Properties

Label 105.3.h.a.76.9
Level 105
Weight 3
Character 105.76
Analytic conductor 2.861
Analytic rank 0
Dimension 12
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) \(=\) \( 105 = 3 \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 105.h (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.86104277578\)
Analytic rank: \(0\)
Dimension: \(12\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{10} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 76.9
Root \(0.378061 - 0.654821i\) of \(x^{12} - 2 x^{11} + 21 x^{10} - 26 x^{9} + 295 x^{8} - 372 x^{7} + 1704 x^{6} - 1074 x^{5} + 5613 x^{4} - 5472 x^{3} + 4950 x^{2} - 1638 x + 441\)
Character \(\chi\) \(=\) 105.76
Dual form 105.3.h.a.76.10

$q$-expansion

\(f(q)\) \(=\) \(q+2.91758 q^{2} -1.73205i q^{3} +4.51225 q^{4} -2.23607i q^{5} -5.05339i q^{6} +(6.13981 + 3.36195i) q^{7} +1.49451 q^{8} -3.00000 q^{9} +O(q^{10})\) \(q+2.91758 q^{2} -1.73205i q^{3} +4.51225 q^{4} -2.23607i q^{5} -5.05339i q^{6} +(6.13981 + 3.36195i) q^{7} +1.49451 q^{8} -3.00000 q^{9} -6.52390i q^{10} -2.58757 q^{11} -7.81544i q^{12} -0.0498225i q^{13} +(17.9134 + 9.80876i) q^{14} -3.87298 q^{15} -13.6886 q^{16} +14.2114i q^{17} -8.75273 q^{18} +14.9314i q^{19} -10.0897i q^{20} +(5.82308 - 10.6345i) q^{21} -7.54942 q^{22} -22.2765 q^{23} -2.58857i q^{24} -5.00000 q^{25} -0.145361i q^{26} +5.19615i q^{27} +(27.7043 + 15.1700i) q^{28} +17.4169 q^{29} -11.2997 q^{30} -6.36515i q^{31} -45.9156 q^{32} +4.48180i q^{33} +41.4628i q^{34} +(7.51756 - 13.7290i) q^{35} -13.5367 q^{36} -7.14160 q^{37} +43.5635i q^{38} -0.0862951 q^{39} -3.34183i q^{40} -74.5035i q^{41} +(16.9893 - 31.0268i) q^{42} +79.2782 q^{43} -11.6757 q^{44} +6.70820i q^{45} -64.9935 q^{46} -81.3603i q^{47} +23.7094i q^{48} +(26.3945 + 41.2835i) q^{49} -14.5879 q^{50} +24.6149 q^{51} -0.224811i q^{52} -67.1978 q^{53} +15.1602i q^{54} +5.78598i q^{55} +(9.17603 + 5.02449i) q^{56} +25.8620 q^{57} +50.8151 q^{58} -4.33175i q^{59} -17.4759 q^{60} +109.670i q^{61} -18.5708i q^{62} +(-18.4194 - 10.0859i) q^{63} -79.2079 q^{64} -0.111407 q^{65} +13.0760i q^{66} -49.1800 q^{67} +64.1253i q^{68} +38.5841i q^{69} +(21.9330 - 40.0555i) q^{70} +97.3864 q^{71} -4.48354 q^{72} -116.398i q^{73} -20.8362 q^{74} +8.66025i q^{75} +67.3742i q^{76} +(-15.8872 - 8.69929i) q^{77} -0.251773 q^{78} +98.8343 q^{79} +30.6087i q^{80} +9.00000 q^{81} -217.370i q^{82} -112.111i q^{83} +(26.2752 - 47.9853i) q^{84} +31.7777 q^{85} +231.300 q^{86} -30.1669i q^{87} -3.86716 q^{88} +77.7603i q^{89} +19.5717i q^{90} +(0.167501 - 0.305901i) q^{91} -100.517 q^{92} -11.0248 q^{93} -237.375i q^{94} +33.3877 q^{95} +79.5282i q^{96} +109.997i q^{97} +(77.0080 + 120.448i) q^{98} +7.76270 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12q - 4q^{2} + 44q^{4} - 8q^{7} + 4q^{8} - 36q^{9} + O(q^{10}) \) \( 12q - 4q^{2} + 44q^{4} - 8q^{7} + 4q^{8} - 36q^{9} - 16q^{11} - 40q^{14} + 92q^{16} + 12q^{18} + 36q^{21} - 88q^{22} - 64q^{23} - 60q^{25} + 88q^{28} + 104q^{29} - 228q^{32} + 60q^{35} - 132q^{36} + 32q^{37} - 24q^{39} - 60q^{42} + 152q^{43} + 192q^{44} + 200q^{46} + 60q^{49} + 20q^{50} + 24q^{51} + 176q^{53} - 368q^{56} - 240q^{57} - 400q^{58} + 24q^{63} - 20q^{64} - 240q^{65} + 168q^{67} - 60q^{70} + 32q^{71} - 12q^{72} + 184q^{74} + 8q^{77} + 456q^{78} + 120q^{79} + 108q^{81} + 108q^{84} + 120q^{85} + 400q^{86} - 536q^{88} + 24q^{91} + 192q^{92} + 48q^{93} + 884q^{98} + 48q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/105\mathbb{Z}\right)^\times\).

\(n\) \(22\) \(31\) \(71\)
\(\chi(n)\) \(1\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.91758 1.45879 0.729394 0.684094i \(-0.239802\pi\)
0.729394 + 0.684094i \(0.239802\pi\)
\(3\) 1.73205i 0.577350i
\(4\) 4.51225 1.12806
\(5\) 2.23607i 0.447214i
\(6\) 5.05339i 0.842231i
\(7\) 6.13981 + 3.36195i 0.877116 + 0.480279i
\(8\) 1.49451 0.186814
\(9\) −3.00000 −0.333333
\(10\) 6.52390i 0.652390i
\(11\) −2.58757 −0.235233 −0.117617 0.993059i \(-0.537525\pi\)
−0.117617 + 0.993059i \(0.537525\pi\)
\(12\) 7.81544i 0.651286i
\(13\) 0.0498225i 0.00383250i −0.999998 0.00191625i \(-0.999390\pi\)
0.999998 0.00191625i \(-0.000609962\pi\)
\(14\) 17.9134 + 9.80876i 1.27953 + 0.700625i
\(15\) −3.87298 −0.258199
\(16\) −13.6886 −0.855539
\(17\) 14.2114i 0.835965i 0.908455 + 0.417982i \(0.137263\pi\)
−0.908455 + 0.417982i \(0.862737\pi\)
\(18\) −8.75273 −0.486263
\(19\) 14.9314i 0.785864i 0.919567 + 0.392932i \(0.128539\pi\)
−0.919567 + 0.392932i \(0.871461\pi\)
\(20\) 10.0897i 0.504484i
\(21\) 5.82308 10.6345i 0.277289 0.506403i
\(22\) −7.54942 −0.343156
\(23\) −22.2765 −0.968545 −0.484273 0.874917i \(-0.660916\pi\)
−0.484273 + 0.874917i \(0.660916\pi\)
\(24\) 2.58857i 0.107857i
\(25\) −5.00000 −0.200000
\(26\) 0.145361i 0.00559081i
\(27\) 5.19615i 0.192450i
\(28\) 27.7043 + 15.1700i 0.989440 + 0.541784i
\(29\) 17.4169 0.600583 0.300291 0.953848i \(-0.402916\pi\)
0.300291 + 0.953848i \(0.402916\pi\)
\(30\) −11.2997 −0.376657
\(31\) 6.36515i 0.205327i −0.994716 0.102664i \(-0.967263\pi\)
0.994716 0.102664i \(-0.0327365\pi\)
\(32\) −45.9156 −1.43486
\(33\) 4.48180i 0.135812i
\(34\) 41.4628i 1.21950i
\(35\) 7.51756 13.7290i 0.214787 0.392258i
\(36\) −13.5367 −0.376020
\(37\) −7.14160 −0.193016 −0.0965081 0.995332i \(-0.530767\pi\)
−0.0965081 + 0.995332i \(0.530767\pi\)
\(38\) 43.5635i 1.14641i
\(39\) −0.0862951 −0.00221270
\(40\) 3.34183i 0.0835459i
\(41\) 74.5035i 1.81716i −0.417713 0.908579i \(-0.637168\pi\)
0.417713 0.908579i \(-0.362832\pi\)
\(42\) 16.9893 31.0268i 0.404506 0.738734i
\(43\) 79.2782 1.84368 0.921840 0.387570i \(-0.126686\pi\)
0.921840 + 0.387570i \(0.126686\pi\)
\(44\) −11.6757 −0.265358
\(45\) 6.70820i 0.149071i
\(46\) −64.9935 −1.41290
\(47\) 81.3603i 1.73107i −0.500848 0.865535i \(-0.666978\pi\)
0.500848 0.865535i \(-0.333022\pi\)
\(48\) 23.7094i 0.493946i
\(49\) 26.3945 + 41.2835i 0.538664 + 0.842521i
\(50\) −14.5879 −0.291758
\(51\) 24.6149 0.482644
\(52\) 0.224811i 0.00432330i
\(53\) −67.1978 −1.26788 −0.633942 0.773381i \(-0.718564\pi\)
−0.633942 + 0.773381i \(0.718564\pi\)
\(54\) 15.1602i 0.280744i
\(55\) 5.78598i 0.105200i
\(56\) 9.17603 + 5.02449i 0.163858 + 0.0897230i
\(57\) 25.8620 0.453719
\(58\) 50.8151 0.876122
\(59\) 4.33175i 0.0734195i −0.999326 0.0367097i \(-0.988312\pi\)
0.999326 0.0367097i \(-0.0116877\pi\)
\(60\) −17.4759 −0.291264
\(61\) 109.670i 1.79787i 0.438082 + 0.898935i \(0.355658\pi\)
−0.438082 + 0.898935i \(0.644342\pi\)
\(62\) 18.5708i 0.299529i
\(63\) −18.4194 10.0859i −0.292372 0.160093i
\(64\) −79.2079 −1.23762
\(65\) −0.111407 −0.00171395
\(66\) 13.0760i 0.198121i
\(67\) −49.1800 −0.734030 −0.367015 0.930215i \(-0.619620\pi\)
−0.367015 + 0.930215i \(0.619620\pi\)
\(68\) 64.1253i 0.943020i
\(69\) 38.5841i 0.559190i
\(70\) 21.9330 40.0555i 0.313329 0.572221i
\(71\) 97.3864 1.37164 0.685819 0.727772i \(-0.259444\pi\)
0.685819 + 0.727772i \(0.259444\pi\)
\(72\) −4.48354 −0.0622714
\(73\) 116.398i 1.59450i −0.603651 0.797249i \(-0.706288\pi\)
0.603651 0.797249i \(-0.293712\pi\)
\(74\) −20.8362 −0.281570
\(75\) 8.66025i 0.115470i
\(76\) 67.3742i 0.886503i
\(77\) −15.8872 8.69929i −0.206327 0.112978i
\(78\) −0.251773 −0.00322785
\(79\) 98.8343 1.25107 0.625534 0.780197i \(-0.284881\pi\)
0.625534 + 0.780197i \(0.284881\pi\)
\(80\) 30.6087i 0.382609i
\(81\) 9.00000 0.111111
\(82\) 217.370i 2.65085i
\(83\) 112.111i 1.35073i −0.737484 0.675365i \(-0.763986\pi\)
0.737484 0.675365i \(-0.236014\pi\)
\(84\) 26.2752 47.9853i 0.312799 0.571254i
\(85\) 31.7777 0.373855
\(86\) 231.300 2.68954
\(87\) 30.1669i 0.346747i
\(88\) −3.86716 −0.0439450
\(89\) 77.7603i 0.873711i 0.899532 + 0.436855i \(0.143908\pi\)
−0.899532 + 0.436855i \(0.856092\pi\)
\(90\) 19.5717i 0.217463i
\(91\) 0.167501 0.305901i 0.00184067 0.00336155i
\(92\) −100.517 −1.09258
\(93\) −11.0248 −0.118546
\(94\) 237.375i 2.52526i
\(95\) 33.3877 0.351449
\(96\) 79.5282i 0.828419i
\(97\) 109.997i 1.13399i 0.823723 + 0.566993i \(0.191893\pi\)
−0.823723 + 0.566993i \(0.808107\pi\)
\(98\) 77.0080 + 120.448i 0.785796 + 1.22906i
\(99\) 7.76270 0.0784111
\(100\) −22.5612 −0.225612
\(101\) 96.7400i 0.957822i 0.877864 + 0.478911i \(0.158968\pi\)
−0.877864 + 0.478911i \(0.841032\pi\)
\(102\) 71.8157 0.704076
\(103\) 106.961i 1.03846i −0.854635 0.519230i \(-0.826219\pi\)
0.854635 0.519230i \(-0.173781\pi\)
\(104\) 0.0744604i 0.000715966i
\(105\) −23.7794 13.0208i −0.226470 0.124008i
\(106\) −196.055 −1.84957
\(107\) 33.0838 0.309195 0.154597 0.987978i \(-0.450592\pi\)
0.154597 + 0.987978i \(0.450592\pi\)
\(108\) 23.4463i 0.217095i
\(109\) −49.8791 −0.457607 −0.228803 0.973473i \(-0.573481\pi\)
−0.228803 + 0.973473i \(0.573481\pi\)
\(110\) 16.8810i 0.153464i
\(111\) 12.3696i 0.111438i
\(112\) −84.0455 46.0205i −0.750407 0.410898i
\(113\) −111.225 −0.984291 −0.492146 0.870513i \(-0.663787\pi\)
−0.492146 + 0.870513i \(0.663787\pi\)
\(114\) 75.4543 0.661880
\(115\) 49.8118i 0.433146i
\(116\) 78.5893 0.677494
\(117\) 0.149468i 0.00127750i
\(118\) 12.6382i 0.107103i
\(119\) −47.7781 + 87.2553i −0.401497 + 0.733238i
\(120\) −5.78823 −0.0482352
\(121\) −114.304 −0.944665
\(122\) 319.971i 2.62271i
\(123\) −129.044 −1.04914
\(124\) 28.7211i 0.231622i
\(125\) 11.1803i 0.0894427i
\(126\) −53.7401 29.4263i −0.426508 0.233542i
\(127\) −69.4347 −0.546730 −0.273365 0.961910i \(-0.588137\pi\)
−0.273365 + 0.961910i \(0.588137\pi\)
\(128\) −47.4323 −0.370565
\(129\) 137.314i 1.06445i
\(130\) −0.325037 −0.00250028
\(131\) 39.7493i 0.303430i 0.988424 + 0.151715i \(0.0484796\pi\)
−0.988424 + 0.151715i \(0.951520\pi\)
\(132\) 20.2230i 0.153204i
\(133\) −50.1988 + 91.6761i −0.377434 + 0.689294i
\(134\) −143.486 −1.07079
\(135\) 11.6190 0.0860663
\(136\) 21.2391i 0.156170i
\(137\) −89.9621 −0.656657 −0.328329 0.944564i \(-0.606485\pi\)
−0.328329 + 0.944564i \(0.606485\pi\)
\(138\) 112.572i 0.815739i
\(139\) 126.585i 0.910684i 0.890317 + 0.455342i \(0.150483\pi\)
−0.890317 + 0.455342i \(0.849517\pi\)
\(140\) 33.9211 61.9488i 0.242293 0.442491i
\(141\) −140.920 −0.999434
\(142\) 284.132 2.00093
\(143\) 0.128919i 0.000901533i
\(144\) 41.0659 0.285180
\(145\) 38.9454i 0.268589i
\(146\) 339.601i 2.32603i
\(147\) 71.5052 45.7166i 0.486430 0.310998i
\(148\) −32.2247 −0.217734
\(149\) −91.3583 −0.613143 −0.306571 0.951848i \(-0.599182\pi\)
−0.306571 + 0.951848i \(0.599182\pi\)
\(150\) 25.2669i 0.168446i
\(151\) 21.2035 0.140421 0.0702104 0.997532i \(-0.477633\pi\)
0.0702104 + 0.997532i \(0.477633\pi\)
\(152\) 22.3152i 0.146811i
\(153\) 42.6342i 0.278655i
\(154\) −46.3520 25.3808i −0.300987 0.164811i
\(155\) −14.2329 −0.0918252
\(156\) −0.389385 −0.00249606
\(157\) 268.749i 1.71178i 0.517159 + 0.855890i \(0.326990\pi\)
−0.517159 + 0.855890i \(0.673010\pi\)
\(158\) 288.357 1.82504
\(159\) 116.390i 0.732013i
\(160\) 102.671i 0.641691i
\(161\) −136.774 74.8927i −0.849526 0.465172i
\(162\) 26.2582 0.162088
\(163\) −51.5630 −0.316338 −0.158169 0.987412i \(-0.550559\pi\)
−0.158169 + 0.987412i \(0.550559\pi\)
\(164\) 336.178i 2.04987i
\(165\) 10.0216 0.0607370
\(166\) 327.091i 1.97043i
\(167\) 91.2114i 0.546176i 0.961989 + 0.273088i \(0.0880450\pi\)
−0.961989 + 0.273088i \(0.911955\pi\)
\(168\) 8.70267 15.8933i 0.0518016 0.0946033i
\(169\) 168.998 0.999985
\(170\) 92.7137 0.545375
\(171\) 44.7943i 0.261955i
\(172\) 357.723 2.07978
\(173\) 120.543i 0.696780i −0.937350 0.348390i \(-0.886729\pi\)
0.937350 0.348390i \(-0.113271\pi\)
\(174\) 88.0143i 0.505830i
\(175\) −30.6990 16.8098i −0.175423 0.0960559i
\(176\) 35.4202 0.201251
\(177\) −7.50281 −0.0423888
\(178\) 226.871i 1.27456i
\(179\) −51.2128 −0.286105 −0.143053 0.989715i \(-0.545692\pi\)
−0.143053 + 0.989715i \(0.545692\pi\)
\(180\) 30.2691i 0.168161i
\(181\) 54.0291i 0.298503i −0.988799 0.149252i \(-0.952314\pi\)
0.988799 0.149252i \(-0.0476864\pi\)
\(182\) 0.488697 0.892489i 0.00268515 0.00490378i
\(183\) 189.954 1.03800
\(184\) −33.2926 −0.180938
\(185\) 15.9691i 0.0863195i
\(186\) −32.1656 −0.172933
\(187\) 36.7730i 0.196647i
\(188\) 367.118i 1.95275i
\(189\) −17.4692 + 31.9034i −0.0924298 + 0.168801i
\(190\) 97.4110 0.512690
\(191\) 43.9113 0.229902 0.114951 0.993371i \(-0.463329\pi\)
0.114951 + 0.993371i \(0.463329\pi\)
\(192\) 137.192i 0.714542i
\(193\) −46.6855 −0.241894 −0.120947 0.992659i \(-0.538593\pi\)
−0.120947 + 0.992659i \(0.538593\pi\)
\(194\) 320.923i 1.65424i
\(195\) 0.192962i 0.000989548i
\(196\) 119.099 + 186.281i 0.607646 + 0.950415i
\(197\) 274.811 1.39498 0.697490 0.716595i \(-0.254300\pi\)
0.697490 + 0.716595i \(0.254300\pi\)
\(198\) 22.6483 0.114385
\(199\) 270.380i 1.35870i −0.733816 0.679348i \(-0.762263\pi\)
0.733816 0.679348i \(-0.237737\pi\)
\(200\) −7.47257 −0.0373628
\(201\) 85.1822i 0.423792i
\(202\) 282.246i 1.39726i
\(203\) 106.936 + 58.5548i 0.526780 + 0.288447i
\(204\) 111.068 0.544453
\(205\) −166.595 −0.812658
\(206\) 312.068i 1.51489i
\(207\) 66.8296 0.322848
\(208\) 0.682002i 0.00327885i
\(209\) 38.6361i 0.184862i
\(210\) −69.3781 37.9892i −0.330372 0.180901i
\(211\) 385.058 1.82492 0.912460 0.409166i \(-0.134180\pi\)
0.912460 + 0.409166i \(0.134180\pi\)
\(212\) −303.213 −1.43025
\(213\) 168.678i 0.791916i
\(214\) 96.5246 0.451050
\(215\) 177.272i 0.824519i
\(216\) 7.76572i 0.0359524i
\(217\) 21.3993 39.0808i 0.0986144 0.180096i
\(218\) −145.526 −0.667551
\(219\) −201.608 −0.920584
\(220\) 26.1078i 0.118672i
\(221\) 0.708048 0.00320384
\(222\) 36.0893i 0.162564i
\(223\) 141.356i 0.633883i −0.948445 0.316941i \(-0.897344\pi\)
0.948445 0.316941i \(-0.102656\pi\)
\(224\) −281.913 154.366i −1.25854 0.689135i
\(225\) 15.0000 0.0666667
\(226\) −324.507 −1.43587
\(227\) 298.664i 1.31570i 0.753149 + 0.657850i \(0.228534\pi\)
−0.753149 + 0.657850i \(0.771466\pi\)
\(228\) 116.696 0.511823
\(229\) 2.37781i 0.0103835i −0.999987 0.00519173i \(-0.998347\pi\)
0.999987 0.00519173i \(-0.00165259\pi\)
\(230\) 145.330i 0.631869i
\(231\) −15.0676 + 27.5174i −0.0652277 + 0.119123i
\(232\) 26.0298 0.112197
\(233\) −368.120 −1.57991 −0.789956 0.613163i \(-0.789897\pi\)
−0.789956 + 0.613163i \(0.789897\pi\)
\(234\) 0.436083i 0.00186360i
\(235\) −181.927 −0.774158
\(236\) 19.5459i 0.0828217i
\(237\) 171.186i 0.722304i
\(238\) −139.396 + 254.574i −0.585698 + 1.06964i
\(239\) 420.588 1.75978 0.879892 0.475174i \(-0.157615\pi\)
0.879892 + 0.475174i \(0.157615\pi\)
\(240\) 53.0158 0.220899
\(241\) 143.604i 0.595868i 0.954586 + 0.297934i \(0.0962976\pi\)
−0.954586 + 0.297934i \(0.903702\pi\)
\(242\) −333.492 −1.37807
\(243\) 15.5885i 0.0641500i
\(244\) 494.858i 2.02811i
\(245\) 92.3128 59.0199i 0.376787 0.240898i
\(246\) −376.495 −1.53047
\(247\) 0.743921 0.00301183
\(248\) 9.51280i 0.0383581i
\(249\) −194.181 −0.779844
\(250\) 32.6195i 0.130478i
\(251\) 298.338i 1.18860i 0.804245 + 0.594298i \(0.202570\pi\)
−0.804245 + 0.594298i \(0.797430\pi\)
\(252\) −83.1130 45.5099i −0.329813 0.180595i
\(253\) 57.6420 0.227834
\(254\) −202.581 −0.797563
\(255\) 55.0405i 0.215845i
\(256\) 178.444 0.697047
\(257\) 189.432i 0.737089i 0.929610 + 0.368545i \(0.120144\pi\)
−0.929610 + 0.368545i \(0.879856\pi\)
\(258\) 400.624i 1.55281i
\(259\) −43.8481 24.0097i −0.169298 0.0927017i
\(260\) −0.502694 −0.00193344
\(261\) −52.2507 −0.200194
\(262\) 115.972i 0.442640i
\(263\) 233.105 0.886332 0.443166 0.896440i \(-0.353855\pi\)
0.443166 + 0.896440i \(0.353855\pi\)
\(264\) 6.69811i 0.0253716i
\(265\) 150.259i 0.567015i
\(266\) −146.459 + 267.472i −0.550596 + 1.00553i
\(267\) 134.685 0.504437
\(268\) −221.912 −0.828030
\(269\) 261.173i 0.970903i −0.874264 0.485451i \(-0.838655\pi\)
0.874264 0.485451i \(-0.161345\pi\)
\(270\) 33.8992 0.125552
\(271\) 172.256i 0.635632i −0.948152 0.317816i \(-0.897050\pi\)
0.948152 0.317816i \(-0.102950\pi\)
\(272\) 194.535i 0.715200i
\(273\) −0.529836 0.290120i −0.00194079 0.00106271i
\(274\) −262.471 −0.957924
\(275\) 12.9378 0.0470467
\(276\) 174.101i 0.630800i
\(277\) 225.774 0.815070 0.407535 0.913190i \(-0.366388\pi\)
0.407535 + 0.913190i \(0.366388\pi\)
\(278\) 369.322i 1.32849i
\(279\) 19.0954i 0.0684424i
\(280\) 11.2351 20.5182i 0.0401253 0.0732794i
\(281\) 156.116 0.555573 0.277787 0.960643i \(-0.410399\pi\)
0.277787 + 0.960643i \(0.410399\pi\)
\(282\) −411.145 −1.45796
\(283\) 94.6516i 0.334458i −0.985918 0.167229i \(-0.946518\pi\)
0.985918 0.167229i \(-0.0534819\pi\)
\(284\) 439.431 1.54729
\(285\) 57.8291i 0.202909i
\(286\) 0.376131i 0.00131514i
\(287\) 250.477 457.437i 0.872744 1.59386i
\(288\) 137.747 0.478288
\(289\) 87.0361 0.301163
\(290\) 113.626i 0.391814i
\(291\) 190.520 0.654707
\(292\) 525.218i 1.79869i
\(293\) 323.853i 1.10530i 0.833413 + 0.552650i \(0.186383\pi\)
−0.833413 + 0.552650i \(0.813617\pi\)
\(294\) 208.622 133.382i 0.709598 0.453679i
\(295\) −9.68609 −0.0328342
\(296\) −10.6732 −0.0360582
\(297\) 13.4454i 0.0452707i
\(298\) −266.545 −0.894445
\(299\) 1.10987i 0.00371195i
\(300\) 39.0772i 0.130257i
\(301\) 486.753 + 266.530i 1.61712 + 0.885481i
\(302\) 61.8629 0.204844
\(303\) 167.559 0.552999
\(304\) 204.391i 0.672338i
\(305\) 245.230 0.804032
\(306\) 124.388i 0.406498i
\(307\) 542.844i 1.76822i −0.467276 0.884112i \(-0.654765\pi\)
0.467276 0.884112i \(-0.345235\pi\)
\(308\) −71.6868 39.2533i −0.232749 0.127446i
\(309\) −185.263 −0.599555
\(310\) −41.5256 −0.133953
\(311\) 405.345i 1.30336i 0.758494 + 0.651680i \(0.225935\pi\)
−0.758494 + 0.651680i \(0.774065\pi\)
\(312\) −0.128969 −0.000413363
\(313\) 44.1040i 0.140907i −0.997515 0.0704536i \(-0.977555\pi\)
0.997515 0.0704536i \(-0.0224447\pi\)
\(314\) 784.096i 2.49712i
\(315\) −22.5527 + 41.1871i −0.0715958 + 0.130753i
\(316\) 445.965 1.41128
\(317\) −244.609 −0.771636 −0.385818 0.922575i \(-0.626081\pi\)
−0.385818 + 0.922575i \(0.626081\pi\)
\(318\) 339.577i 1.06785i
\(319\) −45.0674 −0.141277
\(320\) 177.114i 0.553482i
\(321\) 57.3029i 0.178514i
\(322\) −399.047 218.505i −1.23928 0.678587i
\(323\) −212.196 −0.656955
\(324\) 40.6102 0.125340
\(325\) 0.249113i 0.000766500i
\(326\) −150.439 −0.461470
\(327\) 86.3932i 0.264199i
\(328\) 111.347i 0.339471i
\(329\) 273.530 499.537i 0.831397 1.51835i
\(330\) 29.2388 0.0886024
\(331\) −516.884 −1.56158 −0.780792 0.624791i \(-0.785184\pi\)
−0.780792 + 0.624791i \(0.785184\pi\)
\(332\) 505.871i 1.52371i
\(333\) 21.4248 0.0643388
\(334\) 266.116i 0.796755i
\(335\) 109.970i 0.328268i
\(336\) −79.7099 + 145.571i −0.237232 + 0.433247i
\(337\) −643.730 −1.91018 −0.955089 0.296320i \(-0.904240\pi\)
−0.955089 + 0.296320i \(0.904240\pi\)
\(338\) 493.063 1.45877
\(339\) 192.647i 0.568281i
\(340\) 143.389 0.421731
\(341\) 16.4702i 0.0482998i
\(342\) 130.691i 0.382136i
\(343\) 23.2640 + 342.210i 0.0678249 + 0.997697i
\(344\) 118.482 0.344426
\(345\) 86.2766 0.250077
\(346\) 351.693i 1.01645i
\(347\) −256.423 −0.738971 −0.369485 0.929237i \(-0.620466\pi\)
−0.369485 + 0.929237i \(0.620466\pi\)
\(348\) 136.121i 0.391151i
\(349\) 410.197i 1.17535i −0.809097 0.587675i \(-0.800043\pi\)
0.809097 0.587675i \(-0.199957\pi\)
\(350\) −89.5668 49.0438i −0.255905 0.140125i
\(351\) 0.258885 0.000737565
\(352\) 118.810 0.337528
\(353\) 258.233i 0.731537i 0.930706 + 0.365769i \(0.119194\pi\)
−0.930706 + 0.365769i \(0.880806\pi\)
\(354\) −21.8900 −0.0618362
\(355\) 217.763i 0.613416i
\(356\) 350.873i 0.985599i
\(357\) 151.131 + 82.7541i 0.423335 + 0.231804i
\(358\) −149.417 −0.417366
\(359\) −152.789 −0.425597 −0.212798 0.977096i \(-0.568258\pi\)
−0.212798 + 0.977096i \(0.568258\pi\)
\(360\) 10.0255i 0.0278486i
\(361\) 138.053 0.382417
\(362\) 157.634i 0.435453i
\(363\) 197.981i 0.545403i
\(364\) 0.755806 1.38030i 0.00207639 0.00379203i
\(365\) −260.275 −0.713081
\(366\) 554.206 1.51422
\(367\) 393.499i 1.07220i −0.844153 0.536102i \(-0.819896\pi\)
0.844153 0.536102i \(-0.180104\pi\)
\(368\) 304.935 0.828628
\(369\) 223.510i 0.605719i
\(370\) 46.5911i 0.125922i
\(371\) −412.582 225.916i −1.11208 0.608938i
\(372\) −49.7464 −0.133727
\(373\) 324.962 0.871212 0.435606 0.900137i \(-0.356534\pi\)
0.435606 + 0.900137i \(0.356534\pi\)
\(374\) 107.288i 0.286866i
\(375\) 19.3649 0.0516398
\(376\) 121.594i 0.323389i
\(377\) 0.867754i 0.00230173i
\(378\) −50.9678 + 93.0805i −0.134835 + 0.246245i
\(379\) −146.945 −0.387718 −0.193859 0.981029i \(-0.562100\pi\)
−0.193859 + 0.981029i \(0.562100\pi\)
\(380\) 150.653 0.396456
\(381\) 120.264i 0.315655i
\(382\) 128.115 0.335379
\(383\) 356.582i 0.931025i −0.885041 0.465512i \(-0.845870\pi\)
0.885041 0.465512i \(-0.154130\pi\)
\(384\) 82.1551i 0.213946i
\(385\) −19.4522 + 35.5248i −0.0505252 + 0.0922722i
\(386\) −136.208 −0.352872
\(387\) −237.835 −0.614560
\(388\) 496.332i 1.27921i
\(389\) 99.7568 0.256444 0.128222 0.991745i \(-0.459073\pi\)
0.128222 + 0.991745i \(0.459073\pi\)
\(390\) 0.562981i 0.00144354i
\(391\) 316.581i 0.809670i
\(392\) 39.4470 + 61.6988i 0.100630 + 0.157395i
\(393\) 68.8478 0.175185
\(394\) 801.782 2.03498
\(395\) 221.000i 0.559494i
\(396\) 35.0272 0.0884526
\(397\) 646.374i 1.62815i 0.580763 + 0.814073i \(0.302754\pi\)
−0.580763 + 0.814073i \(0.697246\pi\)
\(398\) 788.855i 1.98205i
\(399\) 158.788 + 86.9468i 0.397964 + 0.217912i
\(400\) 68.4431 0.171108
\(401\) 219.319 0.546931 0.273465 0.961882i \(-0.411830\pi\)
0.273465 + 0.961882i \(0.411830\pi\)
\(402\) 248.526i 0.618223i
\(403\) −0.317128 −0.000786917
\(404\) 436.515i 1.08048i
\(405\) 20.1246i 0.0496904i
\(406\) 311.995 + 170.838i 0.768461 + 0.420783i
\(407\) 18.4794 0.0454039
\(408\) 36.7873 0.0901649
\(409\) 98.2083i 0.240118i 0.992767 + 0.120059i \(0.0383084\pi\)
−0.992767 + 0.120059i \(0.961692\pi\)
\(410\) −486.053 −1.18550
\(411\) 155.819i 0.379121i
\(412\) 482.636i 1.17145i
\(413\) 14.5631 26.5961i 0.0352619 0.0643974i
\(414\) 194.980 0.470967
\(415\) −250.687 −0.604065
\(416\) 2.28763i 0.00549912i
\(417\) 219.252 0.525784
\(418\) 112.724i 0.269674i
\(419\) 397.174i 0.947909i 0.880549 + 0.473955i \(0.157174\pi\)
−0.880549 + 0.473955i \(0.842826\pi\)
\(420\) −107.298 58.7530i −0.255472 0.139888i
\(421\) −149.418 −0.354911 −0.177456 0.984129i \(-0.556787\pi\)
−0.177456 + 0.984129i \(0.556787\pi\)
\(422\) 1123.44 2.66217
\(423\) 244.081i 0.577024i
\(424\) −100.428 −0.236859
\(425\) 71.0570i 0.167193i
\(426\) 492.131i 1.15524i
\(427\) −368.706 + 673.354i −0.863480 + 1.57694i
\(428\) 149.282 0.348791
\(429\) 0.223295 0.000520500
\(430\) 517.203i 1.20280i
\(431\) −241.112 −0.559425 −0.279713 0.960084i \(-0.590239\pi\)
−0.279713 + 0.960084i \(0.590239\pi\)
\(432\) 71.1282i 0.164649i
\(433\) 391.184i 0.903426i −0.892163 0.451713i \(-0.850813\pi\)
0.892163 0.451713i \(-0.149187\pi\)
\(434\) 62.4342 114.021i 0.143858 0.262721i
\(435\) −67.4553 −0.155070
\(436\) −225.067 −0.516208
\(437\) 332.620i 0.761145i
\(438\) −588.206 −1.34294
\(439\) 111.468i 0.253914i 0.991908 + 0.126957i \(0.0405210\pi\)
−0.991908 + 0.126957i \(0.959479\pi\)
\(440\) 8.64722i 0.0196528i
\(441\) −79.1836 123.851i −0.179555 0.280840i
\(442\) 2.06578 0.00467372
\(443\) −25.3173 −0.0571497 −0.0285748 0.999592i \(-0.509097\pi\)
−0.0285748 + 0.999592i \(0.509097\pi\)
\(444\) 55.8148i 0.125709i
\(445\) 173.877 0.390735
\(446\) 412.416i 0.924700i
\(447\) 158.237i 0.353998i
\(448\) −486.321 266.293i −1.08554 0.594405i
\(449\) −486.460 −1.08343 −0.541715 0.840562i \(-0.682225\pi\)
−0.541715 + 0.840562i \(0.682225\pi\)
\(450\) 43.7636 0.0972525
\(451\) 192.783i 0.427456i
\(452\) −501.874 −1.11034
\(453\) 36.7256i 0.0810720i
\(454\) 871.375i 1.91933i
\(455\) −0.684015 0.374544i −0.00150333 0.000823173i
\(456\) 38.6511 0.0847612
\(457\) 352.023 0.770292 0.385146 0.922856i \(-0.374151\pi\)
0.385146 + 0.922856i \(0.374151\pi\)
\(458\) 6.93745i 0.0151473i
\(459\) −73.8446 −0.160881
\(460\) 224.763i 0.488616i
\(461\) 213.924i 0.464043i −0.972711 0.232021i \(-0.925466\pi\)
0.972711 0.232021i \(-0.0745339\pi\)
\(462\) −43.9609 + 80.2841i −0.0951534 + 0.173775i
\(463\) 144.676 0.312474 0.156237 0.987720i \(-0.450064\pi\)
0.156237 + 0.987720i \(0.450064\pi\)
\(464\) −238.413 −0.513822
\(465\) 24.6521i 0.0530153i
\(466\) −1074.02 −2.30476
\(467\) 97.9108i 0.209659i 0.994490 + 0.104830i \(0.0334297\pi\)
−0.994490 + 0.104830i \(0.966570\pi\)
\(468\) 0.674434i 0.00144110i
\(469\) −301.956 165.341i −0.643829 0.352539i
\(470\) −530.786 −1.12933
\(471\) 465.487 0.988296
\(472\) 6.47386i 0.0137158i
\(473\) −205.138 −0.433695
\(474\) 499.448i 1.05369i
\(475\) 74.6571i 0.157173i
\(476\) −215.586 + 393.717i −0.452913 + 0.827137i
\(477\) 201.594 0.422628
\(478\) 1227.10 2.56715
\(479\) 322.314i 0.672890i 0.941703 + 0.336445i \(0.109225\pi\)
−0.941703 + 0.336445i \(0.890775\pi\)
\(480\) 177.831 0.370480
\(481\) 0.355813i 0.000739735i
\(482\) 418.976i 0.869245i
\(483\) −129.718 + 236.899i −0.268567 + 0.490474i
\(484\) −515.770 −1.06564
\(485\) 245.960 0.507134
\(486\) 45.4805i 0.0935813i
\(487\) −349.967 −0.718617 −0.359309 0.933219i \(-0.616987\pi\)
−0.359309 + 0.933219i \(0.616987\pi\)
\(488\) 163.903i 0.335868i
\(489\) 89.3098i 0.182638i
\(490\) 269.329 172.195i 0.549652 0.351419i
\(491\) −487.352 −0.992571 −0.496286 0.868159i \(-0.665303\pi\)
−0.496286 + 0.868159i \(0.665303\pi\)
\(492\) −582.277 −1.18349
\(493\) 247.518i 0.502066i
\(494\) 2.17045 0.00439361
\(495\) 17.3579i 0.0350665i
\(496\) 87.1301i 0.175666i
\(497\) 597.934 + 327.409i 1.20309 + 0.658770i
\(498\) −566.538 −1.13763
\(499\) −15.0073 −0.0300748 −0.0150374 0.999887i \(-0.504787\pi\)
−0.0150374 + 0.999887i \(0.504787\pi\)
\(500\) 50.4484i 0.100897i
\(501\) 157.983 0.315335
\(502\) 870.423i 1.73391i
\(503\) 868.775i 1.72719i 0.504189 + 0.863594i \(0.331792\pi\)
−0.504189 + 0.863594i \(0.668208\pi\)
\(504\) −27.5281 15.0735i −0.0546192 0.0299077i
\(505\) 216.317 0.428351
\(506\) 168.175 0.332362
\(507\) 292.712i 0.577342i
\(508\) −313.307 −0.616745
\(509\) 620.297i 1.21866i −0.792917 0.609330i \(-0.791439\pi\)
0.792917 0.609330i \(-0.208561\pi\)
\(510\) 160.585i 0.314872i
\(511\) 391.326 714.664i 0.765804 1.39856i
\(512\) 710.353 1.38741
\(513\) −77.5859 −0.151240
\(514\) 552.682i 1.07526i
\(515\) −239.173 −0.464413
\(516\) 619.594i 1.20076i
\(517\) 210.525i 0.407206i
\(518\) −127.930 70.0502i −0.246969 0.135232i
\(519\) −208.786 −0.402286
\(520\) −0.166499 −0.000320190
\(521\) 73.0697i 0.140249i 0.997538 + 0.0701245i \(0.0223396\pi\)
−0.997538 + 0.0701245i \(0.977660\pi\)
\(522\) −152.445 −0.292041
\(523\) 600.742i 1.14865i −0.818629 0.574323i \(-0.805265\pi\)
0.818629 0.574323i \(-0.194735\pi\)
\(524\) 179.359i 0.342287i
\(525\) −29.1154 + 53.1723i −0.0554579 + 0.101281i
\(526\) 680.102 1.29297
\(527\) 90.4576 0.171646
\(528\) 61.3497i 0.116193i
\(529\) −32.7560 −0.0619206
\(530\) 438.392i 0.827154i
\(531\) 12.9952i 0.0244732i
\(532\) −226.509 + 413.665i −0.425769 + 0.777566i
\(533\) −3.71195 −0.00696426
\(534\) 392.953 0.735867
\(535\) 73.9777i 0.138276i
\(536\) −73.5002 −0.137127
\(537\) 88.7032i 0.165183i
\(538\) 761.991i 1.41634i
\(539\) −68.2976 106.824i −0.126712 0.198189i
\(540\) 52.4276 0.0970881
\(541\) −628.263 −1.16130 −0.580650 0.814153i \(-0.697202\pi\)
−0.580650 + 0.814153i \(0.697202\pi\)
\(542\) 502.571i 0.927253i
\(543\) −93.5811 −0.172341
\(544\) 652.526i 1.19950i
\(545\) 111.533i 0.204648i
\(546\) −1.54584 0.846448i −0.00283120 0.00155027i
\(547\) −616.326 −1.12674 −0.563370 0.826205i \(-0.690495\pi\)
−0.563370 + 0.826205i \(0.690495\pi\)
\(548\) −405.931 −0.740750
\(549\) 329.010i 0.599290i
\(550\) 37.7471 0.0686311
\(551\) 260.059i 0.471976i
\(552\) 57.6645i 0.104465i
\(553\) 606.824 + 332.277i 1.09733 + 0.600862i
\(554\) 658.714 1.18901
\(555\) 27.6593 0.0498366
\(556\) 571.183i 1.02731i
\(557\) 444.374 0.797799 0.398900 0.916995i \(-0.369392\pi\)
0.398900 + 0.916995i \(0.369392\pi\)
\(558\) 55.7124i 0.0998430i
\(559\) 3.94984i 0.00706591i
\(560\) −102.905 + 187.932i −0.183759 + 0.335592i
\(561\) −63.6926 −0.113534
\(562\) 455.480 0.810464
\(563\) 490.184i 0.870665i 0.900270 + 0.435332i \(0.143369\pi\)
−0.900270 + 0.435332i \(0.856631\pi\)
\(564\) −635.867 −1.12742
\(565\) 248.706i 0.440188i
\(566\) 276.153i 0.487903i
\(567\) 55.2583 + 30.2576i 0.0974573 + 0.0533644i
\(568\) 145.545 0.256242
\(569\) 152.671 0.268315 0.134158 0.990960i \(-0.457167\pi\)
0.134158 + 0.990960i \(0.457167\pi\)
\(570\) 168.721i 0.296002i
\(571\) −348.236 −0.609871 −0.304936 0.952373i \(-0.598635\pi\)
−0.304936 + 0.952373i \(0.598635\pi\)
\(572\) 0.581715i 0.00101698i
\(573\) 76.0567i 0.132734i
\(574\) 730.787 1334.61i 1.27315 2.32510i
\(575\) 111.383 0.193709
\(576\) 237.624 0.412541
\(577\) 216.610i 0.375407i −0.982226 0.187703i \(-0.939896\pi\)
0.982226 0.187703i \(-0.0601044\pi\)
\(578\) 253.934 0.439333
\(579\) 80.8617i 0.139657i
\(580\) 175.731i 0.302985i
\(581\) 376.911 688.338i 0.648728 1.18475i
\(582\) 555.856 0.955078
\(583\) 173.879 0.298249
\(584\) 173.959i 0.297875i
\(585\) 0.334220 0.000571316
\(586\) 944.865i 1.61240i
\(587\) 549.987i 0.936945i −0.883478 0.468473i \(-0.844805\pi\)
0.883478 0.468473i \(-0.155195\pi\)
\(588\) 322.649 206.285i 0.548722 0.350824i
\(589\) 95.0407 0.161359
\(590\) −28.2599 −0.0478981
\(591\) 475.986i 0.805392i
\(592\) 97.7587 0.165133
\(593\) 496.397i 0.837095i −0.908195 0.418547i \(-0.862539\pi\)
0.908195 0.418547i \(-0.137461\pi\)
\(594\) 39.2280i 0.0660403i
\(595\) 195.109 + 106.835i 0.327914 + 0.179555i
\(596\) −412.231 −0.691663
\(597\) −468.313 −0.784443
\(598\) 3.23814i 0.00541495i
\(599\) 837.957 1.39893 0.699463 0.714669i \(-0.253422\pi\)
0.699463 + 0.714669i \(0.253422\pi\)
\(600\) 12.9429i 0.0215714i
\(601\) 643.195i 1.07021i −0.844786 0.535104i \(-0.820272\pi\)
0.844786 0.535104i \(-0.179728\pi\)
\(602\) 1420.14 + 777.621i 2.35904 + 1.29173i
\(603\) 147.540 0.244677
\(604\) 95.6755 0.158403
\(605\) 255.593i 0.422467i
\(606\) 488.865 0.806707
\(607\) 137.690i 0.226837i −0.993547 0.113419i \(-0.963820\pi\)
0.993547 0.113419i \(-0.0361801\pi\)
\(608\) 685.586i 1.12761i
\(609\) 101.420 185.219i 0.166535 0.304137i
\(610\) 715.476 1.17291
\(611\) −4.05358 −0.00663433
\(612\) 192.376i 0.314340i
\(613\) 844.662 1.37792 0.688958 0.724801i \(-0.258068\pi\)
0.688958 + 0.724801i \(0.258068\pi\)
\(614\) 1583.79i 2.57946i
\(615\) 288.551i 0.469188i
\(616\) −23.7436 13.0012i −0.0385448 0.0211059i
\(617\) −601.594 −0.975031 −0.487515 0.873114i \(-0.662097\pi\)
−0.487515 + 0.873114i \(0.662097\pi\)
\(618\) −540.517 −0.874623
\(619\) 389.067i 0.628542i 0.949333 + 0.314271i \(0.101760\pi\)
−0.949333 + 0.314271i \(0.898240\pi\)
\(620\) −64.2223 −0.103584
\(621\) 115.752i 0.186397i
\(622\) 1182.62i 1.90132i
\(623\) −261.426 + 477.433i −0.419625 + 0.766345i
\(624\) 1.18126 0.00189305
\(625\) 25.0000 0.0400000
\(626\) 128.677i 0.205554i
\(627\) −66.9196 −0.106730
\(628\) 1212.66i 1.93099i
\(629\) 101.492i 0.161355i
\(630\) −65.7991 + 120.166i −0.104443 + 0.190740i
\(631\) 394.214 0.624745 0.312372 0.949960i \(-0.398876\pi\)
0.312372 + 0.949960i \(0.398876\pi\)
\(632\) 147.709 0.233717
\(633\) 666.940i 1.05362i
\(634\) −713.664 −1.12565
\(635\) 155.261i 0.244505i
\(636\) 525.180i 0.825755i
\(637\) 2.05685 1.31504i 0.00322896 0.00206443i
\(638\) −131.488 −0.206093
\(639\) −292.159 −0.457213
\(640\) 106.062i 0.165722i
\(641\) 98.0430 0.152953 0.0764766 0.997071i \(-0.475633\pi\)
0.0764766 + 0.997071i \(0.475633\pi\)
\(642\) 167.186i 0.260414i
\(643\) 585.514i 0.910598i 0.890339 + 0.455299i \(0.150468\pi\)
−0.890339 + 0.455299i \(0.849532\pi\)
\(644\) −617.156 337.934i −0.958317 0.524743i
\(645\) −307.043 −0.476036
\(646\) −619.099 −0.958358
\(647\) 1256.79i 1.94248i −0.238099 0.971241i \(-0.576524\pi\)
0.238099 0.971241i \(-0.423476\pi\)
\(648\) 13.4506 0.0207571
\(649\) 11.2087i 0.0172707i
\(650\) 0.726805i 0.00111816i
\(651\) −67.6899 37.0647i −0.103978 0.0569351i
\(652\) −232.665 −0.356848
\(653\) −687.810 −1.05331 −0.526654 0.850080i \(-0.676554\pi\)
−0.526654 + 0.850080i \(0.676554\pi\)
\(654\) 252.059i 0.385411i
\(655\) 88.8822 0.135698
\(656\) 1019.85i 1.55465i
\(657\) 349.195i 0.531499i
\(658\) 798.044 1457.44i 1.21283 2.21495i
\(659\) 757.250 1.14909 0.574545 0.818473i \(-0.305179\pi\)
0.574545 + 0.818473i \(0.305179\pi\)
\(660\) 45.2199 0.0685151
\(661\) 652.355i 0.986922i 0.869768 + 0.493461i \(0.164268\pi\)
−0.869768 + 0.493461i \(0.835732\pi\)
\(662\) −1508.05 −2.27802
\(663\) 1.22637i 0.00184974i
\(664\) 167.551i 0.252336i
\(665\) 204.994 + 112.248i 0.308262 + 0.168794i
\(666\) 62.5085 0.0938566
\(667\) −387.988 −0.581691
\(668\) 411.568i 0.616120i
\(669\) −244.835 −0.365972
\(670\) 320.845i 0.478873i
\(671\) 283.779i 0.422919i
\(672\) −267.370 + 488.288i −0.397873 + 0.726619i
\(673\) −798.483 −1.18645 −0.593227 0.805035i \(-0.702146\pi\)
−0.593227 + 0.805035i \(0.702146\pi\)
\(674\) −1878.13 −2.78654
\(675\) 25.9808i 0.0384900i
\(676\) 762.558 1.12804
\(677\) 512.802i 0.757462i 0.925507 + 0.378731i \(0.123639\pi\)
−0.925507 + 0.378731i \(0.876361\pi\)
\(678\) 562.063i 0.829001i
\(679\) −369.804 + 675.358i −0.544630 + 0.994636i
\(680\) 47.4922 0.0698414
\(681\) 517.301 0.759620
\(682\) 48.0532i 0.0704592i
\(683\) −1332.72 −1.95127 −0.975636 0.219394i \(-0.929592\pi\)
−0.975636 + 0.219394i \(0.929592\pi\)
\(684\) 202.123i 0.295501i
\(685\) 201.161i 0.293666i
\(686\) 67.8743 + 998.424i 0.0989422 + 1.45543i
\(687\) −4.11850 −0.00599490
\(688\) −1085.21 −1.57734
\(689\) 3.34797i 0.00485917i
\(690\) 251.719 0.364810
\(691\) 1065.65i 1.54218i 0.636724 + 0.771092i \(0.280289\pi\)
−0.636724 + 0.771092i \(0.719711\pi\)
\(692\) 543.919i 0.786010i
\(693\) 47.6615 + 26.0979i 0.0687756 + 0.0376593i
\(694\) −748.133 −1.07800
\(695\) 283.053 0.407270
\(696\) 45.0849i 0.0647772i
\(697\) 1058.80 1.51908
\(698\) 1196.78i 1.71459i
\(699\) 637.602i 0.912163i
\(700\) −138.522 75.8498i −0.197888 0.108357i
\(701\) −953.569 −1.36030 −0.680149 0.733074i \(-0.738085\pi\)
−0.680149 + 0.733074i \(0.738085\pi\)
\(702\) 0.755318 0.00107595
\(703\) 106.634i 0.151685i
\(704\) 204.956 0.291130
\(705\) 315.107i 0.446961i
\(706\) 753.413i 1.06716i
\(707\) −325.235 + 593.965i −0.460022 + 0.840120i
\(708\) −33.8545 −0.0478171
\(709\) 68.0675 0.0960050 0.0480025 0.998847i \(-0.484714\pi\)
0.0480025 + 0.998847i \(0.484714\pi\)
\(710\) 635.339i 0.894843i
\(711\) −296.503 −0.417023
\(712\) 116.214i 0.163222i
\(713\) 141.793i 0.198869i
\(714\) 440.935 + 241.441i 0.617556 + 0.338153i
\(715\) 0.288272 0.000403178
\(716\) −231.085 −0.322744
\(717\) 728.480i 1.01601i
\(718\) −445.774 −0.620855
\(719\) 137.609i 0.191389i 0.995411 + 0.0956947i \(0.0305073\pi\)
−0.995411 + 0.0956947i \(0.969493\pi\)
\(720\) 91.8261i 0.127536i
\(721\) 359.599 656.722i 0.498751 0.910849i
\(722\) 402.779 0.557866
\(723\) 248.730 0.344025
\(724\) 243.792i 0.336730i
\(725\) −87.0845 −0.120117
\(726\) 577.625i 0.795627i
\(727\) 853.429i 1.17391i −0.809621 0.586953i \(-0.800328\pi\)
0.809621 0.586953i \(-0.199672\pi\)
\(728\) 0.250333 0.457173i 0.000343864 0.000627985i
\(729\) −27.0000 −0.0370370
\(730\) −759.371 −1.04023
\(731\) 1126.65i 1.54125i
\(732\) 857.120 1.17093
\(733\) 1225.71i 1.67219i −0.548586 0.836094i \(-0.684834\pi\)
0.548586 0.836094i \(-0.315166\pi\)
\(734\) 1148.06i 1.56412i
\(735\) −102.226 159.890i −0.139082 0.217538i
\(736\) 1022.84 1.38973
\(737\) 127.257 0.172668
\(738\) 652.109i 0.883616i
\(739\) −1314.44 −1.77867 −0.889334 0.457258i \(-0.848832\pi\)
−0.889334 + 0.457258i \(0.848832\pi\)
\(740\) 72.0565i 0.0973737i
\(741\) 1.28851i 0.00173888i
\(742\) −1203.74 659.127i −1.62229 0.888312i
\(743\) 1209.47 1.62782 0.813908 0.580994i \(-0.197336\pi\)
0.813908 + 0.580994i \(0.197336\pi\)
\(744\) −16.4766 −0.0221460
\(745\) 204.283i 0.274206i
\(746\) 948.101 1.27091
\(747\) 336.332i 0.450243i
\(748\) 165.929i 0.221830i
\(749\) 203.128 + 111.226i 0.271200 + 0.148500i
\(750\) 56.4986 0.0753315
\(751\) −173.085 −0.230473 −0.115236 0.993338i \(-0.536763\pi\)
−0.115236 + 0.993338i \(0.536763\pi\)
\(752\) 1113.71i 1.48100i
\(753\) 516.736 0.686236
\(754\) 2.53174i 0.00335774i
\(755\) 47.4125i 0.0627981i
\(756\) −78.8255 + 143.956i −0.104266 + 0.190418i
\(757\) 723.857 0.956218 0.478109 0.878301i \(-0.341322\pi\)
0.478109 + 0.878301i \(0.341322\pi\)
\(758\) −428.723 −0.565598
\(759\) 99.8390i 0.131540i
\(760\) 49.8983 0.0656557
\(761\) 187.223i 0.246023i −0.992405 0.123011i \(-0.960745\pi\)
0.992405 0.123011i \(-0.0392552\pi\)
\(762\) 350.881i 0.460473i
\(763\) −306.248 167.691i −0.401374 0.219779i
\(764\) 198.139 0.259344
\(765\) −95.3330 −0.124618
\(766\) 1040.36i 1.35817i
\(767\) −0.215819 −0.000281380
\(768\) 309.074i 0.402441i
\(769\) 94.5845i 0.122997i −0.998107 0.0614984i \(-0.980412\pi\)
0.998107 0.0614984i \(-0.0195879\pi\)
\(770\) −56.7532 + 103.646i −0.0737055 + 0.134606i
\(771\) 328.106 0.425559
\(772\) −210.656 −0.272871
\(773\) 561.473i 0.726356i −0.931720 0.363178i \(-0.881692\pi\)
0.931720 0.363178i \(-0.118308\pi\)
\(774\) −693.901 −0.896513
\(775\) 31.8257i 0.0410655i
\(776\) 164.391i 0.211845i
\(777\) −41.5861 + 75.9471i −0.0535214 + 0.0977440i
\(778\) 291.048 0.374098
\(779\) 1112.44 1.42804
\(780\) 0.870691i 0.00111627i
\(781\) −251.994 −0.322655
\(782\) 923.648i 1.18114i
\(783\) 90.5008i 0.115582i
\(784\) −361.305 565.115i −0.460848 0.720810i
\(785\) 600.942 0.765531
\(786\) 200.869 0.255558