 0.201719i
\(139\) −22.7967 −1.93359 −0.966795 0.255554i \(-0.917742\pi\)
−0.966795 + 0.255554i \(0.917742\pi\)
\(140\) −1.04547 + 0.797185i −0.0883585 + 0.0673745i
\(141\) −1.55911 −0.131301
\(142\) 1.96684 + 3.40666i 0.165053 + 0.285881i
\(143\) 0 0
\(144\) −6.43251 + 11.1414i −0.536043 + 0.928453i
\(145\) −5.07312 8.78691i −0.421300 0.729713i
\(146\) −8.90904 −0.737317
\(147\) −2.40692 2.43634i −0.198519 0.200946i
\(148\) −2.08175 −0.171119
\(149\) −7.20581 12.4808i −0.590323 1.02247i −0.994189 0.107651i \(-0.965667\pi\)
0.403866 0.914818i \(-0.367666\pi\)
\(150\) 1.36165 2.35844i 0.111178 0.192566i
\(151\) 7.62901 13.2138i 0.620840 1.07533i −0.368489 0.929632i \(-0.620125\pi\)
0.989330 0.145695i \(-0.0465417\pi\)
\(152\) 8.23236 + 14.2589i 0.667732 + 1.15655i
\(153\) 2.50197 0.202272
\(154\) −6.92168 + 5.27787i −0.557765 + 0.425303i
\(155\) 6.30048 0.506067
\(156\) 0 0
\(157\) 5.70745 9.88559i 0.455504 0.788956i −0.543213 0.839595i \(-0.682792\pi\)
0.998717 + 0.0506387i \(0.0161257\pi\)
\(158\) 4.72034 8.17587i 0.375530 0.650437i
\(159\) −0.691012 1.19687i −0.0548008 0.0949178i
\(160\) 2.76803 0.218832
\(161\) 8.78205 + 3.66893i 0.692122 + 0.289152i
\(162\) −10.7320 −0.843185
\(163\) −7.20385 12.4774i −0.564249 0.977308i −0.997119 0.0758514i \(-0.975833\pi\)
0.432870 0.901456i \(-0.357501\pi\)
\(164\) 0.320371 0.554899i 0.0250168 0.0433303i
\(165\) −0.616800 + 1.06833i −0.0480178 + 0.0831693i
\(166\) 9.04118 + 15.6598i 0.701731 + 1.21543i
\(167\) −7.77190 −0.601407 −0.300704 0.953718i \(-0.597222\pi\)
−0.300704 + 0.953718i \(0.597222\pi\)
\(168\) 0.406210 + 3.15959i 0.0313398 + 0.243768i
\(169\) 0 0
\(170\) −0.839430 1.45394i −0.0643813 0.111512i
\(171\) −9.23471 + 15.9950i −0.706196 + 1.22317i
\(172\) −1.13286 + 1.96218i −0.0863800 + 0.149615i
\(173\) −3.04731 5.27809i −0.231682 0.401286i 0.726621 0.687039i \(-0.241090\pi\)
−0.958303 + 0.285753i \(0.907756\pi\)
\(174\) 6.47713 0.491030
\(175\) 1.20789 + 9.39526i 0.0913080 + 0.710215i
\(176\) 9.86157 0.743344
\(177\) 2.50643 + 4.34126i 0.188395 + 0.326309i
\(178\) 13.7987 23.9001i 1.03426 1.79139i
\(179\) −9.26488 + 16.0472i −0.692490 + 1.19943i 0.278530 + 0.960428i \(0.410153\pi\)
−0.971020 + 0.239000i \(0.923181\pi\)
\(180\) 0.685909 + 1.18803i 0.0511246 + 0.0885504i
\(181\) −5.60520 −0.416631 −0.208316 0.978062i \(-0.566798\pi\)
−0.208316 + 0.978062i \(0.566798\pi\)
\(182\) 0 0
\(183\) 4.04535 0.299041
\(184\) −4.42650 7.66692i −0.326326 0.565212i
\(185\) 2.97377 5.15071i 0.218636 0.378688i
\(186\) −2.01104 + 3.48322i −0.147456 + 0.255402i
\(187\) −0.958931 1.66092i −0.0701240 0.121458i
\(188\) 1.32903 0.0969295
\(189\) −5.92962 + 4.52141i −0.431317 + 0.328884i
\(190\) 12.3933 0.899102
\(191\) −0.251851 0.436219i −0.0182233 0.0315637i 0.856770 0.515699i \(-0.172468\pi\)
−0.874993 + 0.484135i \(0.839134\pi\)
\(192\) 1.39647 2.41876i 0.100782 0.174559i
\(193\) −1.85622 + 3.21507i −0.133614 + 0.231426i −0.925067 0.379804i \(-0.875991\pi\)
0.791453 + 0.611230i \(0.209325\pi\)
\(194\) −4.82290 8.35351i −0.346264 0.599747i
\(195\) 0 0
\(196\) 2.05172 + 2.07680i 0.146552 + 0.148343i
\(197\) 7.44451 0.530399 0.265200 0.964194i \(-0.414562\pi\)
0.265200 + 0.964194i \(0.414562\pi\)
\(198\) 4.54115 + 7.86550i 0.322725 + 0.558977i
\(199\) −3.75278 + 6.50001i −0.266028 + 0.460773i −0.967832 0.251596i \(-0.919045\pi\)
0.701805 + 0.712369i \(0.252378\pi\)
\(200\) 4.40554 7.63062i 0.311519 0.539566i
\(201\) 0.915789 + 1.58619i 0.0645948 + 0.111881i
\(202\) 11.2290 0.790068
\(203\) −17.9156 + 13.6609i −1.25743 + 0.958807i
\(204\) 0.184925 0.0129473
\(205\) 0.915297 + 1.58534i 0.0639271 + 0.110725i
\(206\) 7.71626 13.3650i 0.537617 0.931181i
\(207\) 4.96545 8.60042i 0.345123 0.597770i
\(208\) 0 0
\(209\) 14.1576 0.979299
\(210\) 2.21253 + 0.924342i 0.152679 + 0.0637857i
\(211\) 3.79063 0.260957 0.130479 0.991451i \(-0.458349\pi\)
0.130479 + 0.991451i \(0.458349\pi\)
\(212\) 0.589037 + 1.02024i 0.0404553 + 0.0700706i
\(213\) 0.618953 1.07206i 0.0424100 0.0734562i
\(214\) −1.71020 + 2.96216i −0.116907 + 0.202489i
\(215\) −3.23658 5.60592i −0.220733 0.382320i
\(216\) 6.93605 0.471938
\(217\) −1.78395 13.8760i −0.121103 0.941965i
\(218\) 21.3704 1.44739
\(219\) 1.40181 + 2.42801i 0.0947258 + 0.164070i
\(220\) 0.525777 0.910673i 0.0354479 0.0613975i
\(221\) 0 0
\(222\) 1.89838 + 3.28809i 0.127411 + 0.220682i
\(223\) −4.86879 −0.326039 −0.163019 0.986623i \(-0.552123\pi\)
−0.163019 + 0.986623i \(0.552123\pi\)
\(224\) −0.783757 6.09624i −0.0523669 0.407322i
\(225\) 9.88390 0.658926
\(226\) −12.5111 21.6699i −0.832228 1.44146i
\(227\) 12.0884 20.9376i 0.802332 1.38968i −0.115745 0.993279i \(-0.536925\pi\)
0.918077 0.396402i \(-0.129741\pi\)
\(228\) −0.682552 + 1.18222i −0.0452031 + 0.0782941i
\(229\) −10.8561 18.8034i −0.717394 1.24256i −0.962029 0.272947i \(-0.912002\pi\)
0.244635 0.969615i \(-0.421332\pi\)
\(230\) −6.66379 −0.439397
\(231\) 2.52750 + 1.05593i 0.166298 + 0.0694752i
\(232\) 20.9564 1.37586
\(233\) −1.89842 3.28816i −0.124370 0.215414i 0.797117 0.603825i \(-0.206358\pi\)
−0.921486 + 0.388411i \(0.873024\pi\)
\(234\) 0 0
\(235\) −1.89851 + 3.28832i −0.123845 + 0.214507i
\(236\) −2.13655 3.70061i −0.139077 0.240889i
\(237\) −2.97093 −0.192983
\(238\) −2.96443 + 2.26041i −0.192155 + 0.146521i
\(239\) −21.9100 −1.41724 −0.708619 0.705592i \(-0.750681\pi\)
−0.708619 + 0.705592i \(0.750681\pi\)
\(240\) −1.35832 2.35268i −0.0876792 0.151865i
\(241\) −10.3744 + 17.9690i −0.668273 + 1.15748i 0.310114 + 0.950699i \(0.399633\pi\)
−0.978387 + 0.206783i \(0.933701\pi\)
\(242\) −5.06980 + 8.78115i −0.325899 + 0.564474i
\(243\) 5.91625 + 10.2472i 0.379527 + 0.657361i
\(244\) −3.44837 −0.220759
\(245\) −8.06935 + 2.10972i −0.515532 + 0.134785i
\(246\) −1.16861 −0.0745077
\(247\) 0 0
\(248\) −6.50661 + 11.2698i −0.413170 + 0.715632i
\(249\) 2.84521 4.92805i 0.180308 0.312302i
\(250\) −7.94719 13.7649i −0.502624 0.870571i
\(251\) 13.2578 0.836827 0.418413 0.908257i \(-0.362586\pi\)
0.418413 + 0.908257i \(0.362586\pi\)
\(252\) 2.42227 1.84701i 0.152589 0.116351i
\(253\) −7.61245 −0.478591
\(254\) −12.1875 21.1094i −0.764713 1.32452i
\(255\) −0.264164 + 0.457546i −0.0165426 + 0.0286526i
\(256\) −4.80213 + 8.31753i −0.300133 + 0.519845i
\(257\) 6.58555 + 11.4065i 0.410795 + 0.711518i 0.994977 0.100105i \(-0.0319178\pi\)
−0.584182 + 0.811623i \(0.698584\pi\)
\(258\) 4.13231 0.257266
\(259\) −12.1858 5.09094i −0.757189 0.316336i
\(260\) 0 0
\(261\) 11.7540 + 20.3585i 0.727555 + 1.26016i
\(262\) −7.41406 + 12.8415i −0.458042 + 0.793352i
\(263\) 9.57028 16.5762i 0.590129 1.02213i −0.404086 0.914721i \(-0.632410\pi\)
0.994215 0.107412i \(-0.0342564\pi\)
\(264\) −1.27396 2.20657i −0.0784069 0.135805i
\(265\) −3.36575 −0.206756
\(266\) −3.50910 27.2946i −0.215157 1.67354i
\(267\) −8.68477 −0.531499
\(268\) −0.780643 1.35211i −0.0476854 0.0825935i
\(269\) 14.2411 24.6663i 0.868296 1.50393i 0.00455867 0.999990i \(-0.498549\pi\)
0.863737 0.503943i \(-0.168118\pi\)
\(270\) 2.61044 4.52141i 0.158866 0.275164i
\(271\) 8.97371 + 15.5429i 0.545114 + 0.944165i 0.998600 + 0.0529014i \(0.0168469\pi\)
−0.453486 + 0.891263i \(0.649820\pi\)
\(272\) 4.22353 0.256089
\(273\) 0 0
\(274\) −4.29811 −0.259658
\(275\) −3.78821 6.56137i −0.228437 0.395665i
\(276\) 0.367005 0.635671i 0.0220911 0.0382629i
\(277\) −6.71943 + 11.6384i −0.403732 + 0.699284i −0.994173 0.107797i \(-0.965620\pi\)
0.590441 + 0.807081i \(0.298954\pi\)
\(278\) −17.7209 30.6934i −1.06283 1.84087i
\(279\) −14.5977 −0.873940
\(280\) 7.15853 + 2.99066i 0.427804 + 0.178726i
\(281\) 29.9530 1.78685 0.893424 0.449214i \(-0.148296\pi\)
0.893424 + 0.449214i \(0.148296\pi\)
\(282\) −1.21197 2.09919i −0.0721716 0.125005i
\(283\) 4.94561 8.56604i 0.293986 0.509199i −0.680763 0.732504i \(-0.738351\pi\)
0.974748 + 0.223306i \(0.0716848\pi\)
\(284\) −0.527613 + 0.913852i −0.0313080 + 0.0542271i
\(285\) −1.95005 3.37758i −0.115511 0.200070i
\(286\) 0 0
\(287\) 3.23235 2.46471i 0.190800 0.145487i
\(288\) −6.41330 −0.377907
\(289\) 8.08931 + 14.0111i 0.475842 + 0.824182i
\(290\) 7.88712 13.6609i 0.463148 0.802195i
\(291\) −1.51774 + 2.62881i −0.0889716 + 0.154103i
\(292\) −1.19494 2.06970i −0.0699288 0.121120i
\(293\) −7.91058 −0.462141 −0.231071 0.972937i \(-0.574223\pi\)
−0.231071 + 0.972937i \(0.574223\pi\)
\(294\) 1.40928 5.13454i 0.0821908 0.299452i
\(295\) 12.2082 0.710788
\(296\) 6.14212 + 10.6385i 0.357003 + 0.618348i
\(297\) 2.98206 5.16508i 0.173037 0.299708i
\(298\) 11.2028 19.4038i 0.648959 1.12403i
\(299\) 0 0
\(300\) 0.730535 0.0421775
\(301\) −11.4299 + 8.71545i −0.658809 + 0.502350i
\(302\) 23.7214 1.36502
\(303\) −1.76685 3.06027i −0.101503 0.175808i
\(304\) −15.5889 + 27.0008i −0.894086 + 1.54860i
\(305\) 4.92598 8.53204i 0.282061 0.488543i
\(306\) 1.94489 + 3.36865i 0.111182 + 0.192573i
\(307\) −1.27238 −0.0726187 −0.0363094 0.999341i \(-0.511560\pi\)
−0.0363094 + 0.999341i \(0.511560\pi\)
\(308\) −2.15451 0.900105i −0.122765 0.0512882i
\(309\) −4.85653 −0.276278
\(310\) 4.89763 + 8.48295i 0.278167 + 0.481799i
\(311\) −12.3817 + 21.4458i −0.702103 + 1.21608i 0.265624 + 0.964077i \(0.414422\pi\)
−0.967727 + 0.252002i \(0.918911\pi\)
\(312\) 0 0
\(313\) −1.18826 2.05812i −0.0671642 0.116332i 0.830488 0.557037i \(-0.188062\pi\)
−0.897652 + 0.440705i \(0.854728\pi\)
\(314\) 17.7466 1.00150
\(315\) 1.10972 + 8.63169i 0.0625259 + 0.486341i
\(316\) 2.53250 0.142464
\(317\) −9.88979 17.1296i −0.555466 0.962096i −0.997867 0.0652782i \(-0.979207\pi\)
0.442401 0.896817i \(-0.354127\pi\)
\(318\) 1.07431 1.86076i 0.0602442 0.104346i
\(319\) 9.00993 15.6057i 0.504459 0.873749i
\(320\) −3.40093 5.89059i −0.190118 0.329294i
\(321\) 1.07638 0.0600779
\(322\) 1.88682 + 14.6762i 0.105149 + 0.817870i
\(323\) 6.06342 0.337378
\(324\) −1.43945 2.49320i −0.0799695 0.138511i
\(325\) 0 0
\(326\) 11.1997 19.3985i 0.620295 1.07438i
\(327\) −3.36258 5.82416i −0.185951 0.322077i
\(328\) −3.78097 −0.208769
\(329\) 7.77967 + 3.25016i 0.428907 + 0.179187i
\(330\) −1.91786 −0.105575
\(331\) 1.96386 + 3.40151i 0.107944 + 0.186964i 0.914937 0.403596i \(-0.132240\pi\)
−0.806993 + 0.590561i \(0.798907\pi\)
\(332\) −2.42533 + 4.20080i −0.133107 + 0.230549i
\(333\) −6.88997 + 11.9338i −0.377568 + 0.653967i
\(334\) −6.04143 10.4641i −0.330572 0.572568i
\(335\) 4.46058 0.243708
\(336\) −4.79688 + 3.65768i −0.261691 + 0.199543i
\(337\) −7.14099 −0.388995 −0.194497 0.980903i \(-0.562308\pi\)
−0.194497 + 0.980903i \(0.562308\pi\)
\(338\) 0 0
\(339\) −3.93718 + 6.81940i −0.213838 + 0.370379i
\(340\) 0.225181 0.390024i 0.0122121 0.0211520i
\(341\) 5.59486 + 9.69059i 0.302979 + 0.524775i
\(342\) −28.7142 −1.55268
\(343\) 6.93120 + 17.1744i 0.374250 + 0.927328i
\(344\) 13.3699 0.720856
\(345\) 1.04853 + 1.81611i 0.0564509 + 0.0977759i
\(346\) 4.73761 8.20578i 0.254695 0.441145i
\(347\) −5.03498 + 8.72085i −0.270292 + 0.468160i −0.968937 0.247309i \(-0.920454\pi\)
0.698644 + 0.715469i \(0.253787\pi\)
\(348\) 0.868758 + 1.50473i 0.0465703 + 0.0806622i
\(349\) 6.28837 0.336609 0.168304 0.985735i \(-0.446171\pi\)
0.168304 + 0.985735i \(0.446171\pi\)
\(350\) −11.7108 + 8.92964i −0.625969 + 0.477310i
\(351\) 0 0
\(352\) 2.45803 + 4.25743i 0.131013 + 0.226922i
\(353\) 17.0836 29.5897i 0.909269 1.57490i 0.0941861 0.995555i \(-0.469975\pi\)
0.815083 0.579345i \(-0.196692\pi\)
\(354\) −3.89671 + 6.74930i −0.207108 + 0.358721i
\(355\) −1.50738 2.61087i −0.0800036 0.138570i
\(356\) 7.40313 0.392365
\(357\) 1.08248 + 0.452236i 0.0572911 + 0.0239349i
\(358\) −28.8080 −1.52255
\(359\) 9.34327 + 16.1830i 0.493119 + 0.854107i 0.999969 0.00792750i \(-0.00252343\pi\)
−0.506850 + 0.862034i \(0.669190\pi\)
\(360\) 4.04750 7.01047i 0.213322 0.369484i
\(361\) −12.8799 + 22.3087i −0.677891 + 1.17414i
\(362\) −4.35716 7.54683i −0.229007 0.396653i
\(363\) 3.19088 0.167478
\(364\) 0 0
\(365\) 6.82788 0.357388
\(366\) 3.14463 + 5.44666i 0.164372 + 0.284701i
\(367\) 15.5305 26.8997i 0.810687 1.40415i −0.101696 0.994816i \(-0.532427\pi\)
0.912384 0.409336i \(-0.134240\pi\)
\(368\) 8.38209 14.5182i 0.436946 0.756813i
\(369\) −2.12067 3.67310i −0.110397 0.191214i
\(370\) 9.24655 0.480705
\(371\) 0.952998 + 7.41264i 0.0494772 + 0.384845i
\(372\) −1.07894 −0.0559404
\(373\) 1.46852 + 2.54355i 0.0760371 + 0.131700i 0.901537 0.432702i \(-0.142440\pi\)
−0.825500 + 0.564403i \(0.809107\pi\)
\(374\) 1.49084 2.58221i 0.0770894 0.133523i
\(375\) −2.50094 + 4.33175i −0.129148 + 0.223691i
\(376\) −3.92126 6.79182i −0.202223 0.350261i
\(377\) 0 0
\(378\) −10.6970 4.46894i −0.550193 0.229858i
\(379\) −10.0851 −0.518036 −0.259018 0.965872i \(-0.583399\pi\)
−0.259018 + 0.965872i \(0.583399\pi\)
\(380\) 1.66227 + 2.87914i 0.0852727 + 0.147697i
\(381\) −3.83534 + 6.64301i −0.196491 + 0.340332i
\(382\) 0.391550 0.678184i 0.0200334 0.0346989i
\(383\) 1.84466 + 3.19504i 0.0942576 + 0.163259i 0.909299 0.416144i \(-0.136619\pi\)
−0.815041 + 0.579403i \(0.803286\pi\)
\(384\) 6.61534 0.337588
\(385\) 5.30477 4.04496i 0.270356 0.206150i
\(386\) −5.77168 −0.293771
\(387\) 7.49888 + 12.9884i 0.381190 + 0.660240i
\(388\) 1.29376 2.24086i 0.0656809 0.113763i
\(389\) −11.3333 + 19.6299i −0.574623 + 0.995277i 0.421459 + 0.906847i \(0.361518\pi\)
−0.996082 + 0.0884295i \(0.971815\pi\)
\(390\) 0 0
\(391\) −3.26027 −0.164879
\(392\) 4.55965 16.6125i 0.230297 0.839060i
\(393\) 4.66633 0.235385
\(394\) 5.78694 + 10.0233i 0.291542 + 0.504965i
\(395\) −3.61767 + 6.26598i −0.182025 + 0.315276i
\(396\) −1.21818 + 2.10995i −0.0612160 + 0.106029i
\(397\) −14.5680 25.2325i −0.731146 1.26638i −0.956394 0.292080i \(-0.905652\pi\)
0.225248 0.974302i \(-0.427681\pi\)
\(398\) −11.6688 −0.584904
\(399\) −6.88654 + 5.25108i −0.344758 + 0.262883i
\(400\) 16.6848 0.834241
\(401\) 4.06026 + 7.03258i 0.202760 + 0.351190i 0.949417 0.314019i \(-0.101676\pi\)
−0.746657 + 0.665209i \(0.768342\pi\)
\(402\) −1.42377 + 2.46603i −0.0710110 + 0.122995i
\(403\) 0 0
\(404\) 1.50611 + 2.60866i 0.0749318 + 0.129786i
\(405\) 8.22499 0.408703
\(406\) −32.3196 13.5024i −1.60399 0.670111i
\(407\) 10.5629 0.523583
\(408\) −0.545614 0.945031i −0.0270119 0.0467860i
\(409\) −4.16131 + 7.20759i −0.205763 + 0.356393i −0.950376 0.311105i \(-0.899301\pi\)
0.744612 + 0.667497i \(0.232634\pi\)
\(410\) −1.42300 + 2.46471i −0.0702769 + 0.121723i
\(411\) 0.676295 + 1.17138i 0.0333592 + 0.0577798i
\(412\) 4.13984 0.203955
\(413\) −3.45670 26.8870i −0.170093 1.32302i
\(414\) 15.4395 0.758808
\(415\) −6.92915 12.0016i −0.340139 0.589138i
\(416\) 0 0
\(417\) −5.57666 + 9.65905i −0.273090 + 0.473006i
\(418\) 11.0053 + 19.0617i 0.538286 + 0.932339i
\(419\) −13.0166 −0.635905 −0.317952 0.948107i \(-0.602995\pi\)
−0.317952 + 0.948107i \(0.602995\pi\)
\(420\) 0.0820216 + 0.637983i 0.00400224 + 0.0311304i
\(421\) 8.89681 0.433604 0.216802 0.976216i \(-0.430437\pi\)
0.216802 + 0.976216i \(0.430437\pi\)
\(422\) 2.94662 + 5.10369i 0.143439 + 0.248444i
\(423\) 4.39870 7.61877i 0.213872 0.370437i
\(424\) 3.47587 6.02038i 0.168803 0.292376i
\(425\) −1.62242 2.81011i −0.0786988 0.136310i
\(426\) 1.92456 0.0932451
\(427\) −20.1855 8.43303i −0.976846 0.408103i
\(428\) −0.917539 −0.0443509
\(429\) 0 0
\(430\) 5.03187 8.71545i 0.242658 0.420296i
\(431\) −4.47872 + 7.75736i −0.215732 + 0.373659i −0.953499 0.301397i \(-0.902547\pi\)
0.737767 + 0.675056i \(0.235880\pi\)
\(432\) 6.56711 + 11.3746i 0.315960 + 0.547259i
\(433\) −0.172909 −0.00830950 −0.00415475 0.999991i \(-0.501323\pi\)
−0.00415475 + 0.999991i \(0.501323\pi\)
\(434\) 17.2959 13.1883i 0.830229 0.633060i
\(435\) −4.96407 −0.238009
\(436\) 2.86636 + 4.96467i 0.137274 + 0.237765i
\(437\) 12.0336 20.8428i 0.575644 0.997045i
\(438\) −2.17938 + 3.77480i −0.104135 + 0.180367i
\(439\) −4.77080 8.26327i −0.227698 0.394384i 0.729428 0.684058i \(-0.239787\pi\)
−0.957125 + 0.289674i \(0.906453\pi\)
\(440\) −6.20515 −0.295819
\(441\) 18.6960 4.88806i 0.890286 0.232765i
\(442\) 0 0
\(443\) 6.93676 + 12.0148i 0.329576 + 0.570842i 0.982428 0.186644i \(-0.0597610\pi\)
−0.652852 + 0.757485i \(0.726428\pi\)
\(444\) −0.509249 + 0.882045i −0.0241679 + 0.0418600i
\(445\) −10.5753 + 18.3170i −0.501319 + 0.868310i
\(446\) −3.78473 6.55534i −0.179212 0.310404i
\(447\) −7.05091 −0.333496
\(448\) −12.0103 + 9.15803i −0.567434 + 0.432676i
\(449\) 21.2913 1.00480 0.502398 0.864636i \(-0.332451\pi\)
0.502398 + 0.864636i \(0.332451\pi\)
\(450\) 7.68318 + 13.3077i 0.362189 + 0.627329i
\(451\) −1.62558 + 2.81558i −0.0765455 + 0.132581i
\(452\) 3.35616 5.81304i 0.157861 0.273423i
\(453\) −3.73251 6.46489i −0.175368 0.303747i
\(454\) 37.5872 1.76406
\(455\) 0 0
\(456\) 8.05539 0.377228
\(457\) 4.84282 + 8.38801i 0.226538 + 0.392375i 0.956780 0.290814i \(-0.0939261\pi\)
−0.730242 + 0.683189i \(0.760593\pi\)
\(458\) 16.8779 29.2334i 0.788652 1.36599i
\(459\) 1.27716 2.21211i 0.0596128 0.103252i
\(460\) −0.893795 1.54810i −0.0416734 0.0721804i
\(461\) 1.37436 0.0640101 0.0320051 0.999488i \(-0.489811\pi\)
0.0320051 + 0.999488i \(0.489811\pi\)
\(462\) 0.543035 + 4.22385i 0.0252643 + 0.196511i
\(463\) −31.7710 −1.47653 −0.738263 0.674513i \(-0.764354\pi\)
−0.738263 + 0.674513i \(0.764354\pi\)
\(464\) 19.8417 + 34.3669i 0.921128 + 1.59544i
\(465\) 1.54126 2.66954i 0.0714742 0.123797i
\(466\) 2.95145 5.11206i 0.136723 0.236812i
\(467\) 14.5605 + 25.2195i 0.673778 + 1.16702i 0.976824 + 0.214042i \(0.0686629\pi\)
−0.303046 + 0.952976i \(0.598004\pi\)
\(468\) 0 0
\(469\) −1.26299 9.82387i −0.0583197 0.453624i
\(470\) −5.90319 −0.272294
\(471\) −2.79238 4.83654i −0.128666 0.222856i
\(472\) −12.6076 + 21.8370i −0.580312 + 1.00513i
\(473\) 5.74820 9.95618i 0.264303 0.457786i
\(474\) −2.30943 4.00006i −0.106076 0.183729i
\(475\) 23.9532 1.09905
\(476\) −0.922738 0.385498i −0.0422936 0.0176693i
\(477\) 7.79816 0.357053
\(478\) −17.0316 29.4995i −0.779005 1.34928i
\(479\) 4.86092 8.41936i 0.222101 0.384690i −0.733345 0.679857i \(-0.762042\pi\)
0.955446 + 0.295167i \(0.0953752\pi\)
\(480\) 0.677132 1.17283i 0.0309067 0.0535320i
\(481\) 0 0
\(482\) −32.2578 −1.46930
\(483\) 3.70286 2.82348i 0.168486 0.128473i
\(484\) −2.71999 −0.123636
\(485\) 3.69627 + 6.40213i 0.167839 + 0.290706i
\(486\) −9.19791 + 15.9313i −0.417226 + 0.722656i
\(487\) −8.55666 + 14.8206i −0.387739 + 0.671584i −0.992145 0.125093i \(-0.960077\pi\)
0.604406 + 0.796676i \(0.293411\pi\)
\(488\) 10.1743 + 17.6224i 0.460568 + 0.797728i
\(489\) −7.04899 −0.318766
\(490\) −9.11318 9.22457i −0.411692 0.416724i
\(491\) −25.7213 −1.16079 −0.580394 0.814336i \(-0.697101\pi\)
−0.580394 + 0.814336i \(0.697101\pi\)
\(492\) −0.156742 0.271485i −0.00706647 0.0122395i
\(493\) 3.85879 6.68361i 0.173791 0.301015i
\(494\) 0 0
\(495\) −3.48033 6.02812i −0.156429 0.270944i
\(496\) −24.6421 −1.10646
\(497\) −5.32329 + 4.05908i −0.238782 + 0.182075i
\(498\) 8.84682 0.396435
\(499\) 2.70198 + 4.67996i 0.120957 + 0.209504i 0.920145 0.391577i \(-0.128070\pi\)
−0.799188 + 0.601081i \(0.794737\pi\)
\(500\) 2.13187 3.69250i 0.0953400 0.165134i
\(501\) −1.90121 + 3.29299i −0.0849396 + 0.147120i
\(502\) 10.3059 + 17.8503i 0.459974 + 0.796699i
\(503\) −12.6169 −0.562562 −0.281281 0.959625i \(-0.590759\pi\)
−0.281281 + 0.959625i \(0.590759\pi\)
\(504\) −16.5857 6.92912i −0.738786 0.308647i
\(505\) −8.60589 −0.382957
\(506\) −5.91749 10.2494i −0.263064 0.455641i
\(507\) 0 0
\(508\) 3.26935 5.66268i 0.145054 0.251241i
\(509\) −0.979379 1.69633i −0.0434102 0.0751887i 0.843504 0.537123i \(-0.180489\pi\)
−0.886914 + 0.461934i \(0.847156\pi\)
\(510\) −0.821385 −0.0363715
\(511\) −1.93329 15.0376i −0.0855236 0.665222i
\(512\) 12.1111 0.535240
\(513\) 9.42794 + 16.3297i 0.416254 + 0.720973i
\(514\) −10.2385 + 17.7335i −0.451599 + 0.782193i
\(515\) −5.91374 + 10.2429i −0.260590 + 0.451356i
\(516\) 0.554255 + 0.959998i 0.0243997 + 0.0422615i
\(517\) −6.74357 −0.296582
\(518\) −2.61812 20.3644i −0.115034 0.894758i
\(519\) −2.98180 −0.130886
\(520\) 0 0
\(521\) 19.5477 33.8576i 0.856401 1.48333i −0.0189387 0.999821i \(-0.506029\pi\)
0.875339 0.483509i \(-0.160638\pi\)
\(522\) −18.2738 + 31.6512i −0.799823 + 1.38533i
\(523\) 4.35634 + 7.54540i 0.190489 + 0.329937i 0.945413 0.325876i \(-0.105659\pi\)
−0.754923 + 0.655813i \(0.772326\pi\)
\(524\) −3.97770 −0.173767
\(525\) 4.27629 + 1.78653i 0.186633 + 0.0779707i
\(526\) 29.7576 1.29749
\(527\) 2.39618 + 4.15030i 0.104379 + 0.180790i
\(528\) 2.41239 4.17839i 0.104986 0.181841i
\(529\) 5.02961 8.71154i 0.218679 0.378763i
\(530\) −2.61634 4.53164i −0.113647 0.196842i
\(531\) −28.2854 −1.22748
\(532\) 5.87028 4.47616i 0.254509 0.194066i
\(533\) 0 0
\(534\) −6.75105 11.6932i −0.292147 0.506013i
\(535\) 1.31070 2.27020i 0.0566665 0.0981493i
\(536\) −4.60652 + 7.97873i −0.198971 + 0.344629i
\(537\) 4.53286 + 7.85114i 0.195607 + 0.338802i
\(538\) 44.2809 1.90909
\(539\) −10.4105 10.5378i −0.448413 0.453894i
\(540\) 1.40052 0.0602689
\(541\) −10.7497 18.6190i −0.462165 0.800493i 0.536904 0.843644i \(-0.319594\pi\)
−0.999069 + 0.0431505i \(0.986260\pi\)
\(542\) −13.9513 + 24.1644i −0.599260 + 1.03795i
\(543\) −1.37118 + 2.37495i −0.0588428 + 0.101919i
\(544\) 1.05273 + 1.82338i 0.0451353 + 0.0781767i
\(545\) −16.3783 −0.701569
\(546\) 0 0
\(547\) −30.2968 −1.29540 −0.647699 0.761896i \(-0.724269\pi\)
−0.647699 + 0.761896i \(0.724269\pi\)
\(548\) −0.576493 0.998514i −0.0246265 0.0426544i
\(549\) −11.4131 + 19.7680i −0.487098 + 0.843679i
\(550\) 5.88947 10.2009i 0.251128 0.434967i
\(551\) 28.4854 + 49.3381i 1.21352 + 2.10187i
\(552\) −4.33134 −0.184354
\(553\) 14.8244 + 6.19327i 0.630396 + 0.263365i
\(554\) −20.8932 −0.887668
\(555\) −1.45492 2.51999i −0.0617579 0.106968i
\(556\) 4.75369 8.23364i 0.201601 0.349184i
\(557\) −8.84201 + 15.3148i −0.374648 + 0.648909i −0.990274 0.139129i \(-0.955570\pi\)
0.615626 + 0.788038i \(0.288903\pi\)
\(558\) −11.3474 19.6543i −0.480374 0.832033i
\(559\) 0 0
\(560\) 1.87330 + 14.5710i 0.0791616 + 0.615737i
\(561\) −0.938317 −0.0396158
\(562\) 23.2838 + 40.3287i 0.982167 + 1.70116i
\(563\) 20.8695 36.1471i 0.879545 1.52342i 0.0277042 0.999616i \(-0.491180\pi\)
0.851841 0.523801i \(-0.175486\pi\)
\(564\) 0.325115 0.563116i 0.0136898 0.0237115i
\(565\) 9.58852 + 16.6078i 0.403392 + 0.698696i
\(566\) 15.3777 0.646375
\(567\) −2.32887 18.1145i −0.0978035 0.760738i
\(568\) 6.22681 0.261271
\(569\) −2.73388 4.73521i −0.114610 0.198510i 0.803014 0.595960i \(-0.203229\pi\)
−0.917624 + 0.397450i \(0.869895\pi\)
\(570\) 3.03171 5.25108i 0.126984 0.219943i
\(571\) −4.67621 + 8.09944i −0.195693 + 0.338951i −0.947128 0.320857i \(-0.896029\pi\)
0.751434 + 0.659808i \(0.229362\pi\)
\(572\) 0 0
\(573\) −0.246437 −0.0102951
\(574\) 5.83112 + 2.43611i 0.243386 + 0.101681i
\(575\) −12.8795 −0.537113
\(576\) 7.87968 + 13.6480i 0.328320 + 0.568667i
\(577\) −1.68462 + 2.91786i −0.0701318 + 0.121472i −0.898959 0.438033i \(-0.855675\pi\)
0.828827 + 0.559505i \(0.189009\pi\)
\(578\) −12.5763 + 21.7829i −0.523107 + 0.906048i
\(579\) 0.908159 + 1.57298i 0.0377418 + 0.0653707i
\(580\) 4.23151 0.175704
\(581\) −24.4702 + 18.6588i −1.01519 + 0.774098i
\(582\) −4.71923 −0.195618
\(583\) −2.98881 5.17676i −0.123784 0.214400i
\(584\) −7.05128 + 12.2132i −0.291784 + 0.505385i
\(585\) 0 0
\(586\) −6.14924 10.6508i −0.254023 0.439980i
\(587\) 13.1528 0.542873 0.271437 0.962456i \(-0.412501\pi\)
0.271437 + 0.962456i \(0.412501\pi\)
\(588\) 1.38185 0.361284i 0.0569866 0.0148991i
\(589\) −35.3769 −1.45768
\(590\) 9.48995 + 16.4371i 0.390695 + 0.676704i
\(591\) 1.82112 3.15427i 0.0749108 0.129749i
\(592\) −11.6308 + 20.1452i −0.478024 + 0.827961i
\(593\) 19.2958 + 33.4213i 0.792384 + 1.37245i 0.924487 + 0.381214i \(0.124494\pi\)
−0.132102 + 0.991236i \(0.542173\pi\)
\(594\) 9.27234 0.380449
\(595\) 2.27194 1.73238i 0.0931403 0.0710207i
\(596\) 6.01038 0.246195
\(597\) 1.83605 + 3.18014i 0.0751447 + 0.130154i
\(598\) 0 0
\(599\) −9.20762 + 15.9481i −0.376213 + 0.651620i −0.990508 0.137457i \(-0.956107\pi\)
0.614295 + 0.789077i \(0.289441\pi\)
\(600\) −2.15542 3.73329i −0.0879946 0.152411i
\(601\) −41.4037 −1.68889 −0.844445 0.535642i \(-0.820070\pi\)
−0.844445 + 0.535642i \(0.820070\pi\)
\(602\) −20.6194 8.61431i −0.840385 0.351093i
\(603\) −10.3348 −0.420865
\(604\) 3.18169 + 5.51085i 0.129461 + 0.224233i
\(605\) 3.88549 6.72987i 0.157968 0.273608i
\(606\) 2.74690 4.75777i 0.111585 0.193271i
\(607\) −6.15255 10.6565i −0.249724 0.432535i 0.713725 0.700426i \(-0.247007\pi\)
−0.963449 + 0.267891i \(0.913673\pi\)
\(608\) −15.5424 −0.630327
\(609\) 1.40556 + 10.9327i 0.0569560 + 0.443017i
\(610\) 15.3167 0.620155
\(611\) 0 0
\(612\) −0.521725 + 0.903654i −0.0210895 + 0.0365280i
\(613\) 13.1112 22.7093i 0.529556 0.917219i −0.469849 0.882747i \(-0.655692\pi\)
0.999406 0.0344720i \(-0.0109749\pi\)
\(614\) −0.989078 1.71313i −0.0399160 0.0691365i
\(615\) 0.895620 0.0361149
\(616\) 1.75696 + 13.6661i 0.0707900 + 0.550621i
\(617\) 18.8252 0.757873 0.378936 0.925423i \(-0.376290\pi\)
0.378936 + 0.925423i \(0.376290\pi\)
\(618\) −3.77519 6.53882i −0.151860 0.263030i
\(619\) −7.90415 + 13.6904i −0.317695 + 0.550263i −0.980007 0.198965i \(-0.936242\pi\)
0.662312 + 0.749228i \(0.269575\pi\)
\(620\) −1.31381 + 2.27559i −0.0527639 + 0.0913898i
\(621\) −5.06935 8.78038i −0.203426 0.352344i
\(622\) −38.4994 −1.54369
\(623\) 43.3353 + 18.1045i 1.73619 + 0.725340i
\(624\) 0 0
\(625\) −2.86003 4.95371i −0.114401 0.198149i
\(626\) 1.84737 3.19973i 0.0738356 0.127887i
\(627\) 3.46331 5.99862i 0.138311 0.239562i
\(628\) 2.38030 + 4.12280i 0.0949843 + 0.164518i
\(629\) 4.52389 0.180379
\(630\) −10.7591 + 8.20392i −0.428651 + 0.326852i
\(631\) 16.6763 0.663875 0.331937 0.943301i \(-0.392298\pi\)
0.331937 + 0.943301i \(0.392298\pi\)
\(632\) −7.47206 12.9420i −0.297222 0.514804i
\(633\) 0.927285 1.60610i 0.0368563 0.0638369i
\(634\) 15.3755 26.6312i 0.610640 1.05766i
\(635\) 9.34050 + 16.1782i 0.370667 + 0.642013i
\(636\) 0.576375 0.0228548
\(637\) 0 0
\(638\) 28.0152 1.10913
\(639\) 3.49248 + 6.04916i 0.138161 + 0.239301i
\(640\) 8.05542 13.9524i 0.318418 0.551517i
\(641\) −24.6232 + 42.6487i −0.972559 + 1.68452i −0.284792 + 0.958589i \(0.591925\pi\)
−0.687767 + 0.725932i \(0.741409\pi\)
\(642\) 0.836720 + 1.44924i 0.0330227 + 0.0571970i
\(643\) −42.8711 −1.69067 −0.845335 0.534236i \(-0.820599\pi\)
−0.845335 + 0.534236i \(0.820599\pi\)
\(644\) −3.15642 + 2.40681i −0.124380 + 0.0948415i
\(645\) −3.16700 −0.124701
\(646\) 4.71336 + 8.16378i 0.185445 + 0.321200i
\(647\) −2.12929 + 3.68804i −0.0837112 + 0.144992i −0.904841 0.425749i \(-0.860011\pi\)
0.821130 + 0.570741i \(0.193344\pi\)
\(648\) −8.49410 + 14.7122i −0.333680 + 0.577950i
\(649\) 10.8409 + 18.7771i 0.425544 + 0.737064i
\(650\) 0 0
\(651\) −6.31572 2.63856i −0.247533 0.103413i
\(652\) 6.00875 0.235321
\(653\) 1.04776 + 1.81477i 0.0410020 + 0.0710176i 0.885798 0.464071i \(-0.153612\pi\)
−0.844796 + 0.535088i \(0.820278\pi\)
\(654\) 5.22776 9.05475i 0.204422 0.354069i
\(655\) 5.68213 9.84174i 0.222019 0.384549i
\(656\) −3.57986 6.20049i −0.139770 0.242089i
\(657\) −15.8196 −0.617183
\(658\) 1.67146 + 13.0010i 0.0651604 + 0.506833i
\(659\) 25.4518 0.991463 0.495732 0.868476i \(-0.334900\pi\)
0.495732 + 0.868476i \(0.334900\pi\)
\(660\) −0.257237 0.445548i −0.0100129 0.0173429i
\(661\) 13.9054 24.0848i 0.540857 0.936792i −0.457998 0.888953i \(-0.651433\pi\)
0.998855 0.0478387i \(-0.0152333\pi\)
\(662\) −3.05319 + 5.28829i −0.118666 + 0.205535i
\(663\) 0 0
\(664\) 28.6234 1.11080
\(665\) 2.68937 + 20.9186i 0.104289 + 0.811187i
\(666\) −21.4235 −0.830143
\(667\) −15.3164 26.5288i −0.593055 1.02720i
\(668\) 1.62064 2.80703i 0.0627044 0.108607i
\(669\) −1.19103 + 2.06293i −0.0460480 + 0.0797574i
\(670\) 3.46740 + 6.00572i 0.133957 + 0.232021i
\(671\) 17.4972 0.675472
\(672\) −2.77473 1.15922i −0.107038 0.0447178i
\(673\) 15.5207 0.598278 0.299139 0.954210i \(-0.403301\pi\)
0.299139 + 0.954210i \(0.403301\pi\)
\(674\) −5.55100 9.61462i −0.213817 0.370341i
\(675\) 5.04536 8.73881i 0.194196 0.336357i
\(676\) 0 0
\(677\) −17.2813 29.9321i −0.664175 1.15038i −0.979508 0.201403i \(-0.935450\pi\)
0.315334 0.948981i \(-0.397884\pi\)
\(678\) −12.2422 −0.470158
\(679\) 13.0533 9.95331i 0.500940 0.381973i
\(680\) −2.65755 −0.101912
\(681\) −5.91425 10.2438i −0.226634 0.392542i
\(682\) −8.69826 + 15.0658i −0.333074 + 0.576900i
\(683\) 23.5032 40.7087i 0.899325 1.55768i 0.0709661 0.997479i \(-0.477392\pi\)
0.828359 0.560198i \(-0.189275\pi\)
\(684\) −3.85135 6.67073i −0.147260 0.255062i
\(685\) 3.29407 0.125860
\(686\) −17.7356 + 22.6825i −0.677148 + 0.866023i
\(687\) −10.6228 −0.405284
\(688\) 12.6587 + 21.9255i 0.482609 + 0.835904i
\(689\) 0 0
\(690\) −1.63013 + 2.82348i −0.0620582 + 0.107488i
\(691\) 9.50301 + 16.4597i 0.361512 + 0.626156i 0.988210 0.153106i \(-0.0489275\pi\)
−0.626698 + 0.779262i \(0.715594\pi\)
\(692\) 2.54177 0.0966235
\(693\) −12.2907 + 9.37183i −0.466886 + 0.356006i
\(694\) −15.6556 −0.594280
\(695\) 13.5813 + 23.5234i 0.515166 + 0.892294i
\(696\) 5.12648 8.87933i 0.194319 0.336570i
\(697\) −0.696205 + 1.20586i −0.0263706 + 0.0456753i
\(698\) 4.88822 + 8.46665i 0.185022 + 0.320467i
\(699\) −1.85761 −0.0702612
\(700\) −3.64523 1.52289i −0.137777 0.0575598i
\(701\) −45.4648 −1.71718 −0.858591 0.512662i \(-0.828659\pi\)
−0.858591 + 0.512662i \(0.828659\pi\)
\(702\) 0 0
\(703\) −16.6976 + 28.9210i −0.629760 + 1.09078i
\(704\) 6.04010 10.4618i 0.227645 0.394293i
\(705\) 0.928851 + 1.60882i 0.0349826 + 0.0605916i
\(706\) 53.1193 1.99917
\(707\) 2.43672 + 18.9534i 0.0916423 + 0.712815i
\(708\) −2.09062 −0.0785702
\(709\) −4.89390 8.47648i −0.183794 0.318341i 0.759375 0.650653i \(-0.225505\pi\)
−0.943170 + 0.332312i \(0.892171\pi\)
\(710\) 2.34351 4.05908i 0.0879504 0.152334i
\(711\) 8.38183 14.5178i 0.314343 0.544459i
\(712\) −21.8427 37.8326i −0.818589 1.41784i
\(713\) 19.0220 0.712378
\(714\) 0.232572 + 1.80900i 0.00870377 + 0.0677000i
\(715\) 0 0
\(716\) −3.86393 6.69252i −0.144402 0.250111i
\(717\) −5.35974 + 9.28334i −0.200163 + 0.346693i
\(718\) −14.5259 + 25.1595i −0.542100 + 0.938945i
\(719\) 13.9201 + 24.1104i 0.519133 + 0.899165i 0.999753 + 0.0222358i \(0.00707846\pi\)
−0.480620 + 0.876929i \(0.659588\pi\)
\(720\) 15.3288 0.571271
\(721\) 24.2331 + 10.1240i 0.902489 + 0.377039i
\(722\) −40.0485 −1.49045
\(723\) 5.07568 + 8.79134i 0.188767 + 0.326953i
\(724\) 1.16883 2.02447i 0.0434391 0.0752388i
\(725\) 15.2439 26.4033i 0.566145 0.980592i
\(726\) 2.48041 + 4.29619i 0.0920566 + 0.159447i
\(727\) −14.5650 −0.540186 −0.270093 0.962834i \(-0.587055\pi\)
−0.270093 + 0.962834i \(0.587055\pi\)
\(728\) 0 0
\(729\) −14.9199 −0.552589
\(730\) 5.30761 + 9.19305i 0.196444 + 0.340250i
\(731\) 2.46185 4.26405i 0.0910547 0.157711i
\(732\) −0.843560 + 1.46109i −0.0311789 + 0.0540034i
\(733\) 8.83030 + 15.2945i 0.326155 + 0.564916i 0.981745 0.190200i \(-0.0609136\pi\)
−0.655591 + 0.755116i \(0.727580\pi\)
\(734\) 48.2902 1.78243
\(735\) −1.08007 + 3.93511i −0.0398390 + 0.145149i
\(736\) 8.35705 0.308045
\(737\) 3.96102 + 6.86069i 0.145906 + 0.252717i
\(738\) 3.29697 5.71052i 0.121363 0.210207i
\(739\) 4.48279 7.76443i 0.164902 0.285619i −0.771718 0.635964i \(-0.780602\pi\)
0.936621 + 0.350345i \(0.113936\pi\)
\(740\) 1.24021 + 2.14811i 0.0455911 + 0.0789661i
\(741\) 0 0
\(742\) −9.23955 + 7.04528i −0.339195 + 0.258640i
\(743\) 26.3679 0.967343 0.483671 0.875250i \(-0.339303\pi\)
0.483671 + 0.875250i \(0.339303\pi\)
\(744\) 3.18337 + 5.51376i 0.116708 + 0.202144i
\(745\) −8.58580 + 14.8710i −0.314560 + 0.544833i
\(746\) −2.28309 + 3.95442i −0.0835898 + 0.144782i
\(747\) 16.0543 + 27.8068i 0.587395 + 1.01740i
\(748\) 0.799847 0.0292453
\(749\) −5.37095 2.24385i −0.196250 0.0819887i
\(750\) −7.77635 −0.283952
\(751\) 10.1438 + 17.5696i 0.370152 + 0.641123i 0.989589 0.143924i \(-0.0459721\pi\)
−0.619436 + 0.785047i \(0.712639\pi\)
\(752\) 7.42536 12.8611i 0.270775 0.468996i
\(753\) 3.24321 5.61740i 0.118189 0.204709i
\(754\) 0 0
\(755\) −18.1801 −0.661642
\(756\) −0.396552 3.08447i −0.0144225 0.112181i
\(757\) 24.9984 0.908584 0.454292 0.890853i \(-0.349892\pi\)
0.454292 + 0.890853i \(0.349892\pi\)
\(758\) −7.83957 13.5785i −0.284746 0.493195i
\(759\) −1.86220 + 3.22543i −0.0675936 + 0.117076i
\(760\) 9.80895 16.9896i 0.355808 0.616277i
\(761\) 10.0711 + 17.4436i 0.365077 + 0.632332i 0.988789 0.149323i \(-0.0477094\pi\)
−0.623712 + 0.781655i \(0.714376\pi\)
\(762\) −11.9255 −0.432016
\(763\) 4.63745 + 36.0711i 0.167887 + 1.30586i
\(764\) 0.210070 0.00760006
\(765\) −1.49056 2.58173i −0.0538914 0.0933426i
\(766\) −2.86786 + 4.96729i −0.103620 + 0.179475i
\(767\) 0 0
\(768\) 2.34945 + 4.06936i 0.0847784 + 0.146840i
\(769\) −8.67220 −0.312727 −0.156364 0.987700i \(-0.549977\pi\)
−0.156364 + 0.987700i \(0.549977\pi\)
\(770\) 9.56976 + 3.99802i 0.344870 + 0.144079i
\(771\) 6.44398 0.232074
\(772\) −0.774139 1.34085i −0.0278619 0.0482582i
\(773\) 1.17283 2.03141i 0.0421839 0.0730647i −0.844163 0.536087i \(-0.819902\pi\)
0.886346 + 0.463023i \(0.153235\pi\)
\(774\) −11.6584 + 20.1930i −0.419053 + 0.725821i
\(775\) 9.46596 + 16.3955i 0.340027 + 0.588945i
\(776\) −15.2688 −0.548119
\(777\) −5.13801 + 3.91780i −0.184325 + 0.140550i
\(778\) −35.2396 −1.26340
\(779\) −5.13935 8.90161i −0.184136 0.318933i
\(780\)