Properties

Label 1512.2.c.g.757.16
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 757.16
Character \(\chi\) = 1512.757
Dual form 1512.2.c.g.757.15

$q$-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 \(0.0475319\pi\)
−0.988872 + 0.148771i \(0.952468\pi\)
\(14\) 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 \(-0.499390\pi\)
0.00191719 + 0.999998i \(0.499390\pi\)
\(18\) 0 0
\(19\) 2.35077i 0.539303i 0.962958 + 0.269651i \(0.0869085\pi\)
−0.962958 + 0.269651i \(0.913092\pi\)
\(20\) 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 \(-0.286944\pi\)
0.620465 + 0.784235i \(0.286944\pi\)
\(24\) 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 \(0.123372\pi\)
−0.925825 + 0.377953i \(0.876628\pi\)
\(38\) −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 \(-0.0967698\pi\)
0.954143 + 0.299350i \(0.0967698\pi\)
\(42\) 0 0
\(43\) 1.97482i 0.301158i −0.988598 0.150579i \(-0.951886\pi\)
0.988598 0.150579i \(-0.0481137\pi\)
\(44\) 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 \(-0.326045\pi\)
0.519696 + 0.854351i \(0.326045\pi\)
\(48\) 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 \(0.0808494\pi\)
−0.967916 + 0.251274i \(0.919151\pi\)
\(62\) 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 \(0.283885\pi\)
−0.627972 + 0.778236i \(0.716115\pi\)
\(68\) −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 \(-0.580606\pi\)
−0.250533 + 0.968108i \(0.580606\pi\)
\(72\) 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 \(-0.504062\pi\)
−0.0127618 + 0.999919i \(0.504062\pi\)
\(90\) 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 \(0.230189\pi\)
−0.749719 + 0.661756i \(0.769811\pi\)
\(110\) −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 \(-0.555993\pi\)
−0.175003 + 0.984568i \(0.555993\pi\)
\(114\) 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 \(-0.689911\pi\)
−0.561853 + 0.827237i \(0.689911\pi\)
\(138\) 0 0
\(139\) 5.29486i 0.449104i −0.974462 0.224552i \(-0.927908\pi\)
0.974462 0.224552i \(-0.0720919\pi\)
\(140\) 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 \(0.220612\pi\)
−0.769285 + 0.638905i \(0.779388\pi\)
\(158\) −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 \(-0.836091\pi\)
0.870324 0.492480i \(-0.163909\pi\)
\(164\) −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 \(-0.266834\pi\)
0.668741 + 0.743495i \(0.266834\pi\)
\(168\) 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 \(-0.642316\pi\)
0.432351 0.901705i \(-0.357684\pi\)
\(182\) −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 \(-0.623846\pi\)
−0.379333 + 0.925260i \(0.623846\pi\)
\(192\) 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 \(-0.755788\pi\)
0.719847 0.694133i \(-0.244212\pi\)
\(212\) 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 \(0.147692\pi\)
−0.894274 + 0.447519i \(0.852308\pi\)
\(230\) 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 \(-0.382590\pi\)
0.360547 + 0.932741i \(0.382590\pi\)
\(234\) 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 \(-0.666393\pi\)
−0.499255 + 0.866455i \(0.666393\pi\)
\(240\) 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 \(-0.391224\pi\)
0.335118 + 0.942176i \(0.391224\pi\)
\(258\) 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 \(-0.649446\pi\)
−0.452439 + 0.891795i \(0.649446\pi\)
\(264\) 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 \(0.0576110\pi\)
−0.983666 + 0.180004i \(0.942389\pi\)
\(278\) 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 \(-0.518291\pi\)
−0.0574309 + 0.998349i \(0.518291\pi\)
\(282\) 0 0
\(283\) 28.2195i 1.67747i 0.544537 + 0.838737i \(0.316705\pi\)
−0.544537 + 0.838737i \(0.683295\pi\)
\(284\) 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 \(-0.850732\pi\)
0.892049 0.451940i \(-0.149268\pi\)
\(308\) 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 \(-0.364527\pi\)
0.412869 + 0.910791i \(0.364527\pi\)
\(312\) 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 \(-0.793961\pi\)
0.797720 0.603027i \(-0.206039\pi\)
\(332\) 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 \(0.109427\pi\)
−0.941489 + 0.337045i \(0.890573\pi\)
\(350\) 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 \(-0.641831\pi\)
−0.430977 + 0.902363i \(0.641831\pi\)
\(354\) 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 \(-0.413418\pi\)
0.268665 + 0.963234i \(0.413418\pi\)
\(360\) 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 \(-0.937134\pi\)
0.980560 0.196218i \(-0.0628661\pi\)
\(374\) 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 \(-0.881891\pi\)
0.931947 0.362594i \(-0.118109\pi\)
\(380\) −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 \(-0.489533\pi\)
0.0328756 + 0.999459i \(0.489533\pi\)
\(384\) 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 \(-0.825416\pi\)
0.853322 0.521385i \(-0.174584\pi\)
\(398\) −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 \(-0.559005\pi\)
−0.184309 + 0.982868i \(0.559005\pi\)
\(402\) 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 \(0.244330\pi\)
−0.719589 + 0.694400i \(0.755670\pi\)
\(422\) 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 \(-0.825613\pi\)
−0.853645 + 0.520855i \(0.825613\pi\)
\(432\) 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 \(-0.477855\pi\)
0.0695154 + 0.997581i \(0.477855\pi\)
\(450\) 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 \(-0.463010\pi\)
0.115947 + 0.993255i \(0.463010\pi\)
\(480\) 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 \(0.0126383\pi\)
−0.999212 + 0.0396939i \(0.987362\pi\)
\(500\) 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 \(-0.691324\pi\)
−0.565519 + 0.824735i \(0.691324\pi\)
\(504\) 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 \(-0.540047\pi\)
−0.125480 + 0.992096i \(0.540047\pi\)
\(522\) 0 0
\(523\) 11.3779i 0.497519i −0.968565 0.248759i \(-0.919977\pi\)
0.968565 0.248759i \(-0.0800229\pi\)
\(524\) 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 \(-0.617309\pi\)
0.360252 0.932855i \(-0.382691\pi\)
\(542\) −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 \(0.129931\pi\)
−0.917841 + 0.396949i \(0.870069\pi\)
\(548\) 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 \(-0.737988\pi\)
−0.679926 + 0.733281i \(0.737988\pi\)
\(570\) 0 0
\(571\) 34.0452i 1.42475i −0.701800 0.712374i \(-0.747620\pi\)
0.701800 0.712374i \(-0.252380\pi\)
\(572\) −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 \(-0.589213\pi\)
−0.276615 + 0.960981i \(0.589213\pi\)
\(594\) 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 \(-0.777571\pi\)
−0.765626 + 0.643285i \(0.777571\pi\)
\(600\) 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 \(-0.936816\pi\)
0.980364 0.197196i \(-0.0631836\pi\)
\(614\) 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 \(-0.594166\pi\)
−0.291535 + 0.956560i \(0.594166\pi\)
\(618\) 0 0
\(619\) 6.72500i 0.270301i 0.990825 + 0.135150i \(0.0431518\pi\)
−0.990825 + 0.135150i \(0.956848\pi\)
\(620\) 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 \(-0.704828\pi\)
−0.599988 + 0.800009i \(0.704828\pi\)
\(642\) 0 0
\(643\) 5.74408i 0.226524i −0.993565 0.113262i \(-0.963870\pi\)
0.993565 0.113262i \(-0.0361300\pi\)
\(644\) −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 \(-0.526306\pi\)
−0.0825494 + 0.996587i \(0.526306\pi\)
\(648\) 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 \(0.304048\pi\)
−0.577449 + 0.816427i \(0.695952\pi\)
\(662\) 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 \(0.307161\pi\)
−0.569438 + 0.822034i \(0.692839\pi\)
\(692\) −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 \(-0.850998\pi\)
0.892426 0.451194i \(-0.149002\pi\)
\(710\) −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 \(-0.734978\pi\)
−0.672961 + 0.739678i \(0.734978\pi\)
\(720\) 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 \(0.0710209\pi\)
−0.975212 + 0.221272i \(0.928979\pi\)
\(734\) −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 \(0.236162\pi\)
−0.737169 + 0.675708i \(0.763838\pi\)
\(740\) −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 \(-0.578428\pi\)
−0.243903 + 0.969800i \(0.578428\pi\)
\(744\) 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 \(0.0467331\pi\)
−0.989242 + 0.146290i \(0.953267\pi\)
\(758\) 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 \(-0.923368\pi\)
−0.971160 + 0.238429i \(0.923368\pi\)
\(762\) 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
\(786\) 0