Properties

Label 1512.2.c.g.757.10
Level 1512
Weight 2
Character 1512.757
Analytic conductor 12.073
Analytic rank 0
Dimension 24
CM no
Inner twists 4

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Newspace parameters

Level: \( N \) = \( 1512 = 2^{3} \cdot 3^{3} \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 1512.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(12.0733807856\)
Analytic rank: \(0\)
Dimension: \(24\)
Coefficient ring index: multiple of None
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 757.10
Character \(\chi\) = 1512.757
Dual form 1512.2.c.g.757.9

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.497658 + 1.32376i) q^{2} +(-1.50467 - 1.31756i) q^{4} -1.25392i q^{5} +1.00000 q^{7} +(2.49294 - 1.33613i) q^{8} +O(q^{10})\) \(q+(-0.497658 + 1.32376i) q^{2} +(-1.50467 - 1.31756i) q^{4} -1.25392i q^{5} +1.00000 q^{7} +(2.49294 - 1.33613i) q^{8} +(1.65989 + 0.624024i) q^{10} -1.55766i q^{11} -1.07281i q^{13} +(-0.497658 + 1.32376i) q^{14} +(0.528080 + 3.96499i) q^{16} -0.0158095 q^{17} -2.35077i q^{19} +(-1.65211 + 1.88674i) q^{20} +(2.06197 + 0.775184i) q^{22} -5.95129 q^{23} +3.42768 q^{25} +(1.42014 + 0.533891i) q^{26} +(-1.50467 - 1.31756i) q^{28} -0.469737i q^{29} +1.69031 q^{31} +(-5.51149 - 1.27416i) q^{32} +(0.00786775 - 0.0209280i) q^{34} -1.25392i q^{35} -4.59800i q^{37} +(3.11185 + 1.16988i) q^{38} +(-1.67540 - 3.12595i) q^{40} -12.2190 q^{41} +1.97482i q^{43} +(-2.05231 + 2.34377i) q^{44} +(2.96171 - 7.87807i) q^{46} -7.12571 q^{47} +1.00000 q^{49} +(-1.70581 + 4.53742i) q^{50} +(-1.41348 + 1.61422i) q^{52} -1.86735i q^{53} -1.95319 q^{55} +(2.49294 - 1.33613i) q^{56} +(0.621818 + 0.233768i) q^{58} -8.54291i q^{59} -3.92502i q^{61} +(-0.841198 + 2.23757i) q^{62} +(4.42952 - 6.66179i) q^{64} -1.34521 q^{65} -12.7403i q^{67} +(0.0237882 + 0.0208300i) q^{68} +(1.65989 + 0.624024i) q^{70} +4.22205 q^{71} +6.51561 q^{73} +(6.08664 + 2.28823i) q^{74} +(-3.09727 + 3.53713i) q^{76} -1.55766i q^{77} -6.15343 q^{79} +(4.97178 - 0.662170i) q^{80} +(6.08088 - 16.1750i) q^{82} -8.88604i q^{83} +0.0198239i q^{85} +(-2.61419 - 0.982787i) q^{86} +(-2.08124 - 3.88316i) q^{88} +0.240788 q^{89} -1.07281i q^{91} +(8.95474 + 7.84117i) q^{92} +(3.54617 - 9.43272i) q^{94} -2.94767 q^{95} +5.86131 q^{97} +(-0.497658 + 1.32376i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24q + 6q^{4} + 24q^{7} + O(q^{10}) \) \( 24q + 6q^{4} + 24q^{7} - 16q^{10} + 2q^{16} + 16q^{22} - 24q^{25} + 6q^{28} + 8q^{31} + 22q^{34} + 26q^{46} + 24q^{49} - 6q^{52} + 16q^{55} - 58q^{58} + 6q^{64} - 16q^{70} + 60q^{76} + 8q^{79} - 28q^{82} + 12q^{88} + 36q^{94} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1512\mathbb{Z}\right)^\times\).

\(n\) \(757\) \(785\) \(1081\) \(1135\)
\(\chi(n)\) \(-1\) \(1\) \(1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.497658 + 1.32376i −0.351897 + 0.936039i
\(3\) 0 0
\(4\) −1.50467 1.31756i −0.752336 0.658779i
\(5\) 1.25392i 0.560770i −0.959888 0.280385i \(-0.909538\pi\)
0.959888 0.280385i \(-0.0904622\pi\)
\(6\) 0 0
\(7\) 1.00000 0.377964
\(8\) 2.49294 1.33613i 0.881388 0.472393i
\(9\) 0 0
\(10\) 1.65989 + 0.624024i 0.524903 + 0.197334i
\(11\) 1.55766i 0.469653i −0.972037 0.234827i \(-0.924548\pi\)
0.972037 0.234827i \(-0.0754522\pi\)
\(12\) 0 0
\(13\) 1.07281i 0.297543i −0.988872 0.148771i \(-0.952468\pi\)
0.988872 0.148771i \(-0.0475319\pi\)
\(14\) −0.497658 + 1.32376i −0.133005 + 0.353789i
\(15\) 0 0
\(16\) 0.528080 + 3.96499i 0.132020 + 0.991247i
\(17\) −0.0158095 −0.00383438 −0.00191719 0.999998i \(-0.500610\pi\)
−0.00191719 + 0.999998i \(0.500610\pi\)
\(18\) 0 0
\(19\) 2.35077i 0.539303i −0.962958 0.269651i \(-0.913092\pi\)
0.962958 0.269651i \(-0.0869085\pi\)
\(20\) −1.65211 + 1.88674i −0.369424 + 0.421888i
\(21\) 0 0
\(22\) 2.06197 + 0.775184i 0.439614 + 0.165270i
\(23\) −5.95129 −1.24093 −0.620465 0.784235i \(-0.713056\pi\)
−0.620465 + 0.784235i \(0.713056\pi\)
\(24\) 0 0
\(25\) 3.42768 0.685537
\(26\) 1.42014 + 0.533891i 0.278512 + 0.104705i
\(27\) 0 0
\(28\) −1.50467 1.31756i −0.284356 0.248995i
\(29\) 0.469737i 0.0872279i −0.999048 0.0436139i \(-0.986113\pi\)
0.999048 0.0436139i \(-0.0138872\pi\)
\(30\) 0 0
\(31\) 1.69031 0.303589 0.151795 0.988412i \(-0.451495\pi\)
0.151795 + 0.988412i \(0.451495\pi\)
\(32\) −5.51149 1.27416i −0.974303 0.225242i
\(33\) 0 0
\(34\) 0.00786775 0.0209280i 0.00134931 0.00358913i
\(35\) 1.25392i 0.211951i
\(36\) 0 0
\(37\) 4.59800i 0.755906i −0.925825 0.377953i \(-0.876628\pi\)
0.925825 0.377953i \(-0.123372\pi\)
\(38\) 3.11185 + 1.16988i 0.504808 + 0.189779i
\(39\) 0 0
\(40\) −1.67540 3.12595i −0.264904 0.494256i
\(41\) −12.2190 −1.90829 −0.954143 0.299350i \(-0.903230\pi\)
−0.954143 + 0.299350i \(0.903230\pi\)
\(42\) 0 0
\(43\) 1.97482i 0.301158i 0.988598 + 0.150579i \(0.0481137\pi\)
−0.988598 + 0.150579i \(0.951886\pi\)
\(44\) −2.05231 + 2.34377i −0.309398 + 0.353337i
\(45\) 0 0
\(46\) 2.96171 7.87807i 0.436680 1.16156i
\(47\) −7.12571 −1.03939 −0.519696 0.854351i \(-0.673955\pi\)
−0.519696 + 0.854351i \(0.673955\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) −1.70581 + 4.53742i −0.241239 + 0.641689i
\(51\) 0 0
\(52\) −1.41348 + 1.61422i −0.196015 + 0.223852i
\(53\) 1.86735i 0.256500i −0.991742 0.128250i \(-0.959064\pi\)
0.991742 0.128250i \(-0.0409360\pi\)
\(54\) 0 0
\(55\) −1.95319 −0.263368
\(56\) 2.49294 1.33613i 0.333133 0.178548i
\(57\) 0 0
\(58\) 0.621818 + 0.233768i 0.0816487 + 0.0306953i
\(59\) 8.54291i 1.11219i −0.831118 0.556096i \(-0.812299\pi\)
0.831118 0.556096i \(-0.187701\pi\)
\(60\) 0 0
\(61\) 3.92502i 0.502547i −0.967916 0.251274i \(-0.919151\pi\)
0.967916 0.251274i \(-0.0808494\pi\)
\(62\) −0.841198 + 2.23757i −0.106832 + 0.284171i
\(63\) 0 0
\(64\) 4.42952 6.66179i 0.553690 0.832723i
\(65\) −1.34521 −0.166853
\(66\) 0 0
\(67\) 12.7403i 1.55647i −0.627972 0.778236i \(-0.716115\pi\)
0.627972 0.778236i \(-0.283885\pi\)
\(68\) 0.0237882 + 0.0208300i 0.00288474 + 0.00252601i
\(69\) 0 0
\(70\) 1.65989 + 0.624024i 0.198395 + 0.0745851i
\(71\) 4.22205 0.501066 0.250533 0.968108i \(-0.419394\pi\)
0.250533 + 0.968108i \(0.419394\pi\)
\(72\) 0 0
\(73\) 6.51561 0.762595 0.381297 0.924452i \(-0.375477\pi\)
0.381297 + 0.924452i \(0.375477\pi\)
\(74\) 6.08664 + 2.28823i 0.707557 + 0.266001i
\(75\) 0 0
\(76\) −3.09727 + 3.53713i −0.355282 + 0.405737i
\(77\) 1.55766i 0.177512i
\(78\) 0 0
\(79\) −6.15343 −0.692315 −0.346158 0.938176i \(-0.612514\pi\)
−0.346158 + 0.938176i \(0.612514\pi\)
\(80\) 4.97178 0.662170i 0.555862 0.0740328i
\(81\) 0 0
\(82\) 6.08088 16.1750i 0.671521 1.78623i
\(83\) 8.88604i 0.975370i −0.873020 0.487685i \(-0.837842\pi\)
0.873020 0.487685i \(-0.162158\pi\)
\(84\) 0 0
\(85\) 0.0198239i 0.00215021i
\(86\) −2.61419 0.982787i −0.281895 0.105977i
\(87\) 0 0
\(88\) −2.08124 3.88316i −0.221861 0.413947i
\(89\) 0.240788 0.0255235 0.0127618 0.999919i \(-0.495938\pi\)
0.0127618 + 0.999919i \(0.495938\pi\)
\(90\) 0 0
\(91\) 1.07281i 0.112461i
\(92\) 8.95474 + 7.84117i 0.933596 + 0.817498i
\(93\) 0 0
\(94\) 3.54617 9.43272i 0.365759 0.972911i
\(95\) −2.94767 −0.302425
\(96\) 0 0
\(97\) 5.86131 0.595126 0.297563 0.954702i \(-0.403826\pi\)
0.297563 + 0.954702i \(0.403826\pi\)
\(98\) −0.497658 + 1.32376i −0.0502711 + 0.133720i
\(99\) 0 0
\(100\) −5.15754 4.51617i −0.515754 0.451617i
\(101\) 3.12870i 0.311317i 0.987811 + 0.155659i \(0.0497500\pi\)
−0.987811 + 0.155659i \(0.950250\pi\)
\(102\) 0 0
\(103\) 2.72832 0.268830 0.134415 0.990925i \(-0.457085\pi\)
0.134415 + 0.990925i \(0.457085\pi\)
\(104\) −1.43341 2.67444i −0.140557 0.262251i
\(105\) 0 0
\(106\) 2.47192 + 0.929302i 0.240094 + 0.0902618i
\(107\) 2.05577i 0.198738i 0.995051 + 0.0993692i \(0.0316825\pi\)
−0.995051 + 0.0993692i \(0.968318\pi\)
\(108\) 0 0
\(109\) 13.8179i 1.32351i −0.749719 0.661756i \(-0.769811\pi\)
0.749719 0.661756i \(-0.230189\pi\)
\(110\) 0.972019 2.58555i 0.0926784 0.246522i
\(111\) 0 0
\(112\) 0.528080 + 3.96499i 0.0498988 + 0.374656i
\(113\) 3.72061 0.350005 0.175003 0.984568i \(-0.444007\pi\)
0.175003 + 0.984568i \(0.444007\pi\)
\(114\) 0 0
\(115\) 7.46244i 0.695876i
\(116\) −0.618905 + 0.706800i −0.0574639 + 0.0656247i
\(117\) 0 0
\(118\) 11.3088 + 4.25145i 1.04106 + 0.391378i
\(119\) −0.0158095 −0.00144926
\(120\) 0 0
\(121\) 8.57368 0.779426
\(122\) 5.19578 + 1.95332i 0.470404 + 0.176845i
\(123\) 0 0
\(124\) −2.54337 2.22709i −0.228401 0.199998i
\(125\) 10.5676i 0.945199i
\(126\) 0 0
\(127\) −19.8627 −1.76253 −0.881264 0.472625i \(-0.843307\pi\)
−0.881264 + 0.472625i \(0.843307\pi\)
\(128\) 6.61421 + 9.17890i 0.584619 + 0.811308i
\(129\) 0 0
\(130\) 0.669456 1.78074i 0.0587152 0.156181i
\(131\) 7.24798i 0.633259i −0.948549 0.316629i \(-0.897449\pi\)
0.948549 0.316629i \(-0.102551\pi\)
\(132\) 0 0
\(133\) 2.35077i 0.203837i
\(134\) 16.8650 + 6.34030i 1.45692 + 0.547718i
\(135\) 0 0
\(136\) −0.0394123 + 0.0211236i −0.00337958 + 0.00181133i
\(137\) 13.1526 1.12371 0.561853 0.827237i \(-0.310089\pi\)
0.561853 + 0.827237i \(0.310089\pi\)
\(138\) 0 0
\(139\) 5.29486i 0.449104i 0.974462 + 0.224552i \(0.0720919\pi\)
−0.974462 + 0.224552i \(0.927908\pi\)
\(140\) −1.65211 + 1.88674i −0.139629 + 0.159459i
\(141\) 0 0
\(142\) −2.10114 + 5.58898i −0.176324 + 0.469017i
\(143\) −1.67107 −0.139742
\(144\) 0 0
\(145\) −0.589012 −0.0489148
\(146\) −3.24255 + 8.62509i −0.268355 + 0.713818i
\(147\) 0 0
\(148\) −6.05813 + 6.91848i −0.497975 + 0.568696i
\(149\) 6.59368i 0.540175i −0.962836 0.270088i \(-0.912947\pi\)
0.962836 0.270088i \(-0.0870526\pi\)
\(150\) 0 0
\(151\) −9.51585 −0.774389 −0.387195 0.921998i \(-0.626556\pi\)
−0.387195 + 0.921998i \(0.626556\pi\)
\(152\) −3.14093 5.86032i −0.254763 0.475335i
\(153\) 0 0
\(154\) 2.06197 + 0.775184i 0.166158 + 0.0624661i
\(155\) 2.11952i 0.170244i
\(156\) 0 0
\(157\) 16.0109i 1.27781i −0.769285 0.638905i \(-0.779388\pi\)
0.769285 0.638905i \(-0.220612\pi\)
\(158\) 3.06231 8.14566i 0.243624 0.648034i
\(159\) 0 0
\(160\) −1.59769 + 6.91097i −0.126309 + 0.546360i
\(161\) −5.95129 −0.469027
\(162\) 0 0
\(163\) 12.5751i 0.984959i 0.870324 + 0.492480i \(0.163909\pi\)
−0.870324 + 0.492480i \(0.836091\pi\)
\(164\) 18.3856 + 16.0992i 1.43567 + 1.25714i
\(165\) 0 0
\(166\) 11.7630 + 4.42221i 0.912984 + 0.343230i
\(167\) −17.2841 −1.33748 −0.668741 0.743495i \(-0.733166\pi\)
−0.668741 + 0.743495i \(0.733166\pi\)
\(168\) 0 0
\(169\) 11.8491 0.911468
\(170\) −0.0262421 0.00986553i −0.00201268 0.000756652i
\(171\) 0 0
\(172\) 2.60194 2.97146i 0.198396 0.226572i
\(173\) 8.78719i 0.668078i 0.942559 + 0.334039i \(0.108412\pi\)
−0.942559 + 0.334039i \(0.891588\pi\)
\(174\) 0 0
\(175\) 3.42768 0.259109
\(176\) 6.17612 0.822570i 0.465542 0.0620036i
\(177\) 0 0
\(178\) −0.119830 + 0.318745i −0.00898166 + 0.0238910i
\(179\) 11.6964i 0.874233i 0.899405 + 0.437117i \(0.144000\pi\)
−0.899405 + 0.437117i \(0.856000\pi\)
\(180\) 0 0
\(181\) 24.2624i 1.80341i 0.432351 + 0.901705i \(0.357684\pi\)
−0.432351 + 0.901705i \(0.642316\pi\)
\(182\) 1.42014 + 0.533891i 0.105267 + 0.0395746i
\(183\) 0 0
\(184\) −14.8362 + 7.95169i −1.09374 + 0.586206i
\(185\) −5.76552 −0.423890
\(186\) 0 0
\(187\) 0.0246260i 0.00180083i
\(188\) 10.7219 + 9.38854i 0.781972 + 0.684730i
\(189\) 0 0
\(190\) 1.46693 3.90201i 0.106423 0.283081i
\(191\) 10.4850 0.758665 0.379333 0.925260i \(-0.376154\pi\)
0.379333 + 0.925260i \(0.376154\pi\)
\(192\) 0 0
\(193\) 12.7092 0.914832 0.457416 0.889253i \(-0.348775\pi\)
0.457416 + 0.889253i \(0.348775\pi\)
\(194\) −2.91693 + 7.75896i −0.209423 + 0.557061i
\(195\) 0 0
\(196\) −1.50467 1.31756i −0.107477 0.0941113i
\(197\) 16.0117i 1.14079i −0.821372 0.570394i \(-0.806791\pi\)
0.821372 0.570394i \(-0.193209\pi\)
\(198\) 0 0
\(199\) −11.1888 −0.793156 −0.396578 0.918001i \(-0.629802\pi\)
−0.396578 + 0.918001i \(0.629802\pi\)
\(200\) 8.54502 4.57983i 0.604224 0.323843i
\(201\) 0 0
\(202\) −4.14164 1.55702i −0.291405 0.109552i
\(203\) 0.469737i 0.0329690i
\(204\) 0 0
\(205\) 15.3217i 1.07011i
\(206\) −1.35777 + 3.61164i −0.0946004 + 0.251635i
\(207\) 0 0
\(208\) 4.25366 0.566527i 0.294938 0.0392816i
\(209\) −3.66170 −0.253285
\(210\) 0 0
\(211\) 20.1657i 1.38827i 0.719847 + 0.694133i \(0.244212\pi\)
−0.719847 + 0.694133i \(0.755788\pi\)
\(212\) −2.46034 + 2.80975i −0.168977 + 0.192974i
\(213\) 0 0
\(214\) −2.72134 1.02307i −0.186027 0.0699355i
\(215\) 2.47627 0.168880
\(216\) 0 0
\(217\) 1.69031 0.114746
\(218\) 18.2915 + 6.87658i 1.23886 + 0.465741i
\(219\) 0 0
\(220\) 2.93891 + 2.57344i 0.198141 + 0.173501i
\(221\) 0.0169606i 0.00114089i
\(222\) 0 0
\(223\) −11.1501 −0.746663 −0.373332 0.927698i \(-0.621785\pi\)
−0.373332 + 0.927698i \(0.621785\pi\)
\(224\) −5.51149 1.27416i −0.368252 0.0851333i
\(225\) 0 0
\(226\) −1.85159 + 4.92518i −0.123166 + 0.327618i
\(227\) 18.7414i 1.24391i −0.783053 0.621955i \(-0.786338\pi\)
0.783053 0.621955i \(-0.213662\pi\)
\(228\) 0 0
\(229\) 13.5444i 0.895038i −0.894274 0.447519i \(-0.852308\pi\)
0.894274 0.447519i \(-0.147692\pi\)
\(230\) −9.87847 3.71374i −0.651367 0.244877i
\(231\) 0 0
\(232\) −0.627629 1.17103i −0.0412058 0.0768816i
\(233\) −11.0070 −0.721094 −0.360547 0.932741i \(-0.617410\pi\)
−0.360547 + 0.932741i \(0.617410\pi\)
\(234\) 0 0
\(235\) 8.93508i 0.582860i
\(236\) −11.2558 + 12.8543i −0.732689 + 0.836743i
\(237\) 0 0
\(238\) 0.00786775 0.0209280i 0.000509991 0.00135656i
\(239\) 15.4366 0.998509 0.499255 0.866455i \(-0.333607\pi\)
0.499255 + 0.866455i \(0.333607\pi\)
\(240\) 0 0
\(241\) 16.0354 1.03293 0.516466 0.856308i \(-0.327247\pi\)
0.516466 + 0.856308i \(0.327247\pi\)
\(242\) −4.26676 + 11.3495i −0.274278 + 0.729573i
\(243\) 0 0
\(244\) −5.17144 + 5.90587i −0.331068 + 0.378085i
\(245\) 1.25392i 0.0801100i
\(246\) 0 0
\(247\) −2.52192 −0.160466
\(248\) 4.21385 2.25848i 0.267580 0.143413i
\(249\) 0 0
\(250\) 13.9890 + 5.25907i 0.884743 + 0.332613i
\(251\) 11.4441i 0.722343i 0.932499 + 0.361172i \(0.117623\pi\)
−0.932499 + 0.361172i \(0.882377\pi\)
\(252\) 0 0
\(253\) 9.27010i 0.582806i
\(254\) 9.88482 26.2934i 0.620229 1.64979i
\(255\) 0 0
\(256\) −15.4423 + 4.18766i −0.965141 + 0.261729i
\(257\) −10.7447 −0.670236 −0.335118 0.942176i \(-0.608776\pi\)
−0.335118 + 0.942176i \(0.608776\pi\)
\(258\) 0 0
\(259\) 4.59800i 0.285706i
\(260\) 2.02411 + 1.77240i 0.125530 + 0.109919i
\(261\) 0 0
\(262\) 9.59457 + 3.60702i 0.592755 + 0.222842i
\(263\) 14.6747 0.904878 0.452439 0.891795i \(-0.350554\pi\)
0.452439 + 0.891795i \(0.350554\pi\)
\(264\) 0 0
\(265\) −2.34151 −0.143838
\(266\) 3.11185 + 1.16988i 0.190800 + 0.0717298i
\(267\) 0 0
\(268\) −16.7860 + 19.1699i −1.02537 + 1.17099i
\(269\) 4.93110i 0.300655i −0.988636 0.150327i \(-0.951967\pi\)
0.988636 0.150327i \(-0.0480328\pi\)
\(270\) 0 0
\(271\) −22.6605 −1.37652 −0.688262 0.725462i \(-0.741626\pi\)
−0.688262 + 0.725462i \(0.741626\pi\)
\(272\) −0.00834870 0.0626847i −0.000506214 0.00380082i
\(273\) 0 0
\(274\) −6.54552 + 17.4109i −0.395429 + 1.05183i
\(275\) 5.33918i 0.321965i
\(276\) 0 0
\(277\) 5.99172i 0.360008i −0.983666 0.180004i \(-0.942389\pi\)
0.983666 0.180004i \(-0.0576110\pi\)
\(278\) −7.00912 2.63503i −0.420379 0.158039i
\(279\) 0 0
\(280\) −1.67540 3.12595i −0.100124 0.186811i
\(281\) 1.92544 0.114862 0.0574309 0.998349i \(-0.481709\pi\)
0.0574309 + 0.998349i \(0.481709\pi\)
\(282\) 0 0
\(283\) 28.2195i 1.67747i −0.544537 0.838737i \(-0.683295\pi\)
0.544537 0.838737i \(-0.316705\pi\)
\(284\) −6.35281 5.56280i −0.376970 0.330092i
\(285\) 0 0
\(286\) 0.831622 2.21209i 0.0491748 0.130804i
\(287\) −12.2190 −0.721265
\(288\) 0 0
\(289\) −16.9998 −0.999985
\(290\) 0.293127 0.779710i 0.0172130 0.0457861i
\(291\) 0 0
\(292\) −9.80386 8.58470i −0.573728 0.502381i
\(293\) 29.0957i 1.69979i −0.526955 0.849893i \(-0.676666\pi\)
0.526955 0.849893i \(-0.323334\pi\)
\(294\) 0 0
\(295\) −10.7121 −0.623685
\(296\) −6.14352 11.4625i −0.357085 0.666247i
\(297\) 0 0
\(298\) 8.72844 + 3.28140i 0.505625 + 0.190086i
\(299\) 6.38458i 0.369230i
\(300\) 0 0
\(301\) 1.97482i 0.113827i
\(302\) 4.73564 12.5967i 0.272506 0.724858i
\(303\) 0 0
\(304\) 9.32076 1.24139i 0.534582 0.0711987i
\(305\) −4.92166 −0.281814
\(306\) 0 0
\(307\) 15.8372i 0.903879i 0.892049 + 0.451940i \(0.149268\pi\)
−0.892049 + 0.451940i \(0.850732\pi\)
\(308\) −2.05231 + 2.34377i −0.116941 + 0.133549i
\(309\) 0 0
\(310\) 2.80573 + 1.05480i 0.159355 + 0.0599084i
\(311\) −14.5620 −0.825737 −0.412869 0.910791i \(-0.635473\pi\)
−0.412869 + 0.910791i \(0.635473\pi\)
\(312\) 0 0
\(313\) 6.47077 0.365749 0.182875 0.983136i \(-0.441460\pi\)
0.182875 + 0.983136i \(0.441460\pi\)
\(314\) 21.1946 + 7.96796i 1.19608 + 0.449658i
\(315\) 0 0
\(316\) 9.25890 + 8.10751i 0.520854 + 0.456083i
\(317\) 11.9823i 0.672994i 0.941685 + 0.336497i \(0.109242\pi\)
−0.941685 + 0.336497i \(0.890758\pi\)
\(318\) 0 0
\(319\) −0.731691 −0.0409669
\(320\) −8.35335 5.55426i −0.466966 0.310493i
\(321\) 0 0
\(322\) 2.96171 7.87807i 0.165049 0.439027i
\(323\) 0.0371646i 0.00206789i
\(324\) 0 0
\(325\) 3.67724i 0.203977i
\(326\) −16.6464 6.25811i −0.921960 0.346605i
\(327\) 0 0
\(328\) −30.4612 + 16.3262i −1.68194 + 0.901461i
\(329\) −7.12571 −0.392853
\(330\) 0 0
\(331\) 21.9422i 1.20605i 0.797720 + 0.603027i \(0.206039\pi\)
−0.797720 + 0.603027i \(0.793961\pi\)
\(332\) −11.7079 + 13.3706i −0.642553 + 0.733806i
\(333\) 0 0
\(334\) 8.60156 22.8799i 0.470657 1.25193i
\(335\) −15.9753 −0.872823
\(336\) 0 0
\(337\) 22.3150 1.21558 0.607788 0.794100i \(-0.292057\pi\)
0.607788 + 0.794100i \(0.292057\pi\)
\(338\) −5.89680 + 15.6853i −0.320743 + 0.853169i
\(339\) 0 0
\(340\) 0.0261192 0.0298285i 0.00141651 0.00161768i
\(341\) 2.63294i 0.142582i
\(342\) 0 0
\(343\) 1.00000 0.0539949
\(344\) 2.63862 + 4.92312i 0.142265 + 0.265437i
\(345\) 0 0
\(346\) −11.6321 4.37302i −0.625347 0.235095i
\(347\) 24.5806i 1.31956i 0.751460 + 0.659779i \(0.229350\pi\)
−0.751460 + 0.659779i \(0.770650\pi\)
\(348\) 0 0
\(349\) 12.5930i 0.674089i −0.941489 0.337045i \(-0.890573\pi\)
0.941489 0.337045i \(-0.109427\pi\)
\(350\) −1.70581 + 4.53742i −0.0911796 + 0.242536i
\(351\) 0 0
\(352\) −1.98471 + 8.58505i −0.105785 + 0.457585i
\(353\) 16.1946 0.861953 0.430977 0.902363i \(-0.358169\pi\)
0.430977 + 0.902363i \(0.358169\pi\)
\(354\) 0 0
\(355\) 5.29412i 0.280983i
\(356\) −0.362308 0.317253i −0.0192023 0.0168144i
\(357\) 0 0
\(358\) −15.4833 5.82083i −0.818316 0.307640i
\(359\) −10.1809 −0.537329 −0.268665 0.963234i \(-0.586582\pi\)
−0.268665 + 0.963234i \(0.586582\pi\)
\(360\) 0 0
\(361\) 13.4739 0.709152
\(362\) −32.1176 12.0744i −1.68806 0.634616i
\(363\) 0 0
\(364\) −1.41348 + 1.61422i −0.0740867 + 0.0846082i
\(365\) 8.17006i 0.427640i
\(366\) 0 0
\(367\) −12.3939 −0.646955 −0.323478 0.946236i \(-0.604852\pi\)
−0.323478 + 0.946236i \(0.604852\pi\)
\(368\) −3.14275 23.5968i −0.163827 1.23007i
\(369\) 0 0
\(370\) 2.86926 7.63216i 0.149166 0.396777i
\(371\) 1.86735i 0.0969480i
\(372\) 0 0
\(373\) 7.57921i 0.392437i 0.980560 + 0.196218i \(0.0628661\pi\)
−0.980560 + 0.196218i \(0.937134\pi\)
\(374\) −0.0325988 0.0122553i −0.00168564 0.000633707i
\(375\) 0 0
\(376\) −17.7640 + 9.52087i −0.916107 + 0.491001i
\(377\) −0.503936 −0.0259540
\(378\) 0 0
\(379\) 14.1179i 0.725187i 0.931947 + 0.362594i \(0.118109\pi\)
−0.931947 + 0.362594i \(0.881891\pi\)
\(380\) 4.43528 + 3.88373i 0.227525 + 0.199231i
\(381\) 0 0
\(382\) −5.21793 + 13.8796i −0.266972 + 0.710140i
\(383\) −1.28678 −0.0657512 −0.0328756 0.999459i \(-0.510467\pi\)
−0.0328756 + 0.999459i \(0.510467\pi\)
\(384\) 0 0
\(385\) −1.95319 −0.0995436
\(386\) −6.32486 + 16.8240i −0.321927 + 0.856318i
\(387\) 0 0
\(388\) −8.81935 7.72262i −0.447735 0.392057i
\(389\) 33.3310i 1.68995i 0.534806 + 0.844975i \(0.320385\pi\)
−0.534806 + 0.844975i \(0.679615\pi\)
\(390\) 0 0
\(391\) 0.0940872 0.00475819
\(392\) 2.49294 1.33613i 0.125913 0.0674847i
\(393\) 0 0
\(394\) 21.1956 + 7.96836i 1.06782 + 0.401440i
\(395\) 7.71591i 0.388230i
\(396\) 0 0
\(397\) 20.7770i 1.04277i 0.853322 + 0.521385i \(0.174584\pi\)
−0.853322 + 0.521385i \(0.825416\pi\)
\(398\) 5.56822 14.8113i 0.279110 0.742425i
\(399\) 0 0
\(400\) 1.81009 + 13.5907i 0.0905045 + 0.679536i
\(401\) 7.38157 0.368618 0.184309 0.982868i \(-0.440995\pi\)
0.184309 + 0.982868i \(0.440995\pi\)
\(402\) 0 0
\(403\) 1.81338i 0.0903308i
\(404\) 4.12225 4.70767i 0.205089 0.234215i
\(405\) 0 0
\(406\) 0.621818 + 0.233768i 0.0308603 + 0.0116017i
\(407\) −7.16213 −0.355014
\(408\) 0 0
\(409\) 31.9846 1.58154 0.790769 0.612114i \(-0.209681\pi\)
0.790769 + 0.612114i \(0.209681\pi\)
\(410\) −20.2822 7.62494i −1.00166 0.376569i
\(411\) 0 0
\(412\) −4.10523 3.59472i −0.202250 0.177099i
\(413\) 8.54291i 0.420369i
\(414\) 0 0
\(415\) −11.1424 −0.546958
\(416\) −1.36693 + 5.91276i −0.0670190 + 0.289897i
\(417\) 0 0
\(418\) 1.82228 4.84721i 0.0891305 0.237085i
\(419\) 14.6646i 0.716413i −0.933642 0.358207i \(-0.883388\pi\)
0.933642 0.358207i \(-0.116612\pi\)
\(420\) 0 0
\(421\) 28.4958i 1.38880i −0.719589 0.694400i \(-0.755670\pi\)
0.719589 0.694400i \(-0.244330\pi\)
\(422\) −26.6945 10.0356i −1.29947 0.488527i
\(423\) 0 0
\(424\) −2.49502 4.65520i −0.121169 0.226076i
\(425\) −0.0541901 −0.00262861
\(426\) 0 0
\(427\) 3.92502i 0.189945i
\(428\) 2.70859 3.09326i 0.130925 0.149518i
\(429\) 0 0
\(430\) −1.23234 + 3.27798i −0.0594286 + 0.158078i
\(431\) 35.4443 1.70729 0.853645 0.520855i \(-0.174387\pi\)
0.853645 + 0.520855i \(0.174387\pi\)
\(432\) 0 0
\(433\) −31.5907 −1.51815 −0.759077 0.651001i \(-0.774349\pi\)
−0.759077 + 0.651001i \(0.774349\pi\)
\(434\) −0.841198 + 2.23757i −0.0403788 + 0.107407i
\(435\) 0 0
\(436\) −18.2059 + 20.7914i −0.871903 + 0.995727i
\(437\) 13.9901i 0.669237i
\(438\) 0 0
\(439\) 23.3732 1.11554 0.557771 0.829995i \(-0.311657\pi\)
0.557771 + 0.829995i \(0.311657\pi\)
\(440\) −4.86918 + 2.60971i −0.232129 + 0.124413i
\(441\) 0 0
\(442\) −0.0224517 0.00844057i −0.00106792 0.000401477i
\(443\) 3.52932i 0.167683i −0.996479 0.0838416i \(-0.973281\pi\)
0.996479 0.0838416i \(-0.0267190\pi\)
\(444\) 0 0
\(445\) 0.301929i 0.0143128i
\(446\) 5.54892 14.7600i 0.262749 0.698906i
\(447\) 0 0
\(448\) 4.42952 6.66179i 0.209275 0.314740i
\(449\) −2.94601 −0.139031 −0.0695154 0.997581i \(-0.522145\pi\)
−0.0695154 + 0.997581i \(0.522145\pi\)
\(450\) 0 0
\(451\) 19.0331i 0.896233i
\(452\) −5.59829 4.90212i −0.263322 0.230576i
\(453\) 0 0
\(454\) 24.8091 + 9.32682i 1.16435 + 0.437729i
\(455\) −1.34521 −0.0630646
\(456\) 0 0
\(457\) −22.1796 −1.03752 −0.518758 0.854921i \(-0.673605\pi\)
−0.518758 + 0.854921i \(0.673605\pi\)
\(458\) 17.9295 + 6.74048i 0.837790 + 0.314962i
\(459\) 0 0
\(460\) 9.83220 11.2285i 0.458429 0.523533i
\(461\) 23.4545i 1.09238i 0.837660 + 0.546192i \(0.183923\pi\)
−0.837660 + 0.546192i \(0.816077\pi\)
\(462\) 0 0
\(463\) −29.2354 −1.35868 −0.679342 0.733822i \(-0.737735\pi\)
−0.679342 + 0.733822i \(0.737735\pi\)
\(464\) 1.86250 0.248058i 0.0864644 0.0115158i
\(465\) 0 0
\(466\) 5.47773 14.5706i 0.253751 0.674972i
\(467\) 5.43057i 0.251297i 0.992075 + 0.125648i \(0.0401011\pi\)
−0.992075 + 0.125648i \(0.959899\pi\)
\(468\) 0 0
\(469\) 12.7403i 0.588291i
\(470\) −11.8279 4.44661i −0.545579 0.205107i
\(471\) 0 0
\(472\) −11.4144 21.2970i −0.525392 0.980273i
\(473\) 3.07611 0.141440
\(474\) 0 0
\(475\) 8.05768i 0.369712i
\(476\) 0.0237882 + 0.0208300i 0.00109033 + 0.000954742i
\(477\) 0 0
\(478\) −7.68214 + 20.4343i −0.351373 + 0.934643i
\(479\) −5.07525 −0.231894 −0.115947 0.993255i \(-0.536990\pi\)
−0.115947 + 0.993255i \(0.536990\pi\)
\(480\) 0 0
\(481\) −4.93276 −0.224914
\(482\) −7.98015 + 21.2270i −0.363486 + 0.966864i
\(483\) 0 0
\(484\) −12.9006 11.2963i −0.586390 0.513470i
\(485\) 7.34962i 0.333729i
\(486\) 0 0
\(487\) −3.23366 −0.146531 −0.0732656 0.997312i \(-0.523342\pi\)
−0.0732656 + 0.997312i \(0.523342\pi\)
\(488\) −5.24433 9.78485i −0.237400 0.442939i
\(489\) 0 0
\(490\) 1.65989 + 0.624024i 0.0749861 + 0.0281905i
\(491\) 32.6437i 1.47319i 0.676335 + 0.736594i \(0.263567\pi\)
−0.676335 + 0.736594i \(0.736433\pi\)
\(492\) 0 0
\(493\) 0.00742632i 0.000334465i
\(494\) 1.25505 3.33841i 0.0564675 0.150202i
\(495\) 0 0
\(496\) 0.892620 + 6.70207i 0.0400798 + 0.300932i
\(497\) 4.22205 0.189385
\(498\) 0 0
\(499\) 1.77339i 0.0793877i −0.999212 0.0396939i \(-0.987362\pi\)
0.999212 0.0396939i \(-0.0126383\pi\)
\(500\) −13.9235 + 15.9008i −0.622677 + 0.711107i
\(501\) 0 0
\(502\) −15.1492 5.69523i −0.676141 0.254191i
\(503\) 25.3666 1.13104 0.565519 0.824735i \(-0.308676\pi\)
0.565519 + 0.824735i \(0.308676\pi\)
\(504\) 0 0
\(505\) 3.92314 0.174578
\(506\) −12.2714 4.61334i −0.545529 0.205088i
\(507\) 0 0
\(508\) 29.8868 + 26.1702i 1.32601 + 1.16112i
\(509\) 14.3204i 0.634739i 0.948302 + 0.317369i \(0.102799\pi\)
−0.948302 + 0.317369i \(0.897201\pi\)
\(510\) 0 0
\(511\) 6.51561 0.288234
\(512\) 2.14152 22.5258i 0.0946427 0.995511i
\(513\) 0 0
\(514\) 5.34719 14.2234i 0.235854 0.627367i
\(515\) 3.42110i 0.150752i
\(516\) 0 0
\(517\) 11.0995i 0.488154i
\(518\) 6.08664 + 2.28823i 0.267431 + 0.100539i
\(519\) 0 0
\(520\) −3.35354 + 1.79738i −0.147062 + 0.0788203i
\(521\) 5.72827 0.250960 0.125480 0.992096i \(-0.459953\pi\)
0.125480 + 0.992096i \(0.459953\pi\)
\(522\) 0 0
\(523\) 11.3779i 0.497519i 0.968565 + 0.248759i \(0.0800229\pi\)
−0.968565 + 0.248759i \(0.919977\pi\)
\(524\) −9.54963 + 10.9058i −0.417178 + 0.476424i
\(525\) 0 0
\(526\) −7.30296 + 19.4257i −0.318424 + 0.847001i
\(527\) −0.0267231 −0.00116408
\(528\) 0 0
\(529\) 12.4178 0.539905
\(530\) 1.16527 3.09959i 0.0506161 0.134638i
\(531\) 0 0
\(532\) −3.09727 + 3.53713i −0.134284 + 0.153354i
\(533\) 13.1086i 0.567797i
\(534\) 0 0
\(535\) 2.57777 0.111447
\(536\) −17.0226 31.7607i −0.735266 1.37186i
\(537\) 0 0
\(538\) 6.52759 + 2.45400i 0.281424 + 0.105800i
\(539\) 1.55766i 0.0670933i
\(540\) 0 0
\(541\) 43.3953i 1.86571i 0.360252 + 0.932855i \(0.382691\pi\)
−0.360252 + 0.932855i \(0.617309\pi\)
\(542\) 11.2772 29.9970i 0.484396 1.28848i
\(543\) 0 0
\(544\) 0.0871342 + 0.0201439i 0.00373585 + 0.000863662i
\(545\) −17.3265 −0.742187
\(546\) 0 0
\(547\) 18.5677i 0.793898i −0.917841 0.396949i \(-0.870069\pi\)
0.917841 0.396949i \(-0.129931\pi\)
\(548\) −19.7904 17.3294i −0.845404 0.740274i
\(549\) 0 0
\(550\) 7.06778 + 2.65709i 0.301371 + 0.113299i
\(551\) −1.10424 −0.0470422
\(552\) 0 0
\(553\) −6.15343 −0.261671
\(554\) 7.93159 + 2.98183i 0.336981 + 0.126686i
\(555\) 0 0
\(556\) 6.97629 7.96703i 0.295860 0.337877i
\(557\) 17.4689i 0.740182i 0.928996 + 0.370091i \(0.120673\pi\)
−0.928996 + 0.370091i \(0.879327\pi\)
\(558\) 0 0
\(559\) 2.11860 0.0896073
\(560\) 4.97178 0.662170i 0.210096 0.0279818i
\(561\) 0 0
\(562\) −0.958209 + 2.54881i −0.0404196 + 0.107515i
\(563\) 26.8370i 1.13105i −0.824733 0.565523i \(-0.808675\pi\)
0.824733 0.565523i \(-0.191325\pi\)
\(564\) 0 0
\(565\) 4.66534i 0.196272i
\(566\) 37.3558 + 14.0437i 1.57018 + 0.590299i
\(567\) 0 0
\(568\) 10.5253 5.64121i 0.441633 0.236700i
\(569\) 32.4375 1.35985 0.679926 0.733281i \(-0.262012\pi\)
0.679926 + 0.733281i \(0.262012\pi\)
\(570\) 0 0
\(571\) 34.0452i 1.42475i 0.701800 + 0.712374i \(0.252380\pi\)
−0.701800 + 0.712374i \(0.747620\pi\)
\(572\) 2.51441 + 2.20173i 0.105133 + 0.0920591i
\(573\) 0 0
\(574\) 6.08088 16.1750i 0.253811 0.675131i
\(575\) −20.3991 −0.850702
\(576\) 0 0
\(577\) 6.09534 0.253752 0.126876 0.991919i \(-0.459505\pi\)
0.126876 + 0.991919i \(0.459505\pi\)
\(578\) 8.46006 22.5036i 0.351892 0.936025i
\(579\) 0 0
\(580\) 0.886271 + 0.776058i 0.0368004 + 0.0322241i
\(581\) 8.88604i 0.368655i
\(582\) 0 0
\(583\) −2.90870 −0.120466
\(584\) 16.2430 8.70570i 0.672142 0.360244i
\(585\) 0 0
\(586\) 38.5156 + 14.4797i 1.59107 + 0.598151i
\(587\) 10.7735i 0.444669i −0.974970 0.222334i \(-0.928632\pi\)
0.974970 0.222334i \(-0.0713677\pi\)
\(588\) 0 0
\(589\) 3.97353i 0.163727i
\(590\) 5.33098 14.1803i 0.219473 0.583793i
\(591\) 0 0
\(592\) 18.2310 2.42811i 0.749290 0.0997946i
\(593\) 13.4720 0.553230 0.276615 0.960981i \(-0.410787\pi\)
0.276615 + 0.960981i \(0.410787\pi\)
\(594\) 0 0
\(595\) 0.0198239i 0.000812701i
\(596\) −8.68755 + 9.92133i −0.355856 + 0.406393i
\(597\) 0 0
\(598\) −8.45164 3.17734i −0.345613 0.129931i
\(599\) 37.4766 1.53125 0.765626 0.643285i \(-0.222429\pi\)
0.765626 + 0.643285i \(0.222429\pi\)
\(600\) 0 0
\(601\) −3.99803 −0.163083 −0.0815415 0.996670i \(-0.525984\pi\)
−0.0815415 + 0.996670i \(0.525984\pi\)
\(602\) −2.61419 0.982787i −0.106546 0.0400554i
\(603\) 0 0
\(604\) 14.3182 + 12.5377i 0.582601 + 0.510151i
\(605\) 10.7507i 0.437079i
\(606\) 0 0
\(607\) 36.8295 1.49486 0.747432 0.664338i \(-0.231287\pi\)
0.747432 + 0.664338i \(0.231287\pi\)
\(608\) −2.99525 + 12.9562i −0.121473 + 0.525444i
\(609\) 0 0
\(610\) 2.44931 6.51509i 0.0991695 0.263788i
\(611\) 7.64451i 0.309264i
\(612\) 0 0
\(613\) 9.76469i 0.394392i 0.980364 + 0.197196i \(0.0631836\pi\)
−0.980364 + 0.197196i \(0.936816\pi\)
\(614\) −20.9647 7.88153i −0.846066 0.318073i
\(615\) 0 0
\(616\) −2.08124 3.88316i −0.0838555 0.156457i
\(617\) 14.4832 0.583070 0.291535 0.956560i \(-0.405834\pi\)
0.291535 + 0.956560i \(0.405834\pi\)
\(618\) 0 0
\(619\) 6.72500i 0.270301i −0.990825 0.135150i \(-0.956848\pi\)
0.990825 0.135150i \(-0.0431518\pi\)
\(620\) −2.79259 + 3.18918i −0.112153 + 0.128081i
\(621\) 0 0
\(622\) 7.24691 19.2766i 0.290575 0.772922i
\(623\) 0.240788 0.00964698
\(624\) 0 0
\(625\) 3.88743 0.155497
\(626\) −3.22023 + 8.56573i −0.128706 + 0.342355i
\(627\) 0 0
\(628\) −21.0953 + 24.0912i −0.841795 + 0.961343i
\(629\) 0.0726923i 0.00289843i
\(630\) 0 0
\(631\) −23.2251 −0.924577 −0.462288 0.886730i \(-0.652971\pi\)
−0.462288 + 0.886730i \(0.652971\pi\)
\(632\) −15.3401 + 8.22178i −0.610198 + 0.327045i
\(633\) 0 0
\(634\) −15.8617 5.96310i −0.629948 0.236825i
\(635\) 24.9062i 0.988373i
\(636\) 0 0
\(637\) 1.07281i 0.0425061i
\(638\) 0.364132 0.968583i 0.0144161 0.0383466i
\(639\) 0 0
\(640\) 11.5096 8.29369i 0.454957 0.327837i
\(641\) 30.3809 1.19998 0.599988 0.800009i \(-0.295172\pi\)
0.599988 + 0.800009i \(0.295172\pi\)
\(642\) 0 0
\(643\) 5.74408i 0.226524i 0.993565 + 0.113262i \(0.0361300\pi\)
−0.993565 + 0.113262i \(0.963870\pi\)
\(644\) 8.95474 + 7.84117i 0.352866 + 0.308985i
\(645\) 0 0
\(646\) −0.0491969 0.0184952i −0.00193563 0.000727686i
\(647\) 4.19948 0.165099 0.0825494 0.996587i \(-0.473694\pi\)
0.0825494 + 0.996587i \(0.473694\pi\)
\(648\) 0 0
\(649\) −13.3070 −0.522345
\(650\) 4.86778 + 1.83001i 0.190930 + 0.0717788i
\(651\) 0 0
\(652\) 16.5685 18.9214i 0.648871 0.741021i
\(653\) 45.2069i 1.76908i 0.466460 + 0.884542i \(0.345529\pi\)
−0.466460 + 0.884542i \(0.654471\pi\)
\(654\) 0 0
\(655\) −9.08839 −0.355113
\(656\) −6.45260 48.4482i −0.251932 1.89158i
\(657\) 0 0
\(658\) 3.54617 9.43272i 0.138244 0.367726i
\(659\) 47.0951i 1.83456i −0.398239 0.917282i \(-0.630379\pi\)
0.398239 0.917282i \(-0.369621\pi\)
\(660\) 0 0
\(661\) 41.9805i 1.63285i −0.577449 0.816427i \(-0.695952\pi\)
0.577449 0.816427i \(-0.304048\pi\)
\(662\) −29.0462 10.9197i −1.12891 0.424408i
\(663\) 0 0
\(664\) −11.8729 22.1524i −0.460758 0.859679i
\(665\) −2.94767 −0.114306
\(666\) 0 0
\(667\) 2.79554i 0.108244i
\(668\) 26.0069 + 22.7728i 1.00624 + 0.881105i
\(669\) 0 0
\(670\) 7.95023 21.1474i 0.307144 0.816996i
\(671\) −6.11386 −0.236023
\(672\) 0 0
\(673\) 30.0898 1.15987 0.579937 0.814661i \(-0.303077\pi\)
0.579937 + 0.814661i \(0.303077\pi\)
\(674\) −11.1052 + 29.5397i −0.427758 + 1.13783i
\(675\) 0 0
\(676\) −17.8290 15.6119i −0.685731 0.600456i
\(677\) 40.5494i 1.55844i 0.626749 + 0.779221i \(0.284385\pi\)
−0.626749 + 0.779221i \(0.715615\pi\)
\(678\) 0 0
\(679\) 5.86131 0.224936
\(680\) 0.0264873 + 0.0494199i 0.00101574 + 0.00189517i
\(681\) 0 0
\(682\) 3.48538 + 1.31030i 0.133462 + 0.0501741i
\(683\) 50.1042i 1.91718i 0.284786 + 0.958591i \(0.408077\pi\)
−0.284786 + 0.958591i \(0.591923\pi\)
\(684\) 0 0
\(685\) 16.4924i 0.630141i
\(686\) −0.497658 + 1.32376i −0.0190007 + 0.0505413i
\(687\) 0 0
\(688\) −7.83015 + 1.04286i −0.298522 + 0.0397588i
\(689\) −2.00330 −0.0763198
\(690\) 0 0
\(691\) 43.2174i 1.64407i −0.569438 0.822034i \(-0.692839\pi\)
0.569438 0.822034i \(-0.307161\pi\)
\(692\) 11.5776 13.2218i 0.440116 0.502619i
\(693\) 0 0
\(694\) −32.5388 12.2328i −1.23516 0.464349i
\(695\) 6.63933 0.251844
\(696\) 0 0
\(697\) 0.193177 0.00731709
\(698\) 16.6701 + 6.26702i 0.630973 + 0.237210i
\(699\) 0 0
\(700\) −5.15754 4.51617i −0.194937 0.170695i
\(701\) 19.4337i 0.734002i −0.930221 0.367001i \(-0.880385\pi\)
0.930221 0.367001i \(-0.119615\pi\)
\(702\) 0 0
\(703\) −10.8088 −0.407662
\(704\) −10.3768 6.89970i −0.391091 0.260042i
\(705\) 0 0
\(706\) −8.05939 + 21.4378i −0.303319 + 0.806821i
\(707\) 3.12870i 0.117667i
\(708\) 0 0
\(709\) 24.0279i 0.902387i 0.892426 + 0.451194i \(0.149002\pi\)
−0.892426 + 0.451194i \(0.850998\pi\)
\(710\) 7.00814 + 2.63466i 0.263011 + 0.0988771i
\(711\) 0 0
\(712\) 0.600271 0.321724i 0.0224961 0.0120571i
\(713\) −10.0595 −0.376733
\(714\) 0 0
\(715\) 2.09539i 0.0783631i
\(716\) 15.4107 17.5993i 0.575927 0.657717i
\(717\) 0 0
\(718\) 5.06663 13.4771i 0.189085 0.502961i
\(719\) 36.0898 1.34592 0.672961 0.739678i \(-0.265022\pi\)
0.672961 + 0.739678i \(0.265022\pi\)
\(720\) 0 0
\(721\) 2.72832 0.101608
\(722\) −6.70539 + 17.8362i −0.249549 + 0.663794i
\(723\) 0 0
\(724\) 31.9671 36.5070i 1.18805 1.35677i
\(725\) 1.61011i 0.0597979i
\(726\) 0 0
\(727\) 36.3230 1.34714 0.673572 0.739122i \(-0.264759\pi\)
0.673572 + 0.739122i \(0.264759\pi\)
\(728\) −1.43341 2.67444i −0.0531256 0.0991214i
\(729\) 0 0
\(730\) 10.8152 + 4.06590i 0.400288 + 0.150486i
\(731\) 0.0312211i 0.00115475i
\(732\) 0 0
\(733\) 11.9814i 0.442544i −0.975212 0.221272i \(-0.928979\pi\)
0.975212 0.221272i \(-0.0710209\pi\)
\(734\) 6.16792 16.4065i 0.227662 0.605575i
\(735\) 0 0
\(736\) 32.8005 + 7.58289i 1.20904 + 0.279509i
\(737\) −19.8451 −0.731002
\(738\) 0 0
\(739\) 36.7377i 1.35142i −0.737169 0.675708i \(-0.763838\pi\)
0.737169 0.675708i \(-0.236162\pi\)
\(740\) 8.67522 + 7.59641i 0.318908 + 0.279250i
\(741\) 0 0
\(742\) 2.47192 + 0.929302i 0.0907471 + 0.0341158i
\(743\) 13.2966 0.487805 0.243903 0.969800i \(-0.421572\pi\)
0.243903 + 0.969800i \(0.421572\pi\)
\(744\) 0 0
\(745\) −8.26795 −0.302914
\(746\) −10.0330 3.77185i −0.367336 0.138097i
\(747\) 0 0
\(748\) 0.0324461 0.0370540i 0.00118635 0.00135483i
\(749\) 2.05577i 0.0751161i
\(750\) 0 0
\(751\) −13.5953 −0.496101 −0.248051 0.968747i \(-0.579790\pi\)
−0.248051 + 0.968747i \(0.579790\pi\)
\(752\) −3.76294 28.2534i −0.137220 1.03029i
\(753\) 0 0
\(754\) 0.250788 0.667090i 0.00913316 0.0242940i
\(755\) 11.9321i 0.434254i
\(756\) 0 0
\(757\) 8.04991i 0.292579i −0.989242 0.146290i \(-0.953267\pi\)
0.989242 0.146290i \(-0.0467331\pi\)
\(758\) −18.6887 7.02588i −0.678803 0.255192i
\(759\) 0 0
\(760\) −7.34838 + 3.93847i −0.266554 + 0.142863i
\(761\) 53.5813 1.94232 0.971160 0.238429i \(-0.0766325\pi\)
0.971160 + 0.238429i \(0.0766325\pi\)
\(762\) 0 0
\(763\) 13.8179i 0.500241i
\(764\) −15.7764 13.8146i −0.570771 0.499793i
\(765\) 0 0
\(766\) 0.640375 1.70338i 0.0231377 0.0615457i
\(767\) −9.16489 −0.330925
\(768\) 0 0
\(769\) 3.40107 0.122646 0.0613229 0.998118i \(-0.480468\pi\)
0.0613229 + 0.998118i \(0.480468\pi\)
\(770\) 0.972019 2.58555i 0.0350291 0.0931766i
\(771\) 0 0
\(772\) −19.1233 16.7452i −0.688261 0.602672i
\(773\) 12.6537i 0.455123i −0.973764 0.227561i \(-0.926925\pi\)
0.973764 0.227561i \(-0.0730752\pi\)
\(774\) 0 0
\(775\) 5.79386 0.208122
\(776\) 14.6119 7.83147i 0.524537 0.281133i
\(777\) 0 0
\(778\) −44.1222 16.5875i −1.58186 0.594689i
\(779\) 28.7240i 1.02914i
\(780\) 0 0
\(781\) 6.57654i 0.235327i
\(782\) −0.0468232 + 0.124549i −0.00167440 + 0.00445385i
\(783\) 0 0
\(784\) 0.528080 + 3.96499i 0.0188600 + 0.141607i
\(785\) −20.0764 −0.716558
\(786\)