Properties

Label 441.2.w.a.251.9
Level $441$
Weight $2$
Character 441.251
Analytic conductor $3.521$
Analytic rank $0$
Dimension $120$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 441 = 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 441.w (of order \(14\), degree \(6\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.52140272914\)
Analytic rank: \(0\)
Dimension: \(120\)
Relative dimension: \(20\) over \(\Q(\zeta_{14})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{14}]$

Embedding invariants

Embedding label 251.9
Character \(\chi\) \(=\) 441.251
Dual form 441.2.w.a.188.9

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.203165 - 0.162019i) q^{2} +(-0.430016 - 1.88402i) q^{4} +(-2.46158 - 1.18543i) q^{5} +(-1.53249 + 2.15673i) q^{7} +(-0.443379 + 0.920685i) q^{8} +O(q^{10})\) \(q+(-0.203165 - 0.162019i) q^{2} +(-0.430016 - 1.88402i) q^{4} +(-2.46158 - 1.18543i) q^{5} +(-1.53249 + 2.15673i) q^{7} +(-0.443379 + 0.920685i) q^{8} +(0.308044 + 0.639659i) q^{10} +(-2.00878 - 1.60195i) q^{11} +(4.63632 + 3.69734i) q^{13} +(0.660778 - 0.189879i) q^{14} +(-3.24295 + 1.56172i) q^{16} +(-1.48891 + 6.52334i) q^{17} -0.418798i q^{19} +(-1.17487 + 5.14742i) q^{20} +(0.148568 + 0.650919i) q^{22} +(-5.32955 + 1.21643i) q^{23} +(1.53666 + 1.92691i) q^{25} +(-0.342899 - 1.50234i) q^{26} +(4.72232 + 1.95982i) q^{28} +(2.32890 + 0.531557i) q^{29} -5.40375i q^{31} +(2.90441 + 0.662912i) q^{32} +(1.35940 - 1.08408i) q^{34} +(6.32900 - 3.49228i) q^{35} +(-1.37636 + 6.03022i) q^{37} +(-0.0678530 + 0.0850850i) q^{38} +(2.18282 - 1.74074i) q^{40} +(-5.97322 - 2.87655i) q^{41} +(-7.06131 + 3.40055i) q^{43} +(-2.15430 + 4.47345i) q^{44} +(1.27986 + 0.616349i) q^{46} +(2.90399 - 3.64149i) q^{47} +(-2.30293 - 6.61033i) q^{49} -0.640448i q^{50} +(4.97219 - 10.3249i) q^{52} +(-13.5007 + 3.08145i) q^{53} +(3.04576 + 6.32459i) q^{55} +(-1.30619 - 2.36719i) q^{56} +(-0.387029 - 0.485319i) q^{58} +(5.52357 - 2.66001i) q^{59} +(-9.77982 - 2.23218i) q^{61} +(-0.875508 + 1.09785i) q^{62} +(4.00571 + 5.02301i) q^{64} +(-7.02971 - 14.5973i) q^{65} -8.37721 q^{67} +12.9304 q^{68} +(-1.85164 - 0.315907i) q^{70} +(6.34846 - 1.44900i) q^{71} +(-5.32281 + 4.24480i) q^{73} +(1.25664 - 1.00213i) q^{74} +(-0.789025 + 0.180090i) q^{76} +(6.53340 - 1.87741i) q^{77} +0.883489 q^{79} +9.83409 q^{80} +(0.747494 + 1.55219i) q^{82} +(6.46744 + 8.10992i) q^{83} +(11.3980 - 14.2927i) q^{85} +(1.98556 + 0.453192i) q^{86} +(2.36554 - 1.13918i) q^{88} +(-1.58193 - 1.98368i) q^{89} +(-15.0793 + 4.33313i) q^{91} +(4.58358 + 9.51791i) q^{92} +(-1.17998 + 0.269322i) q^{94} +(-0.496457 + 1.03090i) q^{95} -3.88426i q^{97} +(-0.603122 + 1.71611i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 120q + 24q^{4} + O(q^{10}) \) \( 120q + 24q^{4} - 32q^{16} - 44q^{22} - 4q^{25} - 56q^{28} + 112q^{34} - 76q^{37} + 28q^{40} + 8q^{43} - 40q^{46} - 84q^{49} - 140q^{52} + 12q^{58} - 84q^{61} + 24q^{64} + 16q^{67} + 112q^{70} - 84q^{76} - 24q^{79} + 140q^{82} - 96q^{85} - 24q^{88} - 112q^{91} - 112q^{94} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/441\mathbb{Z}\right)^\times\).

\(n\) \(199\) \(344\)
\(\chi(n)\) \(e\left(\frac{9}{14}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.203165 0.162019i −0.143659 0.114564i 0.549023 0.835807i \(-0.315000\pi\)
−0.692682 + 0.721243i \(0.743571\pi\)
\(3\) 0 0
\(4\) −0.430016 1.88402i −0.215008 0.942011i
\(5\) −2.46158 1.18543i −1.10085 0.530142i −0.206925 0.978357i \(-0.566346\pi\)
−0.893926 + 0.448215i \(0.852060\pi\)
\(6\) 0 0
\(7\) −1.53249 + 2.15673i −0.579228 + 0.815166i
\(8\) −0.443379 + 0.920685i −0.156758 + 0.325511i
\(9\) 0 0
\(10\) 0.308044 + 0.639659i 0.0974120 + 0.202278i
\(11\) −2.00878 1.60195i −0.605670 0.483005i 0.271983 0.962302i \(-0.412320\pi\)
−0.877653 + 0.479297i \(0.840892\pi\)
\(12\) 0 0
\(13\) 4.63632 + 3.69734i 1.28588 + 1.02546i 0.997693 + 0.0678861i \(0.0216255\pi\)
0.288192 + 0.957573i \(0.406946\pi\)
\(14\) 0.660778 0.189879i 0.176600 0.0507472i
\(15\) 0 0
\(16\) −3.24295 + 1.56172i −0.810738 + 0.390431i
\(17\) −1.48891 + 6.52334i −0.361114 + 1.58214i 0.389260 + 0.921128i \(0.372731\pi\)
−0.750373 + 0.661014i \(0.770126\pi\)
\(18\) 0 0
\(19\) 0.418798i 0.0960788i −0.998845 0.0480394i \(-0.984703\pi\)
0.998845 0.0480394i \(-0.0152973\pi\)
\(20\) −1.17487 + 5.14742i −0.262708 + 1.15100i
\(21\) 0 0
\(22\) 0.148568 + 0.650919i 0.0316748 + 0.138776i
\(23\) −5.32955 + 1.21643i −1.11129 + 0.253644i −0.738487 0.674267i \(-0.764460\pi\)
−0.372800 + 0.927912i \(0.621602\pi\)
\(24\) 0 0
\(25\) 1.53666 + 1.92691i 0.307332 + 0.385382i
\(26\) −0.342899 1.50234i −0.0672481 0.294633i
\(27\) 0 0
\(28\) 4.72232 + 1.95982i 0.892434 + 0.370372i
\(29\) 2.32890 + 0.531557i 0.432466 + 0.0987076i 0.433212 0.901292i \(-0.357380\pi\)
−0.000745584 1.00000i \(0.500237\pi\)
\(30\) 0 0
\(31\) 5.40375i 0.970542i −0.874364 0.485271i \(-0.838721\pi\)
0.874364 0.485271i \(-0.161279\pi\)
\(32\) 2.90441 + 0.662912i 0.513431 + 0.117187i
\(33\) 0 0
\(34\) 1.35940 1.08408i 0.233135 0.185919i
\(35\) 6.32900 3.49228i 1.06980 0.590303i
\(36\) 0 0
\(37\) −1.37636 + 6.03022i −0.226272 + 0.991362i 0.726379 + 0.687295i \(0.241202\pi\)
−0.952651 + 0.304067i \(0.901655\pi\)
\(38\) −0.0678530 + 0.0850850i −0.0110072 + 0.0138026i
\(39\) 0 0
\(40\) 2.18282 1.74074i 0.345134 0.275235i
\(41\) −5.97322 2.87655i −0.932861 0.449242i −0.0952155 0.995457i \(-0.530354\pi\)
−0.837645 + 0.546215i \(0.816068\pi\)
\(42\) 0 0
\(43\) −7.06131 + 3.40055i −1.07684 + 0.518579i −0.886305 0.463102i \(-0.846736\pi\)
−0.190535 + 0.981680i \(0.561022\pi\)
\(44\) −2.15430 + 4.47345i −0.324773 + 0.674398i
\(45\) 0 0
\(46\) 1.27986 + 0.616349i 0.188705 + 0.0908757i
\(47\) 2.90399 3.64149i 0.423590 0.531165i −0.523546 0.851997i \(-0.675391\pi\)
0.947136 + 0.320832i \(0.103963\pi\)
\(48\) 0 0
\(49\) −2.30293 6.61033i −0.328990 0.944333i
\(50\) 0.640448i 0.0905730i
\(51\) 0 0
\(52\) 4.97219 10.3249i 0.689519 1.43180i
\(53\) −13.5007 + 3.08145i −1.85447 + 0.423270i −0.995981 0.0895695i \(-0.971451\pi\)
−0.858485 + 0.512839i \(0.828594\pi\)
\(54\) 0 0
\(55\) 3.04576 + 6.32459i 0.410690 + 0.852807i
\(56\) −1.30619 2.36719i −0.174547 0.316329i
\(57\) 0 0
\(58\) −0.387029 0.485319i −0.0508194 0.0637255i
\(59\) 5.52357 2.66001i 0.719107 0.346304i −0.0382823 0.999267i \(-0.512189\pi\)
0.757390 + 0.652963i \(0.226474\pi\)
\(60\) 0 0
\(61\) −9.77982 2.23218i −1.25218 0.285801i −0.455517 0.890227i \(-0.650545\pi\)
−0.796661 + 0.604426i \(0.793403\pi\)
\(62\) −0.875508 + 1.09785i −0.111190 + 0.139427i
\(63\) 0 0
\(64\) 4.00571 + 5.02301i 0.500714 + 0.627876i
\(65\) −7.02971 14.5973i −0.871928 1.81058i
\(66\) 0 0
\(67\) −8.37721 −1.02344 −0.511719 0.859153i \(-0.670991\pi\)
−0.511719 + 0.859153i \(0.670991\pi\)
\(68\) 12.9304 1.56804
\(69\) 0 0
\(70\) −1.85164 0.315907i −0.221314 0.0377582i
\(71\) 6.34846 1.44900i 0.753424 0.171964i 0.171474 0.985189i \(-0.445147\pi\)
0.581950 + 0.813225i \(0.302290\pi\)
\(72\) 0 0
\(73\) −5.32281 + 4.24480i −0.622987 + 0.496816i −0.883362 0.468692i \(-0.844725\pi\)
0.260374 + 0.965508i \(0.416154\pi\)
\(74\) 1.25664 1.00213i 0.146081 0.116496i
\(75\) 0 0
\(76\) −0.789025 + 0.180090i −0.0905074 + 0.0206577i
\(77\) 6.53340 1.87741i 0.744550 0.213951i
\(78\) 0 0
\(79\) 0.883489 0.0994002 0.0497001 0.998764i \(-0.484173\pi\)
0.0497001 + 0.998764i \(0.484173\pi\)
\(80\) 9.83409 1.09948
\(81\) 0 0
\(82\) 0.747494 + 1.55219i 0.0825469 + 0.171410i
\(83\) 6.46744 + 8.10992i 0.709894 + 0.890179i 0.997719 0.0675041i \(-0.0215036\pi\)
−0.287825 + 0.957683i \(0.592932\pi\)
\(84\) 0 0
\(85\) 11.3980 14.2927i 1.23629 1.55026i
\(86\) 1.98556 + 0.453192i 0.214109 + 0.0488689i
\(87\) 0 0
\(88\) 2.36554 1.13918i 0.252167 0.121437i
\(89\) −1.58193 1.98368i −0.167685 0.210270i 0.690888 0.722962i \(-0.257220\pi\)
−0.858573 + 0.512692i \(0.828648\pi\)
\(90\) 0 0
\(91\) −15.0793 + 4.33313i −1.58074 + 0.454235i
\(92\) 4.58358 + 9.51791i 0.477871 + 0.992310i
\(93\) 0 0
\(94\) −1.17998 + 0.269322i −0.121705 + 0.0277784i
\(95\) −0.496457 + 1.03090i −0.0509354 + 0.105768i
\(96\) 0 0
\(97\) 3.88426i 0.394387i −0.980365 0.197193i \(-0.936817\pi\)
0.980365 0.197193i \(-0.0631827\pi\)
\(98\) −0.603122 + 1.71611i −0.0609245 + 0.173353i
\(99\) 0 0
\(100\) 2.96955 3.72370i 0.296955 0.372370i
\(101\) 9.41819 + 4.53556i 0.937145 + 0.451305i 0.839161 0.543883i \(-0.183046\pi\)
0.0979838 + 0.995188i \(0.468761\pi\)
\(102\) 0 0
\(103\) 3.43174 7.12609i 0.338140 0.702154i −0.660683 0.750665i \(-0.729733\pi\)
0.998823 + 0.0485107i \(0.0154475\pi\)
\(104\) −5.45974 + 2.62927i −0.535371 + 0.257821i
\(105\) 0 0
\(106\) 3.24212 + 1.56132i 0.314903 + 0.151649i
\(107\) 9.87212 7.87275i 0.954374 0.761088i −0.0167017 0.999861i \(-0.505317\pi\)
0.971075 + 0.238773i \(0.0767451\pi\)
\(108\) 0 0
\(109\) −2.69069 + 3.37402i −0.257721 + 0.323172i −0.893812 0.448442i \(-0.851979\pi\)
0.636091 + 0.771614i \(0.280550\pi\)
\(110\) 0.405909 1.77840i 0.0387019 0.169564i
\(111\) 0 0
\(112\) 1.60159 9.38748i 0.151336 0.887034i
\(113\) −10.3065 + 8.21919i −0.969557 + 0.773196i −0.973943 0.226794i \(-0.927175\pi\)
0.00438565 + 0.999990i \(0.498604\pi\)
\(114\) 0 0
\(115\) 14.5611 + 3.32347i 1.35783 + 0.309916i
\(116\) 4.61628i 0.428611i
\(117\) 0 0
\(118\) −1.55317 0.354500i −0.142981 0.0326344i
\(119\) −11.7873 13.2081i −1.08054 1.21079i
\(120\) 0 0
\(121\) −0.978775 4.28829i −0.0889795 0.389845i
\(122\) 1.62526 + 2.03801i 0.147144 + 0.184513i
\(123\) 0 0
\(124\) −10.1808 + 2.32370i −0.914262 + 0.208674i
\(125\) 1.54141 + 6.75337i 0.137868 + 0.604040i
\(126\) 0 0
\(127\) 4.65209 20.3822i 0.412807 1.80862i −0.157883 0.987458i \(-0.550467\pi\)
0.570690 0.821166i \(-0.306676\pi\)
\(128\) 7.62770i 0.674199i
\(129\) 0 0
\(130\) −0.936851 + 4.10461i −0.0821673 + 0.359998i
\(131\) 11.3313 5.45685i 0.990018 0.476768i 0.132479 0.991186i \(-0.457706\pi\)
0.857539 + 0.514418i \(0.171992\pi\)
\(132\) 0 0
\(133\) 0.903232 + 0.641805i 0.0783202 + 0.0556515i
\(134\) 1.70195 + 1.35726i 0.147026 + 0.117250i
\(135\) 0 0
\(136\) −5.34579 4.26313i −0.458398 0.365560i
\(137\) 2.31086 + 4.79856i 0.197430 + 0.409969i 0.976056 0.217521i \(-0.0697969\pi\)
−0.778625 + 0.627489i \(0.784083\pi\)
\(138\) 0 0
\(139\) −1.02034 + 2.11876i −0.0865442 + 0.179711i −0.939749 0.341865i \(-0.888941\pi\)
0.853205 + 0.521576i \(0.174656\pi\)
\(140\) −9.30110 10.4222i −0.786087 0.880841i
\(141\) 0 0
\(142\) −1.52455 0.734184i −0.127937 0.0616113i
\(143\) −3.39040 14.8543i −0.283519 1.24218i
\(144\) 0 0
\(145\) −5.10265 4.06922i −0.423752 0.337931i
\(146\) 1.76914 0.146415
\(147\) 0 0
\(148\) 11.9529 0.982525
\(149\) −10.9789 8.75535i −0.899423 0.717266i 0.0603099 0.998180i \(-0.480791\pi\)
−0.959733 + 0.280914i \(0.909363\pi\)
\(150\) 0 0
\(151\) 4.50982 + 19.7588i 0.367004 + 1.60795i 0.734964 + 0.678107i \(0.237199\pi\)
−0.367960 + 0.929842i \(0.619944\pi\)
\(152\) 0.385581 + 0.185686i 0.0312747 + 0.0150611i
\(153\) 0 0
\(154\) −1.63153 0.677108i −0.131473 0.0545629i
\(155\) −6.40578 + 13.3017i −0.514525 + 1.06842i
\(156\) 0 0
\(157\) −1.46300 3.03795i −0.116760 0.242455i 0.834396 0.551166i \(-0.185817\pi\)
−0.951156 + 0.308711i \(0.900102\pi\)
\(158\) −0.179494 0.143142i −0.0142798 0.0113877i
\(159\) 0 0
\(160\) −6.36358 5.07479i −0.503085 0.401197i
\(161\) 5.54398 13.3586i 0.436927 1.05280i
\(162\) 0 0
\(163\) −16.2148 + 7.80862i −1.27004 + 0.611618i −0.942811 0.333328i \(-0.891828\pi\)
−0.327227 + 0.944946i \(0.606114\pi\)
\(164\) −2.85091 + 12.4907i −0.222619 + 0.975356i
\(165\) 0 0
\(166\) 2.69550i 0.209211i
\(167\) −2.08323 + 9.12724i −0.161205 + 0.706287i 0.828118 + 0.560553i \(0.189411\pi\)
−0.989324 + 0.145734i \(0.953446\pi\)
\(168\) 0 0
\(169\) 4.93237 + 21.6101i 0.379413 + 1.66232i
\(170\) −4.63136 + 1.05708i −0.355209 + 0.0810742i
\(171\) 0 0
\(172\) 9.44319 + 11.8414i 0.720036 + 0.902897i
\(173\) 5.68643 + 24.9139i 0.432332 + 1.89417i 0.447501 + 0.894284i \(0.352314\pi\)
−0.0151690 + 0.999885i \(0.504829\pi\)
\(174\) 0 0
\(175\) −6.51074 + 0.361178i −0.492165 + 0.0273025i
\(176\) 9.01617 + 2.05788i 0.679619 + 0.155119i
\(177\) 0 0
\(178\) 0.659317i 0.0494179i
\(179\) −14.5634 3.32400i −1.08852 0.248447i −0.359640 0.933091i \(-0.617101\pi\)
−0.728878 + 0.684644i \(0.759958\pi\)
\(180\) 0 0
\(181\) −2.80247 + 2.23490i −0.208306 + 0.166118i −0.722086 0.691804i \(-0.756816\pi\)
0.513780 + 0.857922i \(0.328245\pi\)
\(182\) 3.76563 + 1.56279i 0.279127 + 0.115841i
\(183\) 0 0
\(184\) 1.24305 5.44618i 0.0916392 0.401497i
\(185\) 10.5364 13.2123i 0.774654 0.971385i
\(186\) 0 0
\(187\) 13.4409 10.7188i 0.982899 0.783836i
\(188\) −8.10940 3.90528i −0.591439 0.284822i
\(189\) 0 0
\(190\) 0.267888 0.129008i 0.0194346 0.00935923i
\(191\) 2.17795 4.52256i 0.157591 0.327241i −0.807192 0.590289i \(-0.799014\pi\)
0.964783 + 0.263049i \(0.0847280\pi\)
\(192\) 0 0
\(193\) 7.94264 + 3.82497i 0.571724 + 0.275328i 0.697327 0.716753i \(-0.254372\pi\)
−0.125604 + 0.992081i \(0.540087\pi\)
\(194\) −0.629322 + 0.789145i −0.0451827 + 0.0566573i
\(195\) 0 0
\(196\) −11.4637 + 7.18133i −0.818837 + 0.512952i
\(197\) 8.68699i 0.618922i −0.950912 0.309461i \(-0.899851\pi\)
0.950912 0.309461i \(-0.100149\pi\)
\(198\) 0 0
\(199\) −3.05048 + 6.33439i −0.216243 + 0.449033i −0.980668 0.195680i \(-0.937309\pi\)
0.764425 + 0.644713i \(0.223023\pi\)
\(200\) −2.45540 + 0.560429i −0.173623 + 0.0396283i
\(201\) 0 0
\(202\) −1.17860 2.44739i −0.0829260 0.172198i
\(203\) −4.71545 + 4.20820i −0.330960 + 0.295358i
\(204\) 0 0
\(205\) 11.2936 + 14.1617i 0.788778 + 0.989097i
\(206\) −1.85177 + 0.891764i −0.129019 + 0.0621322i
\(207\) 0 0
\(208\) −20.8096 4.74965i −1.44289 0.329329i
\(209\) −0.670892 + 0.841272i −0.0464066 + 0.0581920i
\(210\) 0 0
\(211\) −6.31940 7.92428i −0.435046 0.545530i 0.515184 0.857079i \(-0.327723\pi\)
−0.950230 + 0.311549i \(0.899152\pi\)
\(212\) 11.6110 + 24.1106i 0.797450 + 1.65592i
\(213\) 0 0
\(214\) −3.28120 −0.224298
\(215\) 21.4131 1.46036
\(216\) 0 0
\(217\) 11.6544 + 8.28121i 0.791153 + 0.562165i
\(218\) 1.09331 0.249540i 0.0740481 0.0169010i
\(219\) 0 0
\(220\) 10.6059 8.45796i 0.715053 0.570235i
\(221\) −31.0221 + 24.7393i −2.08677 + 1.66415i
\(222\) 0 0
\(223\) 9.89847 2.25926i 0.662850 0.151291i 0.122157 0.992511i \(-0.461019\pi\)
0.540694 + 0.841220i \(0.318162\pi\)
\(224\) −5.88070 + 5.24810i −0.392921 + 0.350654i
\(225\) 0 0
\(226\) 3.42559 0.227867
\(227\) −8.15525 −0.541283 −0.270641 0.962680i \(-0.587236\pi\)
−0.270641 + 0.962680i \(0.587236\pi\)
\(228\) 0 0
\(229\) 5.17943 + 10.7552i 0.342266 + 0.710723i 0.999060 0.0433472i \(-0.0138022\pi\)
−0.656794 + 0.754070i \(0.728088\pi\)
\(230\) −2.41984 3.03438i −0.159559 0.200081i
\(231\) 0 0
\(232\) −1.52198 + 1.90850i −0.0999230 + 0.125299i
\(233\) −15.7781 3.60125i −1.03366 0.235926i −0.328149 0.944626i \(-0.606425\pi\)
−0.705510 + 0.708700i \(0.749282\pi\)
\(234\) 0 0
\(235\) −11.4651 + 5.52131i −0.747902 + 0.360171i
\(236\) −7.38674 9.26268i −0.480836 0.602949i
\(237\) 0 0
\(238\) 0.254804 + 4.59319i 0.0165165 + 0.297732i
\(239\) −1.43054 2.97056i −0.0925342 0.192149i 0.849565 0.527484i \(-0.176865\pi\)
−0.942099 + 0.335335i \(0.891150\pi\)
\(240\) 0 0
\(241\) −0.422284 + 0.0963835i −0.0272017 + 0.00620861i −0.236100 0.971729i \(-0.575869\pi\)
0.208898 + 0.977937i \(0.433012\pi\)
\(242\) −0.495930 + 1.02981i −0.0318796 + 0.0661987i
\(243\) 0 0
\(244\) 19.3853i 1.24102i
\(245\) −2.16726 + 19.0018i −0.138461 + 1.21398i
\(246\) 0 0
\(247\) 1.54844 1.94168i 0.0985249 0.123546i
\(248\) 4.97515 + 2.39591i 0.315922 + 0.152140i
\(249\) 0 0
\(250\) 0.781011 1.62179i 0.0493955 0.102571i
\(251\) −12.8422 + 6.18449i −0.810594 + 0.390361i −0.792801 0.609480i \(-0.791378\pi\)
−0.0177924 + 0.999842i \(0.505664\pi\)
\(252\) 0 0
\(253\) 12.6545 + 6.09411i 0.795585 + 0.383133i
\(254\) −4.24743 + 3.38721i −0.266507 + 0.212533i
\(255\) 0 0
\(256\) 6.77560 8.49633i 0.423475 0.531021i
\(257\) 2.30160 10.0840i 0.143570 0.629020i −0.851020 0.525134i \(-0.824015\pi\)
0.994589 0.103886i \(-0.0331276\pi\)
\(258\) 0 0
\(259\) −10.8963 12.2097i −0.677061 0.758674i
\(260\) −24.4788 + 19.5212i −1.51811 + 1.21066i
\(261\) 0 0
\(262\) −3.18623 0.727236i −0.196846 0.0449288i
\(263\) 17.7902i 1.09699i −0.836154 0.548495i \(-0.815201\pi\)
0.836154 0.548495i \(-0.184799\pi\)
\(264\) 0 0
\(265\) 36.8859 + 8.41896i 2.26588 + 0.517173i
\(266\) −0.0795208 0.276733i −0.00487573 0.0169676i
\(267\) 0 0
\(268\) 3.60233 + 15.7829i 0.220048 + 0.964091i
\(269\) 9.15874 + 11.4847i 0.558418 + 0.700234i 0.978264 0.207361i \(-0.0664875\pi\)
−0.419846 + 0.907595i \(0.637916\pi\)
\(270\) 0 0
\(271\) 22.7856 5.20067i 1.38413 0.315918i 0.535334 0.844641i \(-0.320186\pi\)
0.848795 + 0.528722i \(0.177329\pi\)
\(272\) −5.35919 23.4801i −0.324948 1.42369i
\(273\) 0 0
\(274\) 0.307969 1.34930i 0.0186051 0.0815143i
\(275\) 6.33238i 0.381857i
\(276\) 0 0
\(277\) 3.44499 15.0935i 0.206989 0.906880i −0.759568 0.650428i \(-0.774589\pi\)
0.966557 0.256452i \(-0.0825535\pi\)
\(278\) 0.550576 0.265143i 0.0330214 0.0159022i
\(279\) 0 0
\(280\) 0.409145 + 7.37542i 0.0244511 + 0.440766i
\(281\) 20.3030 + 16.1911i 1.21117 + 0.965878i 0.999933 0.0115558i \(-0.00367841\pi\)
0.211240 + 0.977434i \(0.432250\pi\)
\(282\) 0 0
\(283\) −17.9985 14.3534i −1.06990 0.853218i −0.0802597 0.996774i \(-0.525575\pi\)
−0.989642 + 0.143556i \(0.954146\pi\)
\(284\) −5.45988 11.3376i −0.323984 0.672760i
\(285\) 0 0
\(286\) −1.71786 + 3.56718i −0.101579 + 0.210932i
\(287\) 15.3579 8.47431i 0.906546 0.500223i
\(288\) 0 0
\(289\) −25.0206 12.0493i −1.47180 0.708783i
\(290\) 0.377388 + 1.65345i 0.0221610 + 0.0970937i
\(291\) 0 0
\(292\) 10.2862 + 8.20296i 0.601954 + 0.480042i
\(293\) 4.47285 0.261307 0.130653 0.991428i \(-0.458293\pi\)
0.130653 + 0.991428i \(0.458293\pi\)
\(294\) 0 0
\(295\) −16.7500 −0.975220
\(296\) −4.94169 3.94086i −0.287230 0.229058i
\(297\) 0 0
\(298\) 0.811989 + 3.55756i 0.0470373 + 0.206084i
\(299\) −29.2071 14.0654i −1.68909 0.813423i
\(300\) 0 0
\(301\) 3.48736 20.4406i 0.201008 1.17818i
\(302\) 2.28506 4.74497i 0.131490 0.273042i
\(303\) 0 0
\(304\) 0.654046 + 1.35814i 0.0375121 + 0.0778947i
\(305\) 21.4277 + 17.0880i 1.22695 + 0.978457i
\(306\) 0 0
\(307\) −12.9156 10.2998i −0.737131 0.587842i 0.181298 0.983428i \(-0.441970\pi\)
−0.918429 + 0.395586i \(0.870541\pi\)
\(308\) −6.34655 11.5018i −0.361628 0.655373i
\(309\) 0 0
\(310\) 3.45656 1.66459i 0.196319 0.0945424i
\(311\) −2.75607 + 12.0751i −0.156282 + 0.684717i 0.834698 + 0.550708i \(0.185642\pi\)
−0.990980 + 0.134009i \(0.957215\pi\)
\(312\) 0 0
\(313\) 0.422739i 0.0238946i 0.999929 + 0.0119473i \(0.00380304\pi\)
−0.999929 + 0.0119473i \(0.996197\pi\)
\(314\) −0.194974 + 0.854237i −0.0110030 + 0.0482074i
\(315\) 0 0
\(316\) −0.379914 1.66451i −0.0213718 0.0936361i
\(317\) 10.4050 2.37488i 0.584406 0.133387i 0.0799117 0.996802i \(-0.474536\pi\)
0.504494 + 0.863415i \(0.331679\pi\)
\(318\) 0 0
\(319\) −3.82672 4.79856i −0.214255 0.268668i
\(320\) −3.90594 17.1130i −0.218348 0.956647i
\(321\) 0 0
\(322\) −3.29067 + 1.81576i −0.183382 + 0.101188i
\(323\) 2.73196 + 0.623552i 0.152010 + 0.0346954i
\(324\) 0 0
\(325\) 14.6153i 0.810713i
\(326\) 4.55941 + 1.04066i 0.252522 + 0.0576366i
\(327\) 0 0
\(328\) 5.29680 4.22405i 0.292467 0.233234i
\(329\) 3.40335 + 11.8437i 0.187633 + 0.652962i
\(330\) 0 0
\(331\) −3.67242 + 16.0899i −0.201854 + 0.884382i 0.767952 + 0.640507i \(0.221276\pi\)
−0.969807 + 0.243875i \(0.921581\pi\)
\(332\) 12.4982 15.6722i 0.685926 0.860124i
\(333\) 0 0
\(334\) 1.90202 1.51681i 0.104074 0.0829963i
\(335\) 20.6211 + 9.93062i 1.12665 + 0.542568i
\(336\) 0 0
\(337\) −21.9232 + 10.5577i −1.19423 + 0.575113i −0.922027 0.387126i \(-0.873468\pi\)
−0.272207 + 0.962239i \(0.587754\pi\)
\(338\) 2.49916 5.18955i 0.135936 0.282274i
\(339\) 0 0
\(340\) −31.8291 15.3281i −1.72618 0.831283i
\(341\) −8.65652 + 10.8549i −0.468777 + 0.587828i
\(342\) 0 0
\(343\) 17.7859 + 5.16349i 0.960348 + 0.278802i
\(344\) 8.00897i 0.431815i
\(345\) 0 0
\(346\) 2.88123 5.98294i 0.154896 0.321645i
\(347\) −4.02560 + 0.918818i −0.216106 + 0.0493247i −0.329203 0.944259i \(-0.606780\pi\)
0.113097 + 0.993584i \(0.463923\pi\)
\(348\) 0 0
\(349\) 4.37881 + 9.09270i 0.234393 + 0.486721i 0.984676 0.174396i \(-0.0557971\pi\)
−0.750283 + 0.661117i \(0.770083\pi\)
\(350\) 1.38127 + 0.981482i 0.0738320 + 0.0524624i
\(351\) 0 0
\(352\) −4.77236 5.98435i −0.254368 0.318967i
\(353\) −32.9080 + 15.8477i −1.75152 + 0.843485i −0.773835 + 0.633387i \(0.781664\pi\)
−0.977680 + 0.210098i \(0.932622\pi\)
\(354\) 0 0
\(355\) −17.3449 3.95886i −0.920572 0.210115i
\(356\) −3.05705 + 3.83341i −0.162023 + 0.203171i
\(357\) 0 0
\(358\) 2.42022 + 3.03486i 0.127912 + 0.160397i
\(359\) 6.54851 + 13.5981i 0.345617 + 0.717681i 0.999234 0.0391446i \(-0.0124633\pi\)
−0.653616 + 0.756826i \(0.726749\pi\)
\(360\) 0 0
\(361\) 18.8246 0.990769
\(362\) 0.931458 0.0489563
\(363\) 0 0
\(364\) 14.6480 + 26.5464i 0.767766 + 1.39141i
\(365\) 18.1344 4.13906i 0.949199 0.216648i
\(366\) 0 0
\(367\) 13.1447 10.4825i 0.686147 0.547184i −0.217183 0.976131i \(-0.569687\pi\)
0.903330 + 0.428947i \(0.141115\pi\)
\(368\) 15.3837 12.2681i 0.801932 0.639520i
\(369\) 0 0
\(370\) −4.28127 + 0.977171i −0.222572 + 0.0508007i
\(371\) 14.0439 33.8396i 0.729123 1.75687i
\(372\) 0 0
\(373\) −14.6161 −0.756794 −0.378397 0.925643i \(-0.623525\pi\)
−0.378397 + 0.925643i \(0.623525\pi\)
\(374\) −4.46737 −0.231002
\(375\) 0 0
\(376\) 2.06510 + 4.28821i 0.106499 + 0.221148i
\(377\) 8.83220 + 11.0752i 0.454881 + 0.570403i
\(378\) 0 0
\(379\) −4.94967 + 6.20670i −0.254248 + 0.318817i −0.892532 0.450984i \(-0.851073\pi\)
0.638284 + 0.769801i \(0.279644\pi\)
\(380\) 2.15573 + 0.492031i 0.110587 + 0.0252407i
\(381\) 0 0
\(382\) −1.17522 + 0.565956i −0.0601295 + 0.0289568i
\(383\) 2.51010 + 3.14756i 0.128260 + 0.160833i 0.841815 0.539766i \(-0.181487\pi\)
−0.713555 + 0.700599i \(0.752916\pi\)
\(384\) 0 0
\(385\) −18.3080 3.12351i −0.933063 0.159189i
\(386\) −0.993948 2.06395i −0.0505906 0.105053i
\(387\) 0 0
\(388\) −7.31803 + 1.67029i −0.371517 + 0.0847963i
\(389\) 15.5635 32.3178i 0.789098 1.63858i 0.0197035 0.999806i \(-0.493728\pi\)
0.769395 0.638774i \(-0.220558\pi\)
\(390\) 0 0
\(391\) 36.5776i 1.84981i
\(392\) 7.10710 + 0.810604i 0.358963 + 0.0409417i
\(393\) 0 0
\(394\) −1.40745 + 1.76489i −0.0709064 + 0.0889139i
\(395\) −2.17477 1.04732i −0.109425 0.0526962i
\(396\) 0 0
\(397\) −1.78352 + 3.70352i −0.0895125 + 0.185875i −0.940919 0.338632i \(-0.890036\pi\)
0.851406 + 0.524506i \(0.175750\pi\)
\(398\) 1.64604 0.792691i 0.0825085 0.0397340i
\(399\) 0 0
\(400\) −7.99261 3.84904i −0.399631 0.192452i
\(401\) −13.0626 + 10.4171i −0.652316 + 0.520205i −0.892803 0.450448i \(-0.851264\pi\)
0.240487 + 0.970652i \(0.422693\pi\)
\(402\) 0 0
\(403\) 19.9795 25.0535i 0.995251 1.24801i
\(404\) 4.49513 19.6945i 0.223641 0.979836i
\(405\) 0 0
\(406\) 1.63982 0.0909676i 0.0813829 0.00451465i
\(407\) 12.4249 9.90852i 0.615879 0.491147i
\(408\) 0 0
\(409\) 14.1052 + 3.21943i 0.697459 + 0.159191i 0.556528 0.830829i \(-0.312133\pi\)
0.140931 + 0.990019i \(0.454990\pi\)
\(410\) 4.70693i 0.232459i
\(411\) 0 0
\(412\) −14.9014 3.40115i −0.734140 0.167563i
\(413\) −2.72792 + 15.9893i −0.134232 + 0.786781i
\(414\) 0 0
\(415\) −6.30634 27.6299i −0.309566 1.35630i
\(416\) 11.0148 + 13.8121i 0.540043 + 0.677192i
\(417\) 0 0
\(418\) 0.272603 0.0622200i 0.0133335 0.00304328i
\(419\) −1.30929 5.73638i −0.0639631 0.280241i 0.932824 0.360331i \(-0.117336\pi\)
−0.996788 + 0.0800903i \(0.974479\pi\)
\(420\) 0 0
\(421\) −0.158030 + 0.692373i −0.00770190 + 0.0337442i −0.978633 0.205616i \(-0.934080\pi\)
0.970931 + 0.239360i \(0.0769375\pi\)
\(422\) 2.63380i 0.128211i
\(423\) 0 0
\(424\) 3.14888 13.7962i 0.152923 0.670000i
\(425\) −14.8578 + 7.15516i −0.720711 + 0.347076i
\(426\) 0 0
\(427\) 19.8017 17.6716i 0.958272 0.855189i
\(428\) −19.0776 15.2139i −0.922151 0.735391i
\(429\) 0 0
\(430\) −4.35039 3.46932i −0.209794 0.167305i
\(431\) 1.24950 + 2.59462i 0.0601865 + 0.124978i 0.928892 0.370350i \(-0.120762\pi\)
−0.868706 + 0.495328i \(0.835048\pi\)
\(432\) 0 0
\(433\) −0.989981 + 2.05572i −0.0475755 + 0.0987915i −0.923402 0.383835i \(-0.874603\pi\)
0.875826 + 0.482627i \(0.160317\pi\)
\(434\) −1.02606 3.57068i −0.0492523 0.171398i
\(435\) 0 0
\(436\) 7.51377 + 3.61844i 0.359844 + 0.173292i
\(437\) 0.509440 + 2.23200i 0.0243698 + 0.106771i
\(438\) 0 0
\(439\) 9.52617 + 7.59686i 0.454659 + 0.362579i 0.823881 0.566763i \(-0.191804\pi\)
−0.369222 + 0.929341i \(0.620376\pi\)
\(440\) −7.17338 −0.341977
\(441\) 0 0
\(442\) 10.3108 0.490436
\(443\) 1.97589 + 1.57572i 0.0938774 + 0.0748647i 0.669304 0.742989i \(-0.266592\pi\)
−0.575426 + 0.817854i \(0.695164\pi\)
\(444\) 0 0
\(445\) 1.54253 + 6.75826i 0.0731229 + 0.320372i
\(446\) −2.37706 1.14473i −0.112557 0.0542047i
\(447\) 0 0
\(448\) −16.9720 + 0.941506i −0.801850 + 0.0444820i
\(449\) 9.03863 18.7689i 0.426559 0.885759i −0.571324 0.820725i \(-0.693570\pi\)
0.997883 0.0650347i \(-0.0207158\pi\)
\(450\) 0 0
\(451\) 7.39080 + 15.3471i 0.348019 + 0.722669i
\(452\) 19.9171 + 15.8834i 0.936822 + 0.747090i
\(453\) 0 0
\(454\) 1.65686 + 1.32130i 0.0777603 + 0.0620118i
\(455\) 42.2555 + 7.20917i 1.98097 + 0.337971i
\(456\) 0 0
\(457\) 19.1035 9.19977i 0.893625 0.430347i 0.0700428 0.997544i \(-0.477686\pi\)
0.823582 + 0.567197i \(0.191972\pi\)
\(458\) 0.690263 3.02424i 0.0322539 0.141313i
\(459\) 0 0
\(460\) 28.8626i 1.34572i
\(461\) 0.625035 2.73846i 0.0291108 0.127543i −0.958285 0.285816i \(-0.907735\pi\)
0.987395 + 0.158273i \(0.0505926\pi\)
\(462\) 0 0
\(463\) −2.91933 12.7904i −0.135673 0.594422i −0.996357 0.0852824i \(-0.972821\pi\)
0.860684 0.509140i \(-0.170036\pi\)
\(464\) −8.38266 + 1.91329i −0.389155 + 0.0888221i
\(465\) 0 0
\(466\) 2.62209 + 3.28800i 0.121466 + 0.152314i
\(467\) 8.40531 + 36.8261i 0.388951 + 1.70411i 0.668278 + 0.743911i \(0.267031\pi\)
−0.279327 + 0.960196i \(0.590111\pi\)
\(468\) 0 0
\(469\) 12.8380 18.0673i 0.592804 0.834272i
\(470\) 3.22387 + 0.735826i 0.148706 + 0.0339411i
\(471\) 0 0
\(472\) 6.26486i 0.288363i
\(473\) 19.6321 + 4.48090i 0.902685 + 0.206032i
\(474\) 0 0
\(475\) 0.806986 0.643550i 0.0370271 0.0295281i
\(476\) −19.8157 + 27.8873i −0.908251 + 1.27821i
\(477\) 0 0
\(478\) −0.190649 + 0.835287i −0.00872008 + 0.0382052i
\(479\) 17.0479 21.3774i 0.778939 0.976759i −0.221060 0.975260i \(-0.570952\pi\)
0.999999 0.00149851i \(-0.000476991\pi\)
\(480\) 0 0
\(481\) −28.6770 + 22.8692i −1.30756 + 1.04274i
\(482\) 0.101409 + 0.0488361i 0.00461906 + 0.00222442i
\(483\) 0 0
\(484\) −7.65835 + 3.68807i −0.348107 + 0.167639i
\(485\) −4.60453 + 9.56140i −0.209081 + 0.434161i
\(486\) 0 0
\(487\) 3.64611 + 1.75587i 0.165221 + 0.0795662i 0.514666 0.857390i \(-0.327916\pi\)
−0.349446 + 0.936957i \(0.613630\pi\)
\(488\) 6.39130 8.01444i 0.289321 0.362796i
\(489\) 0 0
\(490\) 3.51896 3.50936i 0.158970 0.158537i
\(491\) 23.7370i 1.07124i −0.844460 0.535618i \(-0.820079\pi\)
0.844460 0.535618i \(-0.179921\pi\)
\(492\) 0 0
\(493\) −6.93505 + 14.4008i −0.312339 + 0.648579i
\(494\) −0.629177 + 0.143606i −0.0283080 + 0.00646112i
\(495\) 0 0
\(496\) 8.43916 + 17.5241i 0.378929 + 0.786855i
\(497\) −6.60389 + 15.9125i −0.296225 + 0.713772i
\(498\) 0 0
\(499\) 13.3191 + 16.7017i 0.596247 + 0.747670i 0.984788 0.173761i \(-0.0555922\pi\)
−0.388541 + 0.921432i \(0.627021\pi\)
\(500\) 12.0607 5.80812i 0.539370 0.259747i
\(501\) 0 0
\(502\) 3.61109 + 0.824207i 0.161171 + 0.0367862i
\(503\) 13.0531 16.3681i 0.582011 0.729819i −0.400443 0.916321i \(-0.631144\pi\)
0.982454 + 0.186503i \(0.0597153\pi\)
\(504\) 0 0
\(505\) −17.8070 22.3293i −0.792401 0.993639i
\(506\) −1.58360 3.28838i −0.0703996 0.146186i
\(507\) 0 0
\(508\) −40.4009 −1.79250
\(509\) 8.37447 0.371192 0.185596 0.982626i \(-0.440578\pi\)
0.185596 + 0.982626i \(0.440578\pi\)
\(510\) 0 0
\(511\) −0.997701 17.9850i −0.0441357 0.795608i
\(512\) −17.6260 + 4.02303i −0.778968 + 0.177794i
\(513\) 0 0
\(514\) −2.10139 + 1.67580i −0.0926884 + 0.0739165i
\(515\) −16.8950 + 13.4733i −0.744483 + 0.593705i
\(516\) 0 0
\(517\) −11.6669 + 2.66290i −0.513111 + 0.117114i
\(518\) 0.235542 + 4.24598i 0.0103491 + 0.186558i
\(519\) 0 0
\(520\) 16.5564 0.726045
\(521\) −14.5608 −0.637921 −0.318960 0.947768i \(-0.603334\pi\)
−0.318960 + 0.947768i \(0.603334\pi\)
\(522\) 0 0
\(523\) 7.41416 + 15.3957i 0.324198 + 0.673205i 0.997829 0.0658635i \(-0.0209802\pi\)
−0.673630 + 0.739069i \(0.735266\pi\)
\(524\) −15.1535 19.0018i −0.661982 0.830099i
\(525\) 0 0
\(526\) −2.88234 + 3.61434i −0.125676 + 0.157593i
\(527\) 35.2505 + 8.04569i 1.53554 + 0.350476i
\(528\) 0 0
\(529\) 6.20209 2.98677i 0.269656 0.129860i
\(530\) −6.12989 7.68664i −0.266265 0.333886i
\(531\) 0 0
\(532\) 0.820771 1.97770i 0.0355849 0.0857440i
\(533\) −17.0582 35.4217i −0.738872 1.53428i
\(534\) 0 0
\(535\) −33.6336 + 7.67665i −1.45411 + 0.331890i
\(536\) 3.71427 7.71277i 0.160432 0.333141i
\(537\) 0 0
\(538\) 3.81717i 0.164570i
\(539\) −5.96332 + 16.9679i −0.256859 + 0.730858i
\(540\) 0 0
\(541\) −7.15055 + 8.96651i −0.307426 + 0.385500i −0.911412 0.411495i \(-0.865007\pi\)
0.603986 + 0.796995i \(0.293578\pi\)
\(542\) −5.47185 2.63510i −0.235036 0.113187i
\(543\) 0 0
\(544\) −8.64880 + 17.9594i −0.370814 + 0.770004i
\(545\) 10.6230 5.11577i 0.455040 0.219136i
\(546\) 0 0
\(547\) −10.3901 5.00362i −0.444250 0.213939i 0.198366 0.980128i \(-0.436437\pi\)
−0.642616 + 0.766189i \(0.722151\pi\)
\(548\) 8.04689 6.41718i 0.343746 0.274128i
\(549\) 0 0
\(550\) −1.02596 + 1.28652i −0.0437472 + 0.0548573i
\(551\) 0.222615 0.975339i 0.00948371 0.0415509i
\(552\) 0 0
\(553\) −1.35394 + 1.90544i −0.0575754 + 0.0810277i
\(554\) −3.14533 + 2.50831i −0.133632 + 0.106568i
\(555\) 0 0
\(556\) 4.43056 + 1.01125i 0.187897 + 0.0428864i
\(557\) 28.5685i 1.21048i −0.796041 0.605242i \(-0.793076\pi\)
0.796041 0.605242i \(-0.206924\pi\)
\(558\) 0 0
\(559\) −45.3115 10.3421i −1.91647 0.437423i
\(560\) −15.0707 + 21.2094i −0.636852 + 0.896262i
\(561\) 0 0
\(562\) −1.50159 6.57891i −0.0633409 0.277515i
\(563\) −22.0460 27.6448i −0.929128 1.16509i −0.986006 0.166709i \(-0.946686\pi\)
0.0568781 0.998381i \(-0.481885\pi\)
\(564\) 0 0
\(565\) 35.1136 8.01445i 1.47724 0.337171i
\(566\) 1.33116 + 5.83219i 0.0559528 + 0.245145i
\(567\) 0 0
\(568\) −1.48070 + 6.48739i −0.0621290 + 0.272205i
\(569\) 17.6630i 0.740472i 0.928938 + 0.370236i \(0.120723\pi\)
−0.928938 + 0.370236i \(0.879277\pi\)
\(570\) 0 0
\(571\) −9.74752 + 42.7067i −0.407921 + 1.78722i 0.185844 + 0.982579i \(0.440498\pi\)
−0.593765 + 0.804639i \(0.702359\pi\)
\(572\) −26.5279 + 12.7752i −1.10919 + 0.534156i
\(573\) 0 0
\(574\) −4.49317 0.766576i −0.187541 0.0319963i
\(575\) −10.5337 8.40032i −0.439284 0.350317i
\(576\) 0 0
\(577\) 19.5509 + 15.5913i 0.813913 + 0.649074i 0.939324 0.343031i \(-0.111454\pi\)
−0.125411 + 0.992105i \(0.540025\pi\)
\(578\) 3.13110 + 6.50180i 0.130237 + 0.270439i
\(579\) 0 0
\(580\) −5.47229 + 11.3633i −0.227225 + 0.471837i
\(581\) −27.4022 + 1.52011i −1.13683 + 0.0630649i
\(582\) 0 0
\(583\) 32.0563 + 15.4375i 1.32763 + 0.639355i
\(584\) −1.54810 6.78268i −0.0640609 0.280669i
\(585\) 0 0
\(586\) −0.908725 0.724684i −0.0375391 0.0299364i
\(587\) 10.6126 0.438027 0.219014 0.975722i \(-0.429716\pi\)
0.219014 + 0.975722i \(0.429716\pi\)
\(588\) 0 0
\(589\) −2.26308 −0.0932485
\(590\) 3.40300 + 2.71380i 0.140099 + 0.111725i
\(591\) 0 0
\(592\) −4.95407 21.7052i −0.203611 0.892078i
\(593\) −16.6237 8.00554i −0.682652 0.328748i 0.0602163 0.998185i \(-0.480821\pi\)
−0.742869 + 0.669437i \(0.766535\pi\)
\(594\) 0 0
\(595\) 13.3580 + 46.4859i 0.547625 + 1.90574i
\(596\) −11.7742 + 24.4494i −0.482290 + 1.00148i
\(597\) 0 0
\(598\) 3.65500 + 7.58968i 0.149464 + 0.310365i
\(599\) 28.6007 + 22.8083i 1.16859 + 0.931920i 0.998567 0.0535196i \(-0.0170440\pi\)
0.170024 + 0.985440i \(0.445615\pi\)
\(600\) 0 0
\(601\) 7.34653 + 5.85866i 0.299671 + 0.238980i 0.761768 0.647850i \(-0.224331\pi\)
−0.462097 + 0.886829i \(0.652903\pi\)
\(602\) −4.02027 + 3.58780i −0.163854 + 0.146228i
\(603\) 0 0
\(604\) 35.2867 16.9932i 1.43580 0.691443i
\(605\) −2.67415 + 11.7162i −0.108720 + 0.476333i
\(606\) 0 0
\(607\) 9.77984i 0.396951i 0.980106 + 0.198476i \(0.0635991\pi\)
−0.980106 + 0.198476i \(0.936401\pi\)
\(608\) 0.277626 1.21636i 0.0112592 0.0493299i
\(609\) 0 0
\(610\) −1.58478 6.94336i −0.0641658 0.281129i
\(611\) 26.9277 6.14606i 1.08938 0.248643i
\(612\) 0 0
\(613\) 16.9488 + 21.2532i 0.684557 + 0.858407i 0.995765 0.0919348i \(-0.0293051\pi\)
−0.311208 + 0.950342i \(0.600734\pi\)
\(614\) 0.955227 + 4.18512i 0.0385498 + 0.168898i
\(615\) 0 0
\(616\) −1.16826 + 6.84761i −0.0470707 + 0.275898i
\(617\) 8.45955 + 1.93084i 0.340569 + 0.0777326i 0.389385 0.921075i \(-0.372688\pi\)
−0.0488161 + 0.998808i \(0.515545\pi\)
\(618\) 0 0
\(619\) 27.4830i 1.10463i −0.833634 0.552317i \(-0.813744\pi\)
0.833634 0.552317i \(-0.186256\pi\)
\(620\) 27.8154 + 6.34868i 1.11709 + 0.254969i
\(621\) 0 0
\(622\) 2.51633 2.00670i 0.100896 0.0804615i
\(623\) 6.70256 0.371819i 0.268532 0.0148966i
\(624\) 0 0
\(625\) 6.95350 30.4653i 0.278140 1.21861i
\(626\) 0.0684916 0.0858858i 0.00273748 0.00343269i
\(627\) 0 0
\(628\) −5.09445 + 4.06269i −0.203291 + 0.162119i
\(629\) −37.2879 17.9569i −1.48677 0.715989i
\(630\) 0 0
\(631\) 44.8832 21.6146i 1.78677 0.860464i 0.837212 0.546879i \(-0.184184\pi\)
0.949560 0.313585i \(-0.101530\pi\)
\(632\) −0.391720 + 0.813415i −0.0155818 + 0.0323559i
\(633\) 0 0
\(634\) −2.49872 1.20332i −0.0992367 0.0477899i
\(635\) −35.6132 + 44.6575i −1.41327 + 1.77218i
\(636\) 0 0
\(637\) 13.7635 39.1624i 0.545331 1.55167i
\(638\) 1.59490i 0.0631426i
\(639\) 0 0
\(640\) −9.04212 + 18.7762i −0.357421 + 0.742193i
\(641\) −23.9383 + 5.46375i −0.945504 + 0.215805i −0.667361 0.744734i \(-0.732576\pi\)
−0.278143 + 0.960540i \(0.589719\pi\)
\(642\) 0 0
\(643\) −11.9790 24.8747i −0.472407 0.980964i −0.991963 0.126527i \(-0.959617\pi\)
0.519556 0.854436i \(-0.326097\pi\)
\(644\) −27.5518 4.70059i −1.08569 0.185229i
\(645\) 0 0
\(646\) −0.454011 0.569312i −0.0178628 0.0223993i
\(647\) −32.9977 + 15.8909i −1.29727 + 0.624734i −0.949771 0.312945i \(-0.898685\pi\)
−0.347503 + 0.937679i \(0.612970\pi\)
\(648\) 0 0
\(649\) −15.3568 3.50509i −0.602808 0.137587i
\(650\) 2.36796 2.96932i 0.0928789 0.116466i
\(651\) 0 0
\(652\) 21.6842 + 27.1912i 0.849220 + 1.06489i
\(653\) −13.0041 27.0033i −0.508889 1.05672i −0.984226 0.176915i \(-0.943388\pi\)
0.475337 0.879804i \(-0.342326\pi\)
\(654\) 0 0
\(655\) −34.3615 −1.34262
\(656\) 23.8632 0.931703
\(657\) 0 0
\(658\) 1.22745 2.95762i 0.0478510 0.115300i
\(659\) −37.4925 + 8.55743i −1.46050 + 0.333350i −0.877679 0.479249i \(-0.840909\pi\)
−0.582823 + 0.812599i \(0.698052\pi\)
\(660\) 0 0
\(661\) 5.88490 4.69305i 0.228896 0.182539i −0.502325 0.864679i \(-0.667522\pi\)
0.731221 + 0.682140i \(0.238951\pi\)
\(662\) 3.35297 2.67391i 0.130317 0.103924i
\(663\) 0 0
\(664\) −10.3342 + 2.35871i −0.401045 + 0.0915359i
\(665\) −1.46256 2.65057i −0.0567156 0.102785i
\(666\) 0 0
\(667\) −13.0586 −0.505631
\(668\) 18.0918 0.699991
\(669\) 0 0
\(670\) −2.58055 5.35856i −0.0996952 0.207019i
\(671\) 16.0697 + 20.1507i 0.620362 + 0.777910i
\(672\) 0 0
\(673\) −13.2415 + 16.6043i −0.510422 + 0.640048i −0.968544 0.248840i \(-0.919951\pi\)
0.458123 + 0.888889i \(0.348522\pi\)
\(674\) 6.16457 + 1.40702i 0.237450 + 0.0541965i
\(675\) 0 0
\(676\) 38.5929 18.5854i 1.48434 0.714822i
\(677\) 29.2857 + 36.7231i 1.12554 + 1.41138i 0.899312 + 0.437308i \(0.144068\pi\)
0.226228 + 0.974074i \(0.427360\pi\)
\(678\) 0 0
\(679\) 8.37728 + 5.95260i 0.321491 + 0.228440i
\(680\) 8.10542 + 16.8311i 0.310829 + 0.645443i
\(681\) 0 0
\(682\) 3.51740 0.802824i 0.134688 0.0307417i
\(683\) −7.96499 + 16.5395i −0.304772 + 0.632865i −0.995959 0.0898106i \(-0.971374\pi\)
0.691187 + 0.722676i \(0.257088\pi\)
\(684\) 0 0
\(685\) 14.5514i 0.555980i
\(686\) −2.77689 3.93069i −0.106022 0.150074i
\(687\) 0 0
\(688\) 17.5888 22.0556i 0.670566 0.840863i
\(689\) −73.9868 35.6302i −2.81867 1.35740i
\(690\) 0 0
\(691\) −21.2272 + 44.0788i −0.807521 + 1.67684i −0.0739115 + 0.997265i \(0.523548\pi\)
−0.733610 + 0.679571i \(0.762166\pi\)
\(692\) 44.4931 21.4267i 1.69137 0.814523i
\(693\) 0 0
\(694\) 0.966726 + 0.465551i 0.0366964 + 0.0176721i
\(695\) 5.02330 4.00595i 0.190544 0.151954i
\(696\) 0 0
\(697\) 27.6583 34.6824i 1.04763 1.31369i
\(698\) 0.583565 2.55677i 0.0220883 0.0967750i
\(699\) 0 0
\(700\) 3.48019 + 12.1111i 0.131539 + 0.457755i
\(701\) 19.8849 15.8577i 0.751042 0.598936i −0.171341 0.985212i \(-0.554810\pi\)
0.922383 + 0.386275i \(0.126239\pi\)
\(702\) 0 0
\(703\) 2.52544 + 0.576416i 0.0952489 + 0.0217399i
\(704\) 16.5071i 0.622133i
\(705\) 0 0
\(706\) 9.25336 + 2.11202i 0.348255 + 0.0794869i
\(707\) −24.2153 + 13.3617i −0.910709 + 0.502520i
\(708\) 0 0
\(709\) 3.82546 + 16.7604i 0.143668 + 0.629452i 0.994565 + 0.104119i \(0.0332022\pi\)
−0.850897 + 0.525333i \(0.823941\pi\)
\(710\) 2.88247 + 3.61450i 0.108177 + 0.135650i
\(711\) 0 0
\(712\) 2.52774 0.576941i 0.0947311 0.0216218i
\(713\) 6.57331 + 28.7995i 0.246172 + 1.07855i
\(714\) 0 0
\(715\) −9.26305 + 40.5841i −0.346418 + 1.51776i
\(716\) 28.8671i 1.07881i
\(717\) 0 0
\(718\) 0.872721 3.82364i 0.0325697 0.142697i
\(719\) −41.3285 + 19.9028i −1.54129 + 0.742248i −0.995418 0.0956182i \(-0.969517\pi\)
−0.545876 + 0.837866i \(0.683803\pi\)
\(720\) 0 0
\(721\) 10.1099 + 18.3220i 0.376512 + 0.682347i
\(722\) −3.82450 3.04994i −0.142333 0.113507i
\(723\) 0 0
\(724\) 5.41570 + 4.31888i 0.201273 + 0.160510i
\(725\) 2.55447 + 5.30441i 0.0948706 + 0.197001i
\(726\) 0 0
\(727\) 20.1261 41.7923i 0.746435 1.54999i −0.0862692 0.996272i \(-0.527495\pi\)
0.832705 0.553717i \(-0.186791\pi\)
\(728\) 2.69639 15.8045i 0.0999349 0.585753i
\(729\) 0 0
\(730\) −4.35488 2.09720i −0.161181 0.0776209i
\(731\) −11.6693 51.1264i −0.431604 1.89098i
\(732\) 0 0
\(733\) 32.6020 + 25.9992i 1.20418 + 0.960303i 0.999827 0.0185935i \(-0.00591884\pi\)
0.204355 + 0.978897i \(0.434490\pi\)
\(734\) −4.36890 −0.161259
\(735\) 0 0
\(736\) −16.2856 −0.600294
\(737\) 16.8280 + 13.4198i 0.619866 + 0.494326i
\(738\) 0 0
\(739\) 4.98595 + 21.8449i 0.183411 + 0.803577i 0.979991 + 0.199043i \(0.0637835\pi\)
−0.796579 + 0.604534i \(0.793359\pi\)
\(740\) −29.4231 14.1694i −1.08161 0.520877i
\(741\) 0 0
\(742\) −8.33587 + 4.59965i −0.306020 + 0.168858i
\(743\) 5.94655 12.3481i 0.218158 0.453009i −0.762954 0.646453i \(-0.776251\pi\)
0.981111 + 0.193444i \(0.0619658\pi\)
\(744\) 0 0
\(745\) 16.6464 + 34.5667i 0.609878 + 1.26642i
\(746\) 2.96948 + 2.36808i 0.108720 + 0.0867017i
\(747\) 0 0
\(748\) −25.9743 20.7138i −0.949713 0.757371i
\(749\) 1.85042 + 33.3564i 0.0676128 + 1.21882i
\(750\) 0 0
\(751\) −43.7822 + 21.0844i −1.59764 + 0.769381i −0.999488 0.0320048i \(-0.989811\pi\)
−0.598148 + 0.801386i \(0.704097\pi\)
\(752\) −3.73050 + 16.3444i −0.136037 + 0.596018i
\(753\) 0 0
\(754\) 3.68108i 0.134057i
\(755\) 12.3215 53.9839i 0.448424 1.96467i
\(756\) 0 0
\(757\) −3.71116 16.2597i −0.134884 0.590967i −0.996514 0.0834290i \(-0.973413\pi\)
0.861629 0.507538i \(-0.169444\pi\)
\(758\) 2.01120 0.459043i 0.0730501 0.0166732i
\(759\) 0 0
\(760\) −0.729019 0.914161i −0.0264443 0.0331601i
\(761\) 2.33924 + 10.2489i 0.0847974 + 0.371522i 0.999466 0.0326835i \(-0.0104053\pi\)
−0.914668 + 0.404205i \(0.867548\pi\)
\(762\) 0 0
\(763\) −3.15337 10.9737i −0.114160 0.397276i
\(764\) −9.45715 2.15853i −0.342148 0.0780930i
\(765\) 0 0
\(766\) 1.04616i 0.0377992i
\(767\) 35.4440 + 8.08987i 1.27981 + 0.292108i
\(768\) 0 0
\(769\) −26.3184 + 20.9882i −0.949066 + 0.756855i −0.970045 0.242925i \(-0.921893\pi\)
0.0209789 + 0.999780i \(0.493322\pi\)
\(770\) 3.21348 + 3.60083i 0.115806 + 0.129765i
\(771\) 0 0
\(772\) 3.79088 16.6089i 0.136437 0.597768i
\(773\) −26.2873 + 32.9633i −0.945490 + 1.18561i 0.0370050 + 0.999315i \(0.488218\pi\)
−0.982495 + 0.186291i \(0.940353\pi\)
\(774\) 0 0
\(775\) 10.4125 8.30372i 0.374029 0.298279i
\(776\) 3.57618 + 1.72220i 0.128377 + 0.0618233i
\(777\) 0 0
\(778\) −8.39804 + 4.04428i −0.301084 + 0.144994i
\(779\) −1.20469 + 2.50157i −0.0431626 + 0.0896282i
\(780\) 0 0
\(781\) −15.0739 7.25919i −0.539385 0.259754i
\(782\) −5.92625 + 7.43129i −0.211922 + 0.265742i
\(783\) 0 0
\(784\) 17.7918 + 17.8404i 0.635422 + 0.637159i
\(785\) 9.21243i 0.328806i
\(786\) 0 0
\(787\) −14.2218 + 29.5319i −0.506952 + 1.05270i 0.477757 + 0.878492i \(0.341450\pi\)
−0.984709 + 0.174205i \(0.944264\pi\)
\(788\) −16.3665 + 3.73554i −0.583032 + 0.133073i
\(789\) 0 0