Properties

Label 819.2.n.d.100.5
Level $819$
Weight $2$
Character 819.100
Analytic conductor $6.540$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 819 = 3^{2} \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 819.n (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.53974792554\)
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: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 91)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 100.5
Root \(-1.02197 + 1.77010i\) of defining polynomial
Character \(\chi\) \(=\) 819.100
Dual form 819.2.n.d.172.5

$q$-expansion

\(f(q)\) \(=\) \(q+(0.777343 + 1.34640i) q^{2} +(-0.208526 + 0.361177i) q^{4} +(-0.595756 + 1.03188i) q^{5} +(0.337371 - 2.62415i) q^{7} +2.46099 q^{8} +O(q^{10})\) \(q+(0.777343 + 1.34640i) q^{2} +(-0.208526 + 0.361177i) q^{4} +(-0.595756 + 1.03188i) q^{5} +(0.337371 - 2.62415i) q^{7} +2.46099 q^{8} -1.85243 q^{10} -2.11614 q^{11} +(2.86133 + 2.19381i) q^{13} +(3.79541 - 1.58563i) q^{14} +(2.33009 + 4.03583i) q^{16} +(-0.453151 + 0.784881i) q^{17} +6.69028 q^{19} +(-0.248461 - 0.430346i) q^{20} +(-1.64497 - 2.84917i) q^{22} +(1.79866 + 3.11538i) q^{23} +(1.79015 + 3.10063i) q^{25} +(-0.729501 + 5.55783i) q^{26} +(0.877433 + 0.669054i) q^{28} +(4.25772 - 7.37459i) q^{29} +(2.64390 + 4.57937i) q^{31} +(-1.16156 + 2.01189i) q^{32} -1.40902 q^{34} +(2.50682 + 1.91148i) q^{35} +(-2.49579 - 4.32284i) q^{37} +(5.20065 + 9.00778i) q^{38} +(-1.46615 + 2.53944i) q^{40} +(0.768181 - 1.33053i) q^{41} +(-2.71636 - 4.70488i) q^{43} +(0.441269 - 0.764301i) q^{44} +(-2.79636 + 4.84344i) q^{46} +(-1.59337 + 2.75979i) q^{47} +(-6.77236 - 1.77063i) q^{49} +(-2.78312 + 4.82051i) q^{50} +(-1.38901 + 0.575982i) q^{52} +(-1.41239 - 2.44632i) q^{53} +(1.26070 - 2.18360i) q^{55} +(0.830268 - 6.45801i) q^{56} +13.2389 q^{58} +(-5.12298 + 8.87327i) q^{59} -8.26845 q^{61} +(-4.11044 + 7.11949i) q^{62} +5.70861 q^{64} +(-3.96840 + 1.64557i) q^{65} -3.74363 q^{67} +(-0.188987 - 0.327336i) q^{68} +(-0.624956 + 4.86105i) q^{70} +(-1.26510 - 2.19122i) q^{71} +(2.86522 + 4.96271i) q^{73} +(3.88018 - 6.72066i) q^{74} +(-1.39510 + 2.41638i) q^{76} +(-0.713925 + 5.55307i) q^{77} +(-3.03620 + 5.25885i) q^{79} -5.55265 q^{80} +2.38856 q^{82} +11.6309 q^{83} +(-0.539935 - 0.935195i) q^{85} +(4.22310 - 7.31462i) q^{86} -5.20780 q^{88} +(-8.87557 - 15.3729i) q^{89} +(6.72222 - 6.76844i) q^{91} -1.50027 q^{92} -4.95437 q^{94} +(-3.98577 + 6.90356i) q^{95} +(-3.10217 - 5.37312i) q^{97} +(-2.88048 - 10.4947i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12q - 2q^{2} - 4q^{4} - q^{5} + 9q^{7} + 6q^{8} + O(q^{10}) \) \( 12q - 2q^{2} - 4q^{4} - q^{5} + 9q^{7} + 6q^{8} - 8q^{10} + 8q^{11} - 2q^{13} + 2q^{14} + 8q^{16} - 5q^{17} + 2q^{19} + q^{20} - 5q^{22} + q^{23} + 7q^{25} - 5q^{26} - 7q^{28} - 3q^{29} + 16q^{31} - 8q^{32} + 32q^{34} - 8q^{35} - 13q^{37} + 17q^{38} - 5q^{40} + 8q^{41} - 11q^{43} - 21q^{44} + 16q^{46} + q^{47} - 3q^{49} - 6q^{50} - 25q^{52} + 2q^{53} + 9q^{55} + 18q^{56} + 16q^{58} - 13q^{59} + 10q^{61} - 5q^{62} - 30q^{64} - 19q^{65} + 22q^{67} - 29q^{68} - 39q^{70} - 6q^{71} - 30q^{73} + 3q^{74} - 9q^{76} - 11q^{77} + 7q^{79} - 14q^{80} - 2q^{82} + 54q^{83} - q^{85} + 7q^{86} - 4q^{89} - 20q^{91} - 54q^{92} - 90q^{94} + 6q^{95} - 35q^{97} - 62q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/819\mathbb{Z}\right)^\times\).

\(n\) \(92\) \(379\) \(703\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.777343 + 1.34640i 0.549665 + 0.952047i 0.998297 + 0.0583310i \(0.0185779\pi\)
−0.448632 + 0.893716i \(0.648089\pi\)
\(3\) 0 0
\(4\) −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 0
\(7\) 0.337371 2.62415i 0.127514 0.991837i
\(8\) 2.46099 0.870091
\(9\) 0 0
\(10\) −1.85243 −0.585789
\(11\) −2.11614 −0.638040 −0.319020 0.947748i \(-0.603354\pi\)
−0.319020 + 0.947748i \(0.603354\pi\)
\(12\) 0 0
\(13\) 2.86133 + 2.19381i 0.793590 + 0.608453i
\(14\) 3.79541 1.58563i 1.01437 0.423778i
\(15\) 0 0
\(16\) 2.33009 + 4.03583i 0.582521 + 1.00896i
\(17\) −0.453151 + 0.784881i −0.109905 + 0.190362i −0.915732 0.401790i \(-0.868388\pi\)
0.805826 + 0.592152i \(0.201721\pi\)
\(18\) 0 0
\(19\) 6.69028 1.53486 0.767428 0.641135i \(-0.221536\pi\)
0.767428 + 0.641135i \(0.221536\pi\)
\(20\) −0.248461 0.430346i −0.0555575 0.0962284i
\(21\) 0 0
\(22\) −1.64497 2.84917i −0.350708 0.607444i
\(23\) 1.79866 + 3.11538i 0.375048 + 0.649601i 0.990334 0.138702i \(-0.0442930\pi\)
−0.615287 + 0.788303i \(0.710960\pi\)
\(24\) 0 0
\(25\) 1.79015 + 3.10063i 0.358030 + 0.620126i
\(26\) −0.729501 + 5.55783i −0.143067 + 1.08998i
\(27\) 0 0
\(28\) 0.877433 + 0.669054i 0.165819 + 0.126439i
\(29\) 4.25772 7.37459i 0.790639 1.36943i −0.134932 0.990855i \(-0.543082\pi\)
0.925572 0.378573i \(-0.123585\pi\)
\(30\) 0 0
\(31\) 2.64390 + 4.57937i 0.474859 + 0.822479i 0.999585 0.0287913i \(-0.00916583\pi\)
−0.524727 + 0.851271i \(0.675832\pi\)
\(32\) −1.16156 + 2.01189i −0.205337 + 0.355655i
\(33\) 0 0
\(34\) −1.40902 −0.241644
\(35\) 2.50682 + 1.91148i 0.423730 + 0.323099i
\(36\) 0 0
\(37\) −2.49579 4.32284i −0.410306 0.710670i 0.584617 0.811309i \(-0.301245\pi\)
−0.994923 + 0.100639i \(0.967911\pi\)
\(38\) 5.20065 + 9.00778i 0.843656 + 1.46126i
\(39\) 0 0
\(40\) −1.46615 + 2.53944i −0.231818 + 0.401521i
\(41\) 0.768181 1.33053i 0.119970 0.207794i −0.799786 0.600286i \(-0.795054\pi\)
0.919755 + 0.392492i \(0.128387\pi\)
\(42\) 0 0
\(43\) −2.71636 4.70488i −0.414242 0.717488i 0.581107 0.813827i \(-0.302620\pi\)
−0.995349 + 0.0963397i \(0.969286\pi\)
\(44\) 0.441269 0.764301i 0.0665238 0.115223i
\(45\) 0 0
\(46\) −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 \(0.241330\pi\)
\(48\) 0 0
\(49\) −6.77236 1.77063i −0.967480 0.252947i
\(50\) −2.78312 + 4.82051i −0.393593 + 0.681723i
\(51\) 0 0
\(52\) −1.38901 + 0.575982i −0.192621 + 0.0798743i
\(53\) −1.41239 2.44632i −0.194006 0.336029i 0.752568 0.658514i \(-0.228815\pi\)
−0.946574 + 0.322486i \(0.895482\pi\)
\(54\) 0 0
\(55\) 1.26070 2.18360i 0.169993 0.294436i
\(56\) 0.830268 6.45801i 0.110949 0.862988i
\(57\) 0 0
\(58\) 13.2389 1.73835
\(59\) −5.12298 + 8.87327i −0.666956 + 1.15520i 0.311795 + 0.950149i \(0.399070\pi\)
−0.978751 + 0.205052i \(0.934264\pi\)
\(60\) 0 0
\(61\) −8.26845 −1.05867 −0.529333 0.848414i \(-0.677558\pi\)
−0.529333 + 0.848414i \(0.677558\pi\)
\(62\) −4.11044 + 7.11949i −0.522026 + 0.904176i
\(63\) 0 0
\(64\) 5.70861 0.713576
\(65\) −3.96840 + 1.64557i −0.492219 + 0.204108i
\(66\) 0 0
\(67\) −3.74363 −0.457358 −0.228679 0.973502i \(-0.573441\pi\)
−0.228679 + 0.973502i \(0.573441\pi\)
\(68\) −0.188987 0.327336i −0.0229181 0.0396953i
\(69\) 0 0
\(70\) −0.624956 + 4.86105i −0.0746965 + 0.581007i
\(71\) −1.26510 2.19122i −0.150140 0.260050i 0.781139 0.624357i \(-0.214639\pi\)
−0.931279 + 0.364307i \(0.881306\pi\)
\(72\) 0 0
\(73\) 2.86522 + 4.96271i 0.335349 + 0.580841i 0.983552 0.180627i \(-0.0578125\pi\)
−0.648203 + 0.761468i \(0.724479\pi\)
\(74\) 3.88018 6.72066i 0.451061 0.781261i
\(75\) 0 0
\(76\) −1.39510 + 2.41638i −0.160028 + 0.277177i
\(77\) −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 \(0.277635\pi\)
\(80\) −5.55265 −0.620805
\(81\) 0 0
\(82\) 2.38856 0.263773
\(83\) 11.6309 1.27665 0.638327 0.769766i \(-0.279627\pi\)
0.638327 + 0.769766i \(0.279627\pi\)
\(84\) 0 0
\(85\) −0.539935 0.935195i −0.0585642 0.101436i
\(86\) 4.22310 7.31462i 0.455388 0.788755i
\(87\) 0 0
\(88\) −5.20780 −0.555153
\(89\) −8.87557 15.3729i −0.940808 1.62953i −0.763934 0.645295i \(-0.776735\pi\)
−0.176875 0.984233i \(-0.556599\pi\)
\(90\) 0 0
\(91\) 6.72222 6.76844i 0.704680 0.709525i
\(92\) −1.50027 −0.156414
\(93\) 0 0
\(94\) −4.95437 −0.511004
\(95\) −3.98577 + 6.90356i −0.408932 + 0.708291i
\(96\) 0 0
\(97\) −3.10217 5.37312i −0.314978 0.545557i 0.664455 0.747328i \(-0.268664\pi\)
−0.979433 + 0.201771i \(0.935330\pi\)
\(98\) −2.88048 10.4947i −0.290972 1.06012i
\(99\) 0 0
\(100\) −1.49317 −0.149317
\(101\) 7.22266 0.718682 0.359341 0.933206i \(-0.383001\pi\)
0.359341 + 0.933206i \(0.383001\pi\)
\(102\) 0 0
\(103\) −4.96322 + 8.59656i −0.489041 + 0.847044i −0.999921 0.0126084i \(-0.995987\pi\)
0.510879 + 0.859652i \(0.329320\pi\)
\(104\) 7.04170 + 5.39894i 0.690496 + 0.529409i
\(105\) 0 0
\(106\) 2.19582 3.80327i 0.213277 0.369406i
\(107\) −1.10003 1.90531i −0.106344 0.184193i 0.807942 0.589261i \(-0.200581\pi\)
−0.914287 + 0.405068i \(0.867248\pi\)
\(108\) 0 0
\(109\) −6.87291 11.9042i −0.658305 1.14022i −0.981054 0.193734i \(-0.937940\pi\)
0.322749 0.946485i \(-0.395393\pi\)
\(110\) 3.91999 0.373757
\(111\) 0 0
\(112\) 11.3767 4.75293i 1.07500 0.449110i
\(113\) −8.04736 13.9384i −0.757032 1.31122i −0.944358 0.328920i \(-0.893315\pi\)
0.187326 0.982298i \(-0.440018\pi\)
\(114\) 0 0
\(115\) −4.28626 −0.399696
\(116\) 1.77569 + 3.07558i 0.164869 + 0.285561i
\(117\) 0 0
\(118\) −15.9293 −1.46641
\(119\) 1.90677 + 1.45394i 0.174793 + 0.133282i
\(120\) 0 0
\(121\) −6.52196 −0.592905
\(122\) −6.42743 11.1326i −0.581912 1.00790i
\(123\) 0 0
\(124\) −2.20528 −0.198040
\(125\) −10.2235 −0.914420
\(126\) 0 0
\(127\) 7.83921 13.5779i 0.695617 1.20484i −0.274355 0.961628i \(-0.588464\pi\)
0.969972 0.243216i \(-0.0782023\pi\)
\(128\) 6.76067 + 11.7098i 0.597565 + 1.03501i
\(129\) 0 0
\(130\) −5.30041 4.06387i −0.464876 0.356425i
\(131\) −4.76884 + 8.25988i −0.416656 + 0.721669i −0.995601 0.0936976i \(-0.970131\pi\)
0.578945 + 0.815367i \(0.303465\pi\)
\(132\) 0 0
\(133\) 2.25711 17.5563i 0.195716 1.52233i
\(134\) −2.91009 5.04042i −0.251393 0.435426i
\(135\) 0 0
\(136\) −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 \(0.204346\pi\)
\(138\) 0 0
\(139\) 11.3983 + 19.7425i 0.966795 + 1.67454i 0.704714 + 0.709492i \(0.251075\pi\)
0.262081 + 0.965046i \(0.415591\pi\)
\(140\) −1.21312 + 0.506812i −0.102527 + 0.0428335i
\(141\) 0 0
\(142\) 1.96684 3.40666i 0.165053 0.285881i
\(143\) −6.05497 4.64240i −0.506342 0.388217i
\(144\) 0 0
\(145\) 5.07312 + 8.78691i 0.421300 + 0.729713i
\(146\) −4.45452 + 7.71546i −0.368659 + 0.638536i
\(147\) 0 0
\(148\) 2.08175 0.171119
\(149\) 14.4116 1.18065 0.590323 0.807167i \(-0.299000\pi\)
0.590323 + 0.807167i \(0.299000\pi\)
\(150\) 0 0
\(151\) −7.62901 13.2138i −0.620840 1.07533i −0.989330 0.145695i \(-0.953458\pi\)
0.368489 0.929632i \(-0.379875\pi\)
\(152\) 16.4647 1.33546
\(153\) 0 0
\(154\) −8.03161 + 3.35542i −0.647206 + 0.270387i
\(155\) −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 \(0.682792\pi\)
\(158\) −9.44068 −0.751060
\(159\) 0 0
\(160\) −1.38402 2.39719i −0.109416 0.189514i
\(161\) 8.78205 3.66893i 0.692122 0.289152i
\(162\) 0 0
\(163\) −14.4077 −1.12850 −0.564249 0.825605i \(-0.690834\pi\)
−0.564249 + 0.825605i \(0.690834\pi\)
\(164\) 0.320371 + 0.554899i 0.0250168 + 0.0433303i
\(165\) 0 0
\(166\) 9.04118 + 15.6598i 0.701731 + 1.21543i
\(167\) 3.88595 6.73066i 0.300704 0.520834i −0.675592 0.737276i \(-0.736112\pi\)
0.976296 + 0.216442i \(0.0694452\pi\)
\(168\) 0 0
\(169\) 3.37442 + 12.5544i 0.259571 + 0.965724i
\(170\) 0.839430 1.45394i 0.0643813 0.111512i
\(171\) 0 0
\(172\) 2.26573 0.172760
\(173\) −6.09461 −0.463365 −0.231682 0.972791i \(-0.574423\pi\)
−0.231682 + 0.972791i \(0.574423\pi\)
\(174\) 0 0
\(175\) 8.74048 3.65156i 0.660718 0.276032i
\(176\) −4.93078 8.54037i −0.371672 0.643754i
\(177\) 0 0
\(178\) 13.7987 23.9001i 1.03426 1.79139i
\(179\) −18.5298 −1.38498 −0.692490 0.721428i \(-0.743486\pi\)
−0.692490 + 0.721428i \(0.743486\pi\)
\(180\) 0 0
\(181\) −5.60520 −0.416631 −0.208316 0.978062i \(-0.566798\pi\)
−0.208316 + 0.978062i \(0.566798\pi\)
\(182\) 14.3385 + 3.78938i 1.06284 + 0.280887i
\(183\) 0 0
\(184\) 4.42650 + 7.66692i 0.326326 + 0.565212i
\(185\) 5.94753 0.437271
\(186\) 0 0
\(187\) 0.958931 1.66092i 0.0701240 0.121458i
\(188\) −0.664516 1.15097i −0.0484648 0.0839435i
\(189\) 0 0
\(190\) −12.3933 −0.899102
\(191\) −0.503703 −0.0364466 −0.0182233 0.999834i \(-0.505801\pi\)
−0.0182233 + 0.999834i \(0.505801\pi\)
\(192\) 0 0
\(193\) −3.71244 −0.267227 −0.133614 0.991033i \(-0.542658\pi\)
−0.133614 + 0.991033i \(0.542658\pi\)
\(194\) 4.82290 8.35351i 0.346264 0.599747i
\(195\) 0 0
\(196\) 2.05172 2.07680i 0.146552 0.148343i
\(197\) −3.72225 + 6.44713i −0.265200 + 0.459339i −0.967616 0.252427i \(-0.918771\pi\)
0.702416 + 0.711766i \(0.252105\pi\)
\(198\) 0 0
\(199\) −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 0
\(202\) 5.61449 + 9.72458i 0.395034 + 0.684219i
\(203\) −17.9156 13.6609i −1.25743 0.958807i
\(204\) 0 0
\(205\) 0.915297 + 1.58534i 0.0639271 + 0.110725i
\(206\) −15.4325 −1.07523
\(207\) 0 0
\(208\) −2.18668 + 16.6596i −0.151619 + 1.15513i
\(209\) −14.1576 −0.979299
\(210\) 0 0
\(211\) −1.89531 + 3.28278i −0.130479 + 0.225996i −0.923861 0.382728i \(-0.874985\pi\)
0.793383 + 0.608723i \(0.208318\pi\)
\(212\) 1.17807 0.0809105
\(213\) 0 0
\(214\) 1.71020 2.96216i 0.116907 0.202489i
\(215\) 6.47316 0.441466
\(216\) 0 0
\(217\) 12.9089 5.39305i 0.876317 0.366104i
\(218\) 10.6852 18.5073i 0.723695 1.25348i
\(219\) 0 0
\(220\) 0.525777 + 0.910673i 0.0354479 + 0.0613975i
\(221\) −3.01849 + 1.25168i −0.203046 + 0.0841970i
\(222\) 0 0
\(223\) −2.43440 + 4.21650i −0.163019 + 0.282358i −0.935950 0.352133i \(-0.885457\pi\)
0.772931 + 0.634490i \(0.218790\pi\)
\(224\) 4.88762 + 3.72687i 0.326568 + 0.249012i
\(225\) 0 0
\(226\) 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 0
\(229\) 10.8561 18.8034i 0.717394 1.24256i −0.244635 0.969615i \(-0.578668\pi\)
0.962029 0.272947i \(-0.0879985\pi\)
\(230\) −3.33190 5.77101i −0.219699 0.380529i
\(231\) 0 0
\(232\) 10.4782 18.1488i 0.687928 1.19153i
\(233\) 1.89842 3.28816i 0.124370 0.215414i −0.797117 0.603825i \(-0.793642\pi\)
0.921486 + 0.388411i \(0.126976\pi\)
\(234\) 0 0
\(235\) −1.89851 3.28832i −0.123845 0.214507i
\(236\) −2.13655 3.70061i −0.139077 0.240889i
\(237\) 0 0
\(238\) −0.475362 + 3.69748i −0.0308131 + 0.239672i
\(239\) −21.9100 −1.41724 −0.708619 0.705592i \(-0.750681\pi\)
−0.708619 + 0.705592i \(0.750681\pi\)
\(240\) 0 0
\(241\) 10.3744 17.9690i 0.668273 1.15748i −0.310114 0.950699i \(-0.600367\pi\)
0.978387 0.206783i \(-0.0662994\pi\)
\(242\) −5.06980 8.78115i −0.325899 0.564474i
\(243\) 0 0
\(244\) 1.72418 2.98637i 0.110380 0.191183i
\(245\) 5.86175 5.93340i 0.374493 0.379071i
\(246\) 0 0
\(247\) 19.1431 + 14.6772i 1.21805 + 0.933887i
\(248\) 6.50661 + 11.2698i 0.413170 + 0.715632i
\(249\) 0 0
\(250\) −7.94719 13.7649i −0.502624 0.870571i
\(251\) 6.62891 + 11.4816i 0.418413 + 0.724713i 0.995780 0.0917718i \(-0.0292530\pi\)
−0.577367 + 0.816485i \(0.695920\pi\)
\(252\) 0 0
\(253\) −3.80622 6.59257i −0.239295 0.414472i
\(254\) 24.3750 1.52943
\(255\) 0 0
\(256\) −4.80213 + 8.31753i −0.300133 + 0.519845i
\(257\) −6.58555 11.4065i −0.410795 0.711518i 0.584182 0.811623i \(-0.301416\pi\)
−0.994977 + 0.100105i \(0.968082\pi\)
\(258\) 0 0
\(259\) −12.1858 + 5.09094i −0.757189 + 0.316336i
\(260\) 0.233169 1.77644i 0.0144605 0.110170i
\(261\) 0 0
\(262\) −14.8281 −0.916084
\(263\) 19.1406 1.18026 0.590129 0.807309i \(-0.299077\pi\)
0.590129 + 0.807309i \(0.299077\pi\)
\(264\) 0 0
\(265\) 3.36575 0.206756
\(266\) 25.3924 10.6083i 1.55691 0.650438i
\(267\) 0 0
\(268\) 0.780643 1.35211i 0.0476854 0.0825935i
\(269\) −14.2411 + 24.6663i −0.868296 + 1.50393i −0.00455867 + 0.999990i \(0.501451\pi\)
−0.863737 + 0.503943i \(0.831882\pi\)
\(270\) 0 0
\(271\) −8.97371 15.5429i −0.545114 0.944165i −0.998600 0.0529014i \(-0.983153\pi\)
0.453486 0.891263i \(-0.350180\pi\)
\(272\) −4.22353 −0.256089
\(273\) 0 0
\(274\) −4.29811 −0.259658
\(275\) −3.78821 6.56137i −0.228437 0.395665i
\(276\) 0 0
\(277\) −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
\(279\) 0 0
\(280\) 6.16925 + 4.70413i 0.368683 + 0.281126i
\(281\) 29.9530 1.78685 0.893424 0.449214i \(-0.148296\pi\)
0.893424 + 0.449214i \(0.148296\pi\)
\(282\) 0 0
\(283\) −9.89122 −0.587972 −0.293986 0.955810i \(-0.594982\pi\)
−0.293986 + 0.955810i \(0.594982\pi\)
\(284\) 1.05523 0.0626161
\(285\) 0 0
\(286\) 1.54373 11.7611i 0.0912824 0.695451i
\(287\) −3.23235 2.46471i −0.190800 0.145487i
\(288\) 0 0
\(289\) 8.08931 + 14.0111i 0.475842 + 0.824182i
\(290\) −7.88712 + 13.6609i −0.463148 + 0.802195i
\(291\) 0 0
\(292\) −2.38989 −0.139858
\(293\) 3.95529 + 6.85076i 0.231071 + 0.400226i 0.958123 0.286356i \(-0.0924438\pi\)
−0.727053 + 0.686581i \(0.759111\pi\)
\(294\) 0 0
\(295\) −6.10409 10.5726i −0.355394 0.615561i
\(296\) −6.14212 10.6385i −0.357003 0.618348i
\(297\) 0 0
\(298\) 11.2028 + 19.4038i 0.648959 + 1.12403i
\(299\) −1.68797 + 12.8601i −0.0976175 + 0.743716i
\(300\) 0 0
\(301\) −13.2628 + 5.54086i −0.764452 + 0.319370i
\(302\) 11.8607 20.5434i 0.682508 1.18214i
\(303\) 0 0
\(304\) 15.5889 + 27.0008i 0.894086 + 1.54860i
\(305\) 4.92598 8.53204i 0.282061 0.488543i
\(306\) 0 0
\(307\) 1.27238 0.0726187 0.0363094 0.999341i \(-0.488440\pi\)
0.0363094 + 0.999341i \(0.488440\pi\)
\(308\) −1.85677 1.41581i −0.105799 0.0806733i
\(309\) 0 0
\(310\) −4.89763 8.48295i −0.278167 0.481799i
\(311\) 12.3817 + 21.4458i 0.702103 + 1.21608i 0.967727 + 0.252002i \(0.0810888\pi\)
−0.265624 + 0.964077i \(0.585578\pi\)
\(312\) 0 0
\(313\) −1.18826 + 2.05812i −0.0671642 + 0.116332i −0.897652 0.440705i \(-0.854728\pi\)
0.830488 + 0.557037i \(0.188062\pi\)
\(314\) −8.87330 + 15.3690i −0.500749 + 0.867323i
\(315\) 0 0
\(316\) −1.26625 2.19321i −0.0712322 0.123378i
\(317\) −9.88979 + 17.1296i −0.555466 + 0.962096i 0.442401 + 0.896817i \(0.354127\pi\)
−0.997867 + 0.0652782i \(0.979207\pi\)
\(318\) 0 0
\(319\) −9.00993 + 15.6057i −0.504459 + 0.873749i
\(320\) −3.40093 + 5.89059i −0.190118 + 0.329294i
\(321\) 0 0
\(322\) 11.7665 + 8.97212i 0.655722 + 0.499997i
\(323\) −3.03171 + 5.25108i −0.168689 + 0.292178i
\(324\) 0 0
\(325\) −1.67997 + 12.7992i −0.0931882 + 0.709970i
\(326\) −11.1997 19.3985i −0.620295 1.07438i
\(327\) 0 0
\(328\) 1.89049 3.27442i 0.104385 0.180799i
\(329\) 6.70456 + 5.11231i 0.369634 + 0.281851i
\(330\) 0 0
\(331\) 3.92773 0.215888 0.107944 0.994157i \(-0.465573\pi\)
0.107944 + 0.994157i \(0.465573\pi\)
\(332\) −2.42533 + 4.20080i −0.133107 + 0.230549i
\(333\) 0 0
\(334\) 12.0829 0.661145
\(335\) 2.23029 3.86298i 0.121854 0.211057i
\(336\) 0 0
\(337\) −7.14099 −0.388995 −0.194497 0.980903i \(-0.562308\pi\)
−0.194497 + 0.980903i \(0.562308\pi\)
\(338\) −14.2802 + 14.3024i −0.776738 + 0.777948i
\(339\) 0 0
\(340\) 0.450361 0.0244243
\(341\) −5.59486 9.69059i −0.302979 0.524775i
\(342\) 0 0
\(343\) −6.93120 + 17.1744i −0.374250 + 0.927328i
\(344\) −6.68494 11.5787i −0.360428 0.624280i
\(345\) 0 0
\(346\) −4.73761 8.20578i −0.254695 0.441145i
\(347\) 5.03498 8.72085i 0.270292 0.468160i −0.698644 0.715469i \(-0.746213\pi\)
0.968937 + 0.247309i \(0.0795464\pi\)
\(348\) 0 0
\(349\) 3.14418 5.44588i 0.168304 0.291512i −0.769520 0.638623i \(-0.779504\pi\)
0.937824 + 0.347112i \(0.112838\pi\)
\(350\) 11.7108 + 8.92964i 0.625969 + 0.477310i
\(351\) 0 0
\(352\) 2.45803 4.25743i 0.131013 0.226922i
\(353\) −34.1672 −1.81854 −0.909269 0.416210i \(-0.863358\pi\)
−0.909269 + 0.416210i \(0.863358\pi\)
\(354\) 0 0
\(355\) 3.01477 0.160007
\(356\) 7.40313 0.392365
\(357\) 0 0
\(358\) −14.4040 24.9484i −0.761274 1.31857i
\(359\) 9.34327 16.1830i 0.493119 0.854107i −0.506850 0.862034i \(-0.669190\pi\)
0.999969 + 0.00792750i \(0.00252343\pi\)
\(360\) 0 0
\(361\) 25.7599 1.35578
\(362\) −4.35716 7.54683i −0.229007 0.396653i
\(363\) 0 0
\(364\) 1.04285 + 3.83930i 0.0546602 + 0.201234i
\(365\) −6.82788 −0.357388
\(366\) 0 0
\(367\) −31.0611 −1.62137 −0.810687 0.585479i \(-0.800906\pi\)
−0.810687 + 0.585479i \(0.800906\pi\)
\(368\) −8.38209 + 14.5182i −0.436946 + 0.756813i
\(369\) 0 0
\(370\) 4.62327 + 8.00775i 0.240353 + 0.416303i
\(371\) −6.89603 + 2.88100i −0.358024 + 0.149574i
\(372\) 0 0
\(373\) −2.93704 −0.152074 −0.0760371 0.997105i \(-0.524227\pi\)
−0.0760371 + 0.997105i \(0.524227\pi\)
\(374\) 2.98168 0.154179
\(375\) 0 0
\(376\) −3.92126 + 6.79182i −0.202223 + 0.350261i
\(377\) 28.3612 11.7605i 1.46068 0.605698i
\(378\) 0 0
\(379\) −5.04254 + 8.73394i −0.259018 + 0.448632i −0.965979 0.258620i \(-0.916732\pi\)
0.706961 + 0.707252i \(0.250066\pi\)
\(380\) −1.66227 2.87914i −0.0852727 0.147697i
\(381\) 0 0
\(382\) −0.391550 0.678184i −0.0200334 0.0346989i
\(383\) −3.68931 −0.188515 −0.0942576 0.995548i \(-0.530048\pi\)
−0.0942576 + 0.995548i \(0.530048\pi\)
\(384\) 0 0
\(385\) −5.30477 4.04496i −0.270356 0.206150i
\(386\) −2.88584 4.99842i −0.146885 0.254413i
\(387\) 0 0
\(388\) 2.58753 0.131362
\(389\) 11.3333 + 19.6299i 0.574623 + 0.995277i 0.996082 + 0.0884295i \(0.0281848\pi\)
−0.421459 + 0.906847i \(0.638482\pi\)
\(390\) 0 0
\(391\) −3.26027 −0.164879
\(392\) −16.6667 4.35750i −0.841796 0.220087i
\(393\) 0 0
\(394\) −11.5739 −0.583084
\(395\) −3.61767 6.26598i −0.182025 0.315276i
\(396\) 0 0
\(397\) −29.1360 −1.46229 −0.731146 0.682221i \(-0.761014\pi\)
−0.731146 + 0.682221i \(0.761014\pi\)
\(398\) −11.6688 −0.584904
\(399\) 0 0
\(400\) −8.34241 + 14.4495i −0.417120 + 0.722474i
\(401\) 4.06026 + 7.03258i 0.202760 + 0.351190i 0.949417 0.314019i \(-0.101676\pi\)
−0.746657 + 0.665209i \(0.768342\pi\)
\(402\) 0 0
\(403\) −2.48118 + 18.9033i −0.123596 + 0.941641i
\(404\) −1.50611 + 2.60866i −0.0749318 + 0.129786i
\(405\) 0 0
\(406\) 4.46641 34.7408i 0.221664 1.72416i
\(407\) 5.28144 + 9.14773i 0.261791 + 0.453436i
\(408\) 0 0
\(409\) 4.16131 7.20759i 0.205763 0.356393i −0.744612 0.667497i \(-0.767366\pi\)
0.950376 + 0.311105i \(0.100699\pi\)
\(410\) −1.42300 + 2.46471i −0.0702769 + 0.121723i
\(411\) 0 0
\(412\) −2.06992 3.58520i −0.101978 0.176630i
\(413\) 21.5565 + 16.4371i 1.06072 + 0.808816i
\(414\) 0 0
\(415\) −6.92915 + 12.0016i −0.340139 + 0.589138i
\(416\) −7.73731 + 3.20843i −0.379353 + 0.157306i
\(417\) 0 0
\(418\) −11.0053 19.0617i −0.538286 0.932339i
\(419\) −6.50832 + 11.2727i −0.317952 + 0.550710i −0.980061 0.198699i \(-0.936329\pi\)
0.662108 + 0.749408i \(0.269662\pi\)
\(420\) 0 0
\(421\) −8.89681 −0.433604 −0.216802 0.976216i \(-0.569563\pi\)
−0.216802 + 0.976216i \(0.569563\pi\)
\(422\) −5.89323 −0.286878
\(423\) 0 0
\(424\) −3.47587 6.02038i −0.168803 0.292376i
\(425\) −3.24484 −0.157398
\(426\) 0 0
\(427\) −2.78954 + 21.6977i −0.134995 + 1.05002i
\(428\) 0.917539 0.0443509
\(429\) 0 0
\(430\) 5.03187 + 8.71545i 0.242658 + 0.420296i
\(431\) 8.95743 0.431464 0.215732 0.976453i \(-0.430786\pi\)
0.215732 + 0.976453i \(0.430786\pi\)
\(432\) 0 0
\(433\) 0.0864547 + 0.149744i 0.00415475 + 0.00719624i 0.868095 0.496398i \(-0.165344\pi\)
−0.863941 + 0.503594i \(0.832011\pi\)
\(434\) 17.2959 + 13.1883i 0.830229 + 0.633060i
\(435\) 0 0
\(436\) 5.73271 0.274547
\(437\) 12.0336 + 20.8428i 0.575644 + 0.997045i
\(438\) 0 0
\(439\) −4.77080 8.26327i −0.227698 0.394384i 0.729428 0.684058i \(-0.239787\pi\)
−0.957125 + 0.289674i \(0.906453\pi\)
\(440\) 3.10257 5.37382i 0.147909 0.256187i
\(441\) 0 0
\(442\) −4.03166 3.09111i −0.191767 0.147029i
\(443\) −6.93676 + 12.0148i −0.329576 + 0.570842i −0.982428 0.186644i \(-0.940239\pi\)
0.652852 + 0.757485i \(0.273572\pi\)
\(444\) 0 0
\(445\) 21.1507 1.00264
\(446\) −7.56945 −0.358424
\(447\) 0 0
\(448\) 1.92592 14.9803i 0.0909912 0.707751i
\(449\) −10.6456 18.4388i −0.502398 0.870180i −0.999996 0.00277167i \(-0.999118\pi\)
0.497598 0.867408i \(-0.334216\pi\)
\(450\) 0 0
\(451\) −1.62558 + 2.81558i −0.0765455 + 0.132581i
\(452\) 6.71232 0.315721
\(453\) 0 0
\(454\) 37.5872 1.76406
\(455\) 2.97941 + 10.9689i 0.139677 + 0.514228i
\(456\) 0 0
\(457\) −4.84282 8.38801i −0.226538 0.392375i 0.730242 0.683189i \(-0.239407\pi\)
−0.956780 + 0.290814i \(0.906074\pi\)
\(458\) 33.7558 1.57730
\(459\) 0 0
\(460\) 0.893795 1.54810i 0.0416734 0.0721804i
\(461\) −0.687178 1.19023i −0.0320051 0.0554344i 0.849579 0.527461i \(-0.176856\pi\)
−0.881584 + 0.472027i \(0.843523\pi\)
\(462\) 0 0
\(463\) 31.7710 1.47653 0.738263 0.674513i \(-0.235646\pi\)
0.738263 + 0.674513i \(0.235646\pi\)
\(464\) 39.6834 1.84226
\(465\) 0 0
\(466\) 5.90290 0.273446
\(467\) −14.5605 + 25.2195i −0.673778 + 1.16702i 0.303046 + 0.952976i \(0.401996\pi\)
−0.976824 + 0.214042i \(0.931337\pi\)
\(468\) 0 0
\(469\) −1.26299 + 9.82387i −0.0583197 + 0.453624i
\(470\) 2.95160 5.11231i 0.136147 0.235813i
\(471\) 0 0
\(472\) −12.6076 + 21.8370i −0.580312 + 1.00513i
\(473\) 5.74820 + 9.95618i 0.264303 + 0.457786i
\(474\) 0 0
\(475\) 11.9766 + 20.7441i 0.549525 + 0.951804i
\(476\) −0.922738 + 0.385498i −0.0422936 + 0.0176693i
\(477\) 0 0
\(478\) −17.0316 29.4995i −0.779005 1.34928i
\(479\) −9.72184 −0.444202 −0.222101 0.975024i \(-0.571292\pi\)
−0.222101 + 0.975024i \(0.571292\pi\)
\(480\) 0 0
\(481\) 2.34219 17.8444i 0.106795 0.813633i
\(482\) 32.2578 1.46930
\(483\) 0 0
\(484\) 1.36000 2.35558i 0.0618180 0.107072i
\(485\) 7.39254 0.335678
\(486\) 0 0
\(487\) 8.55666 14.8206i 0.387739 0.671584i −0.604406 0.796676i \(-0.706589\pi\)
0.992145 + 0.125093i \(0.0399228\pi\)
\(488\) −20.3486 −0.921137
\(489\) 0 0
\(490\) 12.5453 + 3.27996i 0.566739 + 0.148174i
\(491\) −12.8607 + 22.2753i −0.580394 + 1.00527i 0.415038 + 0.909804i \(0.363768\pi\)
−0.995432 + 0.0954681i \(0.969565\pi\)
\(492\) 0 0
\(493\) 3.85879 + 6.68361i 0.173791 + 0.301015i
\(494\) −4.88057 + 37.1835i −0.219587 + 1.67296i
\(495\) 0 0
\(496\) −12.3210 + 21.3407i −0.553231 + 0.958224i
\(497\) −6.17691 + 2.58057i −0.277072 + 0.115754i
\(498\) 0 0
\(499\) −2.70198 + 4.67996i −0.120957 + 0.209504i −0.920145 0.391577i \(-0.871930\pi\)
0.799188 + 0.601081i \(0.205263\pi\)
\(500\) 2.13187 3.69250i 0.0953400 0.165134i
\(501\) 0 0
\(502\) −10.3059 + 17.8503i −0.459974 + 0.796699i
\(503\) −6.30847 10.9266i −0.281281 0.487193i 0.690420 0.723409i \(-0.257426\pi\)
−0.971700 + 0.236216i \(0.924093\pi\)
\(504\) 0 0
\(505\) −4.30294 + 7.45292i −0.191478 + 0.331650i
\(506\) 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 0
\(511\) 13.9895 5.84450i 0.618861 0.258546i
\(512\) 12.1111 0.535240
\(513\) 0 0
\(514\) 10.2385 17.7335i 0.451599 0.782193i
\(515\) −5.91374 10.2429i −0.260590 0.451356i
\(516\) 0 0
\(517\) 3.37178 5.84010i 0.148291 0.256847i
\(518\) −16.3270 12.4495i −0.717367 0.547001i
\(519\) 0 0
\(520\) −9.76618 + 4.04974i −0.428276 + 0.177593i
\(521\) −19.5477 33.8576i −0.856401 1.48333i −0.875339 0.483509i \(-0.839362\pi\)
0.0189387 0.999821i \(-0.493971\pi\)
\(522\) 0 0
\(523\) 4.35634 + 7.54540i 0.190489 + 0.329937i 0.945413 0.325876i \(-0.105659\pi\)
−0.754923 + 0.655813i \(0.772326\pi\)
\(524\) −1.98885 3.44479i −0.0868834 0.150486i
\(525\) 0 0
\(526\) 14.8788 + 25.7708i 0.648746 + 1.12366i
\(527\) −4.79235 −0.208758
\(528\) 0 0
\(529\) 5.02961 8.71154i 0.218679 0.378763i
\(530\) 2.61634 + 4.53164i 0.113647 + 0.196842i
\(531\) 0 0
\(532\) 5.87028 + 4.47616i 0.254509 + 0.194066i
\(533\) 5.11694 2.12184i 0.221639 0.0919072i
\(534\) 0 0
\(535\) 2.62140 0.113333
\(536\) −9.21304 −0.397943
\(537\) 0 0
\(538\) −44.2809 −1.90909
\(539\) 14.3313 + 3.74690i 0.617291 + 0.161390i
\(540\) 0 0
\(541\) 10.7497 18.6190i 0.462165 0.800493i −0.536904 0.843644i \(-0.680406\pi\)
0.999069 + 0.0431505i \(0.0137395\pi\)
\(542\) 13.9513 24.1644i 0.599260 1.03795i
\(543\) 0 0
\(544\) −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
\(549\) 0 0
\(550\) 5.88947 10.2009i 0.251128 0.434967i
\(551\) 28.4854 49.3381i 1.21352 2.10187i
\(552\) 0 0
\(553\) 12.7757 + 9.74164i 0.543278 + 0.414257i
\(554\) −20.8932 −0.887668
\(555\) 0 0
\(556\) −9.50738 −0.403203
\(557\) 17.6840 0.749296 0.374648 0.927167i \(-0.377764\pi\)
0.374648 + 0.927167i \(0.377764\pi\)
\(558\) 0 0
\(559\) 2.54918 19.4214i 0.107819 0.821437i
\(560\) −1.87330 + 14.5710i −0.0791616 + 0.615737i
\(561\) 0 0
\(562\) 23.2838 + 40.3287i 0.982167 + 1.70116i
\(563\) −20.8695 + 36.1471i −0.879545 + 1.52342i −0.0277042 + 0.999616i \(0.508820\pi\)
−0.851841 + 0.523801i \(0.824514\pi\)
\(564\) 0 0
\(565\) 19.1770 0.806784
\(566\) −7.68887 13.3175i −0.323187 0.559777i
\(567\) 0 0
\(568\) −3.11340 5.39257i −0.130636 0.226267i
\(569\) 2.73388 + 4.73521i 0.114610 + 0.198510i 0.917624 0.397450i \(-0.130105\pi\)
−0.803014 + 0.595960i \(0.796771\pi\)
\(570\) 0 0
\(571\) −4.67621 8.09944i −0.195693 0.338951i 0.751434 0.659808i \(-0.229362\pi\)
−0.947128 + 0.320857i \(0.896029\pi\)
\(572\) 2.93934 1.21886i 0.122900 0.0509630i
\(573\) 0 0
\(574\) 0.805833 6.26795i 0.0336348 0.261619i
\(575\) −6.43976 + 11.1540i −0.268557 + 0.465154i
\(576\) 0 0
\(577\) 1.68462 + 2.91786i 0.0701318 + 0.121472i 0.898959 0.438033i \(-0.144325\pi\)
−0.828827 + 0.559505i \(0.810991\pi\)
\(578\) −12.5763 + 21.7829i −0.523107 + 0.906048i
\(579\) 0 0
\(580\) −4.23151 −0.175704
\(581\) 3.92392 30.5212i 0.162792 1.26623i
\(582\) 0 0
\(583\) 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
\(587\) −6.57639 + 11.3906i −0.271437 + 0.470142i −0.969230 0.246157i \(-0.920832\pi\)
0.697793 + 0.716299i \(0.254165\pi\)
\(588\) 0 0
\(589\) 17.6884 + 30.6373i 0.728840 + 1.26239i
\(590\) 9.48995 16.4371i 0.390695 0.676704i
\(591\) 0 0
\(592\) 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 \(-0.124494\pi\)
\(594\) 0 0
\(595\) −2.63625 + 1.10136i −0.108076 + 0.0451515i
\(596\) −3.00519 + 5.20515i −0.123097 + 0.213211i
\(597\) 0 0
\(598\) −18.6269 + 7.72400i −0.761710 + 0.315858i
\(599\) 9.20762 + 15.9481i 0.376213 + 0.651620i 0.990508 0.137457i \(-0.0438927\pi\)
−0.614295 + 0.789077i \(0.710559\pi\)
\(600\) 0 0
\(601\) 20.7018 35.8566i 0.844445 1.46262i −0.0416571 0.999132i \(-0.513264\pi\)
0.886102 0.463490i \(-0.153403\pi\)
\(602\) −17.7699 13.5498i −0.724248 0.552248i
\(603\) 0 0
\(604\) 6.36338 0.258922
\(605\) 3.88549 6.72987i 0.157968 0.273608i
\(606\) 0 0
\(607\) 12.3051 0.499449 0.249724 0.968317i \(-0.419660\pi\)
0.249724 + 0.968317i \(0.419660\pi\)
\(608\) −7.77119 + 13.4601i −0.315163 + 0.545879i
\(609\) 0 0
\(610\) 15.3167 0.620155
\(611\) −10.6136 + 4.40114i −0.429380 + 0.178051i
\(612\) 0 0
\(613\) 26.2224 1.05911 0.529556 0.848275i \(-0.322358\pi\)
0.529556 + 0.848275i \(0.322358\pi\)
\(614\) 0.989078 + 1.71313i 0.0399160 + 0.0691365i
\(615\) 0 0
\(616\) −1.75696 + 13.6661i −0.0707900 + 0.550621i
\(617\) −9.41259 16.3031i −0.378936 0.656337i 0.611971 0.790880i \(-0.290377\pi\)
−0.990908 + 0.134543i \(0.957043\pi\)
\(618\) 0 0
\(619\) 7.90415 + 13.6904i 0.317695 + 0.550263i 0.980007 0.198965i \(-0.0637580\pi\)
−0.662312 + 0.749228i \(0.730425\pi\)
\(620\) 1.31381 2.27559i 0.0527639 0.0913898i
\(621\) 0 0
\(622\) −19.2497 + 33.3415i −0.771843 + 1.33687i
\(623\) −43.3353 + 18.1045i −1.73619 + 0.725340i
\(624\) 0 0
\(625\) −2.86003 + 4.95371i −0.114401 + 0.198149i
\(626\) −3.69473 −0.147671
\(627\) 0 0
\(628\) −4.76060 −0.189969
\(629\) 4.52389 0.180379
\(630\) 0 0
\(631\) 8.33817 + 14.4421i 0.331937 + 0.574933i 0.982892 0.184184i \(-0.0589644\pi\)
−0.650954 + 0.759117i \(0.725631\pi\)
\(632\) −7.47206 + 12.9420i −0.297222 + 0.514804i
\(633\) 0 0
\(634\) −30.7511 −1.22128
\(635\) 9.34050 + 16.1782i 0.370667 + 0.642013i
\(636\) 0 0
\(637\) −15.4935 19.9236i −0.613877 0.789402i
\(638\) −28.0152 −1.10913
\(639\) 0 0
\(640\) −16.1108 −0.636837
\(641\) 24.6232 42.6487i 0.972559 1.68452i 0.284792 0.958589i \(-0.408075\pi\)
0.687767 0.725932i \(-0.258591\pi\)
\(642\) 0 0
\(643\) −21.4355 37.1275i −0.845335 1.46416i −0.885330 0.464964i \(-0.846067\pi\)
0.0399940 0.999200i \(-0.487266\pi\)
\(644\) −0.506149 + 3.93694i −0.0199450 + 0.155137i
\(645\) 0 0
\(646\) −9.42672 −0.370889
\(647\) −4.25859 −0.167422 −0.0837112 0.996490i \(-0.526677\pi\)
−0.0837112 + 0.996490i \(0.526677\pi\)
\(648\) 0 0
\(649\) 10.8409 18.7771i 0.425544 0.737064i
\(650\) −18.5387 + 7.68744i −0.727148 + 0.301526i
\(651\) 0 0
\(652\) 3.00437 5.20373i 0.117660 0.203794i
\(653\) −1.04776 1.81477i −0.0410020 0.0710176i 0.844796 0.535088i \(-0.179722\pi\)
−0.885798 + 0.464071i \(0.846388\pi\)
\(654\) 0 0
\(655\) −5.68213 9.84174i −0.222019 0.384549i
\(656\) 7.15971 0.279540
\(657\) 0 0
\(658\) −1.67146 + 13.0010i −0.0651604 + 0.506833i
\(659\) 12.7259 + 22.0419i 0.495732 + 0.858632i 0.999988 0.00492170i \(-0.00156663\pi\)
−0.504256 + 0.863554i \(0.668233\pi\)
\(660\) 0 0
\(661\) 27.8108 1.08171 0.540857 0.841115i \(-0.318100\pi\)
0.540857 + 0.841115i \(0.318100\pi\)
\(662\) 3.05319 + 5.28829i 0.118666 + 0.205535i
\(663\) 0 0
\(664\) 28.6234 1.11080
\(665\) 16.7713 + 12.7883i 0.650364 + 0.495911i
\(666\) 0 0
\(667\) 30.6329 1.18611
\(668\) 1.62064 + 2.80703i 0.0627044 + 0.108607i
\(669\) 0 0
\(670\) 6.93481 0.267915
\(671\) 17.4972 0.675472
\(672\) 0 0
\(673\) −7.76033 + 13.4413i −0.299139 + 0.518124i −0.975939 0.218043i \(-0.930033\pi\)
0.676800 + 0.736167i \(0.263366\pi\)
\(674\) −5.55100 9.61462i −0.213817 0.370341i
\(675\) 0 0
\(676\) −5.23802 1.39915i −0.201462 0.0538136i
\(677\) 17.2813 29.9321i 0.664175 1.15038i −0.315334 0.948981i \(-0.602116\pi\)
0.979508 0.201403i \(-0.0645502\pi\)
\(678\) 0 0
\(679\) −15.1465 + 6.32783i −0.581268 + 0.242840i
\(680\) −1.32877 2.30150i −0.0509562 0.0882587i
\(681\) 0 0
\(682\) 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 \(-0.189275\pi\)
\(684\) 0 0
\(685\) −1.64703 2.85275i −0.0629299 0.108998i
\(686\) −28.5114 + 4.01821i −1.08857 + 0.153416i
\(687\) 0 0
\(688\) 12.6587 21.9255i 0.482609 0.835904i
\(689\) 1.32546 10.0982i 0.0504960 0.384713i
\(690\) 0 0
\(691\) −9.50301 16.4597i −0.361512 0.626156i 0.626698 0.779262i \(-0.284406\pi\)
−0.988210 + 0.153106i \(0.951073\pi\)
\(692\) 1.27088 2.20123i 0.0483117 0.0836784i
\(693\) 0 0
\(694\) 15.6556 0.594280
\(695\) −27.1625 −1.03033
\(696\) 0 0
\(697\) 0.696205 + 1.20586i 0.0263706 + 0.0456753i
\(698\) 9.77644 0.370044
\(699\) 0 0
\(700\) −0.503753 + 3.91830i −0.0190401 + 0.148098i
\(701\) 45.4648 1.71718 0.858591 0.512662i \(-0.171341\pi\)
0.858591 + 0.512662i \(0.171341\pi\)
\(702\) 0 0
\(703\) −16.6976 28.9210i −0.629760 1.09078i
\(704\) −12.0802 −0.455290
\(705\) 0 0
\(706\) −26.5597 46.0027i −0.999586 1.73133i
\(707\) 2.43672 18.9534i 0.0916423 0.712815i
\(708\) 0 0
\(709\) −9.78779 −0.367588 −0.183794 0.982965i \(-0.558838\pi\)
−0.183794 + 0.982965i \(0.558838\pi\)
\(710\) 2.34351 + 4.05908i 0.0879504 + 0.152334i
\(711\) 0 0
\(712\) −21.8427 37.8326i −0.818589 1.41784i
\(713\) −9.51099 + 16.4735i −0.356189 + 0.616938i
\(714\) 0 0
\(715\) 8.39768 3.48226i 0.314055 0.130229i
\(716\) 3.86393 6.69252i 0.144402 0.250111i
\(717\) 0 0
\(718\) 29.0517 1.08420
\(719\) 27.8403 1.03827 0.519133 0.854693i \(-0.326255\pi\)
0.519133 + 0.854693i \(0.326255\pi\)
\(720\) 0 0
\(721\) 20.8842 + 15.9245i 0.777770 + 0.593059i
\(722\) 20.0243 + 34.6830i 0.745226 + 1.29077i
\(723\) 0 0
\(724\) 1.16883 2.02447i 0.0434391 0.0752388i
\(725\) 30.4879 1.13229
\(726\) 0 0
\(727\) −14.5650 −0.540186 −0.270093 0.962834i \(-0.587055\pi\)
−0.270093 + 0.962834i \(0.587055\pi\)
\(728\) 16.5433 16.6571i 0.613136 0.617352i
\(729\) 0 0
\(730\) −5.30761 9.19305i −0.196444 0.340250i
\(731\) 4.92370 0.182109
\(732\) 0 0
\(733\) −8.83030 + 15.2945i −0.326155 + 0.564916i −0.981745 0.190200i \(-0.939086\pi\)
0.655591 + 0.755116i \(0.272420\pi\)
\(734\) −24.1451 41.8206i −0.891213 1.54363i
\(735\) 0 0
\(736\) −8.35705 −0.308045
\(737\) 7.92205 0.291812
\(738\) 0 0
\(739\) 8.96559 0.329804 0.164902 0.986310i \(-0.447269\pi\)
0.164902 + 0.986310i \(0.447269\pi\)
\(740\) −1.24021 + 2.14811i −0.0455911 + 0.0789661i
\(741\) 0 0
\(742\) −9.23955 7.04528i −0.339195 0.258640i
\(743\) −13.1839 + 22.8352i −0.483671 + 0.837743i −0.999824 0.0187532i \(-0.994030\pi\)
0.516153 + 0.856497i \(0.327364\pi\)
\(744\) 0 0
\(745\) −8.58580 + 14.8710i −0.314560 + 0.544833i
\(746\) −2.28309 3.95442i −0.0835898 0.144782i
\(747\) 0 0
\(748\) 0.399923 + 0.692688i 0.0146226 + 0.0253272i
\(749\) −5.37095 + 2.24385i −0.196250 + 0.0819887i
\(750\) 0 0
\(751\) 10.1438 + 17.5696i 0.370152 + 0.641123i 0.989589 0.143924i \(-0.0459721\pi\)
−0.619436 + 0.785047i \(0.712639\pi\)
\(752\) −14.8507 −0.541550
\(753\) 0 0
\(754\) 37.8807 + 29.0435i 1.37953 + 1.05770i
\(755\) 18.1801 0.661642
\(756\) 0 0
\(757\) −12.4992 + 21.6493i −0.454292 + 0.786857i −0.998647 0.0519981i \(-0.983441\pi\)
0.544355 + 0.838855i \(0.316774\pi\)
\(758\) −15.6791 −0.569492
\(759\) 0 0
\(760\) −9.80895 + 16.9896i −0.355808 + 0.616277i
\(761\) −20.1422 −0.730154 −0.365077 0.930977i \(-0.618957\pi\)
−0.365077 + 0.930977i \(0.618957\pi\)
\(762\) 0 0
\(763\) −33.5572 + 14.0194i −1.21485 + 0.507537i
\(764\) 0.105035 0.181926i 0.00380003 0.00658184i
\(765\) 0 0
\(766\) −2.86786 4.96729i −0.103620 0.179475i
\(767\) −34.1248 + 14.1505i −1.23217 + 0.510945i
\(768\) 0 0
\(769\) −4.33610 + 7.51034i −0.156364 + 0.270830i −0.933555 0.358435i \(-0.883311\pi\)
0.777191 + 0.629265i \(0.216644\pi\)
\(770\) 1.32249 10.2867i 0.0476594 0.370706i
\(771\) 0 0
\(772\) 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 \(0.153235\pi\)
\(774\) 0 0
\(775\) −9.46596 + 16.3955i −0.340027 + 0.588945i
\(776\) −7.63441 13.2232i −0.274059 0.474685i
\(777\) 0 0
\(778\) −17.6198 + 30.5184i −0.631701 + 1.09414i
\(779\) 5.13935 8.90161i 0.184136 0.318933i
\(780\) 0 0
\(781\) 2.67713 + 4.63693i 0.0957953 + 0.165922i
\(782\) −2.53435 4.38962i −0.0906281 0.156973i
\(783\) 0 0
\(784\) −8.63423 31.4578i −0.308365 1.12349i
\(785\) −13.6010 −0.485440
\(786\) 0 0
\(787\) 17.0583 29.5459i 0.608063 1.05320i −0.383496 0.923543i \(-0.625280\pi\)
0.991559 0.129654i \(-0.0413866\pi\)
\(788\) −1.55237 2.68878i −0.0553009 0.0957840i
\(789\) 0 0
\(790\)