Properties

Label 1183.2.e.g.170.5
Level $1183$
Weight $2$
Character 1183.170
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 170.5
Root \(-1.02197 - 1.77010i\) of defining polynomial
Character \(\chi\) \(=\) 1183.170
Dual form 1183.2.e.g.508.5

$q$-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 \(\left(\mathbb{Z}/1183\mathbb{Z}\right)^\times\).

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

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 −0.448632 0.893716i \(-0.648089\pi\)
0.998297 0.0583310i \(-0.0185779\pi\)
\(3\) 0.244626 + 0.423704i 0.141235 + 0.244626i 0.927962 0.372675i \(-0.121559\pi\)
−0.786727 + 0.617301i \(0.788226\pi\)
\(4\) −0.208526 0.361177i −0.104263 0.180588i
\(5\) −0.595756 + 1.03188i −0.266430 + 0.461470i −0.967937 0.251192i \(-0.919177\pi\)
0.701507 + 0.712662i \(0.252511\pi\)
\(6\) 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 0.980284 0.197595i \(-0.0633130\pi\)
−0.661264 + 0.750153i \(0.729980\pi\)
\(12\) 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 0.915732 0.401790i \(-0.131612\pi\)
−0.805826 + 0.592152i \(0.798279\pi\)
\(18\) −2.14596 3.71691i −0.505808 0.876084i
\(19\) 3.34514 5.79395i 0.767428 1.32922i −0.171525 0.985180i \(-0.554870\pi\)
0.938953 0.344045i \(-0.111797\pi\)
\(20\) 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 −0.990334 0.138702i \(-0.955707\pi\)
0.615287 + 0.788303i \(0.289040\pi\)
\(24\) 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 0.524727 0.851271i \(-0.324168\pi\)
−0.999585 + 0.0287913i \(0.990834\pi\)
\(32\) −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 −0.584617 0.811309i \(-0.698755\pi\)
0.994923 + 0.100639i \(0.0320886\pi\)
\(38\) −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 −0.958519 0.285030i \(-0.907997\pi\)
0.726102 + 0.687587i \(0.241330\pi\)
\(48\) 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 0.946574 0.322486i \(-0.104518\pi\)
−0.752568 + 0.658514i \(0.771185\pi\)
\(54\) 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 −0.978751 0.205052i \(-0.934264\pi\)
0.311795 0.950149i \(-0.399070\pi\)
\(60\) 0.121560 + 0.210548i 0.0156933 + 0.0271816i
\(61\) 4.13423 7.16069i 0.529333 0.916832i −0.470081 0.882623i \(-0.655775\pi\)
0.999415 0.0342093i \(-0.0108913\pi\)
\(62\) −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 0.728738 0.684793i \(-0.240107\pi\)
−0.957417 + 0.288709i \(0.906774\pi\)
\(68\) 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 0.648203 0.761468i \(-0.275521\pi\)
−0.983552 + 0.180627i \(0.942187\pi\)
\(74\) −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 −0.984730 0.174089i \(-0.944302\pi\)
0.643131 + 0.765756i \(0.277635\pi\)
\(80\) 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 −0.176875 + 0.984233i \(0.556599\pi\)
−0.763934 + 0.645295i \(0.776735\pi\)
\(90\) 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 0.987851 0.155405i \(-0.0496682\pi\)
−0.628510 + 0.777802i \(0.716335\pi\)
\(102\) 0.344682 + 0.597007i 0.0341286 + 0.0591125i
\(103\) −4.96322 + 8.59656i −0.489041 + 0.847044i −0.999921 0.0126084i \(-0.995987\pi\)
0.510879 + 0.859652i \(0.329320\pi\)
\(104\) 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 −0.807942 0.589261i \(-0.799419\pi\)
0.914287 + 0.405068i \(0.132752\pi\)
\(108\) −0.587708 1.01794i −0.0565523 0.0979514i
\(109\) 6.87291 + 11.9042i 0.658305 + 1.14022i 0.981054 + 0.193734i \(0.0620598\pi\)
−0.322749 + 0.946485i \(0.604607\pi\)
\(110\) −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 −0.578945 0.815367i \(-0.696535\pi\)
0.995601 + 0.0936976i \(0.0298687\pi\)
\(132\) 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 0.800916 0.598777i \(-0.204346\pi\)
−0.919014 + 0.394225i \(0.871013\pi\)
\(138\) −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 0.403866 + 0.914818i \(0.367666\pi\)
−0.994189 + 0.107651i \(0.965667\pi\)
\(150\) 1.36165 + 2.35844i 0.111178 + 0.192566i
\(151\) 7.62901 + 13.2138i 0.620840 + 1.07533i 0.989330 + 0.145695i \(0.0465417\pi\)
−0.368489 + 0.929632i \(0.620125\pi\)
\(152\) 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 0.998717 0.0506387i \(-0.0161257\pi\)
−0.543213 + 0.839595i \(0.682792\pi\)
\(158\) 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 0.432870 + 0.901456i \(0.357501\pi\)
−0.997119 + 0.0758514i \(0.975833\pi\)
\(164\) 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 −0.958303 0.285753i \(-0.907756\pi\)
0.726621 + 0.687039i \(0.241090\pi\)
\(174\) 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 −0.971020 0.239000i \(-0.923181\pi\)
0.278530 0.960428i \(-0.410153\pi\)
\(180\) 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 −0.874993 0.484135i \(-0.839134\pi\)
0.856770 + 0.515699i \(0.172468\pi\)
\(192\) 1.39647 + 2.41876i 0.100782 + 0.174559i
\(193\) −1.85622 3.21507i −0.133614 0.231426i 0.791453 0.611230i \(-0.209325\pi\)
−0.925067 + 0.379804i \(0.875991\pi\)
\(194\) −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 0.701805 0.712369i \(-0.252378\pi\)
−0.967832 + 0.251596i \(0.919045\pi\)
\(200\) 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 0.918077 + 0.396402i \(0.129741\pi\)
−0.115745 + 0.993279i \(0.536925\pi\)
\(228\) −0.682552 1.18222i −0.0452031 0.0782941i
\(229\) −10.8561 + 18.8034i −0.717394 + 1.24256i 0.244635 + 0.969615i \(0.421332\pi\)
−0.962029 + 0.272947i \(0.912002\pi\)
\(230\) −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 −0.921486 0.388411i \(-0.873024\pi\)
0.797117 + 0.603825i \(0.206358\pi\)
\(234\) 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 −0.978387 0.206783i \(-0.933701\pi\)
0.310114 0.950699i \(-0.399633\pi\)
\(242\) −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 −0.584182 0.811623i \(-0.698584\pi\)
0.994977 + 0.100105i \(0.0319178\pi\)
\(258\) 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 0.994215 + 0.107412i \(0.0342564\pi\)
−0.404086 + 0.914721i \(0.632410\pi\)
\(264\) −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 0.863737 + 0.503943i \(0.168118\pi\)
0.00455867 + 0.999990i \(0.498549\pi\)
\(270\) 2.61044 + 4.52141i 0.158866 + 0.275164i
\(271\) 8.97371 15.5429i 0.545114 0.944165i −0.453486 0.891263i \(-0.649820\pi\)
0.998600 0.0529014i \(-0.0168469\pi\)
\(272\) 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 0.590441 0.807081i \(-0.298954\pi\)
−0.994173 + 0.107797i \(0.965620\pi\)
\(278\) −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 0.974748 0.223306i \(-0.0716848\pi\)
−0.680763 + 0.732504i \(0.738351\pi\)
\(284\) −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 −0.967727 0.252002i \(-0.918911\pi\)
0.265624 0.964077i \(-0.414422\pi\)
\(312\) 0 0
\(313\) −1.18826 + 2.05812i −0.0671642 + 0.116332i −0.897652 0.440705i \(-0.854728\pi\)
0.830488 + 0.557037i \(0.188062\pi\)
\(314\) 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 0.442401 + 0.896817i \(0.354127\pi\)
−0.997867 + 0.0652782i \(0.979207\pi\)
\(318\) 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 −0.806993 0.590561i \(-0.798907\pi\)
0.914937 + 0.403596i \(0.132240\pi\)
\(332\) −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 0.698644 0.715469i \(-0.253787\pi\)
−0.968937 + 0.247309i \(0.920454\pi\)
\(348\) 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 0.815083 + 0.579345i \(0.196692\pi\)
0.0941861 + 0.995555i \(0.469975\pi\)
\(354\) −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 −0.506850 0.862034i \(-0.669190\pi\)
0.999969 + 0.00792750i \(0.00252343\pi\)
\(360\) 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 0.912384 + 0.409336i \(0.134240\pi\)
−0.101696 + 0.994816i \(0.532427\pi\)
\(368\) 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 −0.825500 0.564403i \(-0.809107\pi\)
0.901537 + 0.432702i \(0.142440\pi\)
\(374\) 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 −0.815041 0.579403i \(-0.803286\pi\)
0.909299 + 0.416144i \(0.136619\pi\)
\(384\) 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 −0.996082 0.0884295i \(-0.971815\pi\)
0.421459 0.906847i \(-0.361518\pi\)
\(390\) 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 0.225248 + 0.974302i \(0.427681\pi\)
−0.956394 + 0.292080i \(0.905652\pi\)
\(398\) −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 −0.746657 0.665209i \(-0.768342\pi\)
0.949417 + 0.314019i \(0.101676\pi\)
\(402\) −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 0.744612 0.667497i \(-0.232634\pi\)
−0.950376 + 0.311105i \(0.899301\pi\)
\(410\) −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 0.737767 0.675056i \(-0.235880\pi\)
−0.953499 + 0.301397i \(0.902547\pi\)
\(432\) 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 −0.957125 0.289674i \(-0.906453\pi\)
0.729428 + 0.684058i \(0.239787\pi\)
\(440\) −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 −0.652852 0.757485i \(-0.726428\pi\)
0.982428 + 0.186644i \(0.0597610\pi\)
\(444\) −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 −0.730242 0.683189i \(-0.760593\pi\)
0.956780 + 0.290814i \(0.0939261\pi\)
\(458\) 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 −0.303046 0.952976i \(-0.598004\pi\)
0.976824 0.214042i \(-0.0686629\pi\)
\(468\) 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 0.955446 0.295167i \(-0.0953752\pi\)
−0.733345 + 0.679857i \(0.762042\pi\)
\(480\) 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 0.604406 0.796676i \(-0.293411\pi\)
−0.992145 + 0.125093i \(0.960077\pi\)
\(488\) 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 −0.799188 0.601081i \(-0.794737\pi\)
0.920145 + 0.391577i \(0.128070\pi\)
\(500\) 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 −0.886914 0.461934i \(-0.847156\pi\)
0.843504 + 0.537123i \(0.180489\pi\)
\(510\) −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 0.875339 + 0.483509i \(0.160638\pi\)
−0.0189387 + 0.999821i \(0.506029\pi\)
\(522\) −18.2738 31.6512i −0.799823 1.38533i
\(523\) 4.35634 7.54540i 0.190489 0.329937i −0.754923 0.655813i \(-0.772326\pi\)
0.945413 + 0.325876i \(0.105659\pi\)
\(524\) −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 −0.999069 0.0431505i \(-0.986260\pi\)
0.536904 + 0.843644i \(0.319594\pi\)
\(542\) −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 0.615626 0.788038i \(-0.288903\pi\)
−0.990274 + 0.139129i \(0.955570\pi\)
\(558\) −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 0.851841 + 0.523801i \(0.175486\pi\)
0.0277042 + 0.999616i \(0.491180\pi\)
\(564\) 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 −0.917624 0.397450i \(-0.869895\pi\)
0.803014 + 0.595960i \(0.203229\pi\)
\(570\) 3.03171 + 5.25108i 0.126984 + 0.219943i
\(571\) −4.67621 8.09944i −0.195693 0.338951i 0.751434 0.659808i \(-0.229362\pi\)
−0.947128 + 0.320857i \(0.896029\pi\)
\(572\) 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 0.828827 0.559505i \(-0.189009\pi\)
−0.898959 + 0.438033i \(0.855675\pi\)
\(578\) −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 −0.132102 0.991236i \(-0.542173\pi\)
0.924487 0.381214i \(-0.124494\pi\)
\(594\) 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 0.614295 0.789077i \(-0.289441\pi\)
−0.990508 + 0.137457i \(0.956107\pi\)
\(600\) −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 −0.963449 0.267891i \(-0.913673\pi\)
0.713725 + 0.700426i \(0.247007\pi\)
\(608\) −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 0.999406 + 0.0344720i \(0.0109749\pi\)
−0.469849 + 0.882747i \(0.655692\pi\)
\(614\) −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 0.662312 0.749228i \(-0.269575\pi\)
−0.980007 + 0.198965i \(0.936242\pi\)
\(620\) −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 −0.687767 0.725932i \(-0.741409\pi\)
−0.284792 0.958589i \(-0.591925\pi\)
\(642\) 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 0.821130 0.570741i \(-0.193344\pi\)
−0.904841 + 0.425749i \(0.860011\pi\)
\(648\) −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 −0.844796 0.535088i \(-0.820278\pi\)
0.885798 + 0.464071i \(0.153612\pi\)
\(654\) 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 0.998855 + 0.0478387i \(0.0152333\pi\)
−0.457998 + 0.888953i \(0.651433\pi\)
\(662\) −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 0.315334 + 0.948981i \(0.397884\pi\)
−0.979508 + 0.201403i \(0.935450\pi\)
\(678\) −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 0.828359 + 0.560198i \(0.189275\pi\)
0.0709661 + 0.997479i \(0.477392\pi\)
\(684\) −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 −0.626698 0.779262i \(-0.715594\pi\)
0.988210 + 0.153106i \(0.0489275\pi\)
\(692\) 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 −0.943170 0.332312i \(-0.892171\pi\)
0.759375 + 0.650653i \(0.225505\pi\)
\(710\) 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 −0.480620 0.876929i \(-0.659588\pi\)
0.999753 0.0222358i \(-0.00707846\pi\)
\(720\) 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 −0.655591 0.755116i \(-0.727580\pi\)
0.981745 + 0.190200i \(0.0609136\pi\)
\(734\) 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 0.936621 0.350345i \(-0.113936\pi\)
−0.771718 + 0.635964i \(0.780602\pi\)
\(740\) 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 −0.619436 0.785047i \(-0.712639\pi\)
0.989589 + 0.143924i \(0.0459721\pi\)
\(752\) 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 −0.623712 0.781655i \(-0.714376\pi\)
0.988789 + 0.149323i \(0.0477094\pi\)
\(762\) −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 0.886346 0.463023i \(-0.153235\pi\)
−0.844163 + 0.536087i \(0.819902\pi\)
\(774\) −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
\(780\)